wake behind circular cylinder excited by spanwise non-uniform disturbances takumi kamiyama*, mizuki ino, yudai yokota, jun sakakibara department of mechanical engineering, meiji university higashimita 1-1-1, tamaku, kawasaki, 214-8571, japan abstract we studied a modification of wake behind a circular cylinder using a plasma actuator. the plasma actuators were arranged in the spanwise direction of the cylinder to give temporal periodic disturbances having strouhal number st = 0.18-2.3 with a burst ratio br = 20 and 40%. the reynolds number was set in a rage of re = 4200 to 8400. two types of plasma actuator were prepared; one is a single strip of the actuator placed at each side of the cylinder to give a spanwise uniform disturbance, and another is an array of small piece of actuators placed at the same location to create a spanwise non-uniform disturbance with temporal phase difference, φ = 0 or π, between adjacent electrodes. a conventional two-component piv and stereo piv was used to measure the flow field. figure 1 shows the instantaneous spanwise component of vorticity at re = 4200 evaluated by two-component piv. under no disturbance condition, the laminar shear layer extends straight to around x / d = 1.5 and then forms a wake vortex, as shown in fig.1(a). in the case of spanwise non-uniform forcing with st = 1.09 and φ =π, rapid roll up of the initial shear layer leads to arrangement of wake vortices closer to the cylinder., as shown in fig.1(b). with higher strouhal number case with st = 1.09 and φ = 0, shown in fig.1(c), a series of fine scale vortices are generated behind both side of the cylinder without forming regular karman vortices. the spanwise non-uniform forcing was effective to suppress the formation of large scale vortices just behind the cylinder. figure 2 shows surface of constant vorticity magnitude and vortex lines under st =1.09 and φ = π case. these were computed from a phase-averaged threecomponents velocity field evaluated by stereo piv. the value of the surface was selected to display the boundary layer formed on the cylinder, and the vortex lines are selected to visualize the vortex structure formed in the following shear layer. a bundle of vortex lines are shaped in a wavy pattern along spanwise direction with 180 degrees out of phase to the adjacent bundle upstream of downstream. this structure, so called ‘chain-line fence structure’ was already found in planar free shear layer [nygaard, k.j. and glezer, a., 1990, phys. fluids a, 2, 461] and planar jet [sakakibara, j., anzai, t., 2001, phys. fluids, 13, 1541], but it became evident to create it in the wake of circular cylinder in this study. (a)pa off (b)st=1.09, φ=π (c)st=1.09, φ=0 figure 1 instantaneous vorticity distributions at re = 4200 figure 2 surfaces of constant vorticity magnitude and vortex lines extracted from a phase averaged velocity field line under st =1.09 and φ = π case. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 rayleigh-bénard convection in air: out-of-plane vorticity from stereoscopic piv measurements v. valori1∗, a. thieme1, c. cierpka1, j. schumacher1,2 1 technische universität ilmenau, institute of thermodynamics and fluid mechanics, d-98684 ilmenau, germany 2 new york university, tandon school of engineering, new york city, ny 11201, usa ∗ valentina.valori@tu-ilmenau.de abstract we present results from stereoscopic piv measurements in a rayleigh-bénard convection (rbc) cell filled with (compressed) air at rayleigh numbers: ra = 1.5× 104,2× 104,1× 105,2× 105,5× 105, and prandtl number pr ' 0.7. the three largest rayleigh numbers are obtained pressurising the whole set-up including cameras and objective lenses, up to 4.5 bars. the main goal of this study is to reproduce dns data that are acquired at the same rayleigh numbers to study far-tail events of the out-of-plane vorticity component (ωz). the measurements are performed in a rbc cell with aspect ratio γ = w/h = 10, where w is the width and h = 3 cm is the height of the domain. the cell is equipped with a transparent bottom plate heated by a thin oxide layer (for details see kästner et al. (2018)), which allows us to measure 3c2d velocity fields on a horizontal plane at mid height of the cell. the rbc cell set-up is inserted in the scalex facility of tu ilmenau, a pressure vessel with several optical accesses that can be pressurised up to 10 bars. -10 -5 0 5 10 10 -4 10 -3 10 -2 10 -1 10 0 (a) stereo piv -10 -5 0 5 10 10 -4 10 -3 10 -2 10 -1 10 0 (b) dns figure 1: pdfs of ωz from stereo piv and dns data at ra = 1.5×104,2×104,1×105,2×105,5×105 the experiments aim firstly at improving the quality of previous measurements performed in the same set-up [kästner et al. (2018), cierpka et al. (2019)], regarding the accuracy of the out-of-plane velocity component. this has been realised by positioning the cameras at a larger stereo angle (about 25◦), which is possible by placing them inside the pressure vessel. major challenges of the current measurements are caused by optical distortions due to the temperature gradients that are typical for thermal convection (see valori (2018), valori et al. (2019)). 1900 1950 2000 2050 2100 -10 -5 0 5 (a) time evolution of ωz at (xe,ye) (b) spatial structutre at the time of the extreme event figure 2: visualization of an extreme event of ωz at ra= 2.5×105 from a time evolution serie at the position of the extreme event (xe,ye) and a snapshot of ωz. σ indicates the standard deviation and tf f the free fall time of the flow. arrows in plot (b) show the in-plane velocity. probability density functions (pdfs) of ωz from stereo piv experiments and from dns data are shown respectively in figure 1(a) and 1(b) for all rayleigh numbers studied. we can observe that for both kind of data the tails of the pdf becomes wider while increasing the rayleigh number, which may be connected to intermittency. this crossover from gaussian to intermittent statistic was recently studied in valori and schumacher (2021) from dns. figure2(a) shows the temporal evolution of ωz at the position of its largest (extreme) value at ra = 2.5× 105, while figure2(b) shows the spatial distribution of ωz at the time of its extreme event in the experiments. the experimental results are able to reproduce well the statistics of dns data of the same flow, and allow the study of extreme events of ωz. acknowledgements the work is supported by the priority programme dfg-spp 1881 on turbulent superstructures of the deutsche forschungsgemeinschaft, and the convext marie skłodowska-curie project number 101024531 funded by the european union. references cierpka c, kästner c, resagk c, and schumacher j (2019) on the challenges for reliable measurements of convection in large aspect ratio rayleigh-bénard cells in air and sulfur-hexafluoride. experimental thermal and fluid science 109:109841 kästner c, resagk c, westphalen j, junghähnel m, cierpka c, and schumacher j (2018) assessment of horizontal velocity fields in square thermal convection cells with large aspect ratio. experiments in fluids 59:171 valori v (2018) rayleigh-bénard convection of a supercritical fluid. doctoral thesis. delft university of technology valori v, elsinga ge, rohde m, westerweel j, and van der hagen thjj (2019) particle image velocimetry measurements of a thermally convective supercritical fluid. experiments in fluids 60:143 valori v and schumacher j (2021) connecting boundary layer dynamics with extreme bulk dissipation events in rayleigh-bénard flow. europhysics letters, in press microsoft word ispiv2021_whtien_287f.docx ispiv2021 14th international symposium on particle image velocimetry – ispiv 2021 chicago, u.s.a. visualization of three-dimensional acoustic streaming flow patterns around an inclined triangular obstruction using digital in-line holographic micro-particle tracking velocimetry sheng po hung and wei-hsin tien1 1 department of mechanical engineering, national taiwan university of science and technology, taipei, taiwan whtien@mail.ntust.edu.tw abstract acoustic streaming is a flow phenomenon with many applications in the field of microfluidics, such as micro mixing[1, 2] and particle manipulation[3]. with the manufacturing techniques evolves, more complicated geometries can be designed for microfluidic device and 3-d acoustic streaming patterns may occurs. in this study, 3-d trajectories of particle induced by acoustic streaming around an inclined triangular obstruction in a microchannel were visualized by a volumetric tracking method using digital inline holographic microscopy (dihm)[4-6]. the triangular obstruction has a tip angle of 20° and an inclined angle of 30°. the acoustic streaming is created under 12 khz oscillation of a piezo plate driven by 20v voltage. illuminated by a 450nm continuous laser, the magnified hologram of the motion of 1.79μm tracer particles was recorded by a low-cost 10x industrial microscope with a machine vision camera of 10 fps (frames per second). using rayleighsommerfeld back-propagation method[7], particle locations was reconstructed frame by frame and 3-d tracking of individual particles was performed afterwards. the trajectories of each particle were reconstructed to reveal the vortical structure of the acoustic streaming flow. for the current system setup, the measurable range was estimated to be 550×685×840 μm . the 3d location reconstruction accuracy was verified with a calibration target and the location sensitivity was found to be linear throughout the measurable range. reconstruction at different depth locations show that the dick-shaped calibration dots and the spherical polystyrene particles have different intensity profiles. the calibration dots show local minimum of intensity at the correct depth location, while polystyrene particles show local maximum of intensity instead. resolved particle trajectories show that the acoustic streaming flows cause particles to move with 3-d spiral shaped motions near the side of the triangular obstruction, while particles away from the obstruction shows planar motions. figure 1 (a) experimental setup and (b) calibration results over the measurable range of the dihm system. (a) (b) ispiv2021 14th international symposium on particle image velocimetry – ispiv 2021 chicago, u.s.a. figure 2 (a) device geometry (b) magnified hologram and (c) reconstructed particle trajectories of the acoustic streaming flow around a triangular obstruction. the obstruction has a tip angle of 20° and an inclined angle of 30°. references [1] a. ozcelik et al., "an acoustofluidic micromixer via bubble inception and cavitation from microchannel sidewalls," (in english), analytical chemistry, article vol. 86, no. 10, pp. 5083-5088, 05 / 20 / 2014. [2] x. mao, b. k. juluri, m. i. lapsley, z. s. stratton, and t. j. huang, "milliseconds microfluidic chaotic bubble mixer," (in english), microfluidics and nanofluidics, article vol. 8, no. 1, pp. 139-144, 01 / 01 / 2010. [3] m. v. patel, i. a. nanayakkara, m. g. simon, and a. p. lee, "cavity-induced microstreaming for simultaneous onchip pumping and size-based separation of cells and particles," lab chip, vol. 14, no. 19, pp. 3860-72, oct 7 2014. [4] p. memmolo et al., "recent advances in holographic 3d particle tracking," advances in optics and photonics, vol. 7, no. 4, pp. 713-755, dec 2015. [5] x. yu, j. s. hong, c. g. liu, and m. k. kim, "review of digital holographic microscopy for three-dimensional profiling and tracking," optical engineering, vol. 53, no. 11, nov 2014, art. no. 112306. [6] j. garcia-sucerquia, w. b. xu, s. k. jericho, p. klages, m. h. jericho, and h. j. kreuzer, "digital in-line holographic microscopy," (in english), applied optics, article vol. 45, no. 5, pp. 836-850, feb 2006. [7] f. c. cheong, b. j. krishnatreya, and d. g. grier, "strategies for three-dimensional particle tracking with holographic video microscopy," optics express, vol. 18, no. 13, pp. 13563-13573, jun 2010. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 time-resolved velocity estimation from inflow pressure measurements in a subsonic jet using machine-learning methods songqi li1, wenyan li2, lawrence ukeiley1∗ 1 university of florida, gainesville, florida, usa 2 comcast applied ai research lab, washington dc, usa ∗ ukeiley@ufl.edu the goal of this study is to estimate aspects of the time-resolved (tr) velocity field that is associated with pressure fluctuations measured in a subsonic jet using machine learning (ml) approaches. the experiments were conducted in the anechoic jet test facility at the university of florida using a round converging nozzle operated at at a mach number of 0.3 and red = 3.8× 105. planar piv was utilized to record nontr, 2d velocity snapshots on the streamwise plane. a b&k 4138 1/8” microphone and a gras 46dd 1/8” microphone were employed to measure inflow pressure fluctuations synchronously with the piv. both microphones were equipped with aerodynamically-shaped nosecones and were placed on the upper and lower jet liplines. the nosecone tips were streamwisely aligned and were placed just downstream of the piv window (see figure 1(a)). pressure signals were recorded synchronously with piv, but at different sampling rates, 80 khz and 12 hz, respectively. a total of 8000 piv snapshots were acquired in the experiment. the potential of ml-based techniques to tackle problems in fluid dynamics has been justified in [1; 2]. in this work a ml estimation approach was applied to estimate tr velocity from the experimental dataset (see figure 1(b)). with the application of the snapshot pod [3], the dominant spatial features of velocity were represented by the leading pod modes, which shifts the focus onto the estimation of tr-pod expansion coefficients from time-lagged pressure using proper input-output models. two neural network (nn) architectures were proposed to implement the model. the first model is a multi-layer perceptron (mlp) with two fully connected hidden layers. the second architecture is composed of a two-layered bidirectional long-short-term-memory (bi-lstm) and an output layer stemming from the hidden layer output at the laser burst time. the time-dependent parameter transmission mechanism makes bi-lstm effective to distill information from past and future time steps. an iterative regression approach was utilized to train the models until convergence. tr-pod expansion coefficients were estimated by feeding continuous pressure signals to the trained networks, from which velocity was reconstructed in combination with the pod spatial eigenfunctions. (a) experimental setup of inflow pressure measurements synchronized with piv (b) overview of velocity estimation from pressure inputs figure 1: time-resolved velocity estimation from inflow pressure synchronized measured with piv. (a) r/d = 0 (b) r/d = 0.5 (c) real-time estimation with 2d vorticity (ω d u∞ ) contours and velocity vectors figure 2: (a),(b): a comparison of velocity spectra at x/d = 6 from nn architectures, stochastic estimation, and howtire measurements; (c): instantaneous flow reconstruction from bi-lstm. figures 2(a) and 2(b) display the streamwise velocity spectra estimated from nn architectures using the first 50 pod modes, with the results compared to ones from spectral linear stochastic estimation (slse) [4] and hotwire measurements at same locations. both nn schemes are capable of highlighting the broadband peak at low strouhal numbers. the unique advantage of bi-lstm architecture is featured in the attenuation of high frequency noise with a rapid roll-off. time-resolved velocity reconstruction from the bilstm architecture is exhibited in figure 2(c), where the streamwise convection of coherent structures inside the jet mixing layer is observed as well as the formation of larger eddies downstream of the jet potential core. the estimation result represents the space-time dynamics of the acoustic sources in the jet mixing layer, and is of great importance to enhance the understanding of the noise generation mechanism. acknowledgements the authors at the university of florida acknowledge the support of nsf under award cbet-1704768. references [1] mohan, a. t., and gaitonde, d. v., “a deep learning based approach to reduced order modeling for turbulent flow control using lstm neural networks,” arxiv:1804.09269, 2018. [2] brunton, s. l., noack, b. r., and koumoutsakos, p., “machine learning for fluid mechanics,” annual review of fluid mechanics, vol. 52, no. 1, 2020, pp. 477–508. [3] sirovich, l., “turbulence and the dynamics of coherent structures part i: coherent structures,” quarterly of applied mathematics, vol. 45, no. 3, 1987, pp. 561–571. [4] tinney, c., coiffet, f., delville, j., hall, a., jordan, p., and glauser, m., “on spectral linear stochastic estimation,” experiments in fluids, vol. 41, no. 5, 2006, pp. 763–775. 14th international symposium on particle image velocimetry (ispiv 2021) page 1 of 2 pressure calculation for flows with moving surface boundaries from particle tracking velocimetry (ptv) reza azadi and david s. nobes* applied thermofluids lab., department of mechanical engineering university of alberta, edmonton, canada *david.nobes@ualberta.ca the examples of flow conditions, where an object of a fixed or deformable body moves in a fluid, or the interface between the flow phases instantaneously changes its topology, are numerous in industry and natural sciences. the advent of particle image velocimetry (piv) [1] and particle tracking velocimetry (ptv) [2] enabled the measurement of the instantaneous velocity fields in these types of complicated flow fields. as a next step, several methodologies have been developed in the past decade to calculate the pressure fields from piv or ptv data [3,4]. these methods were developed based on the assumption of a stationary flow domain, with surface boundaries that are fixed and independent of time. this makes the current pressure calculation methods inapplicable to a flow domain with deformable moving surface boundaries. also, for most of the two-phase flows, the capillary forces are significant and the pressure drop over the two-phase interface must be considered. therefore, the current pressure calculators require an improvement in the formulation of the algorithms to account for the deformable volume conditions and the effect of the surface tension force. for the calculation of pressure from sparse ptv velocity data, firstly, a tessellation method is required to interconnect the irregularly spaced vectors in the flow field using a highquality mesh grid. the mesh must be dynamic and adjust itself to the moving boundaries. this tessellation method has already been developed by the current authors [5]. as the next step, equations of motion for a deformable c.v. need to be coupled with the tessellation method to calculate the instantaneous pressures in a two-phase flow field, with a moving interface, which will be the ultimate goal of the current study. the conservation equations of volume, mass, and momentum, governing an isotropic fluid flow, embedded in a control volume (c.v.) with deformable surface boundaries are formulated as [6]: 𝑑𝑉 𝑑𝑡 = ∫ 𝐮s ∙ 𝐧𝑑𝐴𝑆(𝑡) , (1) 𝑑(𝜌𝑉) 𝑑𝑡 + ∫ 𝜌(𝐮 − 𝐮s) ∙ 𝐧𝑑𝐴𝑆(𝑡) = 0, (2) 𝑑(𝜌𝐮𝑉) 𝑑𝑡 + ∫ 𝜌𝐮(𝐮 − 𝐮s) ∙ 𝐧𝑑𝐴𝑆(𝑡) = ∫ (𝜌𝐠 − ∇𝑝 + 𝜎𝜅𝐧)𝑑𝑉 𝑉(𝑡) + ∫ 𝜇(∇𝐮 + ∇𝐮t) ∙ 𝐧𝑑𝐴 𝑉(𝑡) , (3) where 𝑆(𝑡) and 𝑉(𝑡) are the time-dependent control surface (c.s.) and c.v. of a cell. here, 𝐧 is normal to the surface area of 𝐴, pointing outward. the fluid and the control surface velocities are depicted by 𝐮 and 𝐮s, respectively and 𝜌 and 𝜇 are the density and dynamic viscosity of the fluid. 𝑝 is pressure, and 𝐠 is the gravitational acceleration vector. the surface tension coefficient is shown by 𝜎, and the curvature of the interface between two-phases is defined as 𝜅 = ∇ ∙ 𝐧. here, the surface tension force was modeled as a body force [7]. equation (1) acts as a geometrical restrain, describing the changing rate of the volume as a result of moving surface boundaries of the c.v. [6]. the set of equations (2)-(3) can be discretized using high-order schemes, which need to satisfy equation (1) for a dynamic mesh of that time step. different scenarios of a gas-liquid two-phase flow, with the gas phase being the ambient air and the liquid phase a mixture of pure glycerol and distilled water were generated using an experimental setup based on the particle shadow velocimetry (psv) [8]. two versions of capillaries were manufactured using stereolithography apparatus (sla) additive manufacturing technique: a straight square channel with a cross-sectional area of 3 × 3 mm2, and a sinusoidal channel with a throat size of 0.5 mm, depth of 1 mm, amplitude of 1.25 mm and wavelength of 12 mm. the straight and sinusoidal channels were designed to generate a single moving non-deformable bubble, and multiple moving deformable bubbles, respectively. as shown in figure 1, from ptv (or piv) a dense velocity field can be calculated in the liquid phase, which means 𝐮 in equations (1)-(3) becomes a known parameter. information of the fluid volume and the velocity mailto:david.nobes@ualberta.ca 14th international symposium on particle image velocimetry (ispiv 2021) page 2 of 2 of the surface boundaries at each time can be extracted by an accurate image-processing algorithm. identification of the temporal evolution of the two-phase interface makes it feasible to calculate the curvature 𝜅(𝑡) in equation (3). with 𝑉, 𝐮, 𝐮s and 𝜅 known at each time, the set of equations (1)-(3) simplifies to an equation with the pressure as the only unknown, which, with a proper definition of the boundary conditions, and a suitable iterative method is solvable. to do this, the first step is to interconnect the sparse ptv velocity vectors in the flow domain using a high-quality mesh grid, which needs to dynamically adjust to the deformable and moving boundaries of the flow field. this part of the algorithm has been successfully developed and validated, for which the details are given in azadi et al. [5]. figure 1 represents the sample tessellation results for two different snapshots of the gas-liquid flow field in the sinusoidal channel. here, the outline of the bubble moves and deforms with time, which imposes moving boundaries to the control volume embedding the liquid flow, hence demanding a dynamic mesh to tessellate and to solve for pressure. figure 1: snapshots of a gas-liquid flow field, with moving and deformable interfaces in a sinusoidal capillary for two different instants. here, (a) shows the raw images of the seeded liquid field and the outlines of the bubbles. the highquality mesh domains shown in (b) are the results of applying the tessellation method of azadi et al. [5]. (c) the ptv velocity field interpolated on the mesh domains shown in (b), with interpolated uniform vectors drawn on top of them. the resultant dynamic mesh and the interconnected ptv velocity field, shown in figure 1, along with the calculated interface curvature from image processing, can be introduced to each cell in the domain, using equation (3), to calculate for the instantons pressure field. here, the accuracy of the ptv data, the selection of proper discretization schemes, the tessellation and curvature calculation methods used, all impact the final calculated pressure. for the full paper, details of the developed algorithms will be presented, and the applicability of the method will be demonstrated through applying it to several analytical problems and experimental data for flow scenarios in the straight and sinusoidal channels. references [1] raffel m, willert c e, scarano f, kähler c j, wereley s t and kompenhans j 2018 particle image velocimetry (cham: springer international publishing) [2] schanz d, gesemann s and schröder a 2016 shake-the-box: lagrangian particle tracking at high particle image densities exp. fluids 57 70 [3] auteri f, carini m, zagaglia d, montagnani d, gibertini g, merz c b and zanotti a 2015 a novel approach for reconstructing pressure from piv velocity measurements exp. fluids 56 45 [4] schneiders j f g, caridi g c a, sciacchitano a and scarano f 2016 large-scale volumetric pressure from tomographic ptv with hfsb tracers exp. fluids 57 164 [5] azadi r, wong j and nobes d s 2021 determination of fluid flow adjacent to a gas/liquid interface using particle tracking velocimetry (ptv) and a high-quality tessellation approach exp. fluids (in pub) [6] perot b and nallapati r 2003 a moving unstructured staggered mesh method for the simulation of incompressible free-surface flows j. comput. phys. 184 192–214 [7] brackbill j ., kothe d . and zemach c 1992 a continuum method for modeling surface tension j. comput. phys. 100 335–54 [8] estevadeordal j and goss l 2005 piv with led: particle shadow velocimetry (psv) technique 43rd aiaa aerospace sciences meeting and exhibit (reston, virigina: american institute of aeronautics and astronautics) 𝑆 , 𝑆 𝑡 , 𝐮s 𝑡 𝐴 , 𝑡 , 𝑉 , 𝑡 , 𝐧 , 𝑡 , 𝜅 𝑆 , 𝐧 , 𝑡 𝐮 , 𝑡 𝑝 , 𝑡 ?image processing [5] & ptv dynamic meshing & tessellation [5] 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 experimental investigations of the turbulent/non-turbulent interface over surface with spanwise heterogeneity yanguang long1, jinjun wang1∗, chong pan1 1 beijing university of aeronautics and astronautics, fluid mechanics key laboratory of ministry of education, beijing, china ∗ jjwang@buaa.edu.cn abstract the sharp but irregular interface that separates the instantaneous turbulent and irrotational flows is termed as the turbulent/non-turbulent interface (tnti). tnti can be widely observed in various types of flow, such as turbulent boundary layers, jets and combustion flame fronts. due to its importance on the intermittency and entrainment process, tnti has been widely explored in its geometry and dynamic properties (da silva et al., 2014). most of the studies focus on the tntis in smooth plane boundary layer, while few investigate the effects of wall shapes. however, the wall conditions in many engineering applications are complex and heterogeneous, which will induce large-scale heterogeneity (barros and christensen, 2014) and require further investigations. to shed new light on the intermittency and entrainment above complex surfaces, the tnti over spanwise heterogeneity are investigated here with time-resolved stereoscopic piv (tr-spiv). the model and tr-spiv experimental set-up are shown in fig. 1. the experiments are conducted in the low-speed water channel at beijing university of aeronautics and astronautics. the spanwise distance s between two adjacent ridges is s/〈δ〉= 1.35, where 〈δ〉 is the spanwise-averaged boundary layer thickness. this spanwise distance is selected to induced strong secondary vortices (vanderwel and ganapathisubramani, 2015; wangsawijaya et al., 2020). the reynolds number based on the streamwise location x is rex = 7.2×105. the field of view is around 2s×1.8s, and is captured by two cmos cameras (2048×2048 pixel) with sampling rate as 500hz. the averaged resolution is about 8 pixels per kolmogorov scale (calculated at y/〈δ〉 = 0.6), which is high enough for tnti-related research (borrell and jiménez, 2016). the tnti is detected by the magnitude of local enstrophy ω2/2, and the threshold is selected to be the value where changing the threshold has the smallest influence on the tnti-mean-height (watanabe et al., 2018). the time-mean velocity and tnti location are present in fig.2(a). a pair of counter-rotating largescale secondary vortices (svs) are induced over the ridge-type roughness. at the position where svs induce upwash flow, a low-momentum pathway (lmp) can be observed, while the time-mean height of tnti 〈yi〉 is brought higher. as a contrast, where downwash flow induces high-momentum pathway (hmp), 〈yi〉 is lower. camera 1 camera 2 laser plane x z y o z y s u0 h (a) (b) o figure 1: model and tr-spiv experimental set-up. (a): axis view; (b): spanwise-vertical cutaway view figure 2: (a) the time-mean velocity and tnti location. background colormap: streamwise velocity; black vectors: spanwise and vertical velocity; blue curve: tnti location. (b) the p.d.f. of tnti height at three locations denoted in (a); the pink curve is the gaussian distribution. tnti properties are further discussed from two aspect. the geometry properties are firstly investigated. the fractal dimension of the tnti keeps as 2.3 along the spanwise direction. this value is consistent with the result over smooth plate (borrell and jiménez, 2016; wu et al., 2020) and riblets plates(cui et al., 2019), which indicates that the wall shapes do not influence the multiscale properties of the tnti. the streamwise wavelength of the tnti (λi) is further obtained by calculating the streamwise pre-multiplied spectrum of the tnti. it is found that at each spanwise location, λi is identical to the wavelength of streamwise velocity fluctuation at the tnti mean height. this shows that the large-scale fluctuation of tnti is controlled by the large-scale streamwise velocity fluctuation structures. secondly, the p.d.f. of tnti instantaneous height is investigated, as shown in fig. 2(b). it can be observed that the p.d.f. of tnti height above lmp shows a negative skewness, while the p.d.f. above hmp skews positively. a closer look at instantaneous structures shows that the skewness is attributed to the different probability of q2/q4 events in lmp and hmp. acknowledgements this work was supported by national natural science foundation of china (grant number 91852206, 11721202) references barros jm and christensen kt (2014) observations of turbulent secondary flows in a rough-wall boundary layer. journal of fluid mechanics 748:r1 borrell g and jiménez j (2016) properties of the turbulent/non-turbulent interface in boundary layers. journal of fluid mechanics 801:554–596 cui g, pan c, wu d, ye q, and wang j (2019) effect of drag reducing riblet surface on coherent structure in turbulent boundary layer. chinese journal of aeronautics 32:2433–2442 da silva cb, hunt jc, eames i, and westerweel j (2014) interfacial layers between regions of different turbulence intensity. annual review of fluid mechanics 46:567–590 vanderwel c and ganapathisubramani b (2015) effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. journal of fluid mechanics 774:1–12 wangsawijaya dd, baidya r, chung d, marusic i, and hutchins n (2020) the effect of spanwise wavelength of surface heterogeneity on turbulent secondary flows. journal of fluid mechanics 894:a7 watanabe t, zhang x, and nagata k (2018) turbulent/non-turbulent interfaces detected in dns of incompressible turbulent boundary layers. physics of fluids 30:035102 wu d, wang j, cui g, and pan c (2020) effects of surface shapes on properties of turbulent/non-turbulent interface in turbulent boundary layers. science china technological sciences 63:214–222 14th international symposium on particle image velocimetry・august 1-4, 2021 | chicago, il usa large scale piv for confined fires. e. varea, b. betting, c. gobin, g. godard, b. patte-rouland, b. lecordier* normandie univ, insa rouen, unirouen, cnrs, coria, 76000 rouen, france: * correspondent author: bertrand.lecordier@coria.fr keywords: large scale piv, piv processing, fire, enclosure fire. 1. introduction fire safety engineering, including knowledge of fire dynamics and fire-related hazards is crucial for securing people as well as rescue teams during interventions. one of the main critical aspects remains in determining the smoke dynamics at openings where fresh air and hot fumes mix. this particular phenomenon, encountered in many enclosures fires can reveal either wellventilated or under-ventilated fires. the response techniques of rescue teams are different depending on the ventilation status. merci et al. (2016), bengtsson et al. (2001) and pretrel et al. (2012) have studied fire in enclosures that occur in oxygen-limited conditions. generally, smoke dynamics are studied by using different devices or techniques. these include, among others, pitot probes and bidirectional probes or mccaffrey probes, mccaffrey and heskestad (1976). however, these probes are intrusive and potentially affecting the smoke dynamics. moreover, only one-point data are evaluated. to overcome this difficulty, laser techniques such as piv can be set up, see tieszen et al. (2002) , hou et al. (1996) or koched et al. (2012). piv technique has already been used in case of well-ventilated and under-ventilated fires conditions. a natural extension of this technique remains in applying the piv technique close to the outlet of the container in order to highlight exchanges between hot exhaust fumes and fresh incoming air. the objectives of the paper remain threefold: 1. first, we propose a specific design of enclosure fire to ensure large scale piv measurements inside the enclosure. 2. second, the transition from ventilated to under ventilated fire conditions is evaluated 2. experimental setup an experimental test bench is set-up to investigate the smoke dynamics characteristics of enclosure fires. two maritime containers, one for the test cell, one for the measure and control cell are mounted perpendicularly. the standard size of a maritime container is 6m×2.59m×2.45m. these structures have emerged as training tools in rescue services. the volume of these containers is close to that of a room of a standard flat, which is approximately 35m3. in the configuration, only one outlet (opposite to the fire) of 1m², is open. the fuel source consists of 36 propane burners with a surface area of 1m². fire can reach 1mw with temperatures inside the container of 1000°c. fig. 1 : laser and particle image large scale piv is still a complex task and it represents a challenge in terms of seeding, imaging technique and piv processing. indeed, it exists a compromise between spatial resolution and field of view. instantaneous, two-dimensional velocity measurements based on piv processing of alumina particles are used. alumina particles (al2o3) 5μm diameter) are chosen since they withstand high temperature due to combustion, see narayanaswamy and clemens (2013). these particles are injected through an in-house air supply corona, which is positioned below the burner. particles are injected in a such way that the fresh air injection dynamics are not modified. as low as 10 % of air to reach stoichiometric condition is used to feed the burner with particles seeded air. the flow is lightened by a nd:yag laser (quantel qsmart, 2*400 mj/pulse). a -20mm cylindrical lens produces a 0.5mm thick laser sheet. mie scattering from the particles is collected on 4 ccd (charge-coupled device) cameras, (jairm4200, 12 bits, 2048*2048pix2) mounted with 50mm f/1.2 zeiss lens. a 532nm interferential filter reduces noise from ambient light sources. the optical arrangement yields a magnification of 5pix/mm. an illustration is given in fig. 1, more details are available on betting et al. (2019). data are recorded using dantec dynamics software. raw images are post-processed with an in-house piv software developed by dr. b. lecordier. the four individual piv images are first combined into a single frame of around 4kx4k using a reference grid used to determine the camera model. images combination is made using polynomial camera model of 5th order to compensate 14th international symposium on particle image velocimetry・august 1-4, 2021 | chicago, il usa optical distortion and camera tilt. the relative images repositioning has been estimated to 0.1 pixels from analysis of overlapped visualization zones. a specific preprocessing to reduced correlation on identified structures resulting from local soot generation or interfaces due to non-seeded fresh air coming from the opening has been developed. then piv processing is performed using a cross-correlation technique between successive image pairs obtained after images recombination. the size of the piv interrogation windows is 64pix2 with a 50% overlap. a maximum spatial resolution of 2.5cm is reached. the time interval between two consecutive images is in the range of 1 to 2.5ms, depending on the powers and therefore flow velocity. 3. average vertical velocity profiles at the outlet figure 2 shows the vertical component of the velocity profiles for 200kw, 500kw and 800kw input powers. in order to get as close as possible to the outlet, the velocities are measured in the upper part of the laser sheet. velocities are plotted along the x-axis. the colours red, blue and black represent the power of 200 kw, 500 kw and 800 kw, respectively. in fig. 2, one can see that for the three cases, the first 0 to 500 mm reports positive velocities, which corresponds to hot smoke going out from the enclosure. moreover, the higher is the power, the higher velocities are observed. this is linked to the increase of hot fumes that are released with increased powers. in the second part of the image -500 to 1000 mmnegative or positive velocities are observed. a fresh air return for 200kw and 500kw powers therefore exists. for the 800kw power case, no fresh air return is observed. following this observation, hot fumes leaving the volume interfere with the entry of fresh air, but in average only positive velocities are observed. fig. 2 vertical velocity profiles at the outlet. 4. conclusion in this study, the flow topology of a confined fire is evaluated by large scale piv measurements. powers up to 1mw are reached. an experimental setup composed of 4 piv cameras and a high energy laser allows measurement of velocity fields at the exit of the container. the velocity profiles of the vertical component along the x-axis are evaluated for both well-ventilated and under-ventilated conditions, below and above 500kw. for ventilated conditions, it is shown that a wellestablished structure where fresh air and hot fumes enter and exit the cell exists. however, for underventilated conditions, there is no significant fresh air inlet and only the air provided by the injection system facilitates combustion in conclusion, the existence of well-ventilated and under-ventilated conditions from velocity fields is demonstrated, resulting in a flowbased criterion that might make it easier the determination of ventilation status considering large scale confined fires. references 1. b. merci, t. beji, fluid mechanics aspects of fire and smoke dynamics in enclosures, crc press, 2016. 2. b. mccaffrey, g. heskestad, a robust bidirectional low-velocity probe for flame and fire application, combustion and flame 26 (1976) 125 –127. 3. l. bengtsson, enclosure fire, swedish rescue services agency, karlstad, sweden, 2001. 4. h. prétrel, w. l. saux, l. audouin, pressure variations induced by a pool fire in a well-confined and force-ventilated compartment, fire safety journal 52 (2012) 11 – 24. 5. s. tieszen, t. o’hern, r. schefer, e. weckman, t. blanchat, experimental study of the flow field in and around a one meter diameter methane fire, combustion and flame 129 (4) (2002) 378 – 391. 6. x. c. hou, j. p. gore, h. r. baum, measurements and prediction of air entrainment rates of pool fires, vol. 26, 1996, pp. 1453 – 1459. 7. a. koched, h. pretrel, l. audouin, o. vauquelin, f. candelier, application de la piv sur un écoulement de fumée à un passage de porte induit par une source incendie, 13ième congrès de techniques laser, cftl, 2012. 8. v. narayanaswamy and n. clemens, simultaneous lii and piv measurements in the soot formation region of turbulent nonpremixed jet flames. proceedings of the combustion institute, 34(1) :1455–1463, 2013 9. b. betting, e. varea, c. gobin, g. godard, b. lecordier, b. patte-rouland, experimental and numerical studies of smoke dynamics in a compartment fire. fire safety jurnal, 2019, 108, pp.102855. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 fluid structure interactions of a pitching wing at high angle of attack g. acher1∗, patrick braud1∗, ludovic chatellier1∗, lionel thomas1∗, laurent david1∗ 1 institut pprime, upr 3346, cnrs-universit de poitiers-ensma, france ∗ laurent.david@univ-poitiers.fr abstract this paper deals with the study of the flow around a pitching wing at high angle of attack. different pitching amplitudes and frequencies are studied using dic and lpt measurements. the fluid structure interactions are shown and exhibit that the vortex shedding could be reduced by actuating the wing at specific frequencies. 1 introduction in high incidence conditions, wings are subjected to large vortex detachments which promote the dynamic stall leading to a sudden drop in lift. under such conditions it is often necessary to increase the lifting surface so that the effective angle of attack is reduced, or prevent vortex shedding by using actuators such as plasma actuators or micro jets with the objective of moving the point of detachment away from the leading edge. another way to reduce these massive detachments is to force pitching of the profile with a low amplitude around the characteristic frequencies of this vortex shedding. the object of the study is therefore to study the modifications of the flow in the case of a wing pitching around a position of high incidence and to measure the effects of this oscillation on the near wake, and simultaneously to look at the mechanical effects produced on the wing. measurements of the 3d deformation of a naca0015 flexible wing profile installed at a large angle of attack and pitching with small amplitude around the natural vortex shedding frequency at a reynold number of 105 are applied simultaneously with 3d flow measurements. wing time-deformation, volumetric instantaneous velocity fields are measured and correlated to show mutual influence between the flow and the wing. 2 results a wing profile of 146 mm span is placed at 15 angle of attack in the test section of a hydrodynamic tunnel. the naca0015-type wing profile, based on a 80 mm chord, is built of a 140 mm long straight section and its tip is formed by the rotation of the profile around the chord, adding 6mm of wingspan, at the position of maximum thickness. the profile is oscillating with an amplitude of 2 and 4 around the initial angle of incidence at different frequencies around the natural frequency of the vortex shedding (f=5.82 / 8.93 / 12.50 hz ). the surface of the wing is monitored by two high speed cameras so that both the pitching motion and deformations are characterized. four other high speed cameras are used to investigate the instanteous flow fields using lagrangian particle tracking (figure 1). time resolved estimation of the wing motion and deformation is obtained using the piv/dic method described by chatellier et al. (2013),. the technique is based on maximizing the correspondence of two back-projected images on the estimated solid surface. in order to follow the deformation of the wing profile in the test section, a speckle pattern is painted on its pressure side so that the two high speed cameras placed under the water tunnel image the full wingspan. an example of results is presented in the figure 2. the flow velocity field is measured using shake-the-box algorithm schanz et al. (2016), in order to provide 3d time-resolved particle tracks from the four camera recordings. velocity and acceleration are extracted (figure 3) and allow to calculate the main characteristics of the flow in terms of vorticity, q criteria figure 1: tomographic piv and stereo-dic setup as used for the pitching wings experiments figure 2: three-dimensional view of the reconstructed lower surface of the wing superimposed with the undeformed wing shape and pressure-from-piv estimates. correlation between the solid and fluid databases are then calculated to estimate the interaction between the fluid and structure and allow to understand the effect of the flexible wing for wake minimization and drag reduction. 3 conclusions the study of the flow around a pitching wing at high angle of attack has been carried out for different amplitudes and frequencies of the wing. dic and lpt measurements have been recorded to understand the fluid structure interactions and exhibit that the vortex shedding is modified with specific frequencies and allow the drag reduction. acknowledgements the authors would like to thank the project homer : holistic optical metrology for aero-elastic research under the european unions horizon 2020 research and innovation programme (grant agreement no 648161)and the cper numerics program for their fundings. figure 3: lpt sample measurements on the pitching flexible wing (z=70mm, f=5.89hz, =2) references chatellier l, jarny s, gibouin f, and david l (2013) a parametric piv/dic method for the measurement of free surface flowsa parametric piv/dic method for the measurement of free surface flows. experiments in fluids 54:1488 schanz d, gesemann s, and schrder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 introduction results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 on the challenges of precise velocity measurements in vertical convective wall jets h. otto∗, c. cierpka technische universität ilmenau, institute of thermodynamics and fluid mechanics, ilmenau, germany ∗ henning.otto@tu-ilmenau.de abstract for the transition of our energy supply towards a higher share of renewables, thermal energy storage (tes) systems are, besides electric batteries and chemical energy storage systems, one promising solution to overcome the volatile nature of renewable energy sources. for the most efficient operation, the liquid storage material in the tank should be stratified by its temperature-dependent density. as a result, the cold fluid remains at the bottom, and the heated fluid rises to the top (alva et al. (2018)). typically steel tanks are used for tes, and thus, the wall material has a thermal diffusivity that is one to two orders of magnitude higher than that of the storage fluid. consequently, the tank’s sidewalls work as a thermal bridge between the stratified layers. in recent studies, the authors have shown that the resulting heat flux induces two counterdirected, convective wall jets near the sidewalls of the tank, which increase mixing of the stratification and thus lowers the exergy content and the storage efficiency (otto et al. (2019, 2020)). using a model experiment of a tes, the entire vertical extent of the detected wall jets is investigated. hence, the typical flow structures of vertical, natural convection under the influence of non-zero temperature gradients in the ambient fluid can be analyzed, which can help to improve storage tanks in the future. the velocity in the region of the wall jets is measured via 2d particle-image velocimetry (piv) in a rectangular model experiment of 750mm height on a base area of 375mm× 375mm made from polycarbonate. the jets evolve on the surface of an aluminum plate simulating the storage tank’s sidewall. the measuring system consists of four cameras with a resolution of 2160×2560 pixels combined with objective lenses with 100mm focal length capturing the raw images in a plane perpendicular to the aluminum wall. a nd:yag laser with a wavelength of 532nm illuminates the measuring plane. simultaneously using up to four cameras adjacent to each other and stitching their resulting vector fields, the vertical extent of the field of view increases from 38mm up to 140mm. despite this, the field of view is still much smaller than the vertical extent of the model experiment, so that seven consecutive runs are performed to cover the entire height. disturbing reflections of the laser light sheet on the aluminum wall are eliminated using optical filters for the cameras that are opaque for the green laser light in combination with fluorescently (rhodamine b) dyed pmma tracer particles with a diameter between 1–20µm. the particles emit light at a wavelength of 610nm (orange light) and can therefore be detected through the cameras’ filters. during four separate measuring periods, where each lasts for two minutes, double frame images are captured with a time difference of 19.981 ms (maximum possible value) at a measuring frequency of 7 hz. figure 1 shows a schematic of the camera setup next to the model experiment and the measurement and evaluation procedure to finally receive one time-averaged velocity field per measuring period of the full height of the experiment. the raw data evaluation process starts with calculating the vector fields of all cameras used at a certain measuring position and stitching them to one flow field of this position. since the wall jets’ horizontal extents are with 2–7mm relatively small and they show high velocity gradients, the raw images are evaluated in both single-frame and double-frame mode. with a velocity threshold that corresponds to a pixel displacement of 1 4 of the interrogation window size and the time difference of the single-frames, the resulting vector fields are masked and merged into one final vector field. this vector field consists of high velocities evaluated in double-frame mode and low velocities evaluated in single-frame mode (see figure 2) thus minimizing the relative error. the algorithm used in this work is similar to the multi-frame piv approach introduced by hain and kähler (2007). figure 3 shows the time-averaged results of the first measuring period for each of the seven measuring positions in height. measuring plane field of view cameras measurements at 7 different heights 7 hz meas. frequency ∆t ∼ 20 ms double frame single frame masking of double frame and single frame vector fields combined vector field results stitching of 7 measurements → averaged vector field of the entire measuring plane model room + alu. plate figure 1: schematic of the camera setup and the evaluation procedure. figure 2: a) masking areas of single and double frame evaluation. b) resulting vertical velocity field after merging. figure 3: resulting vertical velocity fields of the 7 measurements at different heights. subfigure b) equals figure 2b). each subfigure shows the stitched velocity field of all cameras used during that measurement. acknowledgements the authors acknowledge support from the german research foundation (deutsche forschungsgemeinschaft, dfg) within the priority programme turbulent superstructures spp 1881. references alva g, lin y, and fang g (2018) an overview of thermal energy storage systems. energy 144:341–378 hain r and kähler cj (2007) fundamentals of multiframe particle image velocimetry (piv). experiments in fluids 42:575–587 otto h, resagk c, and cierpka c (2019) convective near-wall flow in thermally stratified hot water storage tanks. in proceedings of the 13th international symposium on particle image velocimetry ispiv2019, munich, germany, july 22-24 otto h, resagk c, and cierpka c (2020) optical measurements on thermal convection processes inside thermal energy storages during stand-by periods. optics 1:155–172 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 simultaneous piv and dic measurements in a towing tank environment with a flexible hydrofoil g. jacobi1∗, a. nila2 1 delft university of technology, ship hydromechanics and structures laboratory, delft, the netherlands 2 lavisionuk ltd, united kingdom ∗ g.jacobi@tudelft.nl abstract due to their good mechanical properties composite materials are increasingly applied for the construction of lifting surfaces in the maritime industry. however, besides improving the strength to weight ratio of a structure, the anisotropic material properties can also exhibit bend-twist coupling, when exposed to higher loads. in order to experimentally measure the fluid structure interaction, the object of investigation needs to exposed to the same fluid loadings, as it would experience during operation. to investigate the possibility to obtain simultaneous deformation and flow field measurements in a large hydrodynamic testing facility simultaneous piv and dic measurements are performed to obtain the deformation of a flexible naca 0008 hydrofoil and to measure the flow field in the wing tip region. for the assessment of the performance of the methods two scenarios are presented including tests in stationary conditions with constant angles of attack and forced plunging oscillations. the calibration of both measurement systems is done independently and the wing tip, visible in the piv images, is used for triangulation to find the position of the wing within the piv coordinate system. the combination of both measurement techniques allows for an accurate determination of tip vortex center positions with respect to the deformed wing and their evolution downstream of the wing. during forced plunging motions, the phase lag of the wing tip and the influence on the wing tip vortex is observed. 1 introduction within the last two decades, the maritime industry has been increasingly investigating the use of composite materials and lightweight structures. with composite materials offering higher strength to weight ratios than traditional materials, propellers and tidal turbines were designed with improved vibration properties and higher fatigue life. especially in performance sailing, but also in the area of passenger transport, composite hydrofoils and lightweight structures lead to the development of fully foiling boats, where the hull is lifted out of the water to reduce its frictional drag. next to an improved strength to weight ratio, due to their anisotropic properties, composite structures may exhibit bend-twist coupling, which leads to a change of the shape of the structure, when exposed to higher loads. this behavior enables a structure to passively adapt its shape to the incoming flow, therefore allowing for an enhanced hydrodynamic performance to be accounted for in the design process. under these circumstances the composite material cannot be modeled as a rigid structure since the hydrodynamic and structural analysis are strongly coupled. to consider the fluid-structure-interactions (fsi) in the design phase, but also to develop a further understanding of the hydrodynamics and structural effects due to the interaction, numerical modeling supported by experimental investigations are needed. despite being interested in the hydrodynamic performance, the fluid structure interaction of hydrofoils at larger scales has only been tested in wind-tunnel facilities, up until now. marimon giovannetti (2017) performed simultaneous particle image velocimetry (piv) and digital image correlation (dic) measurements in a wind tunnel to investigate the structural deformation of a hydrofoil and its influence on the tip vortex at different angles of attack. while testing at an equivalent reynolds number, the flow around the hydrofoil can be correctly analyzed in these facilities. however, the fluid dynamic loads are five times smaller compared to testing in water. to expose the foil to the same fluid loadings as it would experience during operation, marimon giovannetti (2017) proposed to put further effort in the development of a system to simultaneously measure the structural deformation and flow features in a towing tank environment. several tests to measure structural deformations in small cavitation tunnels have been performed (young (2018)). however, due to the small dimensions of these, the size of the investigated object is limited. with piv measurements having become a standard technique for analyzing the flow field during towing tank tests (falchi et al. (2013)), (hallmann et al. (2009)), this paper presents a first application of the combination of the two optical measurement techniques, piv and dic, in a towing tank environment for the analysis of a flexible hydrofoil. 2 test case to test the feasibility of the simultaneous measurement of structural deformations and the herewith associated flow field with an underwater piv and dic system, a flexible naca 0008 hydrofoil is tested in the tu delft towing tank. for a simplified prediction of the expected deformations, the wing profile is manufactured from silicone, with a 1 mm aluminum plate integrated at the camber line. to prevent any sideward forces, the foil is tested in a t-foil configuration. the distance of the hydrofoil to the free surface is 5 chord length. the submerged t-foil with a total wing span of 500 mm is depicted in figure 1 (left), with figure 1 (right) showing the outline of the modified naca 0008 profile with the integrated steel plate. the angle of attack of the foil can be adjusted at the connection of the strut with the foil. figure 1: photograph of the submerged hydrofoil (left) and outline of the modified naca 0008 profile with a 1mm aluminum plate at the camber line (right) for the assessment of the performance of both measurement techniques, two different test scenarios are presented. during the first scenario, the hydrofoil is towed at 1m/s at different angles of attack, varying from 3 to 9 degrees, to obtain the time averaged deformation of the foil, as well as the associated flow field in the wake of the foil. in a second scenario, the hydrofoil is towed with the same velocity of 1 m/s, but is subjected to forced sinusoidal heave oscillations at a frequency of 1 hz. simultaneous dic and piv measurements are used to capture the phase-averaged characteristics of the hydrofoil structure, as well as the flow field in its wake. 3 experimental setup figure 2 (left) gives a general overview of the test setup, showing the towing tank carriage of the towing tank of the tu delft ship hydrodynamics laboratory with the attached foil and the optical measurement equipment. the towing tank is 150 m long with a cross section of 4.5 m width and 2.5 m depth. a more detailed description of the setup can be found in figure 2 (right). the flexible hydrofoil, as well as the dic system are attached to a hexapod mounted on the towing carriage. this allows for the performance of forced oscillatory motions and a repositioning of the hydrofoil in between measurement runs. to capture the deformation of the submerged hydrofoil, the dic system is fitted into a generic ship hull. the piv system, including cameras and laser optics is fitted into a torpedo shaped probe which is towed next to the hydrofoil. figure 2: schematic drawing of the towing tank carriage with the attached measurement configuration (left) and schematic drawing of the detailed measurement setup, including the flexible wing and both optical measurement systems (right) 3.1 deformation measurements a schematic overview of the optical dic setup is presented in figure 3 (left). image acquisition is done with two lavision imager m-lite 2m cameras both looking at the object of investigation under an angle of 45 degrees through water-filled prisms attached to the acrylic glass bottom. as the dic system is oscillating together with the hydrofoil, it is guaranteed, that the speckle pattern on the top of the hydrofoil will stay in focus, also with larger oscillation amplitudes. illumination for the dic measurements is done with two linear illumination units from lavision at a wavelength of 450 nm. recording of the images is done at 25 hz for both, the stationary and oscillation tests. to reduce the interference of the measurement systems, the dic cameras are equipped with bandpass filters. calibration is done with a two-level double-sided 3d calibration plate of 200 x 200 mm. during the calibration of the dic system, the target is horizontally aligned with the wing. prior to mounting the optical setup to the hexapod, the latter has been carefully aligned with the towing tank coordinate system. for measurement of the hydrofoil deformations, a random speckle pattern is a applied to its surface. the pattern is applied manually with spay paint. the final image speckle size is approximately 2 pixels with a standard deviation of ± 1.5 pixels. figure 3 (right) shows a recorded image of the hydrofoil with the speckle pattern. data acquisition and the calculation of deformations from the stereo-image pairs is conducted with the strain master package from lavision. after an initial triangulation to find the initial surface shape, the deformation is calculated with a subset size of 27 pixels and a step size figure 3: detailed schematic overview of the dic setup (left) and recorded raw image of the flexible wing with the applied speckle pattern (right) of 6 pixels. at a resolution of 5 pixels/mm this results in a spatial resolution of approximately 1.25 % of the chord length. to estimate the uncertainty of the obtained deformations, a series of images is recorded without moving the wing. a comparison of the obtained deformations results in a maximum uncertainty of 0.125 % of the chord length. 3.2 flow field measurements the stereo-piv system for the measurement of the flow field in the wake region of the hydrofoil is fitted into a torpedo shaped underwater housing, which together with the strut for the laser optics is towed next to the hydrofoil (figure 2 (right)). a detailed description of the torpedo and its modules is depicted in figure 4 (left). image acquisition is done with two lavision imager mx cameras with a resolution of 4 megapixels equipped with lenses of 28 mm focal length which are mounted to a motorized scheimpflug adapter with attached remote focus and aperture control. in front of the cameras water filled mirror sections are integrated into the torpedo, making both cameras facing the measurement area under an angle of 30 degrees. recording of the double frame images is done at 25 hz and synchronized with the dic system via the lavision programmable timing unit (ptu). as the measurement plane is oriented perpendicular to the towing direction, the time between two successive images is limited by the out-of-plane particle motion, resulting in a time separation of ∆t= 900 µs at a towing tank carriage speed of 1 m/s. figure 4: detailed schematic overview of the piv setup (left) and recorded raw piv images with the detected reference points which are used for triangulation illumination of the measurement area is done with a 50 mj litron nano-piv laser, operating at a wavelength of 532 nm. the laser beam is guided into a separate strut that includes the beam focusing optics and the cylindrical lens for generation of the sheet. the piv system has a stand-off distance of 1000 mm to the center of the measurement area, resulting in a resolution of approximately 6 pixels/mm. to guarantee a uniform distribution of the 50 µm polymer (vestosint) particles in the measurement area, a retractable seeding rake is mounted in front of the carriage. prior to releasing the particles into the towing tank in between measurement runs, they are premixed in a high shear flow to prevent clustering. after every measurement run the tank is reseeded and a waiting time of 25 minutes allows the water to settle in between runs. calibration is done with a two-level double-sided 3d calibration plate of 320x320 mm. the piv calibration target is carefully aligned in an iterative process with the moving direction of the carriage and the laser sheet. mounting the calibration plate to the hexapod allows for an accurate repositioning of the plate during the calibration process. a relation between the dic and piv coordinate systems is established after calibration with fiducial points on the tip of the flexible wing and the usage of the pinhole calibration model. this allows for a triangulation of the identified points, to find their position on the piv coordinate system. figure 4 (right) shows an example of raw images recorded with both cameras and the identified reference points on the leading and trailing edge on the wing tip which are used for triangulation. as no additional filters were used for the piv cameras, the illuminated wing is visible in te background of the images. however, due to the limited focal range of the piv cameras, it is not in focus and can be removed using a sliding average filter which is subtracted from the image prior to vector calculation. the velocity vectors are calculated in an iterative procedure, starting with an interrogation window size of 64x64 pixels with 50 % overlap with a final interrogation window size of 24 x 24 pixels with 75 % overlap. this results in a spatial resolution of 1 vector/mm which is 1.25 % of the hydrofoil chord length. figure 5 shows the final result of the matched coordinate systems with the reconstructed wing surface from the dic measurements and vorticity field in the tip vortex region obtained in multiple planes behind the wing for an angle of attack of 3 degrees. the piv results are obtained from averaging over 400 vector images. the obtained results clearly show the change of the hydrofoil shape due to the hydrodynamic loads and the diffusion of the tip vortex downstream of the hydrofoil. figure 5: reconstructed upper wing surface from dic measurements with time-averaged vorticity fields obtained from piv measurements at multiple stations behind the wing 4 results 4.1 steady motion for a detailed analysis of the influence of the wing shape on the tip vortex the exact shape and deformation of the wing and its position relative to the tip vortex has to be known. for this purpose, the wing shape is reconstructed for angles of attack of 3, 6 and 9 degrees, obtained at a constant translation of 1 m/s. figure 6 (left) shows the reconstructed wing shapes for the tested angles of attack, clearly indicating the upward displacement of the wing tip and the twist which are increasing with increasing angle of attack due to the hydrodynamic load. by considering the wing as an idealized beam with one fixed and one free end and the lift force as a distributed load, a least-squares fit of the bending curve allowed an estimation of the lift forces. the results are show in figure 6 (right), which shows the expected linear distribution within the considered range of angles of attack. a detailed overview of the leading edge displacement which was considered for figure 6: reconstructed upper wing surfaces at 3,6 and 9 degrees of angle of attack (left) and approximated lift coefficient obtained from the deformation measurements figure 7: spanwise distribution of the vertical position of the leading edge (left) and angles of attack (right) for angles of attack of 3,6 and 9 degrees the estimation of forces is presented in figure 7 (left). figure 7 (right) shows the twist angle along the span of the wing which is calculated from the difference of measured leading and trailing edge positions. while at an angle of attack of 3 degrees, the amount of twist is negligible, at 9 degrees, the wing tip is twisted by approximately 2 degrees. having obtained the position of the wing within the piv coordinate system, the flow field of the tip vortex can be accurately related to the deformed wing tip position. figure 8 shows the vertical component of the flow field in the wing tip region two chord lengths behind the wing for angles of attack of 3,6 and 9 degrees. the continuous and the dashed line indicate the leading and trailing edge positions. to determine the position of the tip vortex center with respect to the deformed wing tip, the vortex center is estimated by finding the maximum of the γ1 distribution which is suggested by graftieaux et al. (2001): γ1(p) = 1 n ∑ s (pm∧um) · z ||pm|| · ||um|| , (1) with n being the number of points m within the rectangular area s with center p and um describing the velocity vector. the locations of the identified vortex centers from the measured flow field are included into figure 8. having obtained the flow field in a total of 14 positions behind the wing within the range of x/c=1-14, the position of the vortex center at these positions along the wake is obtained. results are figure 8: measured flow field in the wing tip region at x/c=2 for angles of attack of 3, 6 and 9 degrees with leading and trailing edge positions and the detected center of the tip vortex presented in figure 9 (left), showing the evolution of spanwise and vertical positions of the vortex centers along the wake. due to its robustness, the vortex center identification performs well over the whole length of the wake from x/c=1 to x/c=14, clearly reconstructing the inward motion of the tip vortices towards the root of the wing, which is increasing with increasing angle of attack. the vertical position of the tip vortices is presented in figure 9 (right) together with the wing profiles and their vertical displacement at the wing tip which is obtained from the dic measurements. the vertical tip vortex displacement increases with the upward displacement of the wing tips. while at 3 degrees, the downward motion of the vortices along the wake is negligible, it becomes clearly visible with higher angles of attack. figure 9: evolution of the detected tip vortex centers downstream of the flexible wing 4.2 forced oscillations the combination of the measurement of structural deformations together with the associated flow field becomes of even more importance when the position of the structure changes over time. the instantaneous position of the structure with respect to the flow field has to be known for an analysis of their interaction. phase-averaged oscillation tests are performed to investigate the temporal evolution of the wing tip vortex and its position with respect to the wing which is undergoing a forced plunging motion. to capture a sufficient amount of time steps over one oscillation cycle, the oscillation frequency was set to 1 hz. the angle of attack of the wing was set to 0 degrees. at an oscillation amplitude of 0.024 m this leads to a maximum apparent angle of attack of 8.5 degrees at 90 and 270 degrees of the oscillation cycle. the results from the forced oscillation tests are depicted in figure 10. figure 10 (top) shows the temporal evolution of the vertical position of the hydrofoil at the root and the wing tip. furthermore, the displacement of the wing tip with reference to its non-deformed position is given. as discussed by heathcote et al. (2008), the spanwise flexibility and the deformation resulting from the forced plunging motion results in an equivalent motion of the wing tip, which is varying in phase. due to the low stiffness of the wing used during the experiment, the vertical bending of the wing tip is shifted by 90 degrees and is proportional to the temporal evolution of the apparent angle of attack. the maximum deformation observed at the wing tip is comparable to the deformation observed during the static tests. the deformation results in a phase-lag of the vertical position of the wing tip with respect to the hexapod motion. the influence of the plunging motion on the flow field is depicted in figure 10 (bottom), showing the vorticity contours at two chord lengths behind the hydrofoil at selected phase-angles. the phase-averaged vorticity fields are obtained from a total of 20 oscillation cycles. taking into account the acceleration of the towing tank carriage and the limited length of the tank this is the maximum number of oscillations which could be performed within one measurement run. as the hydrofoil is towed at zero angle of attack, the rotation direction of the tip vortex changes due to the downward ad upward motion. due to the phase-lag of the wing tip with respect to the hexapod motion, the development of the tip vortex is also delayed. figure 10: temporal evolution of the hexapod motion, wing tip bending and total wing tip motion (top) and wing deformation with associated flow field two chord lengths behind the hydrofoil at selected phase angles (bottom). 5 conclusion with increasing use of composite materials in the maritime sector, more fluid structure interaction measurements in towing tanks will be needed in the future to simultaneously assess the structural deformation, as well as the measurement of the flow field. while up to now, the fluid structure interaction of hydrofoils has been only assessed in wind tunnel facilities, this paper presents a first application of simultaneous piv and dic measurements in a towing tank environment, where the object of investigation is exposed to the same fluid loadings as it would experience during operation in water. to obtain a sufficient number of images for the determination of the timeand phase-averaged characteristics of the structure and the flow field, the optical setup cannot be located outside of the towing tank, measuring the flow field at a single location of the tank, when the carriage passes the stationary measurement setup. instead, all optical components have to be attached to the towing tank carriage to be towed next to the investigated object. while both measurement techniques are of optical nature, the interference of both has to be reduced, selecting different wavelength for the illumination of the speckle pattern on the structure and the particles in the flow field. when combining different optical measurement techniques a common coordinate system is necessary. especially, when analyzing flexible structures, an exact knowledge of the position is vital for a low spatial uncertainty. the combination of dic and pic with both having high spatial resolutions and the usage of fiducial markers allows for a highly accurate determination of the position of the measured flow field vectors with respect to the deforming wing. references falchi m, grizzi s, aloisio g, felli m, and f df (2013) critical issues in the application of stereo-piv in large hydrodynamic facilities : study of a catamaran in steady drift. 10th internationnal symposium on particle image velocimetry -piv13 graftieaux l, michard m, and nathalie g (2001) combining piv, pod and vortex identification algorithms for the study of unsteady turbulent swirling flows. measurement science and technology 12:1422–1429 hallmann r, tukker j, and verhulst m (2009) challenges for piv in towing facilities. amt’09, nantes pages 10–22 heathcote s, wang z, and gursul i (2008) effect of spanwise flexibility on flapping wing propulsion. journal of fluids and structures 24:183–199 marimon giovannetti l (2017) fluid structure interaction testing, modelling and development of passive adaptive composite foils. ph.d. thesis. university of southampton young y (2018) load-dependent bend-twist coupling effects on the steady-state hydroelastic response of composite hydrofoils. compos struct 189:pp. 398–418 introduction test case experimental setup deformation measurements flow field measurements results steady motion forced oscillations conclusion 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 volumetric flow rate measurement using surface imaging techniques j. e. chávez-dorado1∗, b. a. johnson1 1 the university of texas at austin, department of civil, architectural & environmental engineering, austin, tx, usa ∗ jechavez@utexas.edu abstract the purpose of our research is to validate an experimental method developed by johnson and cowen (2016) aimed at measuring volumetric discharge in an open channel using surface particle image velocimetry (spiv) combined with turbulent boundary layer analysis to infer the bathymetry and calculate volumetric flow rate, ultimately extending this work to natural systems (hendrickson, 2020). 1 introduction the united states geological survey conducts thousands of streamflow measurements in rivers annually using in situ methods that typically employ intrusive techniques that may affect measurement quality. more modern methods (e.g. acoustic doppler current profilers, multi-beam echosounders) used to measure channel bathymetry provide access to larger bodies of water, but rely on in situ measurements across the channel. the technique developed by johnson and cowen (2016) leverages particle image velocimetry for streamgaging. it utilizes coherent turbulent structures in the instantaneous velocity field, which connect the bed to the free surface, to infer channel bathymetry. the strength of this technique lies in its unobtrusive nature, which allows for reliable and cost-effective data collection across large regions, and thus greater insight about turbulent dynamics across a stream than can be provided by point measurements. 2 methodology tests were performed in a 30 m long, 1.5 m wide, and 0.8 m high outdoor flume with several flow rates. surface flow and boundary layer data were collected via spiv and acoustic doppler velocimetry (adv), respectively. spiv data were captured by a downward-facing jai go 5000m camera above the flume centerline. the time between images, ∆t, ranged from 16 to 33 ms. an adv placed downstream of the spiv field of view (fov) was used to construct the velocity profile (hendrickson, 2020). floating seed particles were used for spiv measurements. the outdoor setting posed major illumination issues during data collection; surface reflections affected particle detection, and shadows on the flume bed obscured the contrast between particles and background. to enhance particle detection, an adaptive binarization algorithm was applied. the surface velocity field was then obtained using pivlab (thielicke and stamhuis, 2014). the volumetric flow rate is calculated using: q = n ∑ i=1 ubiai (1) where q is the total discharge, ai is the ith (or local) cross-sectional area of the n segments into which the entire cross section has been divided, and ubi is the corresponding ith mean velocity measurement. each local velocity component, ubi , was obtained from the relation ub = kusurf (where k is index velocity and usurf is surface velocity). index velocity varies with flow characteristics (johnson and cowen, 2017); thus k was determined at the centerline using ub constructed by the adv data and the surface velocity at the same location. last, k is used with local, spanwise usurf to obtain local depth-averaged velocity across the fov. the local depth across the channel was obtained from the surface velocity field. the integral length scale was used to connect surface dynamics with bathymetry. the integral length scale, l , provides streamwise (l11,1) and spanwise (l22,1) eddy sizes. sparse seeding due to illumination issues affects the averaging process, yielding values of l11,1 and l22,1 outside the theoretical range. l11,1 and l22,1 were used with measured flow depth to build a linear relationship and obtain local flow depths across the fov. 3 results & discussion test l11,1 % difference l22,1 % difference re =ubl/ν 1 0.07 47 38800 2 114 34 89500 3 62 18 118600 4 14 7 133500 5 22 30 59000 table 1: percent difference between estimated and measured discharge (hendrickson, 2020). ν is the kinematic viscosity of water, and l is the hydraulic radius (area over wetted perimeter). the flow rate estimation using l22,1 for obtaining local flow depths, hi, provides a better approximation than l11,1, in particular at high re. the large uncertainty in results (table 1) can be attributed to the difficulty in obtaining high quality images due to seeding inconsistencies and surface reflections, suggesting a need to continue to improve piv algorithms for sparse data in field applications. 4 conclusions spiv measurements were collected in an outdoor channel, in which inconsistent illumination produced sparse seeding and incomplete data sets, following binarization methods to improve image quality. this affected the quality of spiv analysis and the integral length scale. the correlation in the velocity fields is sensitive to factors such as wind, flow dynamics, and seeding, affecting the averaging process and yielding integral length scale values outside the theoretical range. in addition, our aspect channel aspect ratio of almost 1:1 produced a negative slope for the linear relation between l22,1 and channel depth, whereas johnson and cowen’s application in a shallow water channel yielded a positive slope for the same relation. acknowledgements we ackowledge funding provided by the fulbright program. we also thank gregory hendrickson for assisting with experiments and data analysis. references hendrickson g (2020) in-situ determination of volumetric flow rate via surface imaging techniques. master’s thesis. the university of texas at austin johnson ed and cowen ea (2016) remote monitoring of volumetric discharge employing bathymetry determined from surface turbulence metrics. water resources research 52:2178–2193 johnson ed and cowen ea (2017) remote determination of the velocity index and mean streamwise velocity profiles. water resources research 53:7521–7535 thielicke w and stamhuis e (2014) pivlab – towards user-friendly, affordable and accurate digital particle image velocimetry in matlab. journal of open research software 2:e30 introduction methodology results & discussion conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 flow field of impinging sweeping jets g. paolillo1∗, c. s. greco1, g. cardone1 and t. astarita1 1 university of naples “federico ii”, department of industrial engineering, naples 80125, italy ∗gerardo.paolillo@unina.it sweeping jets are oscillating jets generated by fluidic oscillators, i.e., devices designed to produce an oscillation of the flow without the use of any moving parts (raghu, 2013). a typical configuration of such devices consists of an expansion chamber connected to a high-pressure supply via a converging nozzle and provided with feedback channels. the oscillating motion in the expansion chamber is triggered by an inherent flow instability and sustained by the flow rate across the feedback channels. recently, sweeping jets have been studied in flow control applications for noise reduction, separation and circulation control over airfoils, control of resonant cavity oscillations and deflection of jets. the advantageous features of fluidic actuators, among which are the wide range of operating frequencies (up to khz with meso-scale) and the distributed momentum addition, have also stimulated an increasing interest in their application to electronics cooling. several recent studies on the convective heat transfer from impinging sweeping jets (e.g., hossain et al., 2018; park et al., 2018) have shown that, compared to conventional round jets, they offer higher cooling rates with better uniformity at least for small jet-to-plate spacings. in the present study, the flow field of impinging sweeping jets is experimentally investigated using particle image velocimetry (piv) in order to provide insight into their heat transfer capabilities. the investigated sweeping jets are generated by different configurations of fluidic oscillators fabricated with a 3d printer. the geometry of such devices is schematically displayed in figure 1a. the width of the exit throat section w is 10 mm and it is equal to the depth of the sweeping nozzle (the exit throat nozzle is square). the length of the expansion chamber l f is varied from one device to another; specifically, three different values of l f are investigated: l f/w = 2.5, 3.5, 4.5. the fluidic oscillator with the longest expansion chamber (l f = 4.5w) is also provided with tapped holes on its shortest sides, which culminate into the feedback channels. fastening a screw in these holes allows to change the minimum passage area of the feedback channels and correspondingly the head loss across them. such an expedient is used to vary the sweeping jet’s strouhal number, which was observed to be constant for a fixed geometry when varying the reynolds number. the oscillating frequency of the sweeping jet is determined by recording the instantaneous head loss across one feedback channel (the pressure holes used for the differential pressure measurement are also illustrated in figure 1a). the experimental setup for piv measurements is shown in figure 1b. the impingement distance is varied by moving away the plate via a micrometric translational stage; five different spacings are investigated: h/w = 2, 4, 6, 8, 10. the mass flow rate is measured by means of a flow meter and the reynolds number rew, based on the square exit section edge w, is fixed to 1.7×104. (a) (b) laser beamimpingement plate translational stage stagnation chamber pressure probes camera h/w lf pressure holes w figure 1: (a) schematic of the internal geometry of the fluidic oscillators investigated in the present study and (b) experimental setup for the planar piv measurements. 0 1 2 0 1 2 0 1 2 -4 -3 -2 -1 0 1 2 3 4 0 1 2 -4 -3 -2 -1 0 1 2 3 4 (a) (b) (c) (d) (e) (f) (g) (h) x/w x/w x/w x/w y/w y/w u/u0 u/u0 figure 2: streamwise velocity field of the impinging sweeping jet issuing from the fluidic oscillator with l f/w= 4.5 with open (a-d) and closed (e-h) feedback channels: (a, e) time average, (b-d,f-h) phase averages for different phases. u0 is the area-averaged jet exit velocity. rew = 1.7×104, h/w = 2. for lengths of the expansion chamber smaller than 4.5w, a coherently organized oscillating motion is not observed; conversely, the jet resembles more a conventional round jet. this is in agreement with the previous findings of the numerical work of seo et al. (2018). figure 2 shows the effects of reducing the minimum passage area of the feedback channels on the impinging flow field. while the oscillating frequency of the jet is observed to increase when closing the feedback channels, the amplitude of the jet oscillation is strongly reduced, as visible in the phase-averaged fields. as a consequence, the sweeping jet obtained with open feedback channels (figures 2a-d) presents, in the time-averaged field, a larger jet width, although this comes with lower momentum in the jet core. a more uniform and wider distribution of the heat transfer rate is thus expected for this case. in the present experiments, the phase-averaging is performed by calculating the phase angle from the instantaneous differential pressure signal recorded simultaneously with the particle images. a frequency jitter is indeed noticed, which prevents phase-averaging at one fixed frequency. however, the characteristic oscillating modes of the sweeping jet can be determined via proper orthogonal decomposition (pod), which also sheds light on the dynamics of structures with smaller scales. the turbulence statistics are presented in terms of a triple decomposition of the velocity field, thus separating the quasi-periodic coherent fluctuation from the random turbulent one. references hossain ma, prenter r, lundgreen rk, ameri a, gregory jw, and bons jp (2018) experimental and numerical investigation of sweeping jet film cooling. journal of turbomachinery 140 park t, kara k, and kim d (2018) flow structure and heat transfer of a sweeping jet impinging on a flat wall. international journal of heat and mass transfer 124:920–928 raghu s (2013) fluidic oscillators for flow control. experiments in fluids 54:1–11 seo j, zhu c, and mittal r (2018) flow physics and frequency scaling of sweeping jet fluidic oscillators. aiaa journal 56:2208–2219 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 towards capturing a database of respiratory exhalations from flow visualisations prateek bahl1∗, charitha de silva1, c raina macintyre2, abrar ahmad chughtai3, con doolan1 1 unsw sydney, school of mechanical and manufacturing engineering, sydney, australia 2 unsw sydney, biosecurity program, the kirby institute, sydney, australia 3 unsw sydney, school of population health, sydney, australia ∗ p.bahl@unsw.edu.au abstract one of the most common modes of infection transmission is through pathogen laden droplets expelled during natural human respiratory exhalations such as speaking, coughing, and sneezing. infection control guidelines for the prevention of respiratory infection make assumptions about two key parameters: the safe distance between an infected and healthy individual and the size of large and small droplets (bahl et al., 2020). studies in the past have utilised flow visualisation techniques to understand the dynamics of respiratory flows but most of them provide only qualitative data on respiratory droplets and do not provide sufficient detail to estimate accurate flow velocities (bourouiba et al., 2014; vansciver et al., 2011; scharfman et al., 2016). one of the reasons this remains a demanding application is the vast range of droplet sizes that are expelled at various velocities. here, we present an experimental framework using particle tracking to understand the flow dynamics of the expelled droplets. three different illumination techniques were used to capture high-speed frames of different exhalations (see figure 1). the high density of droplets in case of sneezing lead to overlap of droplet trajectories with volume illumination approach, which was resolved using tailored optics to illuminate only a slice of sneeze flow. thereafter, the image processing techniques required for precise ptv were refined to examine droplet dynamics of various exhalations (see figure 2). the techniques were applied to multiple cases of respiratory exhalations to understand subject to subject variability. the results for sneezing revealed a mean droplet velocity of 2 m/s to 5.4 m/s across different subjects. additionally, less than 1% of droplets were expelled at velocities greater than 10 m/s and almost 80% of were expelled at velocities less than 5 m/s. these values were substantially lower than the values usually assumed in studies modelling or replicating sneezes (xie et al., 2007; atkinson and wein, 2008). the results figure 1: schematics of setups used to capture expelled droplets using (a) volume illumination, (b) light sheet illumination, and (c) shadowgraph imaging. figure 2: velocity associated with droplets expelled during (a) sneezing, and (b) singing also revealed a high variation in the droplet dynamics, even among the sneezes from the same subject. flow direction, spread angle, and head movement were also quantified, and the results reveal substantial variation between the subjects. in the case of coughing, maximum droplet velocities observed were in the range of 10−15 m/s however, these high velocities were detected only during the initial 0.05 s. this work addresses the critical gaps in the understanding of the respiratory transmission of infection by providing valuable data on the droplet dynamics of various exhalations, on which the experimental data was very limited in the existing literature. furthermore, this data will aid in numerical modelling of respiratory flows, particularly for sneezes, as studies to date rely only on airflow data of the exhalations. references atkinson mp and wein lm (2008) quantifying the routes of transmission for pandemic influenza. bulletin of mathematical biology 70:820–867 bahl p, doolan c, de silva c, chughtai aa, bourouiba l, and macintyre cr (2020) airborne or droplet precautions for health workers treating coronavirus disease 2019?. the journal of infectious diseases bourouiba l, dehandschoewercker e, and bush jw (2014) violent expiratory events: on coughing and sneezing. journal of fluid mechanics 745:537–563 scharfman b, techet a, bush j, and bourouiba l (2016) visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets. experiments in fluids 57:24 vansciver m, miller s, and hertzberg j (2011) particle image velocimetry of human cough. aerosol science and technology 45:415–422 xie x, li y, chwang at, ho pl, and seto wh (2007) how far droplets can move in indoor environments revisiting the wells evaporation-falling curve. indoor air 17:211–225 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 large scale infrared-based remote sensing of turbulence metrics in surface waters: going beyond mean flow seth a. schweitzer1∗, edwin a. cowen1 1 defrees hydraulics laboratory, school of civil & environmental engineering, cornell university, ithaca, ny ∗ seth.schweitzer@cornell.edu abstract in recent years field-scale applications of image-based velocimetry methods, often referred to as large scale particle image velocimetry (lspiv), have been increasingly deployed. these velocimetry measurements have several advantages—they allow high resolution, non-contact measurement of surface velocity over a large two dimensional area, from which the bulk flow can be inferred. however, visiblelight lspiv methods can have significant limitations. the water surface often lacks natural features that can be tracked in the visible and generally requires seeding with tracer particles, which creates concerns regarding the fidelity with which tracer particles track the flow, and introduces challenges in achieving sufficient and uniform seeding density, in particular in regions with appreciable velocity accelerations such as turbulence. in lspiv, image collection is generally limited to daylight hours, and can suffer from non-uniformity of illumination across the camera’s field of view. due to these issues lspiv often requires spatio-temporal averaging, and as a result is generally able to extracting the mean, but not the instantaneous, velocity field, and hence is often not a suitable tool for calculating turbulence metrics of the flow. figure 1: instantaneous velocity field measured by ir-qiv over several hundred m2 at the surface of a river. background color indicates the local instantaneous velocity. arrows indicate the perturbation from the mean velocity, i.e., u⃗′, the difference between the local instantaneous and mean velocity. we present an alternative to visiblelight lspiv that avoids these seeding and illumination issues: infrared quantitative image velocimetry (ir-qiv), which uses infrared (ir) images to accurately capture temperature patterns at the water surface with high thermal and spatial resolution (schweitzer and cowen, under review). motion of the patterns is tracked over time, from which the surface velocity field is calculated (figure 1). in natural flows small temperature differences are created in the surface skin due to spatial heterogeneity in turbulent stirring and heat exchange between air and water. these spatial differences in temperature form a rich texture of patterns on the water surface that are observable in ir images (figure 2). ir images are a record of radiation emitted by the water surface, with no external illumination, and no concerns of possible differences between motion of tracer particles and the flow. in contrast to lspiv, ir-qiv is able to extract the instantaneous velocity field reliably and robustly. these measurements can be used for a range of applications, including interaction of fish with structures and flow features, and non-contact estimation of bed stress, bathymetry and discharge. in this presentation we will provide an overview of our developed ir-qiv technique and detail the environmental conditions required for high quality ir image collection, and dealing with images collected under sub-optimal environmental conditions. these issues are key for optimizing ir-qiv for accurate turbulence measurements. we use the minimum quadratic difference (mqd) method for pattern matching (gui and merzkirch, 1996, 2000), as it is more suitable than cross-correlation for images containing gradients of intensity and not discrete particles (cowen et al., 2010). this method generates, at each interrogation location, a surface d(m,n) = 1 ṁn ∑m i=1 ∑n j=1(g(i, j)−g′(i+m, j+n))2, where g(i, j) represents a subwindow of dimensions m,n with a corner at pixel-coordinates (i, j), and g′(i+m, j+ n) represents a similar subwindow from a subsequent image, displaced by (m,n) pixels. lower values of the surface d indicate a greater similarity (smaller quadratic difference) between the pattern of pixel intensities in the two images at that displacement. we use a method that considers image entropy to optimize parameters such as the subwindow dimensions m,n, and the temporal separation ∆t between images. figure 2: ir image of a river surface under environmental conditions leading to high (left, top), and low (left, bottom) dynamic range image, and representative surface d for a single location in each of the images (right). in both examples there a local minimum at the coordinate corresponding to zero displacement (marked with a red circle). an important metric of image quality and suitability for ir-qiv is pixel dynamic range (the range of pixel intensities present in the image). in images where the dynamic range is low the signal (of temperature differences at the water surface) can be overwhelmed by noise in the camera’s optical and digitization path, known as fixed pattern noise (fpn). since fpn does not change significantly between consecutive images, it leads to a match between subwindows at a displacement value of zero pixels. a local minimum in match values at a zero displacement is always present (figure 2). when the dynamic range is low this peak can be lower than the match due to comparison of patterns created by temperature patterns at the water surface, leading to incorrect velocimetry results. since this minimum will always be at a coordinate corresponding to zero displacement it can be identified and filtered from the velocimetry record. the dynamic range of ir images is controlled by the range of temperature differences at the water surface, as well as the camera’s sensitivity and position. in the measurement described in this presentation, ir images exhibited high dynamic range when the difference between bulk water temperature and wet-bulb air temperature was greater than ∼3 °c. smaller air-water temperature differences (corrected for latent heat) lead to low dynamic range in the image, and as a result to a large number of zero velocity results. the environmental conditions required for sufficient image quality to avoid zero-displacement issues will vary between measurements, depending on factors including the camera’s sensitivity and internal noise level, optical setup (e.g., viewing angle, distance, and optics), and environmental conditions such as wind velocity and turbulence intensity of the flow. acknowledgements funding for this work was provided by the california department of water resources (dwr). references cowen ea, dudley rd, liao q, variano ea, and liu plf (2010) an insitu borescopic quantitative imaging profiler for the measurement of high concentration sediment velocity. experiments in fluids 49:77–88 gui l and merzkirch w (1996) a method of tracking ensembles of particle images. experiments in fluids 21:465–468 gui l and merzkirch w (2000) a comparative study of the mqd method and several correlation-based piv evaluation algorithms. experiments in fluids 28:36–44 schweitzer sa and cowen ea (under review) instantaneous river-wide water surface velocity field measurements at centimeter scales using infrared quantitative image velocimetry. water resources research 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 characterization of vortex shedding on a hydrofoil using piv measurements h. bonnard1∗, l. chatellier1, l. david1 1institut p’, upr 3346 cnrs université de poitiers isae-ensma, france ∗herve.bonnard@univ-poitiers.fr abstract an experimental study of vortex shedding on a hydrofoil eppler 817 was conducted using two-dimensional two components particle image velocimetry. this foil section’s characteristics are adapted for naval applications but sparsely documented. the characterization of the flow modes was realized based on statistical data such as the mean velocity field and the standard deviation of the vertical velocities. the data were acquired at very low reynolds number which are not often covered for such hydrofoil and at four angles of attack ranging from 2◦ to 30◦. a map of different characteristic flow modes was made for this space of parameters and was used to identify flow configurations exhibiting particular dynamics. 1 introduction while lifting surfaces are already everywhere on ships, from the rudder to the propeller, the last decades have seen an important rise on the uses of hydrofoils, which goal is to lift a boat out of the water just as a plane’s wing. the sailing world has witnessed the high potential of those hydrofoils, as shown by their increasing use in major sailing events such as the america’s cup or the vendée globe. the sections of hydrofoils can be quite different from airfoils as they have to be designed with the specific operating conditions of the sea, such as the presence of the free-surface and the risk of cavitation. the latter can be controlled by designing specific hydrofoils shapes which minimize the pressure loss on the suction side. such profile was for example designed by eppler (1990) and eppler and shen (1979) by prescribing a velocity distribution at different angle of attack and using an inverse method based on a combination of a panel method to analyse a potential flow with a boundary-layer method. the flow characteristic modes of an eppler 817 (e817) hydrofoil were studied experimentally using particles image velocimetry (piv) measurements over a range of low chord-based reynolds numbers 0.4 · 103 ≤ rec ≤ 20 ·103 and four angles of attack α = 2◦,6◦,12◦,30◦. the piv measurements were done on a very large field (about 3.5 chords upstream and downstream of the hydrofoil) even at the cost of a coarser resolution, in order to analyse the whole flow, including a region of the flow with little influence of the hydrofoil. those data are especially useful for an ongoing project on data assimilation for which knowing the upstream conditions is crucial to define the simulation’s inlet. meldi and poux (2017) and suzuki et al. (2018) highlighted the difficulties of assimilating experimental data due to the limited extent of the physical domain covered by the piv data as well as the under-sampling of experimental data compared to the time steps of numerical simulations. the data acquired with this study will allow us to investigate the effect of these parameters on different flows topologies and dynamics. 2 experimental setup the experiments were carried out at the p’ institute on the environmental hydrodynamic platform’s open water channel which dimensions are 7× 0.385× 0.6 m (lxwxh). the channel is equipped with a pcm moineau worm-drive pump controlled with a schneider electric variable-frequency drive up to flow rates of q = 65 l/s. the flow rates are measured with an endress+hauser promag55 electromagnetic flowmeter. the free-surface height is modified by a spillway gate and was set to h = 280 mm for the measures. the hydrofoil (chord c = 40 mm and span s = 355mm) was placed in the middle of the water volume such as the distance between the profile and either the free-surface or the bottom wall was 3.5 chords. the experimental setup is illustrated on figure 1. figure 1: overview of the water channel with wing model support and piv setup. preliminary flow visualizations were performed using a 1 w continuous laser diode in order to describe the main flow characteristics. long exposure images were taken in order to get a representation of the flow topology through the particles’ trajectories. four characteristics flow and vortex shedding regimes were observed: attached flow, trailing-edge vortex, separation bubble and leading-edge vortex (see yarusevych et al. (2009) huang et al. (2001)). the transition between the first two modes can be observed in figure 2. (a) rec = 4700, attached-flow (b) rec = 5200, trailing-edge vortices figure 2: comparison of the flow characteristic regimes at α = 2◦ for two close rec figure 3: photograph of the setup with the laser sheet using the underwater illumination unit piv measurements were carried out using a dantec speedsense 1040 4 mp 100 hz camera on 16 cases (4 reynolds numbers and 4 angles of attack) chosen based on the previous observations. as an opaque 3d-printed abs hydrofoil was used, two lasers were required in order to get the largest illumination. a 2 x 30 mj nd:yag quantel twins ultra (532 nm, 20 hz) was placed below the water channel to illuminate the pressure side of the foil as well as the upstream flow. as the free-surface of the open water tunnel prevent the use of a laser from the top of the experiment, a 2 x 50 mj nd:yag litron nano l 50-50 piv (532 nm, 50 hz) was used with lavision underwater illumination unit in order to view the suction side of the foil and the downstream flow. the measurement equipments are depicted on figure 3. a first series of measurements was performed on the 16 cases using 1000 double-frame images acquired at a very low frequency (2 to 5 hz) in order to provide statistically relevant datasets. then, using only the fastest of the two lasers, time-resolved piv (tr-piv) series of 10 000 images were acquired for the two lowest reynolds numbers at two angles of attack (α = 2◦ and 12◦). a multi-frame piv method was applied to evaluate the time resolved flow fields using a fluid trajectory evaluation based on an ensemble-averaged cross-correlation (ftee) technique, see jeon et al. (2014). those two datasets provide an understanding of both the global mean flow and the dynamics of the flow fluctuations. figure 4: mean normalized velocities (left) and standard deviation of normalized vertical velocities (right) at rec = 1400 for α = 2◦,6◦,12◦,30◦ (rows). the hydrofoil is represented as a dark grey area and the light grey mask corresponds to a zone where data could not be obtained accurately. figure 5: mean normalized velocities (left) and standard deviation of normalized vertical velocities (right) at rec = 6300 for α = 2◦,6◦,12◦,30◦ (rows). the hydrofoil is represented as a dark grey area and the light grey mask corresponds to a zone where data could not be obtained accurately. 3 results the mean normalized velocity field as well as the standard deviation of the normalized vertical velocities are represented on figures 4 and 5 for two of the reynolds numbers studied at all the angle of attack. they both allow to see the time averaged topology of the flow around the hydrofoil at different conditions and can be used to identify the different flow modes. for both chord base reynolds number, at the lowest angle of attack (α = 2◦) we can see an almost symmetrical velocity distribution, and thus pressure distribution, around the hydrofoil. this is due to the asymmetrical section of the eppler 817, which has a negative lift coefficient at an angle of attack of 0◦ and is at zero lift for an angle of attack of approximately 1.5◦. at rec = 1400, when increasing the angle of attack from 2◦ to 12◦, the characteristic flow modes evolve from attached flow to a transitionary state and then a fully developed trailing edge vortex shedding. this can be seen using the standard deviation of the vertical velocity which increases in the wake as the angle of attack increases. while at rec = 6300, we can see that the trailing edge vortex shedding start from the lowest angle of attack, reinforcing the preliminary results obtained with the laser diode showed in figure 2. this is also illustrated by the mean velocity field where the wake is thinner than in the attached flow case from the lower reynolds number. at rec = 6300 and α = 12◦, we observed a new mode: a separation vortex, which did not exist at this angle of attack for the lower reynolds numbers. the standard deviation graph shows that the biggest fluctuations are closer to the hydrofoil, starting from about the third of the chord, which is characteristic of a separation. by comparing the mean velocity fields of the separated cased with the one at rec = 1400 where it did not occur yet, we can see that the wake thicken progressively showing a triangular shape. for all the reynolds numbers studied, there is leading edge vortex shedding at the most extreme angle of attack investigated, α = 30◦. this was expected as the angle chosen is quite high. the figure 6 shows a cartography of the different vortex shedding types observed for all the cases studied. a zoom of the standard deviation of the vertical velocity graphs was added at some points to illustrate the differences between the modes. as there are very few data on this hydrofoil, especially at such low reynolds numbers, our results can be compared, qualitatively, to the ones obtained on a well documented profile such as the naca 0012 (see huang et al. (2001)). most patterns are similar with our study, such as the fact that trailing edge vortices start to appear at lower angle of attack when the reynolds number increases. however, the separation vortices appeared at higher angles of attack, which was partly expected as our zero-lift angle of attack is not zero. figure 6: flows modes observed on our eppler 817 hydrofoil as a function of chord based reynolds number rec and angle of attack α. 4 conclusions and perspectives the present study allowed us to map the different flow topologies around an eppler 817 hydrofoil depending on the reynolds number and angle of attack. this provided a better understanding of the flow characteristics around our hydrofoil and guided us when choosing interesting cases which will be further investigated. a following experiment with a 3d t-shaped hydrofoil, that is a vertical part such as a rudder and a horizontal part at the end to produce lift, will be carried out on the same water channel. we will observe the evolution in behaviour when going from the extruded 2d section to a full 3d shape and the influence of the proximity with the free-surface trough various hydrofoil’s depths. acknowledgements the authors would like to thank the direction générale de l’armement for the funding of hervé bonnard’s phd thesis as well as the european research council (erc) for funding the project homer : holistic optical metrology for aero-elastic research under the european union’s horizon 2020 research and innovation programme (grant agreement no 648161). references eppler r (1990) airfoil design and data. springer berlin heidelberg, berlin, heidelberg eppler r and shen yt (1979) wing sections for hydrofoils—part 1: symmetrical profiles. journal of ship research huang rf, wu jy, jeng jh, and chen rc (2001) surface flow and vortex shedding of an impulsively started wing. journal of fluid mechanics jeon yj, chatellier l, and david l (2014) fluid trajectory evaluation based on an ensemble-averaged crosscorrelation in time-resolved piv. experiments in fluids meldi m and poux a (2017) a reduced order model based on kalman filtering for sequential data assimilation of turbulent flows. journal of computational physics suzuki t, chatellier l, jeon yj, and david l (2018) unsteady pressure estimation and compensation capabilities of the hybrid simulation combining piv and dns. measurement science and technology yarusevych s, sullivan pe, and kawall jg (2009) on vortex shedding from an airfoil in low-reynoldsnumber flows. journal of fluid mechanics introduction experimental setup results conclusions and perspectives 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 3d particle tracking velocimetry applied to droplets generated by breaking waves r.g. ramirez de la torre1∗, a. jensen1 1 university of oslo department of mathematics, oslo, norway ∗ reynar@math.uio.no abstract one of the environmental difficulties of exploring the polar regions is marine icing. the understanding of this phenomenon is important for the safety of installations, ships and people that operates in these environments. one of the main sources of marine icing is wave breaking. therefore, experimental and field work has been conducted to understand the break-up of waves in different situations and some explanation have been proposed to the instabilities that create the spray formation. in this work, two different situations of wave breaking were studied: 1. solitary waves were created and steepened by the use of a beach. the waves impacted on a vertical wall with different wall heights. 2. violent plunging breakers were created by a focusing wave train and a sloping beach. the main objective of these experiments was to quantify the production of droplets from the impact by using particle tracking velocimetry in 3 dimensions. it was found that the initial distribution of droplet sizes is similar in both experiments. these distributions are compared with previous studies, where the distribution of droplet sizes in different experimental cases were approximated by lognormal, weibull or γ-distributions respectively. 1 introduction a large range of two phase flow interactions generate aerosols in the oceanic surface. between this phenomena, wave breaking is a very important source of aerosol and it is also considered the main source to marine icing (rashid et al., 2016; dehghani et al., 2016b; bodaghkhani et al., 2016), which is the main focus of this work. marine icing is produced in polar regions, when the droplets produced after wave breaking are transported by the wind and generate thick layers of ice over the surface of ships and structures; these ice-layers represent a life hazard. therefore, field studies and simulations has been used to address this phenomenon, but its complexity has shown that a deeper understanding of the droplet generation is necessary. to make models of this phenomenon, there is need of more information about the size and velocity distributions of the droplets. it is understood that small aerosols (radius < 1mm) can be transported over long distances and remain in the atmosphere for several days (veron, 2015). but further studies are necessary to comprehend the generation and dynamics of droplets with radius > 1mm because they are relevant to understand the phenomena that occur close to the ocean surface. recent experimental and field studies (ortiz-suslow et al., 2016; lenain and melville, 2017) show that the production rates for droplets with radii∼ 1mm were several orders of magnitude higher than the rates expected from previous investigations (fairall et al., 2009; veron, 2015). these findings may suggest that large droplets have a longer lifetime in the atmospheric boundary layer than previously expected. therefore, the processes from where these larger droplets are created need to be better understood. the present study is an attempt to contribute to the understanding of these droplets behaviour. in particular the generation mechanism and initial size distribution. to measure droplet sizes, optical and non-optical methods can be utilized and some reviews in this topic can be found in the literature (damaschke et al., 2005; tayali and bates, 1990). non-optical methods rely on either physical separation or impact impressions, which cannot obtain information on the kinematics of the particles. on the other hand, optical techniques rely on imaging or holography, and some of them, like the laser-based measurements, allow the retrieval of velocities simultaneously, therefore these techniques have become popular (damaschke et al., 2002; kawaguchi et al., 2002). nonetheless, some applications are not suitable for the use of laser (ramirez de la torre et al., 2020; løken et al., 2021), hence the use of natural light or scattered light should be reconsidered. in this work, the basis for a scattered-light technique to collect droplet sizes is presented and two different experimental setups are used to test the technique. figure 1: diagram of the 3dptv setup in the wave tank. the position of the camera array relative to the tank is shown. an approximation of the fov and the defined cartesian system are also shown. on the right side, examples of the images obtained by the camera array are shown. the jet formation at wave impact and jet break-up into droplets have been less studied because of its complexity. it is common to consider a simplification of the phenomenon by comparing with a planar jet coming out of a nozzle (lozano et al., 1998; sarchami et al., 2010; bodaghkhani et al., 2016) and we can find both numerical and experimental approaches. only few studies have conducted experimental work on the break up of waves impacting on a vertical wall and proposed an explanation of the instabilities that create the spray formation (watanabe and ingram, 2015, 2016). they found that the distribution of droplet sizes at different vertical positions has a lognormal shape and is similar, but not well approximated by distributions proposed by other studies of drop formation. weibull distribution was proposed by studies of droplet crown formation from a single drop impacting the water surface(roisman et al., 2006). a γ-distribution was proposed for the droplets created after the break-up and coalescence of ligaments that detached from the main water bulk of a circular jet (villermaux et al., 2004). in the current work, the size distributions of droplets created after the impact of breaking waves is presented. two significantly different setups are analysed and the results of droplet generation are compared to the previously proposed distributions. 2 materials and methods this section will explain the details of two different experimental setups and the technique used to quantify the sizes of the droplets. all experiments were conducted in the wave tank of the hydrodynamics laboratory at the university of oslo. the wave tank has dimensions 25× 0.52× 1m. in the first set of experiments, solitary waves impacting on a vertical wall were analysed. different wave heights were used to obtain different breaking stages and the wall height is lower than the wave height in all cases. in the second set of experiments, a focusing wave train was forced to overturn by means of a beach. three different amplitudes of the focusing wave train were used and two different wind speeds were also imposed on the air phase. the main objective of these experiments was to quantify the production of droplets from the impact and relate it to the impact characteristics. in contrast to other investigations, the droplets were measured using three dimensional particle tracking velocimetry (3dptv) and shadowgraphy images. 2.1 3dptv to obtain droplet sizes we analyze all the droplets that were visible in the selected field of view (fov) of each experiment, using the setup presented in figure 1. the analysis was made by means of 3dptv with the open source program openptv consortium et al. (2012). highly resolved, high cadence (167 fps) images of the cloud are taken by 4 monochromatic aos promon cameras with 50mm lenses, examples of the obtained images are shown also in figure 1. led lamps and white diffusive sheets were used to illuminate the back of the setup. the position of the fov is always after the impact location and depends on the experimental case. a sequence of 2 seconds during and after the impact is recorded. the droplet size detection was made by combining the trajectories found by 3dptv and additional post processing. in which the pixel size of each detected particle is found and an estimation of its diameter figure 2: diagram of the experimental setup in the wave tank. the position of the beach and the wall is shown. also the camera array and distances to the glass wall are shown. two different fov’s are used to visualize the droplets. the camera array is moved to visualize each fov separately . is made by means of previously established relations. the process is summarized in the following: with the ptv algorithm we define a position of each detected droplet in the three-dimensional space and follow it through time s(t) = (x,y,z). previously to the measurements, a calibration of the system needs to be performed in which relations between all the cameras fov and the cartesian space are established. this calibration can be used to also establish a pixel-to-world transform for each camera i = 1,2,3,4 and a correction due to the light scattering around the droplets depending on the depth of the particle t (i,z). once s(t) is calculated by ptv, the pixel size of the droplet in the vertical and horizontal direction px(s), py(s) can be obtained from the data files of each camera i. then, an estimation of the droplet axes a,b in each camera can be done by applying the defined transformation ai(s) = t (i,z(s); px) and bi(s) = t (i,z(s); py). it is important to mention that droplets are not always spherical and their deformation increases with the size. the equivalent diameter de is commonly used to classify droplet sizes with one unique parameter and is commonly defined as de = √ ab, where a and b are the major and minor axis of the ellipsoid. in addition, a = ai and b = bi, the averaged values from the 4 cameras. to obtain size distributions, we collect all the detected droplets in every time step during the time series and throughout all the repetitions of the experiments. ten repetitions of the same case were developed for the first experiment, while only 5 repetitions were needed for the second experiment. in this way, we obtain one distribution for each analyzed parameter. in other words, we obtain one distribution for each amplitude and wall height in the first experiment, and one distribution for each steepness and wind velocity in the second experiment. 2.2 experiment 1: solitary wave impacts in a vertical wall in the first set of experiments, the mean water level for all experiments was d = 0.2m. the aim of this work was to generate steep solitary waves which will impact in a wall at different stages of the breaking process. to achieve this, solitary waves were made by a horizontal displacement wave paddle, shown in figure 2. a petg (polyethylene terephthalate glycol-modified) beach with an inclination of 5◦ was placed at 8.43 m from the rest position of the paddle. a vertical wall was positioned at 2.05 m from the vertex of the beach. the amplitude (a) to depth (d) ratio, or non dimensional amplitude a = a/d was varied as a = 0.5,0.46,0.4,0.35. two different wall heights h were used for each a, with an amplitude to wall ratio h/a ≈ 0.8,0.9. the produced droplets are observed in two fov’s, after the impact area (marked as fov1 and fov2 in fig. 2). to determine the breaking stage of the input wave, simulations were made with a boundary integral method (bim) pedersen (2008). the wave amplitude was measured with 3 acoustic wave gauges between the beach and the wave paddle. the gauges were positioned at 7.07m, 7.42m and 7.78m from the rest position of the paddle respectively. comparison of the simulations and the gauge measurements was done. far from the wall, the simulations and the experiments are in good agreement. the used bim model cannot simulate the trapped air cavity between the tip and the trough. this is because the simulation cannot handle two contact points between the surface and the boundary. therefore, the velocities in the trough cannot be figure 3: results of the bim model simulation for the breaking stages of the different wave amplitudes a. the wall is represented by the black line. three time steps of the simulations are presented, when the wave is close to the wall position. approximated. in spite of this, there is similarity in the shape and speed of the wave tip approaching the wall until before impacting the wall. from these simulations we can approximate the breaking point and size of the air cavity between the wall and the wave. fast imaging was used to visualize the impact, from the images three different impacts can be distinguished: flip-through (a = 0.35) without air pocket, small air pocket (a = 0.40) and big air pocket (a = 0.46,0.50). with this images we confirm the the simulations are a good approximation to the wall position. h/a = 0.8 h/a=0.9 figure 4: splashing of a wave into the wall, the initial moments of the jet breaking into droplets are visualized in all cases. from the left: a = 0.35,0.40,0.46,0.50. the top row shows the cases with wall of height h/a = 0.8 and to the bottom row, the cases with wall height h/a = 0.9.. figure 4 shows the different impacts obtained in the experiment. after the impact, all cases form a planar jet that shoots upwards in a certain angle. for every impact type we have also two different wall heights that result in a different releasing angle of the planar jet. on top of that, for the cases where there is an air pocket, a second jet is visible when the air cavity is closed, each of these jets has a different ejection angle. the aim of these images is to show the development of the wave after the impact. it is interesting to observe the differences arisen by the different amplitudes and wall heights. the formation of the first jet and the time and angle were the air pockets closed have noticeable changes. 2.3 experiment 2: focusing wave train (fwt) and wind conditions in the second set of experiments, a focusing wave train (fwt, for short) was used to produce breaking waves, the mean water level was d = 0.5m. in the wave train, long waves overtake short waves, then the breaking was made more violent by adding a slope which caused the already focused waves to steepen and overturn. the overturning crest of the wave splashed at the free surface releasing a large number of droplets. further details of this set of experiments can be found in ramirez de la torre, vollestad, and jensen (2020). the wave trains were created using the same methodology as presented in brown and jensen (2001). by using this focusing method, we obtain breaking waves when we reach steepness ak > 0.44. but the breaking created by the selected amplitudes only generated spilling breakers and small overturning. therefore, a shoaling was added to steepen the waves even more as they approach the focusing point. in this way, (a) surface elevation (b) power spectrum (c) energy content figure 5: surface elevation (a) and power spectrum (b) at the focal point for cases without beach (”no beach” label, solid line), with beach and without wind (”beach” label, dotted line), and with beach and wind (”beach+wind” label, dashed line). ak = 0.57 has been selected as example and umax = 6.2ms-1 in the wind case. (c) shows mean power r(0) compared to umax for the three ak, which represented by different markers, the graph shows the increase of energy content with both wind speed and steepness. images extracted from ramirez de la torre, vollestad, and jensen (2020). the waves are forced to overturn. the steepness ak can be used as non dimensional parameter to identify the different wave trains, which are ak = 0.47,0.57,0.66. the wind profiles, without the influence of mechanically generated waves, were measured using particle image velocimetry (piv). the peak horizontal velocity recorded (umax) is correlated to the pressure change (p) obtained by a pressure gauge, and this correlation is used to approximate the mean velocity of the wind during the experiments with the fwt. the wind velocities used in the experiments were umax = 0,5.2 and 6.2ms-1 figure 5 summarizes the results of introducing a beach and wind forcing to the fwt. by comparing the surface elevation for the fwt with and without beach (figure 5(a)), it is visible that there is a steepening effect in the beach cases. this steeper central high component produces a violent plunger breaker that can be studied. the energy content of the wave group can be quantified by means of the power spectrum s( f ), shown in figure 5(b). it is obvious that all cases have the same peak frequency, but the beach cases show evidence of energy dispersion. to quantify the change in energy content of the different cases, we can use the mean power r(0), defined as the area under the spectral curve s( f ), which can be interpreted as the energy content of the wave as r(0) ∝ a2 which is also proportional to the energy. figure 5(c) shows the calculated r(0) compared to the different maximum wave steepness: ak and wind velocities: umax used for this work. the graph shows the effect of wind over the wave energy. in all cases the energy increases with ak. but, it is interesting to see that for umax < 4.5 the total energy of the packet is less than the energy of the packet without the presence of wind. 3 results figure 6 shows the probability distributions of equivalent diameter de for different cases. all distributions are normalized by the mean de. in figure 6(a), the results of experiment 1, with the solitary waves, are presented, and in figure 6(b) the results of experiment 2, with the fwt, are presented. in both cases the distribution has a similar shape, with and extended tail towards larger sizes and a unique maxima that is not centered. for each experiment, the change of parameter shows a displacement of the tail and the maxima. a discussion on the theoretical distributions that can fit the data will be done, but first we will analyze the results for the mean diameter, de, of each case. figure 7 shows the change in de as a function of the parameters determined for each experiment. in the first experiment (fig. 7(a)), two parameters were used: the non dimensional amplitude a = a/d (fig. 7(a)left), and the non dimensional jet speed defined as v jet/c (fig. 7(a)-right), where c is the wave speed, obtained by solitary wave theory (c = √ (d +a)/d) and the jet speed v jet can be estimated by the displacement of the jet in the images divided by the time elapsed between them. for de vs a, a slight peak is visible when a = 0.40 and the values for fov1 are always larger. this is expected as in fov2, the droplets have spend more time flying and further break-up is expected, which corresponds to smaller sizes. for de vs v jet/c, we see a more defined trend where, the mean size of the droplet decreases for v jet/c > 2. dehghani et al. (a) experiment 1 (b) experiment 2 figure 6: probability distribution function of de normalized by the mean for the different experiments. (a) shows the results for experiment 1, with the solitary waves. to the left, the results for fov1 are shown and to the right, the results for fov2 are shown. the different colors describe the wall height: blue for h/a = 0.9 and black h/a = 0.8, the markers show the different a as shown in the graph label. (b) shows the results of experiment 2, with the fwt, the different colors represent the different wind conditions: black for umax = 0, blue for umax = 5.2 and red for umax = 6.2. the different markers shows the different steepness as presented in the label. (2016a) have predicted a similar change of size in the droplets, for larger velocities in the jet, finer droplets are expected. it is also interesting to see that for the cases where v jet/c < 2 the mean droplet size decreases, which suggest that the relation between speed and size is not linear and that the ratio of the jet speed and the wave speed could be a better parameter to represent the sizes on wave impact, but further data would be necessary to test this hypothesis. in the second experiment (fig. 7(b)), r(0) is used as a parameter that quantifies the wave energy. it is observed that de increases with r(0) of the wave. previously, it was found that the mean size of droplets decreases with the presence of high winds mueller and veron (2009); ortiz-suslow et al. (2016); fairall et al. (2009). our findings suggest that the energy of the waves while breaking is also an important parameter on the size distribution and should be considered together with the wind velocity. as for the distribution of droplet sizes in figure 8, three different models from the literature, were used to compare to the data (villermaux et al., 2004; watanabe and ingram, 2016; roisman et al., 2006). without loss of generality, in figure 8, an example case has been selected from each experiment and the three models (a) experiment 1 (b) experiment 2 figure 7: de against the experimental parameters, (a) shows the results of experiment 1, two parameters are defined: non-dimensional amplitude a and non dimensional jet velocity v jet/c (c: wave speed). black represents fov1 and blue for fov2, squares represents h/a = 0.8 and circles represents h/a = 0.9. (b) shows the result for experiment 2 where the main parameter is r(0) an estimate of the wave packet energy. it is important to remember that r(0) depends on umax and ak, as shown in figure 5. (a) experiment 1 (b) experiment 2 figure 8: probability distribution function of de/de compared to theory models. the squares shows the experimental data and the colored lines represent the different models proposed by the references: black for villermaux et al. (2004), blue for roisman et al. (2006) and red for watanabe and ingram (2016). (a) shows results of experiment 1 for the case of a = 0,46, h/a = 0.8, results for fov1 are presented to the left while results for fov2 are presented to the right. (b) shows results for the fwt case, ak = 0.66 and umax = 6.2ms-1 are the parameters in the chosen data set. are fitted to the data. the first model, was presented by villermaux et al. (2004) (black line): pγ(x;n) = nnxn−1e−nx γ(n) (1) where n−1 is the variance and x = de/de is the diameter normalized by the mean. this model describes the ligament-mediated spray formation and was originally thought for a jet of water that creates ligaments and droplets by the effect of wind shear in the surface of the jet. the second model was presented by roisman et al. (2006) (blue line): pweib(x;α,β) = β α ( x α )β−1 e−( x α) β (2) where α = 0.89 and β = 1.94 are empirically found. this model was used to describe the secondary droplets created by the rim instability in crown splashes. the third model was presented in watanabe and ingram (2016) (red line): pl−n(x;µ,λ) = 1 xλ √ 2π e −(lnx−µ)2 2λ2 , (3) where µ = lnx is the mean of the natural logarithm of the normalized size and λ = std[lnx] is the standard deviation. this model was used to describe the generation of droplets from impacting waves on a vertical wall. from figure 8, it is visible that only pγ and pl−n follow closely the data for values larger than the mean, which is the maximum of the distribution, and that only pl−n follows the data more accurately for values smaller than the mean. the experimental data for droplet sizes below 0.5 mm has a larger error because of the cameras resolution, therefore it is more significant to concentrate on the droplets with sizes larger than 0.5 mm. in this case, only pγ seems to resemble closely the distribution without overestimating the probability. a quantitative manner to analyze the closeness of the distribution to the experimental data is to calculate the theoretical quantiles for the different models and compare them to the quantiles of the experimental data, if the model is a good fit the quantiles should align in the identity line q(exp) = q(theory). over all, the first model that corresponds to villermaux et al. (2004), shows the closest similarity for all the quantile values. from this analysis we can conclude that pγ shows the best fit for the data presented in this study. pl−n provides a good fit for the lowest section of the quantiles but separates quite much in the largest values, while pweib shows big difference in the extreme values. acknowledgements funding from the norwegian research council through the project ’rigspray’ (grant number 256435) is gratefully acknowledged. the authors will also like to acknowledge alex liberzon and the openptv software consortium for the help with the use of openptv. the help of olav gundersen in the experimental setup is gratefully acknowledge. references bodaghkhani a, dehghani sr, muzychka ys, and colbourne b (2016) understanding spray cloud formation by wave impact on marine objects. cold regions science and technology 129:114–136 brown mg and jensen a (2001) experiments on focusing unidirectional water waves. journal of geophysical research: oceans 106:16917–16928 consortium o et al. (2012) openptv: open source particle tracking velocimetry. 2012,() damaschke n, nobach h, nonn ti, semidetnov n, and tropea c (2005) multi-dimensional particle sizing techniques. experiments in fluids 39:336–350 damaschke n, nobach h, and tropea c (2002) optical limits of particle concentration for multidimensional particle sizing techniques in fluid mechanics. experiments in fluids 32:143–152 dehghani s, muzychka y, and naterer g (2016a) droplet trajectories of wave-impact sea spray on a marine vessel. cold regions science and technology 127:1–9 dehghani s, naterer g, and muzychka y (2016b) droplet size and velocity distributions of wave-impact sea spray over a marine vessel. cold regions science and technology 132:60–67 fairall c, banner m, peirson w, asher w, and morison r (2009) investigation of the physical scaling of sea spray spume droplet production. journal of geophysical research: oceans 114 kawaguchi t, akasaka y, and maeda m (2002) size measurements of droplets and bubbles by advanced interferometric laser imaging technique. measurement science and technology 13:308 lenain l and melville wk (2017) evidence of sea-state dependence of aerosol concentration in the marine atmospheric boundary layer. journal of physical oceanography 47:69–84 løken tk, ellevold tj, de la torre rgr, rabault j, and jensen a (2021) bringing optical fluid motion analysis to the field: a methodology using an open source rov as a camera system and rising bubbles as tracers. measurement science and technology 32:095302 lozano a, garcıa-olivares a, and dopazo c (1998) the instability growth leading to a liquid sheet breakup. physics of fluids 10:2188–2197 mueller ja and veron f (2009) a sea state–dependent spume generation function. journal of physical oceanography 39:2363–2372 ortiz-suslow dg, haus bk, mehta s, and laxague nj (2016) sea spray generation in very high winds. journal of the atmospheric sciences 73:3975–3995 pedersen g (2008) a lagrangian model applied to runup problems. advanced numerical models for simulating tsunami waves and runup 10:311–314 ramirez de la torre r, kuchta m, and jensen a (2020) experiments on air entrainment produced by a circular free falling jet. international journal of multiphase flow 132:103424 ramirez de la torre rg, vollestad p, and jensen a (2020) experimental investigation of droplet distributions from a plunging breaker with different wind conditions. earth and space science open archive page 17 rashid t, khawaja ha, and edvardsen k (2016) review of marine icing and anti-/de-icing systems. journal of marine engineering & technology 15:79–87 roisman iv, horvat k, and tropea c (2006) spray impact: rim transverse instability initiating fingering and splash, and description of a secondary spray. physics of fluids 18:102104 sarchami a, ashgriz n, and tran h (2010) an atomization model for splash plate nozzles. aiche journal 56:849–857 tayali n and bates c (1990) particle sizing techniques in multiphase flows: a review. flow measurement and instrumentation 1:77–105 veron f (2015) ocean spray. annual review of fluid mechanics 47:507–538 villermaux e, marmottant p, and duplat j (2004) ligament-mediated spray formation. physical review letters 92:074501 watanabe y and ingram d (2015) transverse instabilities of ascending planar jets formed by wave impacts on vertical walls. proceedings of the royal society a: mathematical, physical and engineering sciences 471:20150397 watanabe y and ingram d (2016) size distributions of sprays produced by violent wave impacts on vertical sea walls. proceedings of the royal society a: mathematical, physical and engineering sciences 472:20160423 introduction materials and methods 3dptv to obtain droplet sizes experiment 1: solitary wave impacts in a vertical wall experiment 2: focusing wave train (fwt) and wind conditions results 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 development and uncertainty characterization of rotating 3d velocimetry using a single plenoptic camera m. moaven, a. gururaj, z. p. tan‡, s. morris, b. s. thurow 1∗, v. raghav 2∗ auburn university, department of aerospace engineering, auburn, al, usa 1∗ thurow@auburn.edu 2∗ raghav@auburn.edu abstract rotating 3d velocimetry (r3dv) is a single-camera piv technique designed to track the evolution of flow over a rotor in the rotating reference frame. a high-speed (stationary) plenoptic camera capable of 3d imaging captures the motion of particles within the volume of interest through a revolving mirror from the central hub of a hydrodynamic rotor facility, a by-product being an undesired image rotation. r3dv employs a calibration method adapted for rotation such that during mart reconstruction, voxels are mapped to pixel coordinates based on the mirror’s instantaneous azimuthal position. interpolation of calibration polynomial coefficients using a fitted fourier series is performed to bypass the need to physically calibrate volumes corresponding to each fine azimuth angle. reprojection error associated with calibration is calculated on average to be less than 0.6 of a pixel. experimental uncertainty of cross-correlated 3d/3c vector fields is quantified by comparing vectors obtained from imaging quiescent flow via a rotating mirror to an idealized model based purely on rotational kinematics. the uncertainty shows no dependency on azimuth angle while amounting to approximately less than 0.21 voxels per timestep in the in-plane directions and correspondingly 1.7 voxels in the radial direction, both comparable to previously established uncertainty estimations for single-camera plenoptic piv. 1 motivation there exist countless unsteady fluid dynamics problems involving rotation an action tending to give rise to highly 3d flow features; however, diagnostics of such flows have traditionally been constrained to phaseaveraged piv and time-resolved experiments within a stationary frame of reference (mulleners et al. (2012); percin and oudheusden (2015)). recording the three-dimensional evolution of rotating flows through time is paramount to the success of aerodynamicists in understanding and predicting flows such as that around a helicopter rotor. rotating 3d velocimetry (r3dv) is a technique capable of continuously tracking and reconstructing time-resolved 3d flow over a rotor within the rotating frame of reference. images are captured via a 45◦ inclined mirror that is rotating in conjunction with the wing, thereby transporting the rotating field of view containing the flow as it evolves above the wing through a 90◦ turn and towards a stationary camera (see fig. 1). herein lies the cornerstone of r3dv a high-speed plenoptic camera capable of 3d imaging. the feature that sets a plenoptic camera apart from a conventional camera is an array of microlenses placed between the camera sensor and main lens. this simple modification enables incoming light rays to be encoded based on their angle of incidence with the main lens. as a result, plenoptic images can be decoded to resolve volumetric information (fahringer et al. (2015)) and whilst 3d flow-field measurements have traditionally relied on multi-camera configurations, the plenoptic camera can be the sole imaging device in a 3d-piv experiment. this provides a crucial advantage in an optically restricted environment such as that of the current r3dv implementation. for a more comprehensive discussion of the r3dv technique as well as details of the experimental configuration, the authors would like to point the reader to ”rotating three-dimensional velocimetry” by gururaj et al. (2021). ‡currently at: national yang ming chiao tung university figure 1: r3dv setup schematic including isosurfaces of vorticity (not to scale) the purpose of this paper is to address unique challenges that arise from imaging with the configuration used in r3dv, namely the development of a rotational calibration method and quantification of uncertainty with a potential dependency on rotation. it can be deduced based on intuition that imaging with a stationary camera via a rotating mirror results in a continuously rotating image. fig. 2 illustrates this effect by showing a calibration plate mounted at the position of the wing starting from a position (fig. 2(a)) and undergoing an approximately 40◦ azimuthal rotation (ψ) (fig. 2(b)), resulting in the camera viewing the plate as having been rotated by the same angle ψ. ideally, the rotation should be rectified prior to cross-correlation such that imaged flow particles are not seen as experiencing a false rotation. a simple 2d rotation matrix on plenoptic images would be inappropriate in addressing this as a raw image contains thousands of microlens sub-images meaning any such operation would impose an artificial rotation on the microlens array. as such, an existing volumetric calibration method was adapted to a rotating field of view in order to seamlessly incorporate rotation into camera calibration such that fig. 2(b) is transformed to fig. 2(c) to match the orientation of fig. 2(a). section 3 discusses the details of this method as well as results from an error analysis including a comparison to plenoptic calibration in a stationary frame benchtop setup. in piv experiments designed to examine the growth and formation of a leading-edge vortex (lev) around a 45◦ pitch wing, r3dv was shown to give qualitatively agreeable results with existing literature. of course, the viability of a novel piv implementation cannot be assumed based solely on qualitative observation. as such, images of quiescent flow were recorded via the rotating mirror without the presence of a wing the impetus being to compare resulting vector fields of the perceived rotating flow to a model based on rotational kinematics in order to quantify the uncertainty of the method. with the imaged volume rotating through a wide range of angles, a potential dependency of uncertainty on azimuth angle must simultaneously be investigated. results of the uncertainty analysis and a comparison to single camera plenoptic-piv in the stationary frame are presented in section 4. 2 rotating 3d velocimetry 2.1 technique a typical tomographic or plenoptic-piv experiment begins with recording images of a volume of illuminated particles seeding the flow of interest (fig. 3). a fundamental step specific to processing of plenoptic images involves determining the projected microlens positions on the image sensor. subsequent steps for both tomopiv and plenoptic-piv are based on the same principles of calibrating the volume with respect to the camera, (a) (b) (c) figure 2: rotated field of view (b) resulting from mirror rotation of angle ψ rectified using rotational calibration to generate image (c) with feature point coordinates consistent with that of image (a) using said calibration to reconstruct the volume of interest, and finally cross-correlating consecutive images to yield vector fields of particle displacements. as alluded to in the previous section, the unique nature of r3dv’s rotating field of view is addressed within the volumetric calibration step. here, a rotational calibration technique establishes a relationship between the image and the volume while taking into account its orientation. applying this calibration during volumetric reconstruction generates an intensity field that is dependent on the azimuth angle of the mirror at that instant meaning any rotation of the field of view as a consequence of looking through the rotating mirror is eliminated. as a visual aid for the aforementioned quiescent flow experiments, this results in the camera adopting the perspective of the mirror such that particle images theoretically undergo only translation. 2.2 setup the configuration shown in fig. 1 is an inverted schematic of the arrangement used in this work, with the mirror and wing assembly contained in a 1.2 m × 1.2 m × 1.2 m acrylic water tank and an encoder incorporated to track the mirror’s azimuth angle. the plenoptic camera assembly is composed of a 4096 × 2304 pixel resolution phantom veo 4k 990l camera and a modular plenoptic adaptor (tan et al. (2019)) that houses a 471 × 362 microlens array, an optical relay system, as well as a 200 mm main imaging lens. the calibration plate was held in place by a mounting wing consisting of evenly spaced holes to position the plate at 10.16 mm increments in the depth direction. during uncertainty measurement acquisition, water in the tank was seeded with fluorescent pmma rhodamine particles at a density of approximately 0.04 particles per microlens (ppm). volume illumination was provided by a lavision led-flashlight 300 positioned normal to one of the tank’s sides and a 52 mm tiffen orange 21 lens filter was used to enhance the signal-to-noise ratio of particle images. 2.3 data acquisition and processing parameters the calibration plate was imaged at 9 consecutive positions on the mounting wing, covering a depth of 81.28 mm. the wingless experiments of section 4 designed for uncertainty analysis were performed for two volumes corresponding to two different locations on the wing used in the flow visualization experiments image acquisition of laser illuminated particle volume calibrate microlenses: find all microlens center projections on image sensor volumetric calibration: establish image to object space relationship volumetric reconstruction: generate 3d volume of particle positions cross-correlation of particle motion: generate 3d/3c vector field figure 3: general roadmap of tomographic and conventional plenoptic-piv (left, green) versus additional step exclusive to plenoptic-piv (right, red) (detailed tomographic-piv workflow in elsinga et al. (2006)) of gururaj et al. (2021), across the same range of azimuth angles. volume 1 denotes the volume placing the focal plane near the tip of the wing while volume 2 was centered slightly inboard. experiments for each volume were repeated with three different rotation rates (approximately 1, 3, and 5 rpm) at an image acquisition rate of 200 fps. the theoretical field of view at the focal plane was calculated to be 68 × 38.2 mm and 60.7 × 34 mm for volume 1 and volume 2, respectively. seven iterations of a plenoptic-adapted mart algorithm were used to reconstruct volumes at a grid resolution of 8 vox/mm. the cross-correlation algorithm used here is based on a multi-pass 3d (vodim) scheme. cubic window sizes of [64, 48, 40, 40] voxels in each dimension with overlaps of 75% were applied to generate vector fields of size 52 × 28 × 76 for volume 1 and 44 × 23 × 76 for volume 2, with vector spacings of 1.25 mm. 3 rotational volumetric calibration this section details the calibration technique developed for application in a rotating volume – the necessity of which arises when a field of view is relayed via a rotating mirror to a stationary camera thus causing the image to exhibit in-plane rotation (fig. 2). in a conventional (stationary) field of view, our group employs a technique known as direct light-field calibration (dlfc) to relate a plenoptic image to object space (hall et al. (2018)). here, images of a calibration pattern at known depths relative to the focal plane are captured, covering a total depth that typically encloses the volume of interest. these images are then decoded into perspective views with each perspective representing a discrete location (u,v) on the aperture plane. a generic third-order polynomial is used as a mapping function to pair every location on the microlens plane (s, t) to its corresponding location in object space (x,y,z) via each perspective: s = p(x,y,z,u,v) = as0 +as1x+as2y+as3z+as4u+as5v+as6x 2 +as7xy+ · · · +as55v 3 t = p(x,y,z,u,v) = at0 +at1x+at2y+at3z+at4u+at5v+at6x 2 +at7xy+ · · · +at55v 3 (1) polynomial variables are stored in a matrix a where each row corresponds to a calibration feature point at a unique depth and perspective view. subsequently, the coefficients of eq. 1 are calculated by method of least-squares, as = a/s and at = a/t, where s and t represent vectors of s and t positions. the mapping function is later employed during reconstruction of 3d volumes from plenoptic images. for application to a rotating field of view, a method was devised whereby the coordinate system of the calibration plate was rotated with its azimuth angle (ψ). as the azimuthal rotation is proportional to the orientation of the field of view, assigned object-space coordinates of the calibration plate’s feature points remain constant throughout its angular sweep. for example, fig. 2(b) is imaged at an azimuth angle of ψ≈ 40◦ after fig. 2(a), therefore, the coordinate set (x,y) is rotated by ψ to become (x′,y′). this procedure results in the calibration polynomial being a function of azimuth angle: (s, t) = p(x′,y′,z,u,v,ψ) (2) calibration of the dot card in 2(b) with rotational dlfc results in 2(c) whereby the dot card appears at the same position as 2(a) despite the azimuthal rotation increasing by ψ≈ 40◦. a fixed volume would only require one calibration file whereas a continuously rotating volume with a fine enough angular resolution would require hundreds. the impracticality of physically calibrating volumes at every unique azimuth angle is avoided by exploiting the relationship between the mapping function coefficients and the rotation of the field of view. it was found by imaging a calibration plate through a full revolution that, conveniently, this is a periodic relation meaning that as the mirror rotates and thus the field of view rotates, the coefficients of the mapping function vary sinusoidally, as seen in fig. 4 which shows three examples of coefficients plotted at every 10◦ for 360◦. therefore, in the rotational implementation of dlfc, calibration images are acquired for volumes at relatively broad increments of azimuth angle and mapping functions are generated for any desired in-between angles using interpolation. figure 4: s-coefficient values through a full revolution of calibration plate rotation (gururaj et al. (2021)) a fourier series was chosen as the most suitable representation of a periodic best fit curve and thus is used here to aid interpolation. each mapping function coefficient was initially represented by a four-term fourier series through its rotation: (as,at) = f (ψ) = b0 + n ∑ i=1 bicos(iwψ)+ cisin(iwψ) (3) where w is a measure of the periodicity of a mapping function coefficient, n refers to the selected number of harmonics, and b and c are cosine and sine coefficients, respectively. if the four-term series was deemed to be overfitting the coefficients, the number of terms in the fourier series was dropped to three and subsequently two if overfitting persisted. goodness of fit was determined using a combination of the coefficient of determination (r2) and a comparison of global absolute maxima between the fourier curve and known coefficients. in either case, a user-defined threshold was set, the violation of which resulted in sequentially dropping the number of harmonics. for the rotating experiments presented here, images of the calibration plate were captured across a depth of 81.28 mm at approximately every 10◦ increment for a total sweep of 90◦ while coefficients were interpolated for each intermediate angle at which flow images were acquired according to encoder outputs. for example, in the case of the lowest rotation rate wingless experiment, 982 mapping functions were generated with each corresponding to a different azimuth angle using just 10 physically calibrated volumes. in summary, the rotational dlfc technique involves acquiring images of a calibration plate at discrete yet widely spaced azimuth angles across multiple depths throughout an angle sweep that encompasses the relevant range of rotation of the wing. a mapping function is generated at each of these angles by applying a generic third-order polynomial to the image and object space coordinates of known calibration points via discretized perspective views. coefficients for any angle within the swept range of the calibration plate are interpolated for using a fitted fourier series. this mapping function is then employed during reconstruction meaning the calibrated volume at each azimuth angle is mapped to a common set of in-plane coordinates (x′,y′) thus eliminating the effects of the rotating field of view when tracing particles into the volume. a reprojection error analysis was performed for the physically calibrated volumes in r3dv. as a measure of comparison, the same camera configuration was used to calibrate a stationary volume on a benchtop setup. in the latter, a 300 mm thorlabs motorized translation stage was used to provide positioning of the calibration plate with a precision of 0.5 µm. reprojection error was calculated by applying the corresponding mapping function to known calibration plate feature points in object space (x,y,z) to solve for (srepro j, trepro j), the reprojected image space position. this was compared to (s, t), considered the true image space location, for each feature point. resulting pixel values were then scaled with respect to the plenoptic camera’s perspective view resolution. in the rotational case, no trend in the reprojection error was observed with respect to varying azimuth angles. averaged across all 10 azimuth angles, the errors in rotational dlfc applied with the r3dv setup as well as the benchtop conditions are shown in table 1. for r3dv, an increase in reprojection error of ∼0.15 occurs in the s-direction while the t-axis holds a ∼0.3 increase. possible factors contributing to this rise include needing to image through a much thicker acrylic wall using the r3dv setup relative to the benchtop as well as imperfections in r3dv’s 3d-printed calibration mounting wing. the error in rotational calibration did not show a consistent dependency on ψ. whilst the comparison suggests the rotational calibration configuration has potential for improvements, subpixel accuracy is still obtained and, as section 4 will show, the overall measurement uncertainty of the technique is on par with stationary plenoptic-piv. therefore, the higher error of r3dv’s calibration is considered acceptable albeit a task for future work to reduce. table 1: reprojection errors of r3dv’s rotational dlfc versus conventional dlfc on benchtop setup 4 uncertainty analysis in order to quantify uncertainty of the velocity vector fields, images of quiescent flow were acquired via the mirror undergoing steady rotation. cross-correlation was performed on these images to generate vectors of velocities that represent the displacement in particle position due solely to imaging via the rotating mirror. the initial vectors output in the camera’s rectangular coordinate system were transformed to a cylindrical frame (fig. 5) for convenience as follows: ut = ucosθ+wsinθ (4) uv = v (5) ur = wcosθ−usinθ (6) r′ = r cosθ (7) θ = tan−1( x− x0 r ) (8) where u, v, and w are velocities in the horizontal, vertical, and depth directions of the raw cross-correlated vectors, respectively. similarly, ut , uv, and ur are velocities in the tangential, vertical, and radial directions, respectively, in relation to the cylindrical path of rotation. figure 5: schematic of coordinate transformation from cartesian (left) to cylindrical (right) in quantifying uncertainty, vector fields were compared to a model described by rotational kinematics: ut = ωrotr = ωrot(r−r0) (9) uv = 0 (10) ur = 0 (11) where ωrot is the rotation rate and r is measured relative to r0, the radial distance from the center of rotation to the calibrated center plane. while the location of the in-plane center of rotation, x0, is not known from physical parameters, it can be calculated using rotating images of the calibration board as follows. when assigning object space positions to feature points during dlfc, (0, 0) is chosen arbitrarily as long as it remains consistent to the same feature throughout every calibration image. the objective now becomes to find the distance of the center of rotation to the calibrated (0, 0). this can be achieved by tracking the position of a feature point through a series of images following the rotation of the calibration plate. a leastsquares algorithm is then used to fit a circle to the positions of the rotating dot in order to find its center of rotation (pratt (1987)). finally, the known image magnification is applied to back out x0, the object-space distance of the in-plane center of rotation to the calibrated center position. ωrot and r0 are estimated through a levenberg-marquardt least-squares minimization of velocity vectors after substituting eq. (4) into eq. (9). comparison of the model (fig. 6(a)) to the time-average of the steady-state portion of wingless motion (fig. 6(b)) was determined to give the systematic error in assuming purely rotational motion, ∆u. note the velocity close to the edges of fig. 6(b) drops towards 0 due to this portion of the volume being outside the field of view across most azimuth angles. on average, an error less than 1% of the tangential velocity occurred in the tangential direction, equivalent to less than 0.1 voxels per timestep. the model also assumed zero velocity in the vertical and radial directions. here, the comparison yielded ∆uv and ∆ur less than 0.15 and 0.6 voxels per frame, respectively. voxel error values far below average particle displacements in the direction of motion confirmed the piv measurements obtained using this experimental setup could be accurately modeled by pure rotation. it was noted that the in-plane systematic error increased further from the center of the vector field. as an example, fig. 7 plots the spatial variation of ∆ut normalized with respect to ut for a portion of the center xy-plane of the rpm ≈ 1, volume 2 experimental configuration. no consistent relationship was found with respect to error across the depth direction. after establishing that the system could be described by the rotational model, quantification of measurement uncertainty, δu′, was achieved by generating a model for the vector field at each azimuth angle, u′model , and comparing velocities from the cross-correlated vectors (fig. 6(c)) to their respective ideal values. the standard deviation of residual velocities from this comparison was taken as a value representative of measurement uncertainty. an experimental setup consisting of different imaging conditions at each azimuth (a) (b) (c) figure 6: example of an instantaneous r3dv vector field’s velocity distribution (right) vs time-averaged vector field (center) and a corresponding idealized model (left) calculated based on rotational kinematics angle begs the question as to whether uncertainty possesses a dependency on azimuth angle. fig. 8 plots δu′t for a rotation of approximately 60◦ for volume 2 with the mirror rotating at approximately 5 rpm. clearly, the uncertainty fluctuates randomly around 0.15. this randomness with azimuth angle was seen in all six test cases. similarly, the δu′r and δu′v exhibit no relationship with azimuth angle. accordingly, uncertainty was averaged across all azimuth angles for each volume and each rotation rate to yield a single value for the configurations shown in table 2. here, it is apparent the in-plane uncertainty is consistently higher for the farther volume 1. it was hypothesized this was caused by a slight increase in particle density across the two sets of experiments. interestingly, volume 2 generally possesses a higher radial uncertainty. there also exists a slight trend of increasing tangential uncertainty with higher rotation rates, although in proportion to the mean tangential velocity it actually decreases. due to the limited angular range of perspectives a plenoptic camera can obtain, particle elongation is always expected to cause reduced depth precision relative to that of the in-plane directions in a single-camera plenoptic experiment and this is certainly observed in table 2. overall, the authors assert the uncertainty for the current implementation of r3dv is less than 0.21 voxels per timestep for the in-plane components and better than 1.7 voxels per timestep in the radial direction. these values are comparable to those obtained by fahringer et al. who determined the uncertainty of single-camera plenoptic-piv in a stationary reference frame to be accurate to within 0.2 voxels and 1 voxel in the lateral and depth directions, respectively (fahringer et al. (2015)). 5 conclusions the r3dv technique possesses unique challenges associated with imaging through a rotating mirror using a stationary camera, with one such challenge being an undesired rotation of the images recorded by the camera. the authors propose a rotational calibration method whereby the azimuth angle of the mirror is incorporated in the calibration function to rectify the rotating field of view to a common axis. despite being higher than plenoptic calibration in a benchtop configuration, rotational dlfc’s reprojection errors of less than 0.6 pixels were deemed acceptable for r3dv. a focus for future work will involve reducing this error by improving the physical design of the calibration plate mounting system. quantification of uncertainty was achieved by comparing a model of rotation to vector fields obtained from quiescent flow viewed through a rotating mirror. the error in assuming the motion in the setup adheres purely to laws of rotational kinematics was first assessed and concluded to be insignificant. comparison of instantaneous vector fields to their respective ideal models yielded average uncertainties better than 0.21 and 1.7 voxels per figure 7: spatial variation of systematic error in ut normalized with respect to the model ut across an xyplane of volume 2, rpm ≈ 1 figure 8: variation of uncertainty in tangential velocity across a 60◦ azimuthal rotation timestep in the in-plane and out-of-plane directions, respectively, each with no reliance on azimuth angle. as these values proved comparable to those found in previous work on plenoptic-piv uncertainty estimation, the current implementation of r3dv is seen to be a success. optimization of cross-correlation parameters is currently being explored with the aim of reducing uncertainty. possibilities of future developments include implementing particle tracking velocimetry via the plenoptic ray-bundling triangulation method developed by clifford et al. (2019) as well as investigating the fluid-structure interaction behavior of a rotor during the lev life cycle. table 2: average measurement uncertainty across six wingless r3dv experiments acknowledgements this research was sponsored by the army research office and was accomplished under grant number w911nf-19-1-0052 and w911nf-19-1-0124 (durip) monitored by dr. matthew munson. the views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the army research office or the u.s. government. the u.s. government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation herein. the authors would also like to acknowledge the members of advanced flow diagnostics laboratory, applied fluid research group, dr. chris clifford, dr. eldon triggs and mr. andy weldon in the department of aerospace engineering at auburn university. references clifford c, tan zp, hall em, and thurow bs (2019) particle matching and triangulation using light-field ray bundling. in cj kähler, r hain, s scharnowski, and t fuchs, editors, proceedings of the 13th international symposium on particle image velocimetry elsinga ge, scarano f, wieneke b, and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 fahringer tw, lynch kp, and thurow bs (2015) volumetric particle image velocimetry with a single plenoptic camera. measurement science and technology 26:115201 gururaj a, moaven m, tan zp, thurow b, and raghav v (2021) rotating three-dimensional velocimetry. experiments in fluids hall em, fahringer tw, guildenbecher dr, and thurow bs (2018) volumetric calibration of a plenoptic camera. appl opt 57:914–923 mulleners k, kindler k, and raffel m (2012) dynamic stall on a fully equipped helicopter model. aerospace science and technology 19:72–76 percin m and oudheusden bw (2015) three-dimensional flow structures and unsteady forces on pitching and surging revolving flat plates. experiments in fluids 56:1–19 pratt v (1987) direct least-squares fitting of algebraic surfaces. siggraph comput graph 21:145–152 tan zp, johnson k, clifford c, and thurow bs (2019) development of a modular, high-speed plenopticcamera for 3d flow-measurement. opt express 27:13400–13415 motivation rotating 3d velocimetry technique setup data acquisition and processing parameters rotational volumetric calibration uncertainty analysis conclusions 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 visualization and quantification of the cerebral microcirculation using contrast enhanced ultrasound particle tracking velocimetry z. zhang1, m. hwang2, t. j. kilbaugh3, a. sridharan2, j. katz1* 1 johns hopkins university, department of mechanical engineering, baltimore, usa. 2 children’s hospital of philadelphia, department of radiology, philadelphia, usa. 3 children’s hospital of philadelphia, department of anesthesiology and critical care medicine, philadelphia, usa. * katz@jhu.edu abstract noninvasive measurements of the regional microvascular perfusion might lead to sensitive biomarkers for the changes in intracranial hemodynamics that could guide timely surgical interventions for neonatal brain injuries. the current work utilizes a clinically available contrast enhanced ultrasound (ceus) system and particle tracking velocimetry to perform ultrasound localization microscopy for measuring the microcirculation in piglets. a new deep learning method based on u-net is proposed for enhancing noisy raw ceus images and detecting the microbubbles. subsequently, the bubbles are tracked using a kalman filter based method, which incorporates conditions of spatio-temporal consistency in flow direction and globally optimizes the assignment of bubbles to trajectories. based on analysis of synthetic data, the u-net results demonstrate significant improvement in the processing speed and localization accuracy over a conventional blind deconvolution method. visualization of the microvasculature is performed by superposing the bubble trajectories, enabling depiction of a complex micro-vessel network, where neighboring vessels separated by 40 µm can be distinguished. the corresponding perfusion map shows the velocity distribution in these vessels. based on the current frame rate (44 fps), speeds in the 0.1 to 12 cm/s range can be well captured. these methods show promise as potential clinical tools for bedside measurement of cerebral microcirculation. 1 introduction noninvasive measurements of the cerebral blood flow (cbf) provide vital information about the hemodynamic conditions that could guide timely surgical interventions for various types of neonatal brain injuries. conventionally, magnetic resonance imaging (leliefeld et al. 2008) or computed tomography (dankbaar et al. 2010) are used for mapping the regional distributions of cbf. due to their millimetric scale spatial resolutions, these techniques cannot distinguish the macrovascular perfusions from the microperfusions (demené et al. 2021). flow parameters measured in major cerebral arteries are inadequate for monitoring the complex intracranial dynamic responses under varying hemodynamic conditions (hanlo et al. 1995). in contrast, the microvascular flow in different cerebral regions is sensitive to hemodynamics changes (zaharchuk et al. 1999). therefore, techniques that enable measurements of regional microperfusion might lead to more sensitive markers for various cerebral pathological conditions. as a convenient bedside tool, contrast-enhanced ultrasound (ceus) imaging has been introduced for 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 evaluating the cerebral perfusion in neonatal brains (hwang 2019). ceus utilizes intravascular microbubbles (<5μm in diameter) to visualize the blood flow. several postprocessing techniques have been developed to quantify the flow parameters based on ceus images, including ultrasound imaging velocimetry or echo-piv (crapper et al. 2000; kim et al. 2004; poelma 2017; zhang et al. 2020), and echoparticle tracking velocimetry (sampath et al. 2018; jeronimo et al. 2020), which is also referred to as ultrasound localization microscopy (ulm) in the ceus community (siepmann et al. 2011; christensenjeffries et al. 2014; ackermann and schmitz 2016). the latter uses the bubble trajectories for reconstructing the vascular systems and performing flow measurement in microand macrovessels at very high spatial resolution. the applications of ulm include mapping the cerebral and renal vascular systems in rodent models (errico et al. 2015; foiret et al. 2017; lin et al. 2017), and detecting a small deep-seated human cerebral aneurysm (demené et al. 2021). in the present study, ulm is adopted for visualizing and quantifying the cerebral microcirculation in piglet models. since the width of micro-vessels is comparable to the spatial resolution of the ultrasound systems, application of ulm requires precise localization and robust tracking of the bubbles. previous localization techniques have involved deconvolution (foroozan et al. 2018; zhang et al. 2020), as well as correlation (demené et al. 2021) and peak thresholding (jeronimo et al. 2020). recent studies have shown that preprocessing of the ceus images using deep learning based techniques could reduce the error in bubble localization by 75% (liu et al. 2020), and could be about 60 times faster than blind deconvolution (bd) methods (bai et al. 2019). the robustness and generalizability of deep learning models rely on a training dataset that represents a wide range of circumstances. however, ceus images recorded by different ultrasound systems, contrast agents, and imaging settings, as well as recoded at various depth and organs, involve diverse noise levels, backgrounds, and bubble image morphologies. these variations undermine the robustness of the previous models that are based on specific spatially invariant point spread functions (psf) to describe the bubble image morphologies (liu et al. 2020; van sloun et al. 2020). therefore, further imprvements to these models are needed for ceus images recorded by curved, vector, and curvilinear probes, which have a psf that becomes increasingly elongated with increasing depth and has an orientation that varies with angular position. in terms of bubble tracking, taking advantage of the ultrafast (~1000 frames/s) ultrasound research systems, the nearest-neighbor data association strategy is common in ulm applications (christensen-jeffries et al. 2014; errico et al. 2015). for low-frame-rate clinical systems (~50 frames/s), ackermann et al. (2016) have developed a motion model based modified markov chain monte carlo framework. moreover, a recent work has proposed a kalman filter based tracking method (tang et al. 2020). in the present work, the spatio-temporal consistency conditions in the flow direction are incorporated to the existing kalman filter framework (kim et al. 2015) to improve the bubble tracking. in this paper we utilize echo-ptv to perform ulm for visualizing the cerebral microcirculation in pediatric pig models using a clinical ceus system. a u-net based deep learning model is designed and trained by ceus and synthetic images for bubble detection in images involving a wide range of psfs. the new procedure substantially outperforms blind deconvolution based methods in terms of the processing speed and localization accuracy. the bubble tracking combines a kalman filter, several candidate selection criteria, and globally optimized candidate assignments. the paper concludes with a sample application to visualize the cerebral microcirculation in a piglet. 2 methods 2.1 animal preparation and ceus imaging the current study utilizes a pediatric pig model (female, 4-week-old, 10kg) to visualize and quantify the cerebral micro-perfusion. all of the animal preparation and management protocols, including anesthesia, ventilation, temperature management, cannulation, neuromonitoring, and hemodynamic monitoring, have followed previously published procedures (friess et al. 2015), which have been approved by the institutional animal care and use committee of the children’s hospital of philadelphia. the ceus scans are performed using a siemens acuson sequoia system (siemens medical solutions, malvern, pa) with a 9ec4 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 transducer (siemens medical solutions, malvern, pa). to obtain clear images, a 2.5 cm cranial window is drilled upper right to the midline in the parietal region with intact dura. the field of view is aligned to a coronal plane containing the maximum transverse diameter of the bilateral thalami and is focused on the left hemisphere to maintain image acquisition rate of 44 frames/s. the ultrasound probe is fixed to the experimental table using a stereotactic arm. the piglet’s head is also fixed to the table to minimize its motion. the contrast agents (lumason, bracco diagnostics, nj) are infused at 0.6 ml/min using a veterinary syringe pump (practivet, tempe, arizona, usa) connected to the femoral vein line. this infusion rate is selected, based on a pre-study, to establish a bubble concentration low enough to facilitate detection and tracking of individual bubbles while still maintaining a sufficient number for fully mapping the vascular structures. the ideal concentrations vary between 150 to 200 bubbles per image. the recording lasts for 2 mins with 5760 images collected. the ceus imaging is taken at dual view mode with a ceus image on the left and a normal b-mode image on the right. the b-mode image is used as a reference for crosscorrelation based image stabilization, if needed. 2.2 image preprocessing using u-net in the present study, the u-net creation, training, and validation are performed using the deep learning toolbox in matlab. the current u-net (ronneberger et al. 2015) image enhancement procedure is illustrated in fig. 1. this architecture is widely-used for medical imaging processing tasks, and has been reported to deliver good performances in image enhancement, object detection, and morphometry (falk et al. 2019). as shown in fig. 1(a), u-net consists of encoding (down-sizing) and decoding (up-sizing) steps for converting big and blurred bubble traces with varying sizes to smaller and sharper ones. the current unet model has an encoder-decoder depth of 3, resulting in 45 layers. the inputs, i.e., 128×128 pixels grayscale images, are downsized by half at each encoder level and doubled at each decoder level. the final convolution layer is used to gather the information from the last decoder level, followed by a regression layer, which generates the output. the network is trained by two sets of image pairs: the first set consists of raw ceus images (training input) and the corresponding enhanced images based on blind deconvolution (training reference). to prepare the training set, the background intensity is removed by subtracting the ensemble averaged image, and rejecting pixels with intensity falling below 0.1 (0-1 range), which is considered as noise. then the intensity range for each image is re-normalized to 0-1. a sample of the resulting image is shown in fig. 1(b). these steps ensure standardized inputs from different experiments. the enhanced training reference is generated following a modified blind deconvolution procedure (zhang et al. 2020). specifically, the raw ceus images are modelled as multiple impulse signals blurred by spatially variant psfs with additional noise. by dividing the raw images into smaller windows, a local psf is estimated following pan et al. (2014) in each window. psfs estimated from 20 random raw images are averaged at each location and used to deconvolve the rest of the images. the deconvolved ones are subsequently enhanced using a modified histogram equalization method (roth and katz 2001). then the corresponding pre-processed raw & enhanced images are zeropadded on the right and bottom, and split into 128×128 pixels sub-images with 20% lateral overlapping and 15% vertical overlapping (yellow boxes in fig. 1(b)). these choices ensure that at least one of the neighboring sub-images contains a complete psf. the size of the sub-image is selected to maintain the smallest psf larger than 2 pixels after the three encoding phases of the u-net. splitting of the images avoids large training datasets and computational cost caused by treating the whole image as a training input. moreover, it is more focused on the local features of the psf without depth and angular position information, making this model more robust to the various psf shapes and orientations. the second training set consists of synthetic images generated based on the psf estimated by bd (fig. 1(c)). the purpose of including synthetic images in the training data is to enhance the u-net model with cases where the precise location and morphology information are known. to mimic the result of bd and generate the training reference, 2d gaussian signals with peak intensity of 1 and diameters of 7 to 10 pixels are randomly placed on the 128×128 pixels black background (fig. 1(c)). the bubble densities in the synthetic data are set as 8.5, 25.5, and 42.5 bubbles/cm2, corresponding to sparse, normal, and dense bubble distributions in the raw ceus images. then, the previously determined, spatially varying psf (fig. 1(c), left side) is used for generating the training inputs. these psfs are further randomly rotated in the -20° to 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 +20° range, resized with a factor in the 0.8 to 2 range, and given a peak intensity in 0.1-1 range to simulate the uneven illumination of the bubbles in the actual ceus images. such broadening of image conditions is designed to expand the capability of the u-net model to handle varying psf morphologies, orientations, and image qualities. a sample synthetic image pair is presented in fig. 1(c), with the blurred image on top being the training input, and the corresponding training reference, in the bottom. the training process is based on 400000 pairs of raw & enhanced ceus sub-images along with 64000 of synthetic image pairs. the training set consists of 70% of both types of images, and the rest (30%) are used as the validation set. the adam optimization algorithm, which is provided in the deep learning toolbox of matlab, is used to train the model, with a total of 40 epochs. for each epoch, the dataset is randomly shuffled to increase the randomness in the training and bypass local optima. the training procedure involves a minibatch size of 64, and initial learning rate of 0.001. a learning rate decay strategy is used to reduce the learning rate by half when the training loss plateaus (shin et al. 2016). during the training, the intermediate result is validated twice per epoch. the training stops when the loss does not keep decreasing for the next 5 validations. all the calculations are carried out on a pc, equipped with a nvidia geforce rtx 2080ti gpu (11 gb ram), 1 intel i9-7920x cpu (2.9 ghz), and 128 gb ddr4 ram. due to current amount of data and gpu ram size, the training takes 19 h to converge. the final validation root-mean-squared-error for each pixel is 1.15×10-9. figure 1 schematics depicting the overall structure of the current deep learning model. (a) an illustration of the structure of the u-net with encoder depth of 3 and 45 layers in total. (b) training data based on the actual ceus images. the raw and enhanced images are divided into 128×128 sub-images with 20% lateral overlapping and 15% vertical overlapping (yellow box). a sample sub-image pair of the training data is shown on the right, with the raw image (top) as training input and enhanced image (bottom) as training reference. (c) training data based on the synthetic images. the psf (left column) used for generating the synthetic images are estimated by the blind deconvolution. the increasing elongation of the psf with depth are evident in both (b) and (c). the synthesized images at the same location in (b) is presented in the right column of (c). all raw & enhanced images pairs (both ceus and synthetic) are gathered and shuffled before training. 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 2.3 tracking of the microbubbles due to the complexity of the microvasculature, the following procedure has been used for bubble tracking. the raw ceus images (fig. 2(a)) are enhanced using the u-net described above to obtain the image shown in fig. 2(b). here, the elongated bubble traces are replaced by sharp images where adjacent bubbles are sufficiently separated. subsequently, intensity-weighted center of each bubble is used for generating a heatmap of bubble locations (fig. 2(c)), which restricts the likely locations of blood vessels during the bubble tracking process. the procedures for bubble tracking are illustrated in fig. 2(d). the trajectories are initialized by exhaustively searching for candidates within a prescribed maximum displacement range for the first three exposures (fig. 2(d)). the corresponding candidates in the fourth and subsequent exposures are updated using a kalman filter (kim et al. 2015). removal of the most unlikely candidate tracks is based on a minimum kalman filter tracking score, overlap with the heatmap (<90% for major vessels and <50% for other regions), deviations in bubble radius (>50%) and directions of velocity (>60°), as well as magnitude of acceleration (>30% of prescribed maximum displacement). these thresholds are selected based on previous experiences (zhang et al. 2020), and examination of numerous images. considering that in some cases the same bubble is assigned to multiple tracks, a data association procedure is used for determining the global optimal bubble assignment (fig. 2(e)). this step involves: i) generating an undirected weighted graph by assigning each possible trajectory to a node, assigning a weight to each node based on its tracking score representing the likelihood of being the correct trajectory, and linking nodes that share the same bubble; and ii) solving for the maximum weighted independent set (papageorgiou and salpukas 2009) of this graph. the latter is the largest subset of the nodes that are not interconnected and have the maximum figure 2 schematics depicting the bubble tracking procedures. (a) a sample raw ceus image. (b) the u-net output showing the enhanced images of (a). (c) the bubble center heatmap used as one of the references for bubble tracking. (d) an illustration of the bubble tracking strategy. for the initial 3 time steps, all candidates within a prescribed maximum displacement range are selected. starting from the 4th time step, the candidates are selected within the validation gate of the predicted location by kalman filter. several criteria, including the overlap percentage with the bubble center heatmap, continuity in flow speed and direction, bubble morphology, and deviation from the reference flow direction, are used for removing the most unlikely candidates. (e) global optimum data assignment. the strategy in (d) yields the same bubble being assigned to different trajectories. here each trajectory is modeled as a node of an undirected graph, the tracking score from kalman filter as the weight of each node, and two nodes are linked if they share the same bubble. the maximum weight independent set of this graph is the global optimized assignment of the bubbles. 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 average weight. therefore, the outcome of this method gives the globally optimized candidate-trajectory association. next, a reference flow direction map is generated after processing the first 25% of images. then, the whole analysis is initiated again, with an additional criterion limiting the deviation in flow direction to less than 15° from that of the reference. finally, the vascular structures are visualized by super-positioning all the trajectories consisting of at least 4 exposures. the corresponding velocity map is generated by averaging the bubble velocities at each pixel. 3 result & discussion 3.1 evaluation of the u-net to evaluate the performance of the u-net model, 900 synthetic images pairs are generated following the procedures described in section 2.2 and processed using both u-net and bd methods. comparisons between the two methods are presented in fig. 3. fig. 3(a) a visualization of the synthetic reference images (green) and the outputs of both the u-net (red) and bd (yellow). the images are shown separately on the right side, and superimposed on the synthetic blurred images on the left. it is evident that the u-net result is much sharper and closer to the reference than the bd based result. the processing speed of u-net is 131 frames/s using a gpu, while that of bd is 0.55 frames/s using 12 core cpu. a gpu based bd code is not available. figure 3 evaluation and comparison of the u-net results with bd. (a) an illustration of the image enhancement and bubble localization result of u-net (red) and bd (yellow). several issues regarding bubble detection including miss detection, generation of ghost points, and failure to separate adjacent bubbles are noted. (b) comparisons of the localization error, percentage of miss detections and ghost points between u-net and bd at different depth and bubble densities. 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 further acceleration of the u-net model could be easily achieved by expanding the ram of the gpu. several issues are listed regarding the bubble detection on the left panel of fig. 3(a). while both techniques detect most of the bubbles, the bd method is more prone to miss detections than the u-net. moreover, a ghost point, i.e., erroneous detection caused by enhancement of the pixels which do not belong to a real bubble, has been generated by the bd method. furthermore, while both methods fail to completely separate densely packed bubbles, u-net evidently outperforms bd. quantitative analysis of these observations is presented in fig. 3(b) for varying bubble densities (columns), and image depths, i.e., various sizes of the psf (see fig. 2(c)). here, a successful detection is defined as the closest detection to a prescribed center as long as it is smaller than 6 pixels. miss detections are the prescribed centers that cannot find a successful match, and ghost points are detections without a prescribed center in the 6 pixel range. therefore, for three adjacent bubbles being identified by the bd method as one bubble, the result would be two misses and one successful detection. as the first row of fig. 3(b) shows, for all bubble densities and depths, the mean and standard deviations of bd’s localization error are much higher than those of the u-net. as expected, the error in bd increases with depth, while that of the u-net remains at the similar level for all depths. for both methods, the error increases with bubble density. however, for low (8.5 bubbles/cm2) and normal (25.5 bubbles/cm2) densities, the errors for u-net are less than 1 pixel. furthermore, bd also has more miss detections than u-net (second row of fig. 3(b)). while the average miss detections for u-net are typically less than 5%, those of bd not only increase with depth, but also increase significantly with bubble density. as for the ghost points (3rd row in fig. 3(b)), u-net is not prone to have such an issue for all the tested depths and densities, and bd shows about 5% of ghost points at large depth. clearly, u-net outperforms bd in terms of both processing speed and accuracy in enhancing ceus images and detecting microbubbles. 3.2 visualization and quantification of the cerebral microcirculation the visualization of the vasculature is presented in fig. 4(a), and the corresponding time-averaged velocity map is demonstrated in the fig. 4(b). major blood vessels (~1 mm width) with time-averaged speeds of more than 5 cm/s and moderate vessel (~ 300 µm width) with speeds in 1-2 cm/s range are evident. figure 4 visualization and quantification of the cerebral microcirculation. (a) a visualization of the blood vasculatures. (b) the corresponding blood velocity map of (a). (c) a magnified view of the region in the yellow box of (a), showing the complex microvascular networks. line 1 is the cross section (red bar plot) of a moderate blood vessel, and the result for line 2 shows that the current work is able to distinguish micro-vessels departed by 40µm. 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 the speeds for micro-vessels are usually below 1cm/s. a closer look at the micro-vessel networks is presented in fig. 4(c), where a magnified view of the region in the yellow box of fig. 4(a) is demonstrated. two lines are indicated on the zoomed view to demonstrate the spatial resolution of the current result. line 1 is the cross section of a moderate sized blood vessel, and the bar plot of the numbers of trajectories along this line shows that the in-plane width of this vessel is around 300 µm. the corresponding velocity profile shows a parabolic shape, which is consistent with the expected poiseuille flow profile. line 2 is placed across two parallel micro-vessels that are very close to each other. the results of line 2 shows that the spatial resolution of the current method is sufficient to distinguish two neighboring micro-vessels that are 40 µm apart. 4 conclusions in conclusion, the current work has proposed a u-net based image processing method and a kalman filter based bubble tracking method for performing echo-ptv using clinically available ceus images. the unet model has significantly improved the processing speed and accuracy in bubble detection. we have demonstrated the application of the currently proposed method for measuring the cerebral microcirculation on a piglet. neighboring micro-vessels that are 40 µm apart from each other can be successfully detected. acknowledgements misun hwang acknowledges support from nih grants r01 ns119473-01, and joseph katz acknowledges support from the department of mechanical engineering at johns hopkins university. references ackermann d, schmitz g (2016) detection and tracking of multiple microbubbles in ultrasound b-mode images. ieee transactions on ultrasonics, ferroelectrics, and frequency control 63:72–82 bai c, liu c, yu x, peng t, min j, yan s, dan d, yao b (2019) imaging enhancement of light-sheet fluorescence microscopy via deep learning. ieee photonics technology letters 31:1803–1806 christensen-jeffries k, browning rj, tang m-x, dunsby c, eckersley rj (2014) in vivo acoustic superresolution and super-resolved velocity mapping using microbubbles. ieee transactions on medical imaging 34:433–440 crapper m, bruce t, gouble c (2000) flow field visualization of sediment-laden flow using ultrasonic imaging. dynamics of atmospheres and oceans 31:233–245 dankbaar jw, de rooij nk, rijsdijk m, velthuis bk, frijns cjm, rinkel gje, van der schaaf ic (2010) diagnostic threshold values of cerebral perfusion measured with computed tomography for delayed cerebral ischemia after aneurysmal subarachnoid hemorrhage. stroke 41:1927–1932 demené c, robin j, dizeux a, heiles b, pernot m, tanter m, perren f (2021) transcranial ultrafast ultrasound localization microscopy of brain vasculature in patients. nature biomedical engineering 5:219–228 errico c, pierre j, pezet s, desailly y, lenkei z, couture o, tanter m (2015) ultrafast ultrasound localization microscopy for deep super-resolution vascular imaging. nature 527:499–502 falk t, mai d, bensch r, çiçek ö, abdulkadir a, marrakchi y, böhm a, deubner j, jäckel z, seiwald k (2019) u-net: deep learning for cell counting, detection, and morphometry. nature methods 16:67–70 foiret j, zhang h, ilovitsh t, mahakian l, tam s, ferrara kw (2017) ultrasound localization microscopy to image and assess microvasculature in a rat kidney. scientific reports 7:1–12 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 foroozan f, o’reilly ma, hynynen k (2018) microbubble localization for three-dimensional superresolution ultrasound imaging using curve fitting and deconvolution methods. ieee transactions on biomedical engineering 65:2692–2703 friess sh, bruins b, kilbaugh tj, smith c, margulies ss (2015) differing effects when using phenylephrine and norepinephrine to augment cerebral blood flow after traumatic brain injury in the immature brain. journal of neurotrauma 32:237–243 hanlo pw, gooskens r, nijhuis ijm, faber jaj, peters rja, van huffelen ac, tulleken caf, willemse j (1995) value of transcranial doppler indices in predicting raised icp in infantile hydrocephalus. child’s nervous system 11:595–603 hwang m (2019) introduction to contrast-enhanced ultrasound of the brain in neonates and infants: current understanding and future potential. pediatric radiology 49:254–262 jeronimo md, najjari mr, rival de (2020) echo-lagrangian particle tracking: an ultrasound-based method for extracting path-dependent flow quantities. measurement science and technology 31:54008 kim c, li f, ciptadi a, rehg jm (2015) multiple hypothesis tracking revisited. in: proceedings of the ieee international conference on computer vision. pp 4696–4704 kim h-b, hertzberg jr, shandas r (2004) development and validation of echo piv. experiments in fluids 36:455–462 leliefeld ph, gooskens rhjmjm, vincken kl, ramos lmpp, van der grond j, tulleken caff, kappelle lj, hanlo pw (2008) magnetic resonance imaging for quantitative flow measurement in infants with hydrocephalus: a prospective study. journal of neurosurgery: pediatrics 2:163–170 lin f, shelton se, espíndola d, rojas jd, pinton g, dayton pa (2017) 3-d ultrasound localization microscopy for identifying microvascular morphology features of tumor angiogenesis at a resolution beyond the diffraction limit of conventional ultrasound. theranostics 7:196 liu x, zhou t, lu m, yang y, he q, luo j (2020) deep learning for ultrasound localization microscopy. ieee transactions on medical imaging 39:3064–3078 pan j, hu z, su z, yang m-h (2014) deblurring text images via l0-regularized intensity and gradient prior. in: proceedings of the ieee conference on computer vision and pattern recognition. columbus, oh, usa, pp 2901–2908 papageorgiou dj, salpukas mr (2009) the maximum weight independent set problem for data association in multiple hypothesis tracking. in: optimization and cooperative control strategies. springer, pp 235– 255 poelma c (2017) ultrasound imaging velocimetry: a review. experiments in fluids 58:1–28 ronneberger o, fischer p, brox t (2015) u-net: convolutional networks for biomedical image segmentation bt medical image computing and computer-assisted intervention – miccai 2015. in: navab n, hornegger j, wells wm, frangi af (eds). springer international publishing, cham, pp 234– 241 roth gi, katz j (2001) five techniques for increasing the speed and accuracy of piv interrogation. measurement science and technology 12:238 sampath k, harfi tt, george rt, katz j (2018) optimized time-resolved echo particle image velocimetry– particle tracking velocimetry measurements elucidate blood flow in patients with left ventricular thrombus. journal of biomechanical engineering 140:41010 shin h-c, roth hr, gao m, lu l, xu z, nogues i, yao j, mollura d, summers rm (2016) deep convolutional neural networks for computer-aided detection: cnn architectures, dataset characteristics 14th international symposium on particle image velocimetry -ispiv 2021 august 1--5, 2021 and transfer learning. ieee transactions on medical imaging 35:1285–1298 siepmann m, schmitz g, bzyl j, palmowski m, kiessling f (2011) imaging tumor vascularity by tracing single microbubbles. in: 2011 ieee international ultrasonics symposium. ieee, pp 1906–1909 tang s, song p, trzasko jd, lowerison m, huang c, gong p, lok u-w, manduca a, chen s (2020) kalman filter-based microbubble tracking for robust super-resolution ultrasound microvessel imaging. ieee transactions on ultrasonics, ferroelectrics, and frequency control 67:1738–1751 van sloun rjg, solomon o, bruce m, khaing zz, wijkstra h, eldar yc, mischi m (2020) super-resolution ultrasound localization microscopy through deep learning. ieee transactions on medical imaging 40:829–839 zaharchuk g, mandeville jb, bogdanov aa, weissleder r, rosen br, marota jj (1999) cerebrovascular dynamics of autoregulation and hypoperfusion. an mri study of cbf and changes in total and microvascular cerebral blood volume during hemorrhagic hypotension. stroke 30:2195–2197 zhang z, zhou x, suarez-pierre a, lui c, kearney s, yeung e, halperin h, choi cw, katz j (2020) timeresolved echo-particle image/tracking velocimetry measurement of interactions between native cardiac output and veno-arterial ecmo flows. journal of biomechanical engineering 143: 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 measurement of the acoustic streaming pattern in a standing surface acoustic wave field s. sachs1∗, c. cierpka1, j. könig1 1 technische universität ilmenau, institute of thermodynamics and fluid mechanics, ilmenau, germany ∗ sebastian.sachs@tu-ilmenau.de 1 introduction the application of standing surface acoustic waves (ssaw) has enabled the development of many flexible and easily scalable concepts for the fractionation of particle solutions in the field of microfluidic lab-ona-chip devices. in this context, the acoustic radiation force (arf) is often employed for the targeted manipulation of particle trajectories, whereas acoustically induced flows complicate efficient fractionation in many systems [sehgal and kirby (2017)]. therefore, a characterization of the superimposed fluid motion is essential for the design of such devices. the present work focuses on a structural analysis of the acoustically excited flow, both in the center and in the outer regions of the standing wave field. for this, experimental flow measurements were conducted using astigmatism particle tracking velocimetry (aptv) [cierpka et al. (2010)]. through multiple approaches, we address the specific challenges for reliable velocity measurements in ssaw due to limited optical access, the influence of the arf on particle motion, and regions of particle depletion caused by multiple pressure nodes along the channel width and height. variations in frequency, channel geometry, and electrical power allow for conclusions to be drawn on the formation of a complex, three-dimensional vortex structure at the beginning and end of the ssaw. 2 experimental microfluidic setup the investigated microfluidic system (see fig. 1) consists of a straight channel made of polydimethylsiloxan (pdms) with a rectangular cross-section (500 µm in width, heights between 85 µm and 480 µm) centrally located between two interdigital transducers (idt) on a piezoelectric substrate consisting of linbo3. two coherent counter propagating surface acoustic waves (saw) were excited that superimposed in the region of the microchannel to form a standing wave field within the carried fluid. to study the influence of the frequency, different pairs of idts with resonance frequencies ranging from 25.72 mhz to 194.8 mhz were used. a syringe pump (nemesys, cetoni gmbh) was employed to provide a mixture of 80 % v/v de-ionized water and 20 % v/v glycerol at a constant flow rate. the glycerol was added to match the density between the fluid and suspended 1.14 µm polystyrene particles. in this way, not only sedimentation was reduced but also the influence of arf due to a lower acoustic contrast factor. 3d3c flow measurements are performed by aptv in three distinct regions of interest (roi) through the birefringent linbo3, which requires the use of an additional polarization filter [kiebert et al. (2017)]. figure 1: schematic illustration of the microfluidic device with the observed regions at the beginning (roi1), center (roi2) and the end (roi3) of the ssaw. the directions of saw propagation are indicated by arrows. figure 2: experimentally determined particle motion transverse to the main flow in roi2 for frequencies of 194.8 mhz (a) and 25.72 mhz (b). flow field in sectional planes lengthwise (c, x′ = 250 µm) and crosswise (d, y′ = 90.7 µm) to the microchannel at the beginning (dashed line) of the ssaw. 3 results the flow field transverse to the imposed main flow at the center of the ssaw (roi2) is depicted for frequencies of 194.8 mhz and 25.72 mhz in fig. 2a and 2b, respectively. the irregularly distributed velocity vectors were interpolated onto a regular grid with a voxel size of 10×800×10 µm3. white areas indicate regions where no particles were detected. while two acoustically induced vortex pairs in fig. 2a extend across the entire channel cross-section, periodic structures are visible in the center of the channel as the frequency decreases. with regard to the beginning of the ssaw (roi1, fig. 2c), a 3d vortex is visible, which has significant velocity components in the main flow direction. combined with fig. 2d, it is evident that recirculation occurs near the channel ceiling, while two separate maxima are formed at the lower corners. 4 conclusion and outlook in this study, the acoustically induced velocity field in the center and outer regions of the ssaw was revealed by 3d3c aptv measurements. more advanced investigations of the complex 3d vortices and results on the variation of frequency, channel geometry and electrical power will be presented at the conference. acknowledgements the authors thank the deutsche forschungsgemeinschaft (dfg) for financial support within the priority program spp2045 ”mehrdimpart” (ci 185/8-1). furthermore, support by the center of microand nanotechnologies (zmn), a dfg-funded core facility of tu ilmenau, is gratefully acknowledged. references cierpka c, segura r, hain r, and kähler cj (2010) a simple single camera 3c3d velocity measurement technique without errors due to depth of correlation and spatial averaging for microfluidics. meas sci technol 21:045401 kiebert f, wege s, massing j, könig j, cierpka c, weser r, and schmidt h (2017) 3d measurement and simulation of surface acoustic wace driven fluid motion: a comparison. lab on a chip 17:2104–2114 sehgal p and kirby bj (2017) separation of 300 and 100 nm particles in fabry-perot acoustofluidic resonators. analytical chemistry 89:12192–12200 introduction experimental microfluidic setup results conclusion and outlook 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 flow field study of a top heated immiscible liquid layer adjacent to ice hamed f. farahani *a, tatsunori hayashi b, hirotaka sakaue b, ali s. rangwala a a department of fire protection engineering, worcester polytechnic institute, worcester, ma 01609, usa a department of aerospace and mechanical engineering, university of notre dame, notre dame, in 46556, usa *hfarmahinifaraha@wpi.edu abstract a series of experiments were conducted to investigate the flow field of a top-heated liquid fuel adjacent to an ice block. the experimental setup consisted of a borosilicate container containing an ice wall and a layer of n-heptane heated from above. particle image velocimetry (piv) and background oriented schlieren (bos) measurements were conducted on the liquid-phase. piv measurements showed a surface flow toward the ice caused by surface-tension forces, which is driven by the horizontal temperature gradients on the liquid surface. a recirculation zone was observed under the free surface and near the ice. the combination of the two flow patterns caused lateral intrusion in the ice, instead of a uniform melting across ice surface. bos measurements indicated presence of density gradients below the free surface of n-heptane and in regions near the ice block. these density gradients were created by local small-scale temperature gradients. the current experiments were conducted to explore the processes that influence the ice melting by immiscible liquid layers. 1. introduction arctic multi-year sea ice is already at risk of being lost due to global warming (fig. 1). spill of the oil in ice-infested waters of the arctic is catastrophic for the environment. oil spills contaminate the ocean and disturb ecosystems. also, they bring about thermophysical alterations to the arctic melting processes (blankenet al., 2017). in particular, presence of oil adjacent to ice can fundamentally alter melting of ice sheets by increase of energy absorption from the sunlight. also, spilled oil transfers this energy to the ice differently than the water. this is because, most hydrocarbon fuels are immiscible in water, thereby, melting of ice adjacent to immiscible liquids is dissimilar to conventional melting as the melt layer does not mix in the ambient liquid, i.e. without diffusion of melt. additionally, interfacial forces between the two liquids and air can cause significant convective flows, which intensifies heat transfer to the ice (farahani et al., 2017). thus, understanding the heat transfer from an immiscible liquid to ice requires knowledge of the ambient mailto:*hfarmahinifaraha@wpi.edu 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 liquid flow field. the goal of the current study is to analyze the flow field of a liquid fuel that is adjacent to an ice wall and exposed to radiation from above, which mimic an oil spill scenario. figure 1: melting of towering ice in arctic in warm seasons (baker, 2021). 2. experimental setup particle image velocimetry (piv) and background oriented schlieren (bos) measurement techniques were employed to study the flow field of a top-heated hydrocarbon liquid adjacent to an ice wall. experiments were conducted under an ir radiant panel heater capable for delivery of a relatively uniform heat flux in the range of 1-30 kw/m2. below the ir heater panel, a squareshaped open top borosilicate container with side length of 10 cm and depth of 5 cm was used to hold the ice wall and the fuel as shown in fig. 2. experiment used a 10 cm × 6 cm × 3 cm ice wall placed on the left side of the container adjacent to ~4 cm deep layer of n-heptane (c7h16). the velocity field on the mid-plane of the liquid fuel perpendicular to the ice wall was obtained by piv measurements. a laser sheet was produced by a green diode laser and seeding particles (glass spheres 10 µm diameter) were added to the fuel layer prior to pouring it in the glass container. a dslr camera with recording rate of 30 fps was focused to the laser sheet. bos experiments utilized the same camera and a randomly generated dotted camera as shown in fig. 2 b-c. the bos method attains the first spatial derivative of the index of refraction. the index of refraction is then related to density by the gladstone-dale relation. the video files were processed to obtained individual frames in black and white and the piv post-process was performed by pivlab (thielicke and stumhuis, 2014) on the obtained images. cross correlation scheme with interrogation window size of 16 by 16 pixels was used for most of the postprocess efforts. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 figure 2: a) schematics of the experimental apparatus (not to scale). b) background of the random dot pattern used as imaged by the 1924 × 1080 pixels camera. the magnification (c) represents 32 × 32 pixels, and 4 interrogation windows of size 16 × 16 pixels. 3. results the radiation of the ir heater on the surface of n-heptane increased its temperature. this heat was transferred to the ice and provided the energy for the ice wall to start melting (farahani et al., 2019). figure 3 a-d shows side view of the ice wall and the sequence of its melting captured by the camera with intervals of 1 minute. note that the ice wall is placed on the left and the liquid to a depth of 4 cm is on the right side separated with a solid yellow line. as can be seen in this figure, most of the melting occurred near the free surface of the liquid creating a lateral intrusion in the ice at the final stage of the melting (fig. 3d). this means the heat transfer is mostly occurring near the free surface of the ice. figure 3: sequence of melting shape of ice (left) adjacent to heptane (right) with approximately 1-minute intervals under 3.1 kw/m2 incident heat flux. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a previous parametric study on melting by immiscible layers has revealed that viscosity of liquid has a reverse correlation with melting rate (farahani et al., 2018). the adverse correlation of the melting velocity to the viscosity implies that transfer of energy is mostly through convection rather conduction. piv results of experiments with n-heptane exposed to radiation intensity of 1.5 and 3.1 kw/m2 are shown in fig. 4 and 5. the ice is masked with color red. for the case of 1.5 kw/m2, convective flows were mostly observed near the free surface of the liquid traveling toward the ice. this is due to the strong surface-tension forces at the interface of liquid-air towards the ice wall. the arriving flow stagnated near the ice and returned to the bulk of liquid forming a recirculation zone near the ice wall. streamlines of vorticity show a strong recirculation zone at the free surface of the liquid and near the ice, as can be seen in fig 4b. the velocity magnitude and vorticity in other regions of the liquid-phase were found to show minimal impact from the impinging radiation. figure 4: flow field of n-heptane exposed to 1.5 kw/m2 radiation from above showing (a) vector field with background color map of velocity and (b) streamlines of vorticity with background of vorticity (1/s). with increase of the radiation intensity, the melting rates were also increased. figure 5a shows the vector field of n-heptane exposed to 3.1 kw/m2 radiation adjacent to an ice wall with background of velocity magnitude. vector field of figure 5a was averaged for 3 seconds due to optical distortions that eliminated a number of considerable number of particles from the field of view. as the heating intensity was increased, the density gradients that were created in the liquid caused optical interferences that adversely affects the piv images. these interferences caused blockage and distortion of scattered lights from seeding particles. thus, portion of the signal was 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 lost and obtaining the full image of the vector field was not possible. averaging in this situation provided an opportunity to see the general flow field, however, velocity magnitudes reported for the average results are reduced by averaging. figure 5b shows the streamlines of vorticity in a background of vorticity map. as can be seen, the recirculation zone near the ice is present and the downward directed flow created another recirculation zone deeper in the liquid. figure 5: flow field of n-heptane exposed to 3.1 kw/m2 radiation from above showing (a) vector field with background color map of velocity and (b) streamlines of vorticity with background of vorticity (1/s). assessment of the piv results show that regions of higher melting rate correspond to locations of higher liquid velocity and vorticity. however, due to presence of density gradients, the optical field is distorted and thereby scattered light from seeding particles are not captured entirely. this effect is intensified at higher radiation levels, which renders piv measurement unusable. nevertheless, averaging the results gives a qualitative understanding of flow patterns. loss of piv signal, which has also been observed previously in a similar type experiments [4], is due to significant temperature differences that are caused by impingements of the ir heater and presence of ice. the intrinsic thermal disparity of this system leads to density gradients and subsequently change in the index of refraction of the liquid that causes distortion and obstructions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 in the field of view. although it is not possible to correct these issues occurring for piv, bos can be used to identify regions of significant gradients. as can be seen in fig. 6 from the results of bos measurements (reported by pixel/frame displacement), density gradients are mostly present below the surface of the liquid and near the ice wall, which exactly overlaps with the regions of weak piv signal. figure 6. a) raw background image of bos showing distortions of the pattern near free surface, b) instantaneous, color map of pixel displacement (pixel/frame) in n-heptane. 4. conclusions a series of experiments were conducted to investigate the flow field of an immiscible liquid layer exposed to radiation from above. fluid flow characteristics of the adjacent immiscible nheptane layer were obtained by using piv and bos methods. piv measurements of convective flows in the immiscible liquid showed a surface flow toward the ice, which is caused by surfacetension forces. presence of recirculation zones enhanced the melting and assisted the return flow in the bulk of the liquid. the results indicated the combination of piv and bos techniques is an effective method in scrutinizing the liquid-phase convection and identifying the regions with temperature gradients. however, acquiring quantitative data can be difficult due the density gradients that cause significant distortions in the field of view. the qualitative results that are obtained allow for an informed analysis of heat transfer from the liquid to the ice. understanding the melting heat transfer by immiscible liquids is a necessary step toward understanding the 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 impacts of oil spills in the arctic. this research is planned to continue with the mentioned experiments to obtain more results with the combination of the two techniques. acknowledgement this material is based upon work supported by the national science foundation under grant no. 1938980. any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the national science foundation. references blanken, h., et al., modelling the long-term evolution of worst-case arctic oil spills. marine pollution bulletin, 2017. 116(1-2): p. 315-331. baker, h., https://www.livescience.com/amp/arctic-ice-arches-melting-fast.html yamada, m., et al., (1998) melting heat transfer characteristics of a horizontal ice cylinder immersed in an immiscible liquid. 27(5): p. 336-352. farahani, h.f. fu, y., jomaas, g., rangwala a., (2018) convection-driven cavity formation in ice adjacent to externally heated flammable and non-flammable liquids. cold regions science and technology, 2018. 154: p. 54-62. farahani, h.f., alva, w., rangwala, a., jomaas g., (2017), convection-driven melting in an noctane pool fire bounded by an ice wall. combustion and flame, 179: p. 219-227. farahani, h. f., torero, j. l., jomaas, g., rangwala, a., (2019) scaling analysis of ice melting during burning of oil in ice-infested waters, international journal of heat and mass transfer, volume 130, pages 386-392. thielicke, w., and stamhuis e. j., (2014) "pivlab – towards user-friendly, affordable and accurate digital particle image velocimetry in matlab," journal of open research software, vol. 2. https://www.livescience.com/amp/arctic-ice-arches-melting-fast.html 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 measurement of kinetic constant of protein binding using microfluidics and particle diffusometry hui ma1, steven t. wereley2, jacqueline c. linnes1∗, tamara l. kinzer-ursem1† 1 weldon school of biomedical engineering, purdue university, west lafayette, indiana, 47907, usa 2 department of mechanical engineering and birck nanotechnology center, purdue university, west lafayette, indiana 47907, usa ∗ jlinnes@purdue.edu † tursem@purdue.edu abstract protein-protein interaction is widely used in biological science and biomedical engineering researchmoreira et al. (2007). accurate measurement of binding kinetics is essential for understanding protein-protein interactions. current gold standard assays, such as surface plasmon resonance (spr),bio-layer interferometry (bli) and quartz crystal microbalance (qcm), can generate precise and real-time kinetics data. however, these methods usually require expensive instruments housed in core facilities and high-level expertise, which is not convenient for most labs to implement. we developed a new method based on microfluidics and particle diffusometry (pd) to measure protein binding kinetics, which only needs very general lab equipment including a fluorescent microscope to take photos, a syringe pump to inject solutions, capillary tubing, a simple chip made on a glass slide and a computer to process images. to measure the binding rate of a protein pair, both proteins are conjugated with beads of different sizes, respectively. the bead solutions are diluted to appropriate concentrations and injected into a y-junction channel by a syringe pump. in the microchannel, the two kinds of beads will meet at the interface and bind due to surface protein interactions. therefore, the size of the beads in solution gradually increases and the brownian motion will be less and less drastic until the reaction is saturated. taking photos recording this dynamic process, the apparent change in size of the beads can be measured by particle diffusometry and used for extracting binding kinetics. particle diffusometry is a correlation-based and non-intrusive optical detection method to analyze properties of fluid and particle such as viscosity, temperature and particle diameterchamarthy et al. (2009); clayton et al. (2016, 2017b,a); hohreiter et al. (2002). it was initially developed to determine errors caused by thermal noise in particle image velocimetry (piv). pd always analyzes image pairs. a single image of a particle laden flow is first used to do auto-correlation, correlating with itself, which will generate a high and sharp peak. then it is cross-correlated with a successive image with a known time interval ∆t. because particles slightly deviate away from the initial positions after time ∆t, due to brownian motion, the correlation peak is lower and broader than that of auto-correlation. autoand cross-correlation peaks are fit into gaussian function to find peak widths, by which the particle size can be computed as long as the viscosity and temperature do not change. processing the image sets of the protein-conjugated particles’ binding process, we acquire the relation of particle size and time, which can be used to solve protein binding kinetics. an equation of protein interaction and particle volume is derived to work out association rate from particle diameter data acquired by pd. in this study, we measured streptavidin-biotin binding rate. streptavidin is conjugated with 20nm beads and biotin is immobilized onto 200nm beads. proteins on the two kinds of beads bind rapidly after mixing in the main channel. it is necessary to choose a narrow area at the interface of particle streams that diffusion does not limit the reaction. since the liquid is flowing, there is both brownian motion and advection in particle images. we used edpiv, a software package developed by prof. steven wereley’s lab, to measure advection velocity. when doing pd analysis, images are shifted following the piv data to catch up with the flow. the photos are taken at the center layer in the middle of the channel, where there is no velocity gradient. measuring a series of photo sets along the main channel at several points with known distances to each other, the relation of complex bead size and time can be acquired. solving for the association constant, the measured value is 1.74 ×10 7m−1s−1, which is close to that of current gold standard assays. this novel pd-based method is accurate and requires only general lab facilities, making protein binding kinetics measurements accessible and practical for biological and biomedical labs. figure 1: a. y-junchtion channel fabricated from glass, pdms, and pressure sensitive adhesive. solutions are injected through the two arms and meet in the main channel. b. matlab model of 20nm streptavidinbeads bound to 200nm biotinylated bead. particle size increases due to binding can be measured by pd. c. experiment setup. solutions are injected by a syringe pump. a fluorescent microscope is used to take photos. d. pd mechanism. an interrogation window correlates with itself (auto-correlation), generating a high and sharp peak. an interrogation window correlated with the next successive image (cross-correlation), producing a lower and border peak due to the particles’ brownian motion. pd can be employed to calculate particle size. e. measured experiment data of bead size with the binding of streptavidin and biotin beads over time. references chamarthy p, garimella sv, and wereley st (2009) non-intrusive temperature measurement using microscale visualization techniques. experiments in fluids 47:159–170 clayton kn, berglund gd, linnes jc, kinzer-ursem tl, and wereley st (2017a) dna microviscosity characterization with particle diffusometry for downstream dna detection applications. analytical chemistry 89:13334–13341 clayton kn, lee d, wereley st, and kinzer-ursem tl (2017b) measuring biotherapeutic viscosity and degradation on-chip with particle diffusometry. lab on a chip 17:4148–4159 clayton kn, salameh jw, wereley st, and kinzer-ursem tl (2016) physical characterization of nanoparticle size and surface modification using particle scattering diffusometry. biomicrofluidics 10:054107 hohreiter v, wereley s, olsen m, and chung j (2002) cross-correlation analysis for temperature measurement. measurement science and technology 13:1072 moreira is, fernandes pa, and ramos mj (2007) hot spots—a review of the protein–protein interface determinant amino-acid residues. proteins: structure, function, and bioinformatics 68:803–812 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 investigation of turbulent boundary layer flows with adverse pressure gradient by means of 3d lagrangian particle tracking with shake-the-box m. novara1∗, d. schanz1, r. geisler1, j. agocs1, f. eich2, m. bross2, c. j. kähler2, a. schröder1 1 german aerospace center (dlr), inst. of aerodynamics and flow technology, göttingen, germany 2 universität der bundeswehr, inst. of fluid mechanics and aerodynamics, münchen, germany ∗ matteo.novara@dlr.de abstract a large-scale 3d lagrangian particle tracking (lpt) investigation of a turbulent boundary layer (tbl) flow developing across different pressure gradient regions is presented in this study. three high-speed multi-camera imaging systems, led illumination and helium-filled soap bubbles (hfsb) tracers have been adopted to produce time-resolved sequences of particle images over a large volume encompassing approximately 3 m in the streamwise direction, 0.8 m in the spanwise direction and 0.25 m in the wall-normal direction. individual tracers have been reconstructed and tracked within the imaged volume by means of the shake-the-box algorithm (stb, schanz et al. (2016)); the flowfit data assimilation algorithm (gesemann et al. (2016)) has been used to evaluate the spatial velocity gradients and to interpolate the scattered lpt results onto a regular grid. thanks to the large size of the investigated volume and to the time-resolved nature of the recorded images, the entire spatial extent of the large-scale coherent motions within the logarithmic region of the tbl (i.e. superstructures) could be captured and their dynamics investigated during their development over several boundary layer thickness in the streamwise direction, from the zero pressure gradient region (zpg) to the adverse pressure gradient region (apg). two free-stream velocities were investigated, namely 7 and 14 m/s, corresponding to reτ ≈ 3,000 and 5,000 respectively. the results confirm the location and scale of the elongated highand low-momentum structures in the logarithmic region, as well as their meandering in the spanwise direction. two-point correlation statistics show that the width and spacing of the superstructures are not affected by the transition from the zpg to the apg region. the analysis of the instantaneous flow realizations from both a lagrangian and eulerian perspective indicates the presence of significant fluid particle elements exchange across the interfaces of the large-scale structures. 1 introduction the understanding of turbulent boundary layers subjected to an adverse pressure gradient (apg), particularly at high reynolds numbers, is of high relevance for many aerodynamic applications ranging from lift and thrust generation to wind energy harvesting. unlike for the zero pressure gradient case (zpg), a general consensus about a scaling framework (which could largely benefit the development of near-wall models and wall-functions for rans numerical simulations knopp et al. (2015)) is still missing. of great interest is also the understanding of the flow separation mechanism, in particular regarding the role played by localized near-wall reverse flow events that might represent the nucleus for the generation of the macroscopic flow separation (bross et al. (2019)). furthermore, the interaction between large-scale coherent motions within the logarithmic region of the turbulent boundary layer (i.e. superstructures, adrian (2007), hutchins and marusic (2007), marusic et al. (2010)) and the near-wall flow structures in the viscous and buffer layers has been receiving increasing attention (bross et al. (2019)). these considerations motivate the need to perform accurate flow measurements in the near-wall region at relevant reynolds numbers. the three-dimensional nature of the flow structures (e.g. strong correlation between near-wall reverse flow events and large span-wise velocity component, diaz-daniel et al. (2017)) calls for the adoption of multi-point volumetric techniques allowing for the evaluation of spatial correlations and structural analysis. based on these requirements, 3d lagrangian particle tracking (lpt) approaches appear to be ideal candidates when the choice of the measurement technique is concerned. in particular, the shake-the-box algorithm (stb, schanz et al. (2016)) enables 3d lpt at relatively high seeding densities (huhn et al. (2017) among others), comparable and exceeding those typically employed for cross-correlation based techniques. unlike for cross-correlation-based methods, particle tracking approaches can deliver reliable measurements in close proximity of interfaces, walls and strong shear layers ( kähler et al. (2012a), kähler et al. (2012b), cierpka et al. (2013)). in the present study the attention is directed at the investigation of the large-scale coherent motions within the logarithmic region of the tbl (i.e. superstructures, bross et al. (2019) and marusic et al. (2010) among others); the main questions concern the influence of the pressure gradient on the occurrence and scaling of the large-scale structures (lss), the interaction of these structures with the small-scales close to the wall and local backflow events, and whether or not an exchange of fluid elements occurs across the interface of the large-scale structures a large-scale 3d time-resolved investigation has been performed with stb making use of twelve highspeed cameras, helium-filled soap bubbles (hfsb) and led illumination to cover the flow development over nearly three meters along the streamwise direction (from a zero-pressure gradient region and into an apg region). the experimental campaign took place in the atmospheric wind tunnel (awm) at the university of armed forces (munich) over the same model designed within the scope of the dlr project victoria (previous results from this project can be found in schröder et al. (2018)). the experimental setups are presented here together with results in terms of analysis of the instantaneous 3d particle tracks and flow structures (identified by interpolating the scattered lpt results to a regular grid by means of the flowfit algorithm gesemann et al. (2016)), and flow statistics (obtained via ensemble-averaging of lpt data). figure 1: left: sketch of the model (top) and pressure distribution measured at the awm facility (bottom). right: model installed in the awm test section and led illumination. 2 experimental setup a sketch of the wind-tunnel model installed on the side wall of the awm facility test section is shown in figure 1-top-left; the closed test section of the open circuit facility is 22m long and has a cross-sectional area of 1.8×1.8 m2. in order to qualify the model, the pressure distribution at the wall was measured; results are shown in figure 1-bottom-left. after a canonical zpg region developing over a 4 m long flat plate, two curvilinear deflections cause a small favorable pressure gradient (fpg) followed by an apg region over the 763mm flat plate inclined by 18°. a system of twelve high-speed cameras was installed outside of the tunnel, opposite to the model, figure 2-left. the cameras are organized into three imaging systems; the overlapping volumetric field-of-views figure 2: left: twelve high-speed cameras installed outside the awm test-section. right: sketch of the model and imaging system; the three camera systems (a, b, c) and the relative imaged volumes are indicated in black, red and blue respectively. reproduced from schanz et al. (2019). (figure 2-right) cover a continuous volume from the middle of the zpg plate to the apg region (≈ 2.90 m streamwise, 0.8 m span-wise and 0.25 m wall-normal). the cameras were operated at a constant repetition rate of 1khz and recorded continuous data for 1382 images; several statistically independent individual runs were acquired in order to produce the flow statistics. the most upstream camera system (a) consisted of four veo 4k l cameras, which provide a 4096× 2160 pixels resolution at 1 khz. due to the high spatial resolution and the elongated shape of the sensors, this system was able to capture the full zpg-region at a length of 1.80 m, using f = 35 mm carl zeiss distagon lenses, mounted in scheimpflug-adapters. the two subsequent systems (b and c) each consisted of four pco dimax cameras (2016× 2016 pixels) and each covered around 1 m in streamwise direction, being equipped with f = 50 mm carl zeiss planar lenses. the magnification ranges between 2.0 to 2.5 px/mm for the whole system. the wall-normal extent of the recorded volume is defined by the illumination, consisting of 10 highpower led arrays (hardsoft ilm 501cg, stasicki et al. (2017)), installed above window inserts on the wind tunnel roof; mirrors at the wind tunnel floor provided back-reflection, figure 1-right. two different free stream velocities were considered, u∞ ≈ 7 and 14 m/s. at the lowest velocity, particle shifts of around 19 px were found in the free stream. in order to limit the shift for the higher velocity, a double illumination scheme was applied, motivated by its successful application on double frame cameras for the investigation of high-speed flows (novara et al. (2019)). while the cameras retained the rate of 1 khz, the leds were operated at 2 khz, thus imaging each particle twice per camera image. seeding of the flow was realized by several arrays of hfsb-nozzles (250 nozzles in total). for the lower velocity, most of the seeding rakes (200 nozzles) were installed close to the contraction before the test section. while ensuring a high seeding concentration, a downside of this position is an interaction of the rakes with the incoming boundary layer that might persist in the measurement region. for the run at higher reynolds number the seeding system was moved further upstream; the bubbles had to pass through several layers of meshes, minimizing any flow disturbances, but also reducing the number of bubbles reaching the measurement volume. in both cases, 50 additional nozzles were installed in a cabinet close to the contraction region, seeding the near-wall parts of the boundary layer through a thin slit in the wind tunnel wall. for the u∞ ≈ 7 m/s case 24 runs of 1382 images each were recorded in single illumination mode. the leds were operated only in short bursts of 40µs per image (4% duty cycle, at 45a power), in order to avoid any motion blurring for the fastest particles. at the higher velocity the seeding concentration is reduced both due to the increased mass flow and the different position of the main seeding system; however, the particle image density is doubled due to the two light pulses. for u∞ ≈ 14 m/s 68 runs of 1382 recordings (corresponding to 2764 time-steps) were recorded. figure 3: instantaneous result from stb (left) and flowfit (right) for the 7 m/s case. left: ≈ 600,000 tracked particles color-coded with streamwise velocity. right: iso-surface of q-criterion at 2000 1/s2. 3 results the stb algorithm was adapted to seamlessly triangulate (via iterative particle reconstruction, ipr wieneke (2012)) and track the bubbles over the whole volume (across the three imaging systems) and to cope with the double-exposed recordings for u∞ = 14 m/s. a detailed description of the processing strategy and parameters can be found in schanz et al. (2019). the particle image density ranged between 0.04 and 0.06 particles-per-pixel (ppp); a number of approximately 620,000 and 200,000 tracked particles was found within the complete measurement volume for the singleand double-exposed recordings respectively. particle positions along the tracks were filtered by the trackfit spline-interpolation scheme (gesemann et al. (2016)) in order to deliver continuous position, velocity and acceleration measurements. an example of an instantaneous result from tr-stb is presented in figure 3-left for the 7 m/s case; approximately 600,000 tracks are color-coded by the stream-wise velocity component. the application of the flowfit data assimilation algorithm (gesemann et al. (2016)) allows for the identification of instantaneous 3d flow structures in the tbl; figure 3-right shows an example of instantaneous iso-surfaces of q-criterion color-coded by the stream-wise velocity component. medium-scale structures in the outer part of the boundary layer appear to be well resolved; as a consequence of the large measurement domain and the size of the hfsb tracers (300µm diameter) an under sampling of the flow gradients in the near-wall region is expected. the scattered results from lpt can be used to evaluate flow statistics by means of an ensemble averaging approach. in figure figure 4-left the mean streamwise velocity component for the 14 m/s is presented; 3d bins, of 10×10×10mm3 size, were employed and approximately 100,000 samples per bin used to evaluate the flow statistics. in order to characterized the tbl, a 2d ensemble averaging analysis was carried out making use of bins encompassing the whole spanwise dimension (z), 5 mm along the streamwise direction figure 4: results from ensemble averaging of stb results for the 14 m/s case. left: mean streamwise velocity component (10×10×10mm3 bins). right: wall-normal streamwise velocity and reynolds stresses component from 2d ensemble averaging analysis (5×0.1 mm2 bins in xy plane) in zpg, fpg and apg. figure 5: two views of instantaneous large-scale structures in the logarithmic layer for the 14m/s case; highand low-momentum structures visualized by iso-surfaces of positive and negative wall-parallel fluctuation velocity component (u∗ ′ =±1 m/s). (x) and 0.1mm along the zpg-wall-normal direction (y ); approximately 35,000 samples per bin were found for the 14 m/s case. mean streamwise velocity and reynolds stresses profiles along the local wall-normal direction (y∗) are presented in figure 4-right for three locations in the zpg, fpg and apg respectively (blue, orange and green curves). the slight acceleration of the flow caused by the fpg at x ≈ −1500 mm can be observed, followed by the deceleration experienced when entering the apg region. the streamwise component of the reynolds stresses shows that, despite the large size of the measurement volume, the first peak of the fluctuations can be resolved in the zpg region. as expected, in the apg region the u′u′ peak is broader and located further away from the wall. the clauser chart analysis (clauser (1956)) of the incoming boundary layer (zpg region, x = −2650 mm) allowed for the evaluation of the viscous unit size (l+ ≈ 60 and 30 µm for 7 and 14 m/s respectively) and the friction velocity (uτ ≈ 0.26 and 0.5 m/s for 7 and 14m/s respectively). the incoming boundary layer thickness δ99 was found to be approximately 170mm for the 14 m/s case. the reynolds numbers based on the friction velocity (reτ) was estimated at approximately 3400 and 5400 for the lower and higher free-stream velocity respectively. due to the disturbance to the outer flow caused by the seeding rakes installed before the test section for the 7m/s case, the tbl profile was not canonical, and the tbl thickness could not be estimated accurately. on the other hand, a comparison of the tbl profiles with numerical and experimental results from the literature (sillero et al. (2013), samie et al. (2018)) confirmed that, for both free-stream velocities, the tbl profile behaves as expected over the whole logarithmic region, where the superstructures are located. two views of an instantaneous realization of the flowfit result are presented in figure 5, where isosurfaces of wall-parallel velocity fluctuations (u∗ ′ ) in the logarithmic layer are shown for the 14 m/s case. as reported by bross et al. (2019) among others, the highand low-momentum regions (in white and black respectively in figure 5) are elongated in the streamwise direction and can extend up to several boundary layer thicknesses when instantaneous flow fields are considered (up to 10− 20 · δ99). the results shown in figure 5 also confirm the meandering of the superstructures in the spanwise direction. at high reynolds numbers, these superstructures strongly contribute to the second peak in the streamwise velocity fluctuations. the average size, orientation and spanwise spacing of large-scale coherent structures in the tbl can be estimated by analyzing the 3d two-point spatial cross-correlation coefficient of the streamwise velocity fluctuations ru′u′ (chen (2019)). an ensemble averaging approach was employed to evaluate two-point cross-correlation maps from the lagrangian data offered by stb. three locations along the streamwise direction (i.e. zpg, fpg and apg region) were selected for the reference points and the two-point correlation coefficient was evaluated over the entire 3d field at different locations along the wall-normal direction. in order to investigate the influence of the pressure gradient on the average structural topology, the relevant length scales calculated from the analysis of the two-point correlation coefficient maps, are shown in figure 6 as a function of the wall-normal position. the length scale in the streamwise direction corresponds to the total length of the correlation up to a threshold value (l1) or to the length of the correlation in a section plane parallel to the wall (l2); due to the inclination of the structures relative to the wall, l1 is always larger than l2. the spanwise separation λ2 is the distance between the minima of the correlation coefficient along the spanwise direction z. finally, the figure 6: length scales l1 (a) and l2 (b) calculated from two-point correlations ru′u′ . relative structure inclination angle (c) and spanwise distance of the large-scale structures calculated from the minima of the ru′u′ correlation (d). relative tilt angle is calculated by approximating the positive ru′u′ correlation contour at a given threshold with an ellipse; the angle φ corresponds to the angle of the major semi-axis relative to the wall. the length scales l1 and l2 are normalized using the boundary layer thickness in the zpg (δ99,zpg) in order to allow comparing the structures in the different pressure gradient regions despite the change in the local boundary layer thickness. for both l1 (figure 6a) and l2 (figure 6b), there is almost no difference between the zpg and fpg regions, where the maximum values are located at approximately y/δ99,loc = 0.25. in contrast, l1 and l2 are significantly smaller at the apg position if they are scaled with δ99,zpg; the shortening of the structures is due to the strong deceleration of the flow caused by the apg. this behavior is also visible in the representation of the relative angle of inclination in figure 6c. for the zpg and fpg regions, the maximum relative angle of inclination is approximately 10°, while the inclination angle in the apg is about twice as large for each distance from the wall. interestingly, the structure distance λ2 shown in figure 6d is similar for all pressure gradient cases, particularly for the wall positions y/δ99,loc < 0.5. it can therefore be stated that the structural pattern in the spanwise direction does not physically change under the influence of an apg compared to the zpg and fpg regions, the time-resolved 3d fields obtained from the combined stb and flowfit approaches offer the unique opportunity to investigate the dynamic behavior of the superstructures travelling across the different pressure regions over the wind-tunnel model. the results presented in figure 7 show the evolution of a portion of the flow field (approximately 200 mm long in the streamwise direction) followed as it is advected downstream with a fixed local average flow velocity of≈ 6m/s across the zpg, fpg and apg regions; the location of the flow field patch is shown in yellow in the sketches in figure 7-top. the superstructures are shown with isosurfaces of u∗ ′ , while instantaneous vortical structures are identified by iso-surfaces of vortex identification criterion q, color-coded by streamwise velocity component; by observing the temporal evolution of the flow structures, it appears that streets of vortices ride on top of low-momentum structures while maintaining a rather stable spatial organization. figure 7: instantaneous lsss (iso-surfaces of u∗ ′ = ±0.6 m/s) and vortical structures (iso-surface of q = 2,500 1/s2) color-coded by streamwise velocity component for the 7 m/s case. same flow patch advected downstream shown in the zpg (left), fpg (center) and apg (right) region. location of the flow patch (in yellow) with respect to the pressure gradient regions (black, blue and red for zpg, fpg and apg respectively) shown on top. the eulerian coherence of the turbulent superstructures, inferred by the visualization of time-resolved sequences, can be quantified by evaluating the two-point space-time correlation coefficient of the streamwise velocity fluctuations which provides an indication about the memory of the process (chen (2019)). a fixed reference point is chosen in the zpg region (at different wall-normal locations, namely y+ ≈ 1,000, 2,600 and 5,300) and the cross-correlation coefficient is computed for a series of time separations, namely 0, 100, 200 and 300 ms. the results, relative to the 14 m/s case, are presented in terms of positive and negative iso-surfaces of ru′u′ in figure 8; the elongated shape of the correlation coefficient iso-surfaces reflects the shape of the superstructures, while the stronger correlation values attained in proximity of 0.5 · δ99 (figure 8-middle) confirm the location of the superstructures in the upper logarithmic layer. figure 8: iso-surfaces of two-point space-time correlation coefficient for the 14 m/s case for different locations of the reference point (black dot) along the wall-normal direction in the zpg (x =−2420mm) and for different time separations (∆t). positive values of ru′u′ = 0.12/0.2/0.3 in blue and negative ones in orange (ru′u′ =−0.055/−0.07/−0.1). in order to assess the presence of fluid element exchange across the interfaces of the superstructures, the dual nature of the stb and flowfit results (i.e. lagrangian and eulerian views of the flow) can be taken advantage of. when a time-resolved sequence of realizations is considered, similarly to what is presented in figure 7, iso-surfaces of u∗ ′ obtained from the flowfit interpolation can be visualized for the lowand highfigure 9: instantaneous lsss (iso-surfaces of u∗ ′ = ±0.6 m/s) and particles color-coded by wall-parallel velocity fluctuation component for the 7m/s case. same flow patch advected downstream shown in the zpg (left), fpg (center) and apg (right) region. particles within the lsss showed as spherical markers: top: all instantaneous particles within the superstructures, bottom: subset of particles already present at t = 0 ms. momentum superstructures (in blue and red in figure 9 respectively) for the same portion of the flow field imaged at different instants across its path from the zpg to the apg region. at the same time, individual particle tracers from stb can be visualized by spherical markers color-coded by u∗ ′ values; only particles within the superstructures are shown in figure 9. when all instantaneous particles exhibiting a large value of wall-parallel turbulent fluctuation are considered, figure 9-top, it can be observed, as expected, that the instantaneous superstructures are populated by a rather homogeneous number of individual tracers. on the other hand, when the plotted tracers are limited to those already present at the beginning of the time sequence (i.e. t = 0ms, figure 9-top-left), a progressively decreasing number of particles is found within the structures as they are advected downstream (figure 9-bottom). this visualization allows to conclude that, despite looking quite stable when moving downstream during the observation time of the stb recording sequence in the eulerian frame of reference (see persisting vortical and streaky flow structures in figure 7), the turbulent superstructures are sustained by particles belonging to different individual tracks, therefore confirming the presence of fluid particle elements exchange across the interfaces of the lsss. a similar conclusion can be drawn when complete individual tracks crossing a high(figure 10-left) or low-momentum (figure 10-right) superstructure at a given time instant (larger blue and red markers in figure 10) are visualized, color-coded by the wall-normal velocity fluctuation value. the locations marked in gray along the trajectory indicate that the particle is located outside of a superstructure, while portions of the same track colored in red and blue show how the particle can enter different types of structures during its travel across the investigated domain. figure 10 also shows that particles that are spatially relatively close to each other at one particular time instant occupy significantly different regions of space when the wall-normal (y∗) and spanwise (z) directions are considered at different time instants (i.e. streamwise locations). this dispersion can be quantified by performing a single-particle dispersion analysis (zhang and xiao (2018)) where the quadratic distances along y∗ and z for each position of a particle along a track are computed with respect to the particle position at a reference time (τ = 0 ms).when a statistical analysis is performed by averaging the dispersion results over multiple tracks, single-particle dispersion curves as presented in figure 11 can be obtained. for each track, the reference time was chosen as the time at which the particle passed close to a specific location (i.e. reference point) within the fpg; the choice of the fpg region was dictated by the fact that this position, being the fpg located approximately at the center of the fov along the streamwise direction, would allow figure 10: selection of complete tracks color-coded by wall-parallel velocity fluctuation component; particle locations at a chosen time instant where particles belong to a high(left) or low-momentum (right) superstructures are shown using larger markers. for the evaluation of both backward (τ < 0) and forward (τ > 0) dispersion. the dispersion analysis was performed for several reference points distributed along the wall-normal direction up to y∗ = δ99,zpg with a spacing of 20 mm from each other; all particle tracks crossing an area of 50×10 mm2 in the xy∗ plane around the reference point over a full time-resolved recording sequence were included in the dispersion analysis. figure 11: backward and forward single-particle dispersion in the wall-normal (top) and spanwise direction (bottom); reference volumes located in the fpg (x=−1750mm) at different locations along the wall-normal direction y∗. the wall-normal and spanwise dispersion results are shown in figure 11 (top and bottom respectively); dispersion curves are color-coded based on the reference point location in the wall-normal direction. given the location of the reference point at x =−1750mm (fpg), negative values of the time separation τ indicate results relative to particles coming from the zpg region, while positive τ values show the particles dispersion as the tracers enter the apg region. results show that the spanwise dispersion is larger than the wall-normal one for |τ|< 30 ms; on the other hand, when particles enter the apg region, they exhibit a larger deviation in terms of their relative wall-normal distance from the wall. furthermore, both the wall-normal and the spanwise dispersion attain a maximum value within the logarithmic region for |τ| < 30 ms, which can be associated to the meandering nature of the superstructures and their inclination in the xy∗ plane. 4 conclusions and outlook the adoption of three high-speed multi-camera imaging systems, led illumination and helium-filled soap bubbles, in combination with the shake-the-box 3d lpt algorithm, allowed for the investigation of an unprecedented large-scale volume within a tbl flow crossing three pressure gradient regions (zpg, fpg and apg). the three-dimensional nature of the experiment enabled capturing large-scale coherent structures in the logarithmic layer (i.e. superstructures) in their entirety; the time-resolved recording sequences made it possible to investigate the flow dynamics. visual inspection of the instantaneous flow realizations and the results from two-point spatial correlation statistics confirmed the presence of the large-scale structures and suggested that their spatial organization is not affected by the transition across the pressure gradient regions. the availability of both lagrangian and eulerian data allowed to determine that significant fluid elements exchange occurs across the interfaces of the superstructures. single-particle dispersion analysis of individual tracks confirmed the meandering nature of the lsss and their increased inclination in the apg region. together with the analysis of two-particle dispersion (salazar and collins (2009)), spatial clustering algorithms could be applied to further characterize the behavior of the turbulent superstructures in the tbl (schneide et al. (2018)). furthermore, conditional ensemble averaging approaches based on the detection of individual sweep (q4) and ejection (q2) events would allow to investigate the relation between the superstructures and the turbulence production at varying distances from the wall. furthermore, two-point cross-correlation analysis involving velocity and instantaneous pressure from the flowfit algorithm will be employed to investigate the role of the pressure fluctuations induced by the large-scale structures for the local and global separation processes at the wall. acknowledgements the present work has been partially funded by the dfg-project “analyse turbulenter grenzschichten mit druckgradient bei großen reynolds-zahlen mit hochauflösenden vielkameramessverfahren” (grant no. schr 1165/3-2 and ka1808/14-2). the wind tunnel model was laid out by tobias knopp and installed as part of the dlr project victoria. references adrian rj (2007) hairpin vortex organization in wall turbulence. physics of fluids 19:041301 bross m, fuchs t, and kähler cj (2019) interaction of coherent flow structures in adverse pressure gradient turbulent boundary layers. journal of fluid mechanics 873:287–321 chen j (2019) two-point statistics of coherent structure in turbulent flow. arxiv preprint arxiv:190805422 cierpka c, lütke b, and kähler cj (2013) higher order multi-frame particle tracking velocimetry. experiments in fluids 54:1–12 clauser fh (1956) the turbulent boundary layer. in advances in applied mechanics. volume 4. pages 1–51. elsevier diaz-daniel c, laizet s, and vassilicos jc (2017) wall shear stress fluctuations: mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer. physics of fluids 29:055102 gesemann s, huhn f, schanz d, and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser and imaging techniques to fluid mechanics, lisbon, portugal. pages 4–7 huhn f, schanz d, gesemann s, dierksheide u, van de meerendonk r, and schröder a (2017) large-scale volumetric flow measurement in a pure thermal plume by dense tracking of helium-filled soap bubbles. experiments in fluids 58:1–19 hutchins n and marusic i (2007) evidence of very long meandering features in the logarithmic region of turbulent boundary layers. journal of fluid mechanics kähler cj, scharnowski s, and cierpka c (2012a) on the resolution limit of digital particle image velocimetry. experiments in fluids 52:1629–1639 kähler cj, scharnowski s, and cierpka c (2012b) on the uncertainty of digital piv and ptv near walls. experiments in fluids 52:1641–1656 knopp t, buchmann n, schanz d, eisfeld b, cierpka c, hain r, schröder a, and kähler cj (2015) investigation of scaling laws in a turbulent boundary layer flow with adverse pressure gradient using piv. journal of turbulence 16:250–272 marusic i, mckeon bj, monkewitz pa, nagib hm, smits aj, and sreenivasan kr (2010) wall-bounded turbulent flows at high reynolds numbers: recent advances and key issues. physics of fluids 22:065103 novara m, schanz d, geisler r, gesemann s, voss c, and schröder a (2019) multi-exposed recordings for 3d lagrangian particle tracking with multi-pulse shake-the-box. experiments in fluids 60:1–19 salazar jp and collins lr (2009) two-particle dispersion in isotropic turbulent flows. annual review of fluid mechanics 41:405–432 samie m, marusic i, hutchins n, fu m, fan y, hultmark m, and smits a (2018) fully resolved measurements of turbulent boundary layer flows up toreτ = 20,000). journal of fluid mechanics 851:391–415 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 schanz d, schröder a, novara m, geisler r, agocs j, eich f, bross m, and kähler cj (2019) large-scale volumetric characterization of a turbulent boundary layer flow. in proceedings of the 13th international symposium on particle image velocimetry. 182. pages 251–265. universität der bundeswehr münchen: atheneforschung schneide c, pandey a, padberg-gehle k, and schumacher j (2018) probing turbulent superstructures in rayleigh-bénard convection by lagrangian trajectory clusters. physical review fluids 3:113501 schröder a, schanz d, novara m, philipp f, geisler r, knopp t, schroll m, and willert c (2018) investigation of a high reynolds number turbulent boundary layer flow with adverse pressure gradients using piv and 2d-and 3d-shake-the-box. in 19th international symposium on the application of laser and imaging techniques to fluid mechanics. 257 sillero ja, jiménez j, and moser rd (2013) one-point statistics for turbulent wall-bounded flows at reynolds numbers up to δ+ ≈ 2000. physics of fluids 25:105102 stasicki b, schröder a, boden f, and ludwikowski k (2017) high-power led light sources for optical measurement systems operated in continuous and overdriven pulsed modes. in optical measurement systems for industrial inspection x. volume 10329. page 103292j. international society for optics and photonics wieneke b (2012) iterative reconstruction of volumetric particle distribution. measurement science and technology 24:024008 zhang q and xiao z (2018) single-particle dispersion in compressible turbulence. physics of fluids 30:040904 introduction experimental setup results conclusions and outlook microsoft word schanz_etal_ispiv21_paper2.docx 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa shake-the-box particle tracking with variable time-steps in flows with high velocity range (vt-stb) d. schanz1,*, m. novara1, a. schröder1 1: german aerospace center (dlr), inst. of aerodynamics and flow technology, göttingen, germany *daniel.schanz@dlr.de abstract we present a novel evaluation mode for lagrangian particle tracking methods in general, applied to the shake-thebox method specifically. the aim is to attain high levels of accuracy and a removal of false (‘ghost’) tracks in flow situations, where significant amounts of particles show small relative movement with respect to each other in consecutive time-steps. an iterative approach using variable time separations is employed, which starts by tracking particles at high timeseparations, followed by an iterative reduction of time separation, while feeding the particle tracked within the previous iterations. the process allows for applying tracking parameters fine-tuned to the different flow regimes tracked within each iteration. experimental validation was performed using a dataset on impinging jet flow, created in collaboration with the school of mechanical engineering of pusan national university. evaluation of this flow with high velocity range shows distinct advantages in reduction of ghost tracks and in tracking accuracy. 1. introduction lagrangian tracking of tracer particles (lpt) has been conducted since more than three decades (often termed as 3d ptv; nishino et al. 1989; maas et al. 1993; malik et al. 1993). typically, particle positions were determined using triangulation (maas et al. 1993); the extraction of particle trajectories was carried out as a secondary step by searching for connected paths within the series of particle clouds reconstructed from each time-step individually (see e.g. ouellette et al. 2006). experiments were typically limited to low tracer particle concentrations, as with increasing particle image density more and more ambiguities are created by the triangulation step (creation of 'ghost particles' at positions where no true particle is present) and the subsequent tracking step (creation of ‘ghost tracks’). the particle image density �� was typically limited to approx. 0.005 particles per pixel (ppp, meaning that each particle image is described by 200 camera pixels on average) and results were limited to averaged quantities. the introduction of iterative particle reconstruction (ipr, wieneke 2013, jahn et al. 2021) was a first major step towards particle position determination in concentrations that allow resolving unsteady flow dynamics by means of the analysis of individual snapshots. this method represents an iterative approach to the triangulation process with intermediate position optimization and ghost particle removal, allowing to limit the occurrence of ghost particles. the limitations in particle image density for lpt were ultimately pushed by the 'shake-the-box' (stb) algorithm (schanz et al. 2016), which utilizes a comprehensive prediction of the particle cloud in future time-steps in order to seize temporal information given by the physical consistence and coherence of each particle trajectory. the errors introduced by the prediction can be corrected using an image matching scheme ('shaking', wieneke 2013, jahn et al. 2021), thus distinctly facilitating the reconstruction process of each individual time-step, as only particles that are not yet tracked need to be reconstructed using ipr. in its converged phase, stb can be regarded as an integrated process, where the determination of particle trajectories and the reconstruction of the 3d particle field are conducted quasisimultaneously for the large majority of particles. applying the stb algorithm, particles can be tracked in large numbers, with a nearly complete suppression of ghost particles. using synthetic data, images with �� up to 0.2 ppp could be processed (see digital content of raffel et al. 2018), for experimental data particle image densities of up to �� = 0.15 ppp were reached at well-controlled experimental conditions (huhn et al. 2017, bosbach et al. 2019). the ability of the algorithm to discern real particles from ghost particles is largely stemming from the observation that the vast majority of real particles follow reasonably straight trajectories (the change of acceleration is small between time-steps), while ghost particles are generated in quasi-random locations all over the measurement volume. in order 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa to register a new track, stb requires the presence of a particle in four consecutive time-steps with limited total acceleration. therefore, the generation of a ghost track from at least four ghost particles is unlikely in most flow scenarios. however, this assumption only holds if the particle field exhibits a certain amount of movement of the particles relative to each other, such that the ambiguities caused by a certain particle image distribution ‘de-correlate’ within few time-steps. in many flows this assumption holds, however flows with a high velocity range can exhibit regions in space with only very little movement of the particles from image to image. jet flows for example typically show a steep gradient of the velocities in the jet center in relation to the outer flow. as the time separation between successive frames has to be chosen such that the fast particles within the jet can be reliably tracked (limiting their movements to e.g. 10-20 pixels), particles in the surrounding flow might move only a fraction of a pixel in the same time. other examples would be separated or cavity flows, or even boundary layers with particles moving in the bulk at significant velocity but low relative shift due to small velocity gradients. in such a situation a ghost particle, generated by particles from the outer cloud, might be present in several successive frames, therefore potentially generating a ghost track. another potentially problematic effect of slowly moving particle clouds is that situations of overlapping particle images are retained over several time-steps. when the images of two particles overlap within a certain camera, the position accuracy of the involved particles is compromised. we will call the local overlapping of two or more particle images a particle image cluster (pic). in case the pic corresponds approximately to the sum of the single particle images, the shaking process is able to efficiently resolve the overlap situation. this condition is typically met in synthetically generated particle images and selected experiments, e.g. imaging helium-filled soap bubbles (hfsb) which are illuminated by an incoherent light source (typically leds). however, for most experimental conditions, the presence of several particles in the same line-of-sight of a camera influences the imaging of each of these particles. for large tracer particles (e.g. in water) a particle close to the camera might cause shadowing of particles located further away. in case coherent laser light is used for illumination, the light scattered on the involved particles might interfere and cause e.g. a speckle pattern. in any of these cases, the pic will not be the sum of the single particle images of the involved particles and the shaking process will be compromised, resulting in a 3d displacement of the tracked particle in the time-step where the overlap situation occurs. if such a situation is limited to a single time-step ��, stb is typically stable enough to still predict a location at ���� that is accurate enough for the shaking process to converge to the true position. however, if an overlap situation is sustained over several time-steps, the bias in particle position will have a stronger influence on the position prediction (the prediction uses a wiener-filter over the last 10 time-steps with increasing weights towards the current time-step). therefore the risk increases of predicting a particle position with an error that cannot be recovered by the shaking process (the original particle image and the back-projected image of the particle at the assumed position has to overlap on all camera projections). in such a case, several things can happen: (a) ) if the location backprojects to the same coherently moving pic, a position bias effect of the residual minimization scheme can occur; (b) if the back-projected location lies outside the pic, the intensity of the predicted particle either could be quickly decreased by the shaking process, as the images do not support the predicted location or (c) the particle still could find sufficient energy on the images of one or more cameras, thereby remaining above the intensity limit despite a corrupted 3d position. a phenomenon that can sometimes be observed is that such a rogue particle takes the energy, required to survive over multiple time-steps from one specific camera, in which a particle image is moving only slowly. in this case, the particle trajectory is diverted into a direction following the line-of-sight of this camera. such line-of-sight tracks were quite common in early stb evaluations, before the omission of the brightest camera during the intensity update was introduced (see section 2.2.3 in schanz et al. 2016). this measure avoids such effects in most flows, however when a whole region of the particle field is barely moving, the effect can still occur. 2. variable time-step particle tracking using the shake-the-box method (vt-stb) from the thoughts above we can conclude that a slowly moving particle field is detrimental to the tracking process in multiple ways. in this work we propose an extension to the standard stb evaluation, which applies multiple iterations of particle tracking with variable time-separation. the concept is applicable to other tracking methods as well. the idea is to start the evaluation with a time separation such that the slowest particles of the flow can be optimally tracked. from there, the time-separation is iteratively reduced, tracking faster and faster particles with every iteration. finally, the original time-separation of the recording is reached, where only the fastest particles whose velocity initially determined the recording rate remain to be tracked. the involved steps are detailed in the following 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa 1. choose a suitable temporal δ�, �� such that the slowest particles move at least one particle image diameter from image to image, where δ�, �� indicates the number of snapshots omitted from the original time-series for this first iteration (e.g. δ�, �� = 50: processing of every 50th snapshot) 2. perform particle tracking on the selected subset of snapshots. 3. filter the gained trajectories using a fitting method with a suitable kernel-size. in our case trackfit (gesemann et al. 2016) was used with an adapted cross-over frequency. 4. choose a finer temporal resolution δ�, �� < δ�, for the next iteration. 5. interpolate the filtered trajectories from δ�, to the time-steps given by δ�, �� 6. perform particle tracking on the snapshots given by δ�, ��, while feeding the interpolated particle clouds from the previous iteration as a partial pre-solution to the reconstruction of each snapshot 7. repeat steps from 3 to 6 until δ�, �� = 1 is reached. by this approach, the particles from different velocity regimes are always tracked with an optimal time separation. in the process, a few details have to be considered, but also a number of further advantages arise.  in case a particle is transported from a slowly moving region into a region of higher activity, it's track might be lost within the current iteration as the time-separation becomes too large for the now higher velocities. in order to ensure a reliable, uninterrupted tracking in such situations, the tracking is continued within the next iteration: when within iteration i the end of a track copied from iteration i-1 is reached, the track is added to the list of predicted particles and will from there on be continued by the normal stb procedure of iteration i. for this purpose it is beneficial to delete the last one or two time-steps from the end of all tracks that were lost in-between the time-series, as the trajectories might already have been compromised a few time-steps before the particle ultimately fell below the intensity threshold and the track was ended.  the tracking within each iteration can optionally be conducted using a two-pass approach (first walking forwards in time, then reversing and elongating the found tracks backwards in time). this approach is recommended as it provides more symmetric tracking results by counter-acting the slow build-up of tracks at the beginning of the time-series (see schanz et al. 2016 for details).  in order to avoid small-scale noise effects due to e.g. overlap situations, the shaking process can be deactivated for copied particles at lower values of δ�. this means that the intensity is still updated, however the particle position remains unchanged for the particles taken from the previous iteration. please note that this measure represents a filtering effect on slowly moving particles, as only a sub-set of the available time-steps is used for the creation of the filtered trajectory. therefore the interaction of the chosen filtering and the sampling rate at which shaking of copied particles is turned off has to be characterized and adapted to the flow. an automated procedure for defining these parameters is still under development. however, in general, the possibility to adapt filtering strength to the velocity of the particles is welcome, as in most flows, the dynamics scale with velocity and a stronger filtering can be applied to slow particles. lagrangian particle tracking using stb can be divided into two different modes, for which separate parameters exist. some of these can and have to be chosen independently for the different iterations : 1. finding new tracks:  �: shift vector applied to a given particle position ������⃗ , at time-step i for a search of connected particles p' in the next time-step. within the initialization phase, p is constant over the volume (e.g. [0,0,0]); once the tracking system is established, p is given locally by the averaged velocities of neighboring tracked particles.  �: search radius around p. all particles p' in the cloud of yet untracked particles at time-step i+1 are identified that satisfy �������⃗ + � − ��������⃗ � < �. for every such particle a track candidate is created. the process is repeated in the following time-steps, elongating track candidates in case particles that satisfy the condition are found in each time-step.  �� !: minimum shift of track. excludes particles found in the particle cloud of time-step i+1 that are closer than �" � to the previous coordinate (e.g. a particle has to move at least one pixel at �" � = 1).  $!%: smoothness threshold for new tracks. once a track candidate reaches a length of four time-steps, a function &(������⃗ ) (typically 2nd order) is fitted to the four coordinates ������⃗ . a track is assumed to be found in case the average difference of the particle positions to the fitted ones )*+�����⃗ = � � ∙ ∑ |&(������⃗ ) − ������⃗ |� satisfies 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa )*+�����⃗ < )�/. )�/ is given in pixel; typical values range from 0.2 to 1.5, depending on the flow. this step can be regarded as limiting the allowed acceleration of the track fragment in relation to a 2nd order fit. in case a particle is part of several valid track candidates, the one with the lowest )*+�����⃗ is chosen. 2. elongating existing tracks:  $01: deviation threshold from prediction. all particles p for which a valid track exists at time-step i are predicted to i+1 by fitting and extrapolating a function to the last (up to ten) known time-steps. to this end, a wiener-filter approach is used with increasing weight towards the current time-step, which is extrapolated to i+1, yielding a coordinate ��2������⃗ . all predicted coordinates are inserted as particles into the ipr process of timestep i+1 and are treated by several iteration of the position optimization process (shaking). this way, the errors introduced by the prediction are corrected. in case the error is too large, the particle is either deleted as its intensity is reduced or it randomly walks in 3d-space, following some residuals on the particle images. the parameter )�2 defines, how much deviation from the prediction point is allowed for a tracked particle. the one particle p that minimizes �������⃗ − ��2,/��������⃗ � < )�2 for a given track t is chosen for continuing t in the current time-step. if no such particle exists within the cloud generated by ipr, t is ended.  34: outlier filter. in order to identify and terminate tracks that have deviated from the real particle positions as quickly as possible, an outlier filter is employed, as explained in (schanz et al. 2016): for each tracked particle, 56789�⃗ = :� � ∑ (;⃗ − ;⃗<9=)� signifies the root mean squared deviation of the velocities of the n neighbouring particles with ;⃗<9= being their average. the current particle p is regarded an outlier if �;⃗� − ;⃗<9=� > ?@ ∙ 56789�⃗ . in a single-iteration evaluation with δ� = 1 the parameters for outlier detection and track identification have to be chosen uniformly and in such a way that particles that exhibit the highest acceleration can be tracked and are not discarded as outliers. for large parts of the volume these values could typically be lowered, which would decrease the likelihood of ghost track creation. with vt-processing this discrimination becomes possible and furthermore is not restricted to pre-defined regions in space, as the method intrinsically determines the regions of low and high flow velocities. in the next paragraph the vt-stb approach is applied to an experimental dataset, measuring the flow of a small diameter jet impinging on a circular cylinder. the described features and advantages of vt-processing are heavily connected to experimental difficulties, e.g. particle images not summing up perfectly, particle reprojection not perfectly matching the real particle image (despite a proper calibration of the optical transfer function (otf, schanz et al. 2013), differences between the perceived particle intensity from the different cameras, and more. as it is difficult to simulate all the mentioned effects accurately it was decided to directly move to the evaluation of experimental data, without a prior test on synthetic data. 3. experimental validation 3.1 experimental setup the experimental setup is submerged in water within a regular cylindrical 16-faces glass tank. a jet is generated by a nozzle of diameter d = 3 mm and is impinging onto a circular cylinder with diameter dc = 52 mm at an angle of 45°. the velocity of the jet flow was varied, however for the remainder of this work, we will only consider a case with a maximum jet velocity vmax of 6 m/s, corresponding to a reynolds number of 17,875, with re being defined by a bc defg 8/i, where q is the volumetric flow rate and i the kinematic viscosity. the height h of the jet over the cylinder was fixed at h = 4 d. for a more detailed description, see (kim et al. 2018), where a comparable setup was employed in air. the flow impinges onto the cylinder and attaches to the surface due to the coandă effect. separation occurs only at the bottom part of the cylinder. the flow is seeded with 40μm oragasol polyamide particles, which are illuminated by two high-power arrays of white leds (stasicki et al. 2017). the two arrays are positioned on both sides of the water tank, each being collimated by a lens with f = 1000 mm focal length (see fig. 1), illuminating a volume of 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa fig. 1: setup for the water jet experiment. left: four phantom v2640 cameras viewing into the water tank, which is illuminated from two sides by high-power white led arrays, each collimated by a 1000 mm – lens. right: 16-face water tank with submerged cylinder (dc = 52 mm) and d = 3mm nozzle at 45° impinging angle. approx. 160 mm height and 50 mm depth. this measurement region comprises the jet, half of the cylinder in lateral direction and a wake region below the cylinder. see fig. 2 for a schematical depiction of the measurment region. the measurement volume is observed by a system of four phantom v2640 high-speed cameras, equipped with 60 mm carl zeiss macro lenses in scheimpflug mounts. the cameras are operated at 4 khz repetition rate at a resolution of 1152 × 1952 px. the volume seen by all cameras comprises approx. 80 × 160 × 50 mm3. the internal memory of 144 gb allows for time-series of 45,407 consecutive time-steps. the camera system is calibrated using a two-plane calibration plate. the geometrical calibration was refined using volume self calibration (wieneke 2008) and calibration of the optical transfer function (schanz et al. 2013). the flow generated by the jet exhibits a very high velocity range (vr): particles located within the central axis of the jet move at approx. 6 m/s, while particles in the outer part of the volume show very little movement, in the order of 0.01 m/s. the repetition rate was chosen such that the fastest particles can still be tracked reliably, moving not more than approx. 18 pixels between frames. therefore the particles in the bulk move only approx. 0.03 pixels per timestep, leading to a virtually static particle ditributions in these regions which are large, due to the small mass-flow of the jet. fig. 2: schematical experimental setup from top view (a), front view (b) and side view (c). the cylinder is depicted in blue, the nozzle in yellow, the centerline flow in red and the illuminated area as a dashed line. the camera system (c1-c4, not to scale) is setup as an inline-configuration, centered to the illuminated volume. 3.2 evaluation vt-stb was applied in the following fashion: 5 iterations were performed, starting with a time separation of δ�,� = 79 time-steps (the slowest particle move approx. 2.4 pixel in this interval, corresponding to approx. one particle image diameter). the following iterations feature time separations of δ�, = [36, 14, 6, 1] time-steps. a time-series of 10,000 images was reconstructed. 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa iteration jk peak � �� ! $!% $01 34 s. c. co vt-stb [counts] [px] [px] [px] [px] [5678;⃗] 1 79 13 12.6 0.0 0.3 3.5 6 yes 0.75 2 36 13 12.6 0.0 0.3 3.5 6 yes 0.6 3 14 13 12.6 0.0 0.3 3.5 7.5 yes 0.5 4 6 13 12.6 1.0 0.3 3.5 9.5 no 0.4 5 1 20 18 1.0 0.5 5.5 40 no 0.15 stb 1 20 18 0.0 0.5 5.5 20 0.15 table 1: parameters used for processing of the different iterations of vt-stb and of normal stb. jk signifies the time-step separation, peak the required intensity on the image of an identified peak (in counts) for triangulation, � the search radius around the prediction point for new tracks, �� ! the required minimum velocity of new tracks, $!% the allowed average deviation from a second order fit for new tracks, $01 the search radius around the prediction point for existing tracks, 34 the outlier filter parameter for existing track, s. c. (shake copied) if the positions of particles from previous iterations are optimized by shaking and co the crossover-frequency used for filtering the found tracks (see gesemann et al. 2016). the parameters applied at each iteration are given in table 1, as well as the ones used by a standard stb-evaluation, conducted for comparison. for vt-stb processing, parameters need to be set for every iteration. in order to simplify this process, the search radii r for each time separation of δ� > 1 are set as � = 0.7 ⋅ δ"<* = 12.6 pixel in relation to the assumed maximum displacement of a particle at the original sampling rate δ"<*= 18 pixel. only for the last iteration � = δ"<* is applied, as this iteration mainly tracks the fast particles in the jet core and the shear layer, where large velocity gradients are present. )�/ is set to 0.3 pixels, except for the last iteration, where )�/= 0.5 pixels is applied. )�2 uses a value of 3.5 pixels for δ� > 1, while 5.5 pixels is used in the last iteration. �" � is set to zero for all iterations, except the last two, where it is assumed that all slowly moving particles have already been identified. this measure prevents the creation of ghost tracks from the residuals of slowly moving particle clouds, as explained above. ?@ is slowly increased from 6 to 9.5 for iterations 1-4 and then set to 40 for iteration 5, to account for the high local velocity differences in the shear layer. the normal stb evaluation mainly uses the parameters of the last vtstb iteration, except that ?@ is reduced to 20 in order to allow at least some suppression of deviated tracks. all iterations of vr-stb and stb consist of two passes, going once forwards and once backwards in time. fig. 3: instantaneous flowfield as gained with vt-stb. shown are particle tracks over 50 consecutive time-steps, color-coded by the velocity in downward direction; (b-d): slices used for visualizations in fig. 5, fig. 7 and fig. 8. d) c) b) a) 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa vt-stb, iteration 1  δ� = 79 time-steps  number of particles: approx. 24,500 vt-stb, iteration 2  δ� = 36 time-steps  number of particles: approx. 42,600 vt-stb, iteration 3  δ� = 14 time-steps  number of particles: approx. 65,000 vt-stb, iteration 4  δ� = 6 time-steps  number of particles: approx. 77,300 vt-stb, iteration 5  δ� = 1 time-step  number of particles: approx. 80,500 fig. 4: vt-stb tracking with 5 iterations. from top to bottom: tracking results in 10 mm middle slice of coanda water jet for successive iterations. parameters of each iteration given in table 1.200 out of 45407 times-steps shown fig. 3 (left) shows an instantaneous tracking result of the end-result of vt-stb. the impinging jet flow is captured, which rapidly broadens from the impingement point, creating small-scale flow structures advecting over the cylinder. the fastest particles indeed move at around 6 m/s, however the color-scale has been adapted for better visibility. the 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa flow separates below the centerline of the cylinder and a wake is formed beneath it. vast regions of slowly moving particles exist above and below the cylinder. the operating principle of vt-stb is illustrated in fig. 4. for each iteration, a 10mm thick slice of the volume, centered around the nozzle is visualized, showing particle tracks over approx. 500 time-steps (based on the original sampling; the effective length varies slightly due to the different time separations). the particles tracked at δ�,� = 79 are located in the entrainment region and below the cylinder, far from the wake of the jet. approx. 24,500 particles are captured instantaneously. maximum velocities of approx. 0.12 m/s are attained, corresponding to a shift of approx. 30 pixels at the given δ�(and 0.37 pixel at δ�= 1). this velocity significantly exceeds the initial search radius of δ = 12.6 pixels, as (a) tracked particles can accelerate and (b) the neighborhood predictor expands the trackable regime to higher velocities with time. particles accelerating to even higher velocities are typically lost, as the prediction can no longer follow the acceleration at this δ�. feeding the particles tracked in the first iteration to the tracking system of the next one (δ�,q = 36) and performing again two passes of tracking expands the field of tracked particles towards larger velocities. a further number of approx. 18,100 particles is tracked. here, particles up to 0.3 m/s are found. when moving to iteration 3 (δ�,r = 14), maximum velocities of 0.7 m/s can be tracked. large parts of the wake region below the cylinder appear, with an additional number of 22,400 tracked particles. at δ�,b = 6 (iteration 4), most of the flow on the cylinder surface can be tracked, singular particles approach velocities of 1.5 m/s. the tracking system is complemented by 12,300 further particles. from this iteration on, the tracked particles being read from the previous iteration are no longer treated by the shaking process, i.e. their positions remain unchanged; only the intensity is updated. finally, when δ�,s = 1 is reached in iteration 5, the remaining fast particles from the jet and it's direct surroundings are tracked. maximum velocities of 6 m/s are seen, as expected. these particles comprise only a small subset of the particles; approx. 3,200 particles are added to the tracking system at each time instant. a total number of just over 80,000 particles is reached. fig. 5: stb processing (left) vs. vt-stb processing (right), showing tracks for 200 consecutive time-steps in a 10mm-thick slice in the x-y plane, located as indicated in fig. 3 b). detail view in fig. 6 marked by rectangle 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa 3.3 comparison to standard evaluation in order to assess the benefits of vt-stb over regular processing using δ� = 1, the results are compared to a normal stb evaluation over 1,000 images, with parameters given in table 1. the normal stb processing finds approx. 1,500 particles less compared to vt-stb, for a total of 79,000 instantaneous particles. fig. 5 compares the tracking results in a 10 mm-thick x-y plane, with the cylinder being cut by the plane. shown are particle tracks for 200 consecutive time-steps. both evaluations correctly capture the vast majority of the tracks, however for stb a relevant amount of tracked particles appears within the cylinder, indicating ghost tracks. for vt-stb this region is nearly completely void. within the particle clouds, stb shows traces of falsely tracked particles, clearly standing out from the surroundings. this becomes more evident, when focusing on a smaller region (see fig. 6). while the stb-result is interspersed with both outliers, as well as a sizeable number of tracks with velocities close to zero, appearing in regions with visibly higher flow velocity, the vt-stb results is free of both types of abnormal particle tracks. at the same time, the tracks of slow particles exhibit less noise, as the filtering is carried out on a broader kernel, minimizing the effects of long-lasting overlap situations. fig. 6: stb processing (left) vs. vt-stb processing (right). excerpt from fig. 5 at marked position fig. 7: stb processing (top) vs. vt-stb processing (bottom), showing tracks for 200 consecutive time-steps in a 10mm-thick slice in the y-z plane, located as indicated in fig. 3 c). 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa these findings are supported by fig. 7, which shows a 10 mm-thick slice in the y-z plane for both evaluations. again it is obvious that vt-stb was able to efficiently suppress the generation of low-velocity ghost tracks and outliers, which are especially obvious in the outer regions and the cylinder for the stb evaluation. finally, fig. 8 compares the two evaluations in a x-z plane located on the upper edge of the measurement volume, above the jet (viewing from top). a vortical structure that is induced by the impingement of the jet and reaches up to the water surface is clearly visible in both reconstructions. the stb evaluation shows clear signs of ‘line-of-sight’tracks, where particles follow the viewing direction of a singular camera, as their intensity is mostly supported by a peak on that specific camera, as argued in the introduction. the approximate camera positions in relation to the view in fig. 8 can be taken from fig. 2 a). furthermore, it can be seen that some of the particles in the center of the vortex that are present for vt-stb are missing for the stb evaluation, which might be attributed to the lower choice of ?@ or the general lower reliability of stb in this case. the fact that the edges of the volume (where particles are not seen by all cameras) are not filled up for the stb case can be attributed to the shorter time-series that was evaluated (1,000 vs. 10,000 images). such regions, where no new particles are triangulated have to be filled up by particles convecting from regions visible by more cameras. these missing regions also explain, why stb is tracking less particles, despite the non-negligible number of ghost particles. fig. 8: stb processing (left) vs. vt-stb processing (right), showing tracks for 200 consecutive time-steps in a 10mm-thick slice in the x-z plane, located as indicated in fig. 3 d). it could be argued that using stricter parameters for normal stb might gain better results. while this is true in terms of obvious outliers, it has been found that reducing e.g. � leads to a significant loss of high-velocity particles in the jet and the shear layer. low-velocity ghost particles cannot be reduced by such measures. finally, it has to be stressed that the presented experimental case represents an extreme case in terms of velocity range and volume ratio of fast and (very) slow moving particles. for most experimental investigations, normal stb evaluations will show significantly less ghost particles, as such vast regions of slowly moving particles are not often found. however, we expect benefits of vt-stb processing in most flows, as a number of advantages (adjustable parameters for different velocity regimes, velocity-adapted filtering) still persist. a direct comparison of reconstruction times was not conducted due to the different lengths of the used time-series. however, it can be stated that vt-stb uses only moderately more processing time. the first iterations are fast, as the time-separation is large. in the later iterations, the particles from the previous ones are fed, thereby limiting the amount of work done by ipr. in case the shaking of particles from previous iterations is deactivated further gains in evaluation speed are attained. 6. acknowledgements this work was supported by the deutsche forschungsgemeinschaft (dfg) through grant no. schr 1165/5-1 as part of the priority programme on turbulent superstructures (dfg spp 1881). we thank janos agocs, reinhard geisler, tobias kleindienst and carsten fuchs for their contributions to constructing the water tank and the optical set-up. we specially thank kyung chun kim, mirae kim and eunseop yeom for their contributions to the layout and setup of the experiment. 14th international symposium on particle image velocimetry • august 1-4, 2021 • chicago, il usa references bosbach j, schanz d, godbersen p, schröder a (2019) dense lagrangian particle tracking of turbulent rayleigh bénard convection in a cylindrical sample using shake-the-box. 17th european turbulence conference (etc 2019), 3.-6. sept. 2019, torino, italy. gesemann s, huhn f, schanz d, schroder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. 18th int. symp. on appl. of laser and imaging tech. to fluid mech. lisbon, portugal, july 4 – 7 2016 huhn, f., schanz, d., gesemann, s., dierksheide, u., van de meerendonk, r., & schröder, a. (2017). large-scale volumetric flow measurement in a pure thermal plume by dense tracking of helium-filled soap bubbles. exp. fluids, 58(9), 116. jahn, t. schanz, d., schröder, a. (2021) advanced iterative particle reconstruction for lagrangian particle tracking, submitted to exp. fluids kim, m., kim, h. d., yeom, e., & kim, k. c. (2018). flow characteristics of three-dimensional curved wall jets on a cylinder. journal of fluids engineering, 140(4), 041201. maas hg, grün a, papantoniou d (1993) particle tracking in three dimensional turbulent flows—part i: photogrammetric determination of particle coordinates. exp fluids 15:133–146 malik n, dracos t, papantoniou d (1993) particle tracking in three dimensional turbulent flows—part ii: particle tracking. exp fluids 15:279–294 nishino k, kasagi n, hirata m (1989) three-dimensional particle tracking velocimetry based on automated digital image processing. trans asme j fluid eng 111:384–390 ouellette nt, xu h, bodenschatz e (2006) a quantitative study of three-dimensional lagrangian particle tracking algorithms. exp fluids 40(2):301–313 raffel, m., willert, c. e., scarano, f., kähler, c. j., wereley, s. t., & kompenhans, j. (2018). particle image velocimetry: a practical guide. springer. schanz d, gesemann s, schröder a, wieneke b, novara m (2013) non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. meas sci technol 24:024009 schanz d, gesemann s, schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. exp fluids 57(5), 70. stasicki b, schroder a, boden f, ludwikowski k (2017) high-power led light sources for optical measurement systems operated in continuous and overdriven pulsed modes, optical measurement systems for industrial inspection x 10329, 103292 wieneke b (2007) volume self-calibration for 3d particle image velocimetry. exp fluids 45:549–556 wieneke b (2013) iterative reconstruction of volumetric particle distribution. meas sci technol 24:024008 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 error propagation dynamics of piv-based pressure field calculation (3): what is the minimum resolvable pressure in a reconstructed field? zhao pan1∗, jared p. whitehead3, geordie richards2, barton l. smith2† 1 university of waterloo, department of mechanical and mechatronics engineering, on n2l 3g1, canada 2 utah state university, mechanical and aerospace engineering, logan, ut 84322, usa 3 brigham young university, mathematics department, provo, ut 84602, usa ∗ zhao.pan@uwaterloo.ca † barton.smith@usu.edu abstract an analytical framework for the propagation of velocity errors into piv-based pressure calculation is established. based on this framework, the optimal spatial resolution and the corresponding minimum field-wide error level in the calculated pressure field are estimated. this minimum error is viewed as the smallest resolvable pressure. we find that the optimal spatial resolution is a function of the flow features, geometry of the flow domain, and the type of the boundary conditions, in addition to the error in the piv experiments, making a general statement about pressure sensitivity is difficult. the minimum resolvable pressure is affected by competing effects from the experimental error due to piv and the truncation error from the numerical solver. this means that piv experiments motivated by pressure measurements must be carefully designed so that the optimal resolution (or close to the optimal resolution) is used. flows (re=1.27× 104 and 5×104) with exact solutions are used as examples to validate the theoretical predictions of the optimal spatial resolutions and pressure sensitivity. the numerical experimental results agree well with the analytical predictions. 1 introduction experimental pressure measurements are useful for determining loads on structures and for examination of acoustic effects. however, it has not been possible to measure the pressure field away from surfaces until recently. in the last decades, it has been shown that the pressure field may be determined from velocity data measured using particle image velocimetry (piv). piv-based pressure calculation techniques have received significant recent interest because the output provides field measurements with high frequency response (van oudheusden, 2013). the accuracy of pressure fields derived from piv data has improved with the piv technique itself, as hardware improvements provide increased spatial and temporal resolution and new techniques have provided a fully three-dimensional velocity field (scarano, 2012). with these recent advances, a natural inquiry is “how accurate is the pressure field obtained from piv?” or “how do errors in the velocity field affect the errors of the computed pressure field?” or “what is the minimum measurable pressure?” this work will attempt to address these questions. but first we briefly survey the state-of-the-art in piv-based pressure field calculations. velocimetry-based pressure reconstruction is a straight-forward idea that can be traced back to schwabe (1935). technical limitations of the imaging technique in schwabe (1935) (i.e., low spatial and temporal resolution, etc.) and consequently large error in the velocity field measurement, led to a calculated pressure that was not reliable enough to ensure any quantitative confidence at the time. after decades of development, piv has become a reliable non-invasive velocity field measurement technique, which not only provides the vector velocity field measurements but also describes the uncertainty of these measurements (sciacchitano et al., 2013; charonko and vlachos, 2013; wieneke, 2015). built on these advancements in piv techniques, calculation of the piv-based pressure field has become common. piv-based pressure field reconstruction methods are divided into two categories: i) integrating the pressure gradient from the navier-stokes equations, and ii) integrating the poisson equation derived from the navier-stokes equations to obtain the scalar pressure field. recent algorithmic considerations investigate alternative ‘numerical methods’ such as a least square solver (jeon et al., 2015), spectral decomposition (wang et al., 2017), and data assimilation (e.g., he et al. (2020)) to achieve a robust or fast pressure solution. pressure-poisson-equation-based methods often involve well-defined explicit boundary conditions, which have a straightforward physical and mathematical interpretation. examples may be found in, for example, de kat and van oudheusden (2012); pröbsting et al. (2013). for either the pressure gradient integration or the poisson equation approach, the state-of-the-art implementation uses time-resolved 2d and/or 3d piv data and numerically optimized solvers. taking advantage of the advancing velocimetry techniques and velocimetry-based pressure reconstruction algorithms, piv-based pressure reconstruction techniques have been increasingly applied to various fields of study. examples in classic topics include pressure field and loads on airfoils (jeon et al., 2016; lignarolo et al., 2014), water slamming pressure of boat hull (porfiri and shams, 2017), as well as pressure distribution in turbulent boundary layers (ghaemi et al., 2012; zhang et al., 2017). the extended applications cover aero-acoustics with acoustic analogies (léon et al., 2017), and compressible flows van oudheusden et al. (2007); van gent et al. (2018). fundamental research on piv-based pressure calculations has shed insight into design of experiments and algorithms. for example, charonko et al. (2010) benchmarked several different pressure field reconstruction algorithms and found that the performance of the piv-based pressure calculations are affected by almost every factor involved in the experiments (e.g., type of flow, spatial and temporal resolutions, filtering of the piv data, the type of numerical solver, and error level in the piv data). there is no universal optimal experimental setup for all applications, although, as shown below for a specific problem, optimal spatial and temporal resolutions do exist that minimize the error in the calculated pressure field. de kat and van oudheusden (2012) pointed out that a numerical poisson solver acts as a low-pass filter, which tends to eliminate the high frequency data (both signal and noise) from the piv experiments. in subsequent work, matthew faiella and pan (2021) showed that this low-pass filter is not only due to the specific numerical scheme of the poisson filter, but is rooted in the properties of the poisson operator. thus, low frequency error due to piv measurements should be avoided to minimize the error that propagates to the calculated pressure. a more general study of error propagation of the piv-based pressure field calculation showed that the fundamental features of the domain such as geometry (dimension, shape, and size) of the domain and the configuration of boundary conditions impact the error propagation as well (pan et al., 2016). despite numerous recent studies on piv-based pressure calculations as a quantitative measurement technique, the uncertainty of the technique and how it depends on the accuracy of the velocity measurement has not been sufficiently addressed. only a few works have covered this topic. azijli et al. (2016) proposed a posteriori uncertainty quantification method of piv-based pressure calculations under a bayesian framework. pan et al. (2016) introduced an upper bound on the error in the calculated pressure field which is a function of some fundamental factors of the flow field, such as geometry of the domain and the type of boundary conditions. even though the upper bound is not always apparent and could overestimate the error, it can be considered an a priori estimate of the worst possible error level in the reconstructed pressure field and thus aid the experimental design and optimization. more recently, (mcclure and yarusevych, 2017) proposed an estimation of the optimal spatial and temporal resolution that minimize the error in the pressure field, but did not provide the minimum error in the reconstructed pressure, which can be interpreted as the sensitivity of the pressure reconstruction. in the current study, we will begin to answer one of the fundamental questions posed above: “what is the minimum resolution or the sensitivity of the piv-based pressure calculation for a given experimental setup, and what is the optimal spatial resolution for a piv experiment with pressure reconstruction being the end goal?” flows with exact solutions will be used for validation. based on analytical predictions, practical solutions will be given for real engineering applications. 2 problem setup and definitions piv-based pressure calculation is rooted in the navier-stokes equations. arranging the nondimensionalized navier-stokes equations we have ∇p = − ( ∂uuu ∂t +(uuu ·∇)uuu− 1 re ∇2uuu ) , where uuu is the velocity field, which is obtained from experiments, and p is the pressure field, which is to be determined. re is the reynolds number. as noted above, current piv-based pressure field calculation methods fall into two categories: i) direct integration of the pressure gradient (∇p) (e.g., liu and katz (2006)) from the navier-stokes equations, ii) applying the divergence operator to ∇p and solving the corresponding poisson equation with respect to the pressure field p: ∇ 2 p = f (uuu) =−∇ · ( ∂uuu ∂t +(uuu ·∇)uuu− 1 re ∇ 2uuu ) , (1) where the right hand side, f (uuu), is called the “data” (see pan et al. (2016)). we will adopt this terminology hereafter in the current work. in this study, we focus on the latter method. to prevent any confusion, we will address the experimental data from piv as “experimental results” or “piv results”. eq. (1) must be solved with proper boundary conditions (bcs). a complete description of the problem in a domain ω can be described as ∇2 p = f (uuu) in ω, with neumann bcs ∇p ·n = g(uuu) on ∂ω (enforced pressure gradient on the boundary), and/or dirichlet bcs p = h(uuu) on ∂ω (enforced pressure on the boundary), where f (uuu), g(uuu) and h(uuu) are corresponding functions of the velocity field. clearly, the error from experimental measurements will propagate to the calculated pressure field. however, the typical propagation analysis using taylor series method or monte carlo methods (coleman and steele, 2009) are difficult. in the current study, we directly analyze the error propagation of the piv-based pressure calculation using the underlying governing equations (1) and corresponding boundary conditions. denoting the error in the measured velocity field as εεεu and the true value of the velocity field as uuu, the error contaminated velocity measurement ũuu can be modeled as ũuu = uuu+ εεεu. similarly, the pressure field with errors p̃ can be modeled as p̃ = p+ εp, where εp is the error in the calculated pressure field and p is the unknown true value. with measurement error considered, the pressure field reconstruction problem are implemented, in practice, as ∇2 p̃ = f (ũuu) in ω, with neumann bcs, ∇p̃ ·n = g(ũuu) on ∂ω, and/or dirichlet bcs p̃ = h(ũuu) on ∂ω. we will further quantify the relationship between εεεu and εp. to adequately perform this comparison, we use the space-averaged l2-norm of a field on the domain ω defined as ||ε||l2(ω) = √∫ ε2dω/|ω|, where |ω| denotes the area or volume of the domain depending on the dimensions of the domain. 3 error estimation of reconstructed pressure field in practice, a piv experiment is associated with spatial and temporal resolutions. solving pressure field from piv results is often numerically achieved and involves three important factors: spatial resolution, temporal resolution, and the numerical scheme of the pressure solver. in the current work, we focus on an analytical investigation on the impact of spatial resolution of piv experiments on the error propagation of piv-based pressure field reconstruction. 3.1 theory: error propagation, minimum error, and optimal spatial resolution we consider a two dimensional (2d) flow on a structured mesh with grid spacing h×h. we assume that the measured velocity field from the piv experiments has point-wise zero-mean gaussian noise with variance σu and σv in the two cardinal directions. the expected error level in the calculated pressure field can be estimated as ‖εp‖(l2(ω)) . ‖εp,t‖l2(ω)+‖εp,e‖l2(ω) ≈c1 (∥∥∥∥∂2 p ∂x2 ∥∥∥∥ l2(ω) +2 ∥∥∥∥∇ −2 ∂4 p ∂2x∂2y ∥∥∥∥ l2(ω) + ∥∥∥∥∂2 p ∂x2 ∥∥∥∥ l2(ω) ) hm ︸ ︷︷ ︸ truncation error contribution + piv error contribution︷ ︸︸ ︷ c0c2 σ2 u +σ2 v 2 hn , (2) where ||εp,t ||l2(ω) is the truncation error of the numerical scheme arising from the poisson solver, and the second term (||εp,e ||l2(ω)) includes the effect of the experimental errors in the measured velocity field (the derivation of this estimate with greater details can be found in pan et al. (2018)). for a specific example, a flow in an l×l square domain, with pure dirichlet boundary conditions, the pressure field is solved by a second order finite difference poisson solver with central difference scheme. in this setting, (2) leads to a more particular form with specific parameters: ‖εp‖(l2(ω)) . 1 12 (∥∥∥∥∂2 p ∂x2 ∥∥∥∥ l2(ω) +2 ∥∥∥∥∇ −2 ∂4 p ∂2x∂2y ∥∥∥∥ l2(ω) + ∥∥∥∥∂2 p ∂x2 ∥∥∥∥ l2(ω) ) h2 +0.9012 l2 2π2 σ2 u +σ2 v 2 h−2. (3) the physical and/or mathematical interpretations of the terms and variables in (2) or (3) can be found in table 1. the results above are developed for the non-dimensional setup. the dimensional equivalent estimates can be recovered by multiplying the variables by corresponding characteristic scales (e.g., ||ε∗p||l2(ω) = ||εp||l2(ω)p0, x∗ = xl0, u∗ = uu0, etc., where p0, l0 and u0 are characteristic pressure, length, and velocity respectively). for convenience, the superscript ([ ]∗) denoting dimensional variables will be dropped here after without special note and the non-dimensional variables will be written explicitly (e.g., p/p0 is the non-dimensional pressure, where p is the corresponding dimensional variable). table 1: variables and terms in (2) and the corresponding specific values in (3) and the physical/mathematical interpretations. variables or terms value mathematical/physical interpolation affected by εp error field in the calculated pressure field everything ||εp||l2(ω) global measure of the error level of the calculated pressure field everything c1 1 12 the constant of truncation error contribution numerical scheme ∂2 p ∂x2 , etc. 2nd order derivative of the pressure field flow field c0 0.9012 amplification ratio of point-wise gaussian error to the “most dangerous mode” of the error in the data* dimension, type of bcs of the domain c2 l2 2π2 optimal poincaré constant (highest possible amplification ratio of error in the reconstructed pressure field to the error in the data) dimension, area, shape, type of bcs σ2 u, etc. variance of error of the experimental data quality of piv h spatial resolution piv experiment setup and post-processing m 2 scaling constant of grid spacing for the contribution from the truncation error numerical scheme n −2 scaling constant of grid spacing for the contribution from the experimental error numerical scheme * details about the derivative, calculation, and physical interpretation of c0 can be found in matthew faiella and pan (2021). equation (2) can be written as a function of the spatial resolution: ||εp||l2(ω) = fun(h) ≈ ahm +bhn, where a, b, m, and n are constants once the experimental setup, parameters, and pressure solver are determined. for example, for eq. (3), a = 1 12 (∥∥∥ ∂2 p ∂x2 ∥∥∥ l2(ω) + ∥∥∥∇−2 ∂4 p ∂2x∂2y ∥∥∥ l2(ω) + ∥∥∥ ∂2 p ∂y2 ∥∥∥ l2(ω) ) , b = 0.9012 l2 2π2 σ2 u+σ2 v 2 , m = 2, and n =−2. clearly, ||εp||l2(ω) is not monotonic in h, leaving several open questions: i) what is the minimum error (||εp||l2(ω))? and ii) when is the minimum approached in terms of spatial resolution (h)? we note that ah2 +bh−2 ≥ 2 √ ab, where equality is reached if and only if ah2 = bh−2, and we thus have the optimal spatial resolution hopt ≈ 4 √ b/a, which leads to an estimate of the minimum error level in the calculated pressure field: ||εp||min l2(ω) ≈ 2 √ ab. this minimum error level can be interpreted as the overall sensitivity of the pressure reconstruction, meaning that any pressure reconstruction results smaller than this sensitivity are not meaningful. in other words, this sensitivity of the reconstructed pressure field is a global measure of the best possible accuracy of the current piv-based pressure reconstruction. 3.2 validation consider a taylor vortex in 2d. assuming pressure at the far field vanishes (p∞ = 0), the velocity and pressure fields are defined as uθ(r, t) = hr 8πνt2 exp ( − r2 4νt ) and p(r, t) = −ρ hr2 64π2νt3 exp ( − r2 2νt ) , respectively, where h = m/2ρν is a constant that measures the amount of angular momentum m in the vortex (panton, 2006). the time is t, the distance from the center of the vortex is r, and ρ, and ν are density and kinematic viscosity of the fluid, respectively. we non-dimensionalize the variables as ζ = r/l0, ξ = u/u0, and η = p/p0, where l0 = √ 2νt, u0 = h/(2πl0t), and p0 = ρu2 0 , are the characteristic scales. scaling uθ and pθ leads to ξ∗ θ = 1 2 ζexp ( − ζ2 2 ) , and η∗ =− 1 8 exp ( −ζ2 ) , respectively. now we consider a ‘realistic’ flow in water with parameters shown in the table (see fig. 1), and the 2d non-dimensional representation of the flow (velocity and pressure field) is also shown in the same figure. we again consider point-wise gaussian errors added to the velocity field with zero-mean and constant standard deviation (i.e., εu ∼ n (0,σ2 u), εv ∼ n (0,σ2 v), σu/u0 = σv/u0 ≈ 7.85× 10−3). we refer to this numerical setup (i.e., referring the flow described in table 2, and this specific errors) as setup 1 hereafter. we vary the spatial resolution (h) of the domain and run the numerical experiments 5,000 times for each resolution. the normalized error level in the calculated pressure field (||εp||ω(l2)/p0) versus the normalized spatial resolution (h/l0) of the domain is shown in the box plot in fig. 2(a). as mentioned, each box represents 5,000 independent numerical experiments. the theoretical predictions of the error level in the calculated pressure agree well with these numerical experiments. the blue dashed line (slope = 2) indicates the first term in eq. (3), which represents the contribution from the truncation error, which is affected by both the numerical schemes and the flow field. the blue dash-dot line (slope = −2), which is mainly affected by the property of the poisson operator and the experimental error. the black line indicates the theoretical predication of the total error (see eq. (3)) in the calculated pressure field. the intersection of the piv error contribution (blue dash-dot line) and the truncation error contribution (blue dashed line) is marked by the blue circle indicating the optimal spatial resolution where the minimum global error in the calculated pressure field is achieved. the minimum error in the calculated pressure field is ||εp||min l2(ω)/p0 ≈ 2.35× 10−3 in this specific example. for a characteristic pressure p0 = 64.85 pa, the best possible sensitivity of the pressure field reconstruction is approximately 0.15 pa. this implies that a well designed and conducted piv experiment with an accurate pressure solver could achieve high fidelity pressure reconstructions and rival the sensitivity of pressure sensors. due to the ‘velocity-to-pressure’ computation in the piv-pressure approach, the reconstructed pressure field is scalable with the characteristic pressure (p0 = ρu2 0 ). this feature indicates that piv-based pressure reconstruction techniques are particularly attractive for applications involving small pressure changes (e.g., slow air flows introduce relatively low values of ρ and u0, and thus low p0), which often requires high cost instrumentally when using high-sensitivity pressure transducer arrays. for example, assuming an air flow having the same velocity field as the setup 1, the low density of the fluid media (e.g., ρ≈ 1 kg/m3) leads to a low characteristic pressure (p0 ≈ 0.065 pa). the corresponding pressure measurement sensitivity in such a piv-pressure calculation can be approximately as high as ∼1.5× 10−4 pa. therefore, in addition to the ability to measure pressure anywhere in a flow field, pressure from piv has the potential for superior accuracy for slow flows. remembering the dynamic range (d) is the ratio between the maximum measurable (pmax) and the sensitivity (||εp||min l2(ω)), we define the dynamic range of the piv-based pressure calculation techniqes in the current work as d = pmax/||εp||min l2(ω) we expect that piv-based pressure calculation techniques have following features: i) the maximum measurable pressure is determined by the velocity field and the fluid density, and is scalable to ρu2 0 . in other words, pmax is flow dependent; ii) noting that the sensitivity of the measurement is affected by many factors (see fig. 1 and eq. (2)), the sensitivity is not a fixed value either; iii) thus, the piv-based pressure reconstruction techniques has a “dynamic” dynamic range, which depends on many factors including the nature of the flow. this property is distinct to conventional pressure transducers’ fixed dynamic range. the dynamic range of the piv-based pressure reconstruction could be high if the experiment and pressure solver are carefully designed. for example, in the example presented above, the dynamic range is d = 4.3×105, which is comparable to (or even greater than) a typical pressure gauges. since the contribution from truncation error scales as ||εp,t ||l2(ω) ∼ o(h2), and the contribution from measurement error in the velocity field scales as ||εp,e ||l2(ω) ∼ o(h−2), we expect there to be a competition between the two errors in terms of the resolution h. this phenomena has been observed previously (charonko et al., 2010; pan, 2016; mcclure and yarusevych, 2017), as well as in the current study (e.g., fig. 2(a)). in the following we provide an explicit interpretation based on a rigorous analysis (e.g., eq. (2)). when the spatial resolution is too small (e.g., h/l0→ 0), the error in the pressure is dominated by the error from the errors in the velocity field (green patched regime in fig. 2(a)). when the spatial resolution is relatively large (e.g., h/l0→ 1), the spatial resolution is comparative to the length scale of the flow structure, and the truncation error due to the discrete scheme is the dominant error source (blue patched regime). when the spatial resolution is even larger (e.g., h/l0� 1), the insufficient sampling lower than the nyquist frequency causes aliasing and unreliable, or more precisely, meaningless pressure field reconstructions. the normalized histograms of the error level in the calculated pressure field at three different values of the spatial resolution as indicated in fig. 2(a) (marked by orange, green, and blue frames), are shown -3 0 3 -3 0 3 (b) pressure field -3 0 3 -3 0 3 (b) pressure field -3 0 3 -3 0 3 0 0.1 0.2 0.3 (a) velocity field -3 0 3 0 0.1 0.2 0.3 (a) velocity field |u|/u0 x/l0 y/ l 0 (p p∞)/p0 -0.12 -0.08 -0.02 y/ l 0 figure 1: parameter space for the numerical experiments (table to the left) and 2d visualization of the non-dimensional flow field in a box. (a) velocity quiver plot over the magnitude and (b) the pressure field. in fig. 2(b-d), respectively. these histograms are normalized by ||εp||l2(ω)/p0× 100%. they represent the probability density function (pdf) of the relative error (percentage compared to the characteristic pressure). one of the error fields in the reconstructed pressure drawn from the 5,000 independent numerical experiments for the three typical spatial resolutions are shown in fig. 2(e-g), respectively. more general validations can be achieved by varying the error level in the velocity field (e.g., different σ2 u and σ2 v) and adjusting the flow field (e.g., a flow with different characteristic scales). we consider i) the same flow used in the above example (fig. 1), but with larger error with different statistics (i.e., εu ∼ n (0,σ2 u),εv ∼n (0,σ2 v), where σu/u0 = 1.57×10−2 and σv/u0 = 3.93×10−3, called setup 2 hereafter); ii) the younger stage (t = 312.5 sec) of the same decaying vortex (see the able in fig. 1 for detailed parameters) in the same dimensional domain (meaning a larger non-dimensional size of the domain), and the same dimensional error level as setup 1 (i.e., εu ∼ n(0,σ2 u),εv ∼ n(0,σ2 v), where σu/u0 = σv/u0 = 0.98×10−3, called setup 3 hereafter). table 2: parameters of two different flows for validation (setup 1 & 2, and a younger vortex for setup 3). parameters setup 1 & 2 setup 3 units l0 = √ 2νt 0.05 0.025 [m] u0 = h 2πl0t 0.25 2.04 [m/s] p0 = ρu2 0 64.85 4,150 [pa] upeak 0.1 0.87 [m/s] ppeak− p∞ −8.1 −518.8 [pa] re 1.27×104 5.0×104 similar numerical experiments are conducted and the results are shown in fig. 3(a). the results from the numerical experiments agree with the theoretical predictions well for various flows and piv error statistics. comparing setup 1 and 2, which share the same flow field but different error statistics in the velocity field, we note that when the spatial resolution is large (e.g., larger than the optimal resolution of the setup 2, marked by the green circle in fig. 3(a)), the truncation error dominates and the numerical experimental results collapse onto the same dashed line, which is solely determined by the nature of the flow. when the spatial resolution is small, the error in the velocity field from the piv measurements is the major contributor to the error in the calculated pressure field. thus, setup 2 introduces more error than setup 1, and the (e) (f) (g)(e) (f) (g) (d) 22 1 (b) (c) 1 (a) figure 2: error level in the calculated pressure field vs. spatial resolution. (a) box plot of the error level in the calculated pressure field. each box represents 5000 independent simulations. the green region is dominated by the error from the piv measurements due to the spatial resolution being too fine. the blue region is the regime where the truncation error dominates because the resolution is too coarse. the red region indicates aliasing due to insufficient sampling lower than the nyquist frequency. the dashed line represents the theoretical prediction of the truncation error, and the dash-dot line indicates the theoretical contribution from piv measurement errors in the velocity field. the solid line represents the theoretical prediction of the total error in the calculated pressure field. (b-d) normalized histograms of the relative error in the calculated pressure field for typical spatial resolutions (corresponding to the orange, green, and blue frames in fig. 2(a), respectively). (e-g) relative error field in pressure at several spatial resolutions (corresponding to (b-d), respectively.) optimal spatial resolution is coarser than it is for setup 1 (the green circle is on the right of the blue circle). comparing setup 1 and 3, a smaller characteristic length (radius of the vortex) of the flow in setup 3 implies that the optimal resolution for setup 3 is finer than setup 1 or 2 since a smaller scale flow structure must be resolved (the red circle is on the left of the green and blue circles). we emphasize that the vertical axis in fig. 3(a) is a non-dimensional error level, not the dimensional value. instead, ||εp||l2(ω)/p0 is a “error level” comparing the error to the corresponding characteristic pressure. noting that setup 3 has significantly higher characteristic pressure than setup 1 and 2, it is not surprising that the minimum error level (or sensitivity of the pressure measurement) for setup 3 is lower than the other two setups (the red circle is located lower than the green and blue ones). however, this does not necessarily mean that the absolute pressure sensitivity for setup 3 is low. a more intuitive presentation can be found in fig. 3(b), which is reconstructed from fig. 3(a), but with physical dimensions included. figure 3(b) shows the error in the calculated pressure field versus spatial resolution for setup 1 (blue), 2 (green), and 3(red). when the spatial resolution is small (e.g., to the left of the red circle in fig. 3(b)), the numerical experimental results (blue boxes and the red boxes) are collapsed onto the same dash-dot line because the same error statistics are shared as well as the same domain properties (e.g., size of the domain, type of bcs, etc.). the error in setup 2 is higher than that from setups 1 and 3 when the spatial resolution is small due to the larger random error in the velocity field. when the spatial resolution is high (e.g., to the setup 2: more piv error setup 3: younger vortex setup 2: more piv error setup 3: younger vortex setup 1 setup 1 (a) (b) figure 3: non-dimensional (a) and dimensional (b) error in the calculated pressure field vs. non-dimensional spatial resolution. numerical experiments of setup 1 (blue), 2 (green), and 3 (red). the dashed lines indicate the contribution from truncation error, and the dash-dot lines indicate the contribution of the error from the piv measurement in the velocity field. the optimal spatial resolutions are marked by the circles at the intersections of the dashed lines and the dash-dot lines, with corresponding color schemes. right of the green circle), the numerical experimental results from setup 1 and 2 (blue and green boxes) are collapsed onto the same theoretical prediction since they have the same flow field, despite these two setups have different error statistics in the velocity field. more importantly, fig. 3(b) clarifies how the flow field and error in the piv measurements affect the optimal spatial resolution and the pressure reconstruction sensitivity (note the vertical positions of the colored circles) for the three different setups. the larger error in the piv measurements requires coarser optimal spatial resolution and leads to lower pressure reconstruction sensitivity (comparing the positions of blue and the green circle). the smaller dominant flow structures in the flow require finer spatial resolution, however, leading to worse minimum resolvable pressure (comparing the positions of blue and the red circle). a qualitative illustration of how the error from the piv experimental measurement and the truncation error from the numerical solver compete against each other for the optimal spatial resolution, and at the same time, contribute together to the minimum error in the pressure field is shown in fig. 4. larger truncation error (e.g. due to a flow with higher spatial frequency) would shift the dashed lines up (fig. 4(a)) and lead to a requirement for finer spatial resolution to achieve the minimum error in the pressure field (see the locus marked by the red circles and arrow head in fig. 4(a)). more error in the velocity field from the piv experiments will shift the dash-dot line up and require coarser spatial resolution for the minimum error in the calculated pressure field (see the locus marked by the red circles and arrow head in fig. 4(b)). based on the above observations, an intuitive impression is that one of the most challenging piv experimental results for piv-based pressure reconstruction is a flow with small scale dominant structures (usually leading to small characteristic length scales and more significant contributions from the truncation error) and high uncertainties in velocity field. more truncation error more piv error (a) (b) finer optimal spatial resolution, higher minimum error in pressure coarser optimal spatial resolution, higher minimum error in pressure e rr o r le v el i n t h e c al cu la te d p re ss u re f ie ld spatial resolution spatial resolution figure 4: qualitative illustration of the contributions and/or competition of the truncation error and piv error. more truncation error in the domain leads to finer optimal spatial resolution, and higher minimum error in the calculated pressure field (marked by the red circles and arrow head in (a)). more error from the piv experiments leads to coarser optimal resolution and higher minimum error in the pressure field. 4 discussion and conclusions we have provided a rigorous framework that decouples the contribution of numerical truncation and experimental error to the pressure field reconstructed from piv experiments. based on this framework, we point out that the error propagation from the piv-based velocity field measurements to the calculated pressure field is affected by many factors. for instance, beyond the quality of the piv experiments, the geometry and boundary conditions of the domain, the physical profile of the flow, and the numerical scheme (e.g., grid spacing) of the pressure solver play a significant role. in this paper we have focused on one of these factors: how the spatial resolution of the velocity vector field from piv impacts the error propagation. specifically, we give a precise description of the competition between the truncation error from the numerical schemes and the experimental error from piv experiments over the different spatial resolutions. when the spatial resolution is relatively fine, the error from the experimental data dominates the error propagation and when the spatial resolution is relatively coarse, truncation error due to the numerical scheme of the pressure solver governs the error propagation. thus there is an optimal spatial resolution that minimizes the error propagation of a given flow. the corresponding minimum field-wide error level in the calculated pressure field can be considered the minimum resolvable pressure for the calculated field, or the effective sensitivity of the reconstructed pressure field. we emphasize that the current research mainly focuses on a general framework that decouples error from the true value in the calculated pressure field. the uncertainties in the calculated pressure field can then be directly analyzed. although the framework in this work is general, the specific form of some of the pertinent equations (e.g., (3)) depends on the specific numerical schemes of the solver (e.g., second order central finite difference with structural grid spacing for the current consideration), and the error model (e.g., point-wise gaussian noise at each grid point) is not general. different numerical schemes and more sophisticated models of the velocity field piv-measure error will not fundamentally change the main results discussed above, and the approach taken here provides a guide for future investigations of such setups. references azijli i, sciacchitano a, ragni d, palha a, and dwight rp (2016) a posteriori uncertainty quantification of piv-based pressure data. experiments in fluids 57:1–15 charonko jj, king cv, smith bl, and vlachos pp (2010) assessment of pressure field calculations from particle image velocimetry measurements. measurement science and technology 21:105401 charonko jj and vlachos pp (2013) estimation of uncertainty bounds for individual particle image velocimetry measurements from cross-correlation peak ratio. measurement science and technology 24:065301 coleman hw and steele wg (2009) experimentation, validation, and uncertainty analysis for engineers. john wiley & sons, hoboken, nj de kat r and van oudheusden b (2012) instantaneous planar pressure determination from piv in turbulent flow. experiments in fluids 52:1089–1106 ghaemi s, ragni d, and scarano f (2012) piv-based pressure fluctuations in the turbulent boundary layer. experiments in fluids 53:1823–1840 he c, liu y, and gan l (2020) instantaneous pressure determination from unsteady velocity fields using adjoint-based sequential data assimilation. physics of fluids 32:035101 jeon y, earl t, braud p, chatellier l, and david l (2016) 3d pressure field around an inclined airfoil by tomographic tr-piv and its comparison with direct pressure measurements. in 18th international symposium on the application of laser techniques to fluid mechanics. lisbon, portugal. pages 4–7 jeon yj, chatellier l, beaudoin a, and david l (2015) least-square reconstruction of instantaneous pressure field around a body based on a directly acquired material acceleration in timeresolved piv, 11th int. in symp. part. image velocim.-piv15 léon o, piot e, sebbane d, and simon f (2017) measurement of acoustic velocity components in a turbulent flow using ldv and high-repetition rate piv. experiments in fluids 58:72 lignarolo l, ragni d, krishnaswami c, chen q, ferreira cs, and van bussel g (2014) experimental analysis of the wake of a horizontal-axis wind-turbine model. renewable energy 70:31–46 liu x and katz j (2006) instantaneous pressure and material acceleration measurements using a fourexposure piv system. experiments in fluids 41:227–240 matthew faiella jpw corwin g j macmillan and pan z (2021) error propagation dynamics of velocimetrybased pressure field calculations (2): on the error profile. measurement science and technology 26:074002 mcclure j and yarusevych s (2017) optimization of planar piv-based pressure estimates in laminar and turbulent wakes. experiments in fluids 58:62 pan z (2016) error propagation dynamics of piv-based pressure field calculation. ph.d. thesis. brigham young university pan z, whitehead j, thomson s, and truscott t (2016) error propagation dynamics of piv-based pressure field calculations: how well does the pressure poisson solver perform inherently?. measurement science and technology 27:084012 pan z, whitehead jp, richards g, truscott tt, and smith bl (2018) error propagation dynamics of pivbased pressure field calculation (3): what is the minimum resolvable pressure in a reconstructed field?. arxiv preprint arxiv:180703958 panton rl (2006) incompressible flow. john wiley & sons, hoboken, nj porfiri m and shams a (2017) new york university brooklyn, brooklyn, ny, united states. dynamic response and failure of composite materials and structures page 395 pröbsting s, scarano f, bernardini m, and pirozzoli s (2013) on the estimation of wall pressure coherence using time-resolved tomographic piv. experiments in fluids 54:1–15 scarano f (2012) tomographic piv: principles and practice. measurement science and technology 24:012001 schwabe m (1935) über druckermittlung in der nichtstationären ebenen strömung. ingenieur-archiv 6:34– 50 sciacchitano a, wieneke b, and scarano f (2013) piv uncertainty quantification by image matching. measurement science and technology 24:045302 van gent pl, van oudheusden bw, and schrijer ff (2018) determination of mean pressure from piv in compressible flows using the reynolds-averaging approach. experiments in fluids 59:1–14 van oudheusden b (2013) piv-based pressure measurement. measurement science and technology 24:032001 van oudheusden bw, scarano f, roosenboom ew, casimiri ew, and souverein lj (2007) evaluation of integral forces and pressure fields from planar velocimetry data for incompressible and compressible flows. experiments in fluids 43:153–162 wang cy, gao q, wei rj, li t, and wang jj (2017) spectral decomposition-based fast pressure integration algorithm. experiments in fluids 58:84 wieneke b (2015) piv uncertainty quantification from correlation statistics. measurement science and technology 26:074002 zhang c, wang j, blake w, and katz j (2017) deformation of a compliant wall in a turbulent channel flow. journal of fluid mechanics 823:345–390 introduction problem setup and definitions error estimation of reconstructed pressure field theory: error propagation, minimum error, and optimal spatial resolution validation discussion and conclusions extending the frequency limits of “postage-stamp” piv to mhz rates steven j. beresh,* russell w. spillers, melissa m. soehnel, and seth m. spitzer sandia national laboratories, albuquerque, nm, u.s.a. * sjberes@sandia.gov abstract the effective frequency limits of postage-stamp piv, in which a pulse-burst laser and very small fields of view combine to achieve high repetition rates, have been extended by increasing the piv acquisition rate to very nearly mhz rates (990 khz) by using a faster camera. charge leaked through the camera shift register at these framing rates but this was shown not to bias the measurements. the increased framing rate provided oversampled data and enabled use of multi-frame correlation algorithms for a lower noise floor, increasing the effective frequency response to 240 khz where the interrogation window size begins to spatially filter the data. the velocity spectra suggest turbulence power-law scaling in the inertial subrange steeper than the theoretical -5/3 scaling, attributed to an absence of isotropy. introduction the measurement of turbulent velocity spectra in high-speed flows requires that very high frequencies must be reached at small spatial scales. the most common means of measuring velocity spectra such as hot-wire anemometry and laser doppler velocimetry generally fail to achieve the necessary frequency response, which can require 100 khz or more. in contrast, time-resolved particle image velocimetry (trpiv) using a pulse-burst laser [1] recently has demonstrated an ability to directly measure spectral content at 400 khz by confining the laser energy to a small field of view and windowing the camera to a small array [2]. image sequences exceeding 4,000 frames were acquired, but by necessity for a small array of only 128 × 120 pixels, giving rise to the moniker of “postage-stamp piv.” still, the postage-stamp piv data reached frequency limitations of approximately 120-130 khz due to interference from the noise floor of the measurement. noise reduction schemes were found inadequate to the present case [3]. therefore, postage-stamp piv remains in need of a means of increasing its effective frequency limitation due to the noise floor. an earlier version of the present paper [4] offered a means of accomplishing this by employing an interpolation scheme based upon the temporal super-sampling of scarano and moore [5]. by drawing measurements from multiple spatial and temporal locations, errors that are not spatially correlated will average out and the noise floor is decreased. success was indicated in reducing the impact of measurement noise, which raised the effective frequency response of previous 400-khz measurements from about 120 khz to 200 khz. more recent explorations generate questions about the generalizability of this approach to flows with stronger turbulence and out-of-plane motion. a second, more robust approach is simply to use the increased speeds of the most recently available cameras to obtain data at a sampling rate of 990 khz. previous mhz-rate pulse-burst piv systems have been developed by wernet and opalski [6] and by brock et al [7], but these could only acquire 8 and 14 images, respectively, and therefore were unsuited to obtaining spectral content. willert [8] also used this emerging high-speed camera technology coupled with a continuously pulsed laser in an incompressible free jet to obtain spectral content up to 420 khz. but to achieve such high imaging rates for long sequences, the cameras possess drawbacks that can have unfortunate properties for accurate piv measurements. these must be characterized to ensure no biases are induced as a by-product of raising the effective frequency response of postage-stamp piv. experimental configuration previous 400-khz postage-stamp piv measurements a brief description of postage-stamp piv is provided here, with the full details to be found in beresh et al [2]. present tests were conducted in sandia’s trisonic wind tunnel (twt) of a mach 3.73 jet exhausting transversely into a mach 0.8 crossflow. measurements were conducted in the center streamwise plane in the far-field of the jet interaction. the coordinate axes originate at the centerpoint of the nozzle exit plane; the u component is in the streamwise direction and v component is positive away from the top wall of the tunnel. the twt is seeded by a thermal smoke generator (corona vi-count 5000) delivering particles whose in-situ response showed the particle size to be 0.7 0.8 µm. stokes numbers have been estimated as at most 0.05 based on a posteriori analysis of piv measurements, which is sufficiently small to render particle lag errors negligible. a burst-mode laser (quasimodo-1000, spectral energies, llc) with both diodeand flashlamppumped nd:yag amplifiers was used to produce a high-energy pulse train at 532 nm. the pulse-burst laser generates a burst of maximum duration 10.2 ms once every 8-12 seconds with a maximum repetition rate of 500 khz. in the original postage-stamp piv configuration, it was operated to deliver single pulses at 400 khz with an energy of about 8 mj per pulse at 532 nm, creating a time between successive pulses of 2.5 µs. the laser sheet was narrowed to a slender width of perhaps 1 cm to concentrate the available energy and had a sheet thickness of 1 mm. a total of about 150 bursts of data were acquired. images were acquired using high-speed cmos cameras (photron sa-z) which have an array of 1024 × 1024 pixels at a full framing rate of 20 khz. when operated at 400 khz, they were windowed down to a small array of only 128 × 120 pixels; hence the use of the term “postage-stamp piv.” two-component measurements are shown in the present work using a single camera equipped with a 200-mm focal length lens and anti-peak-locking diffuser plates [9]. data were processed using lavision’s davis v8.3.1 or v8.4.0. in each case, image pairs were background corrected, intensity normalized, and then interrogated with an initial pass using 64 × 64 pixel interrogation windows, followed by two iterations of gaussian-weighted 24 × 24 pixel interrogation windows. a 50% overlap in the interrogation windows was used as well. the resulting vector fields were validated based upon signal-to-noise ratio, nearest-neighbor comparisons, allowable velocity range, and a median filter in both space and time. mhz-rate postage-stamp piv measurements since the original postage-stamp piv measurements were published, ix cameras released the model ix 726, which is capable of reaching a framing rate of 1 mhz with windowed arrays similarly to the photron sa-z that was used previously. the ix 726 also is a cmos camera, in this case with a native resolution of 2048 × 1536 digitized at 12 bits. unfortunately, the ix 726 cannot be windowed effectively in an approximately square aspect ratio as can the sa z. to achieve its high framing rate, the design of the horizontal shift register leaks charge between rows when the horizontal resolution is decreased to small values. although the ix 726 can operate in a nearly square aspect ratio of 112 × 108 pixels at 1 mhz, it creates serious ghosting problems in the image. these artifacts can have damaging consequences to piv accuracy when cross-correlations are computed between frames to determine velocity vectors. as the horizontal dimension is increased, the charge leakage and ghosting problems diminish. for the present experiments, the camera was operated in one of two modes, either 336 × 42 pixels or 504 × 30 pixels. the consequences of both the long aspect ratio of the images and the residual charge leakage both are examined as part of the present study. in addition, the ix 726 has a rigid limit of 1 mhz framing rate in its trigger pulse counter. due to small discrepancies and phase differences between clocks when operating at 1 mhz, it tends to drop frames occasionally and therefore contaminate the image sequences. for this reason, it must be operated at slightly less than 1 mhz. resolution limitations on the timing pulse generator used for the pulse-burst laser made 990 khz a sensible choice for a pulse rate compatible with both the camera and the laser. these measurements are still termed “mhz-rate” as they are within a small rounding error of 1 mhz. the pulse-burst laser was modified slightly to produce pulse frequencies of 990 khz and still achieve adequate laser pulse energy. this was accomplished by shortening the seed pulse duration from 10 ns to 4 ns and by using a tighter telescope to focus the beam on the second-harmonic generator. both of these modifications improved the conversion efficiency of the doubling process and achieved 5.5 mj per pulse at 532 nm. the laser was operated for 10.2 ms duration bursts, with 12 seconds required between bursts to dissipate heat sufficiently to maintain reasonable beam quality burst-to-burst. it should be noted that other very-high-speed cameras exist, such as the shimadzu hpv-x2, which can reach framing rates of 10 mhz, and the kirana from specialized imaging, which can reach 5 mhz. however, these cameras can only acquire sequences of 256 and 180 images, respectively. such short record lengths are not suitable for obtaining frequency spectra with a broad range of scales. although they potentially could be used to measure just the high-frequency spectral regime as a supplement to previous postage-stamp piv measurements, a very large quantity of image sequences would be required to achieve reasonable convergence of the high-frequency spectra. in combination with the low duty cycle of the pulseburst laser and the low duty cycle of the blowdown wind tunnel, acquisition of sufficient image sequences is impractical. for this reason, such cameras were deemed inappropriate to the spectral goals of the postagestamp piv measurements. experimental results previous 400-khz postage-stamp piv measurements the field of view for the postage-stamp piv is shown in fig. 1. the full extent of the jet-in-crossflow experiment is given using conventional 10-hz piv [10], with the vertical component of the mean velocity field shown positioned in its far-field location. superposed are the fields of view for both the 25-khz pulseburst piv described in [1] and the postage-stamp piv [2]. the small size of the postage-stamp piv window is evident, little more than a point measurement. this measurement will reveal little about the structure of the flow given its minimal extent, but this is a necessary sacrifice to achieve the very high framing rate that can yield high-frequency spectral content. the power spectra of the velocity fluctuations that are measured by the two-component postage-stamp piv are shown in fig. 2. in the present case, the properties of the jet interaction change very little within the far-downstream field of view and it suffices to examine the spectra at a single point near the center of the field of view where no edge effects interfere with computing correlations as particles may exit the field of view. slopes for -1 and -5/3 power law dependencies are provided as well. also shown are spectra for the interpolated time series, which will be described subsequently. for both velocity components in fig. 2, the spectral content of the flow is visible to high frequencies until the noise floor intrudes at about 120 khz. the vertical component of the spectra peak at 4 khz, which corresponds to one full period between pairs of turbulent eddies convecting through the flow [11]. following the peak, the spectra then exhibit a -1 slope dependence to about 60-70 khz before gradually fig. 1: field of view of the 25-khz pulse-burst piv and the postage-stamp piv measurement within the larger jet-in-crossflow experiment superposed on a conventional piv mean vector field. transitioning to an apparent -5/3 slope dependence. the presence of the -5/3 region is well-known and expected as a consequence of the inertial subrange of turbulence decay (e.g., pope [12]). the -1 dependence, on the other hand, is an unanticipated discovery and lasts for at least one full decade, from approximately 4 – 60 khz. it is discussed in more detail in [2]. the streamwise component also appears to be supportive of a -1 slope dependence but its lack of a peak means this region does not initiate until about 8 khz. the -5/3 slope dependence at high frequencies is somewhat less convincing for the streamwise component than for the vertical component. this is because the overall intensity of the streamwise velocity fluctuations is reduced compared to the vertical velocity fluctuations, and therefore the impact of the noise floor is felt sooner. mhz-rate camera performance improving technologies in high-speed cameras recently have produced the ix 726, which can reach mhz rates using approximately the same pixel count as in the previous experiments. the advantage of a mhz-rate postage-stamp piv system is not immediately obvious in that it cannot be expected to reduce the noise floor. in fact, it is understood that the noise actually is increased for such faster data transfers. but the increased framing rate will oversample the data for the frequencies of interest in the flow and therefore a conventional image-pair correlation to produce velocity vectors is no longer required to maintain frequency response. instead, multiple-frame image interrogation may be used, of which a number of algorithms have been developed [13-19]. the increased accuracy of these methods should lower the noise floor and therefore reveal higher-frequency content even well short of the nyquist frequency of 500 khz. however, the ix 726 camera leaks charge through the shift register as a consequence of its mhz-rate capability. this tends to smear out the subject matter being viewed; for piv images, this will create ghost particles. for the desired aspect ratio near unity, a field of view of 112 × 108 pixels is possible at 1 mhz. figure 3 shows the effect of the charge leakage when viewing a resolution target; the unadulterated image is shown in fig. 3a extracted from a full field of view at slower acquisition whereas fig. 3b shows the distorted image due to the small image. clearly, this is not a viable configuration for successful imaging. the degree of shift leakage is dominantly a function of the horizontal dimension of the image. however, to maintain the required 1 mhz framing rate, the vertical dimension must be reduced to compensate. a 336 × 42 pixel field of view of the resolution target is shown in fig. 3c and exhibits much less shift leakage than the 112 × 108 pixel field of view, though it is still present. for a 504 × 30 pixel field of view, the shift leakage is nearly negligible but the vertical dimension is becoming untenably small; this image is not shown. treating the shift leakage requires use of a high-aspect-ratio field of view rather than an approximately square field of view as in the 400-khz postage-stamp piv measurements. however, this has two consequences that are detrimental to piv measurements. first, even aligned with the dominant convective direction, this presents the possibility of numerous particles leaving the field of view and increasing the measurement noise due to their loss. worse, a bias error may occur if the most energetic motions, or the most vertically aligned motions, are selectively lost. second, even with these high-aspect-ratio images, some amount of charge will leak between rows. this creates ghost particles in the images, which also can increase measurement noise and may create biases in the correlation peaks if the ghosts occur selectively in one direction. in fact, these ghost particles do occur aligned to the vertical direction because the leakage occurs across entire horizontal rows, mirrored above or below. the impact of both of these image features on piv data quality must be tested. fig. 2: 400-khz postage-stamp piv power spectra of velocity fluctuations for the jet in crossflow for both streamwise and vertical components [2]. first, the characteristics of the shift leakage must be identified. to accomplish this, sequences of images of particles suspended in ambient room air were acquired for both 112 × 108 pixel and 336 × 42 pixel fields of view. autocorrelations were found of the images and then averaged over each sequence, with the results given in fig. 4 both as two-dimensional fields and as profiles sliced through the center of the correlation peaks. figure 4 shows that the ghosting occurs very repeatably spaced every third row. this is true for both fields of view (and others tested, though not shown). no ghosting displacement is observed along the x axis. the correlation magnitudes of the ghost peaks are considerably weaker for the 336 × 42 pixel case than for the 112 × 108 pixel case. in addition, tests have shown ghosting always occurs towards the horizontal centerline of the image. this can be observed in close inspection of fig. 3c. but no ghosting occurs within a six-pixel core of the image where no shifting of charge is required prior to readout. magnitudes of the ghost images cannot be effectively determined by autocorrelations. instead, images were acquired on the benchtop from grids of narrow lines or small dots, from which the ghost patterns were well separated and their intensities easily measured. by altering the lighting, the ghost intensity could be tracked as a function of image intensity and a relationship defined between the signal and ghost intensities. this relationship is shown in fig. 5 for the 336 × 42 pixel field of view. fourteen different cases are included in which the imaged lines or dots were located at different rows of the camera image, but no pattern could be found as a function of position on the camera array. still, the data points scatter reasonably closely around a linear fit and this was used to define the intensity of ghost images. two effects needed to be captured by simulations of shift leakage. first, the effect of particle dropout through the narrow vertical extent of the images must be examined. and secondly, the presence of ghost particles upon the velocity data must be tested. rather than generating synthetic piv images, the actual piv images from the 400-khz data set were modified to simulate the effects of shift leakage. this allowed tests upon real piv data and reduced the risk that the simulations may miss some relevant feature. the 128 × 112 pixel images native to the 400-khz data simply were cropped top and bottom to reduce them to a narrow vertical extent, then reprocessed through the piv interrogation algorithm and compared to the original spectrum. the two image sizes tested in the present work at 990 khz were 336 × 42 pixels and 504 × 30 pixels, so these two vertical extents were simulated from the 400 khz data as well. figure 6a shows the results. the impact of a narrower image is seen only in an elevated noise floor at the highest frequencies, which is emphasized in the magnified scale of the inset plot. the noise floor rises just a little when cropped to a 42-pixel extent and rises somewhat further when cropped to 30 pixels. this is indicative of a greater number of particles departing the images in the narrower field of view. it also may reflect greater uncertainty when warping the narrow image between interrogation iterations where less information is available along a given axis. regardless, a major impact to the spectrum is not observed and suggests that a significant problem is not posed by the size of the long, narrow field of view necessitated by the ix 726. (c) (a) (b) fig. 3: image distortion of a resolution target due to charge leakage through the shift register of the ix 726. (a) uncorrupted image (extracted from larger image) for a 112 × 108 pixel field of view; (b) shift leakage for a 112 × 108 pixel f.o.v.; (c) shift leakage for a 336 × 42 pixel f.o.v. (a) fig. 4: autocorrelations of particle fields showing patterns of image ghosting; both twodimensional fields and one-dimensional slices through the x=0 line are provided; (a, b) 112 × 108 pixel field of view; (c, d) 336 × 42 pixel field of view. (c) (d) (b) fig. 5: ghost intensity vs signal intensity on the ix 726 camera. fourteen different camera rows are represented by the various data points but no trend between them was identified. also shown in fig. 6a is a spectrum that crops the images to a 42-pixel extent and adds simulated ghosting. ghosting was implemented by copying every particle outside the six-pixel centerline of the image, multiplying it by the image intensity relationship found in fig. 5, then adding the resulting intensity to a pixel shifted three rows towards the centerline. this was performed on every image of every burst in the data set, then interrogated again for velocity vectors. no special analysis or additional vector validation was used to account for the ghost correlation peak. as fig. 6a shows, the noise floor is elevated from the spectrum that is only cropped to 42 pixels but otherwise no distortion to the spectrum is created that would be indicative of a bias. from this, it is concluded that the shift register leakage adds noise but the camera is still serviceable for piv. at least, this conclusion is valid for the present flow, which is dominated by convection. the mean displacement of the flow is 12 pixels in the streamwise direction, with the smallest instantaneous displacement still more than half that value. therefore, the signal correlation peak can be expected to always remain distant from the ghost correlation peak lying three pixels above or below the zerodisplacement point. might the ghost correlation interfere with the velocity measurement if the flow motion at some point in time is nearly three pixels vertically? to answer this question, a flow would need to be tested with the ix 726 in an experimental configuration that induced particle displacements of three pixels vertically. alternatively, to avoid crafting an experiment merely to answer this question, the simulated camera behavior was modified to suit the flow behavior for the present jet in crossflow. the ghost displacement was assumed to be 12 pixels in the horizontal direction rather than three pixels in the vertical direction, but otherwise exhibiting the same behavior as already observed. thus an interference from the ghosting may be tested. these results are given in fig. 6b. five different displacements were tested: 10, 11, 12, 13, and 14 pixels; this allowed a study of the sensitivity of the spectrum to the proximity of a ghost correlation peak. the latter two cases are omitted from the plot because they were found to be indistinguishable from the first two cases. when the ghost particles are near the mean flow displacement but not directly overlapping it (10and 11-pixel ghosting) the noise floor is raised modestly but to a level less than that from a threepixel ghost displacement. the noise probably falls below that of three-pixel ghosting because fewer ghost particles are present in an interrogation window when the ghost displacement is large. when the ghost particle displacement exactly matches the integer mean flow displacement (12-pixel ghosting), the noise floor rises further and exceeds that found from any other simulation. nonetheless, this elevated noise is still relatively modest and importantly, no distortions to the spectrum are found that might be indicative of the presence of the ghost particles biasing the correlation. in short, the ghost particles do not “pull” the (a) (b) fig. 6: power spectra from vertically cropped images of the 400-khz postage-stamp piv to simulate the ix 726 camera aspect ratios, as well as simulated ghosting due to shift register leakage. correlation to a fixed value that alters the spectrum. this indicates that even for flows in which the measured motion intersects with the ghosting due to shift leakage, the impact on the spectrum is mild and the ix 726 camera remains useful for piv. as a final note, the tests of the ix 726 camera described here were conducted in 2019. since then, manufacturer enhancements to the camera may have improved its performance in comparison to the present reported results. in addition, even newer camera models, by this manufacturer and others, promise improved performance at ultra-high speeds. nonetheless, the present tests indicate that some leakage of charge in the shift register and a narrow image aspect ratio need not prevent viable piv measurements. mhz-rate piv results once the ix 726 camera was confirmed to be suitable for piv despite its aspect ratio and shift register leakage, measurements were acquired of the jet-in-crossflow interaction. at 990 khz and the 10.2-ms burst duration from the laser, about 10,100 frames were acquired per burst. four bursts could be acquired per wind tunnel run and a little more than 30 tunnel runs were conducted for each of the 336 × 42 pixel and 504 × 30 pixel fields of view. the mhz-rate postage-stamp piv spectra are shown in fig. 7 using the 336 × 42 field of view and are compared to the earlier 400-khz spectra. at first glance, it does not appear that the mhz-rate data represent an improvement over the 400-khz data. the noise floor actually is slightly higher from the mhz-rate data as a consequence of the narrow vertical extent and the particle ghosting as demonstrated in the previous sub-section (as well as the increased camera noise when transferring charge so rapidly). though excluded from fig. 7 for clarity, spectra acquired from the 504 × 30 field of view overlay the 336 × 42 spectra that are shown save that the noise floor is slightly higher, as predicted by fig. 6. despite the modestly elevated noise floor, the mhz-rate data offer an important advantage: the increased framing rate provides oversampled data with respect to the frequencies of interest. this allows application of multi-frame interrogation algorithms. several different algorithms have been explored, but the pyramid correlation offers the most flexibility and accuracy [14]; results from it are added to fig. 7. this algorithm functions by ensemble-averaging the correlation over multiple frames to improve its precision. the number of frames and their temporal separation are chosen at each time step through the image sequence to optimize the dynamic range and signal-to-noise ratio. here, the pyramid correlation was conducted using n=5 frames and a maximum of two levels of correlations. other parameters also have been explored but are omitted because their spectra exhibited characteristics of low-pass filtering; the results shown in fig. 7 have proven most valuable. (a) (b) fig. 7: power spectra from the mhz-rate postage-stamp piv compared to the 400-khz postage stamp piv, including analysis using the pyramid correlation [14] for the mhz-rate data. (a) streamwise component; (b) vertical component. figure 7 shows that the noise floor is lowered by more than an order of magnitude when using the pyramid multi-frame correlation algorithm. with the greatly reduced interference from the noise floor, a region of roughly constant slope emerges for the v component in fig. 7b beginning at approximately 80 khz and extending perhaps to about 250-300 khz where the slope diminishes yet again. this latter effect appears to be the point at which the spatial resolution limit due to the size of the interrogation window begins to noticeably filter the data. for the previous 400-khz piv, this was estimated to be 220 khz [2]. the present camera configuration uses a magnification about 10% greater as compared to the previous 400-khz measurement, which reduces the spatial extent of an interrogation window and thereby raises its expected frequency response to 240 khz. similar effects are observed in the u component of fig. 7a. most encouragingly, the pyramid correlation analysis of the mhz-rate data aligns quite well with the interpolated 400 khz spectra up to its limit at 200 khz. the self-consistency suggests that both analysis methods are functioning well and returning valid spectra well beyond the previous effective frequency limit of about 120-130 khz. the slope beyond 70 khz in both plots of fig. 7 is steeper than that predicted by the -5/3 theory, but as noted earlier, this may be because the turbulent fluctuations have not yet reached isotropy. in the high frequency range where onset of the inertial subrange may be expected, from about 70 khz to perhaps 150 khz, it can be seen that the spectrum for v has a larger magnitude than for u; therefore, the flow is not yet isotropic and a key assumption of the theoretical -5/3 slope has been violated. therefore, the -5/3 slope of theory may not be descriptive of the present flow. furthermore, strictly speaking, the -5/3 relationship of the inertial subrange was derived from wavenumber theory rather than the frequency-space acquisition common to time-series data. in fact, quite a number of studies both experimental and computational have established that even within the high-frequency range associated with the inertial subrange, anisotropic behavior may be found as well as intermittent behavior due to small-scale coherent structures passing through the flow. as a consequence, the power-law slope has been found in some cases to deviate from the theoretical -5/3 value. a lengthier discussion may be found in [4]. further validation of the multi-frame correlation techniques is warranted prior to stating high-frequency power-law behavior with confidence. the pyramid correlation has been shown to be more accurate than conventional two-frame correlation or a fixed-interval multi-frame correlation on a point-by-point basis [14], but its accuracy has not been evaluated in the spectral domain. initial steps in this direction offer a note of caution that low-pass filtering effects in multi-frame algorithms may be difficult to distinguish from creditable flow physics [20]. at this juncture, the mhz-rate piv indicates that the inertial subrange powerlaw likely is steeper than -5/3, consistent with a number of low-speed studies, but the precise scaling law is not yet definitive. particle response the elevated frequency response of the mhzrate piv is only helpful if the particle response time can match it. in situ measurements of the particle response time have established a frequency response of 500-700 khz, but application of melling’s analysis [21] or mei’s analysis [22] suggest the limitation may be 200 khz or less when the energy contributions of fluctuations are considered. this is demonstrated in fig. 8, which reproduces melling’s fig. 3 and is annotated for conditions in the present experiment. based on the measured particle size and flow characteristics, a curve representing the actual particles in the present flow is superposed. mei suggests an appropriate, if semi-arbitrary, choice of frequency cutoff is that at which the energy response of the velocity fig. 8: melling’s fig. 3 [21] of particle response time and velocity fluctuation sensitivity, annotated for conditions in the present experiment. fluctuations falls to 50%. this is marked by the brown line in fig. 8 and corresponds to a frequency limit of 100 khz; beyond this point, the measurements will lose sensitivity to the velocity fluctuations. this suggests the present mhz-rate measurements do not possess adequate particle response to achieve the measurements of behavior in the inertial subrange. however, the intensity of velocity fluctuations at these high frequencies and small scales is much less than the maximum velocity fluctuations of the flow as a whole. this means such fluctuations contain considerably lower energy and do not require the same particle response to measure them. examining any of the spectra presented herein, it can be seen that the energy at 100 khz and above is at least an order of magnitude reduced from the peak energy of the flow. re-examining fig. 8, if only 10% of the peak energy must be measured, a higher frequency response is achieved. this is shown by the green line, suggesting that a particle frequency response of 1 mhz is possible should they need only measure velocity fluctuations of 10% of the peak. therefore, the present measurements can achieve the superior particle response required for high-frequency content. conclusions the effective frequency limits of postage-stamp piv, in which a pulse-burst laser and very small fields of view are combined to achieve high repetition rates, have been extended from the previous 400-khz measurements to very nearly mhz rates (990 khz). this never previously has been accomplished in a manner that can yield spectral content. the mhz-rate measurement is achieved using a faster camera, but to achieve these framing rates it leaks charge through the shift register. to minimize this effect, it must be operated with a high aspect ratio. existing piv images were modified to simulate the camera performance. their analysis established that the narrow vertical extent of the images and the ghost particles due to residual charge leakage both add a tolerable degree of noise to the measurements, but neither introduces any bias errors into the spectra. the increased framing rate provided oversampled data and enabled use of multi-frame correlation algorithms for increased measurement precision and a lower noise floor. the pyramid correlation increased the effective frequency response to at least 240 khz, at which point the finite extent of the interrogation window is estimated to begin spatially filtering the data. particle response time also was shown to be sufficient to measure velocity fluctuations at these very high frequencies. the measured velocity spectra reveal the power-law scaling of the turbulence as the flow reaches the inertial subrange, suggestive of scaling steeper than the theoretical -5/3 scaling. this is attributed to an absence of isotropy even in this high frequency range, which is a requirement of the -5/3 theory but is known not to be universally present in turbulent flows. the present very-high-frequency measurements establish the power of “postage-stamp piv” to reveal turbulence scaling laws for compressible flows. acknowledgements the authors would like to thank todd rumbaugh and drew l’esperance of hadland imaging for their assistance with the ix 726 camera. the authors also would like to thank john henfling, recently retired from sandia, for his contributions to earlier phases of this effort that made the present data possible. sandia national laboratories is a multi-mission laboratory managed and operated by national technology and engineering solutions of sandia, llc., a wholly owned subsidiary of honeywell international, inc., for the u.s. department of energy’s national nuclear security administration under contract de-na0003525. references [1] beresh, s. j., kearney, s. p., wagner, j. l., guildenbecher, d. r., henfling, j. f., spillers, r. w., pruett, b. o. m., jiang, n., slipchenko, m., mance, j., and roy, s., “pulse-burst piv in a high-speed wind tunnel,” measurement science and technology, vol. 26, no. 9, 2015, pp. 095305. [2] beresh, s. j., henfling, j. f., and spillers, r. w., “postage-stamp piv: small velocity fields at 400 khz for turbulence spectra measurements,” measurement science and technology, vol. 29, no. 3, 2018, pp. 034011. [3] beresh, s. j., “denoising 400-khz ‘postage-stamp piv’ using uncertainty quantification,” aiaa paper 2018-2034, january 2018. [4] beresh, s. j., spillers, r. w., soehnel, m. m., and spitzer, s. m., “extending the frequency limits of ‘postage-stamp’ piv to mhz rates,” aiaa paper 2020-1018. [5] scarano, f., and moore, p., “an advection-based model to increase the temporal resolution of piv time series,” experiments in fluids, vol. 52, no. 4, 2012, pp. 919-933. [6] wernet, m. p., and opalski, a. b., “development and application of a mhz frame rate digital particle image velocimetry system,” aiaa paper 2004-2184, january 2004. [7] brock, b., haynes, r. h., thurow, b. s., lyons, g., and murray, n. e., “an examination of mhz rate piv in a heated supersonic jet,” aiaa paper 2014-1102, january 2014. [8] willert, c. e., “’profile piv’ – more than just an optical hotwire: new potentials of piv in boundary layer research,” 18th international symposium on flow visualization, zurich, switzerland, june 26-29, 2018. [9] michaelis, d., neal, d. r., and wieneke, b., “peak-locking reduction for particle image velocimetry,” measurement science and technology, vol. 27, no. 10, 2016, pp. 104005. [10] beresh, s. j., henfling, j. f., erven, r. j., and spillers, r. w., “penetration of a transverse supersonic jet into a subsonic compressible crossflow,” aiaa journal, vol. 43, no. 2, 2005, pp. 379-389. [11] beresh, s. j., wagner, j. l., henfling, j. f., spillers, r. w., and pruett, b. o. m., “turbulent eddies in a compressible jet in crossflow measured using pulse-burst particle image velocimetry,” physics of fluids, vol. 28, no. 2, 2016, pp. 025102. [12] pope, s. b., turbulent flows, cambridge university press, 2000, pp. 228-242. [13] hain, r., and kähler, c. j., “fundamentals of multiframe particle image velocimetry (piv)”, experiments in fluids, vol. 42, no. 4, 2007, pp. 575-587. [14] sciacchitano, a., scarano, f., and wieneke, b., “multi-frame pyramid correlation for time-resolved piv,” experiments in fluids, vol. 53, no. 4, 2012, pp. 1087-1105. [15] lynch, k., and scarano, f., “a high-order time-accurate interrogation method for time-resolved piv,” measurement science and technology, vol. 24, no. 3, 2013, pp. 035305. [16] haynes, r. h., brock, b. a., and thurow, b. s., “application of mhz frame rate, high dynamic range piv to a hightemperature, shock-containing jet,” aiaa paper 2013-0774, january 2013. [17] meinhart, c. d., wereley, s. t., and santiago, j. g., “a piv algorithm for estimating time-averaged velocity fields,” journal of fluids engineering, vol. 122, no. 2, 2000, pp. 285-289. [18] westerweel, j., elsinga, g. e., and adrian, r. j., “particle image velocimetry for complex and turbulent flows,” annual review of fluid mechanics, vol. 45, 2013, pp. 409-436. [19] scarano, f., bryon, k., and violato, d., “time-resolved analysis of circular and chevron jets transition by tomo-piv”, 15th international symposium on applications of laser techniques to fluid mechanics, lisbon, portugal, 2010. [20] beresh, s. j., neal, d. r., and sciacchitano, a., “validation of multi-frame piv image interrogation algorithms in the spectral domain,” aiaa paper 2021-19, january 2021. [21] melling, a., “tracer particles and seeding for particle image velocimetry,” measurement science and technology, vol. 8, no. 12, 1997, pp. 1406-1416. [22] mei, r , “velocity fidelity of flow tracer particles,” experiments in fluids, vol. 22, no. 1, 1996, pp. 1-13. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 dense flow field interpolations from ptv data in the presence of generic solid boundaries bora o. cakir1,2∗, gabriel gonzalez2, andrea sciacchitano2, bas van oudheusden2 1 von karman institute for fluid dynamics, turbomachinery and propulsion department, sint-genesius-rode, belgium 2 delft university of technology, faculty of aerospace engineering, delft, the netherlands ∗ bora.orcun.cakir@vki.ac.be abstract three-dimensional flow measurements by particle tracking velocimetry (ptv) provide scattered flow information, that often needs to be interpolated onto a regular grid. therefore, the use of experimental data assimilation approaches such as vic+ (schneiders and scarano, 2016) were proposed to enhance the instantaneously available spatial resolution limits beyond that of the ptv measurements. nevertheless, there exists no prior attempt to perform the data assimilation when the flow is in direct contact with physical objects. thus, in order to handle generic solid body intrusions within the flow fields of vic+ application, the utilization of arbitrary lagrangian-eulerian and immersed boundary treatment approaches of the computational fluid-structure interaction (fsi) frameworks are proposed. the introduced variants over the standard vic+ are assessed with a high fidelity numerical test case of flow over periodic hills. the accuracy superiority of the flow field reconstructions with the proposed approaches are denoted especially in close proximity of the interaction surface. an experimental application of the introduced methods is demonstrated to compute the pressure distribution over an unsteadily moving elastic membrane surface, revealing the time-resolved interaction between the flow structures and the membrane deformations. 1 introduction tomographic piv (tomo-piv) (elsinga et al., 2006) allows acquisition of flow information over a three dimensional measurement domain. however, tomo-piv measurements are accompanied by stringent limitations on the maximum achievable measurement volume due to the dispersed intensity of light illumination, limited light scattering performance of tracer particles and resolution characteristics of recorded images (tokarev et al., 2013). accordingly, introductory applications of tomo-piv were performed in a volume of 13 cm3, while the maximum measurement volume size achieved with micrometric tracer particles is documented to be 6×22×8 cm3 where the acceptable signal-to-noise ration distribution already limited the effective depth to 5 cm (fukuchi, 2012). hence, in order to enable large scale applications of tomo-piv experiments, the use of neutrally buoyant helium filled soap bubbles (hfsb) as tracers for piv experiments was proposed (scarano et al., 2015; caridi et al., 2016). their controllable larger size and density, provided a great opportunity of achieving suitable flow tracing qualities and superior light scattering characteristics. nevertheless, exploiting large scale ptv techniques, the limited production rate and seeding rate of the hfsb restrict the concentration of tracer particles within the measurement domain which in turn alleviates the instantaneously available spatial resolution. thus, the reliability and accuracy of volumetric reconstruction might be compromised. considering the spatial scarcity of hfsb particles, employing a particle tracking approach enables a greater level of accuracy in terms of determining particle location, velocity and acceleration. however, the data obtained from ptv results in a scattered formation over the measurement domain. although linear interpolation of scattered data might resolve the problem of increasing the spatial resolution of fluidic information, the independency of this approach from statistical or physical characteristics of the flow in measurement would comprise significant numerical errors that results in incoherent and unphysical flow structures. therefore, advanced interpolation methods are required for increasing the spatial resolution of the available experimental data which would provide greater accuracy and physical coherence of the dense flow field information. accordingly, multiple interpolation frameworks were developed based on the statistical formulations of various spatial averaging and data fitting approaches. the adaptive gaussian windowing (agw) proposed by agui and jimenez (1987), captures the scattered information in a measurement volume on a predefined grid using a gaussian weight averaging over the windows of euclidean distances defined with respect to the grid location of interest. furthermore, gaussian windowing is further elaborated on using gaussian radial basis functions (rbf) in which casa and krueger (2013) utilized an iterative optimization procedure to obtain the best fit of data interpolation on a grid structure with respect to the original scattered data. on the other hand, more convoluted approaches in the context of incorporating the physical description of fluid dynamics to the interpolation procedure. (gesemann et al., 2016) introduced the use of 3d cubic bsplines for increasing signal-to-noise ratio of particle information reconstruction over particle velocity and accelerations. the method includes two main steps referred to as trackfit and flowfit. trackfit initiates the reconstruction algorithm with a noise reduction of the particle intensity signals. then, 3d b-splines are calculated for velocity and acceleration (or pressure) information by minimizing a cost function while enforcing divergence free field constraints for incompressible flows. another application of flow physics based experimental data assimilation is introduced by schneiders et al. (2015) where the temporal information is used to enrich the spatial information for elevated accuracy of flow field reconstruction at higher spatial resolution levels. the resultant vic+ method, utilizes the vortexin-cell (vic) model presented by christiansen (1973) for coupling vorticity and velocity field information of the fluid of interest enabling the representation of the fluid behavior on a global sense over the prescribed computational domain, provided that appropriate boundary conditions are imposed. moreover, the vorticity transport equation allows the computation of local time derivative component for the lagrangian acceleration term only by means of velocity and vorticity fields via eliminating the contribution of pressure gradients. hence, vic+ also provides an opportunity to increase the resolution of material derivative information as its optimization procedure is based on maximizing the proximity of not only the velocity vectors to the measured values but also the accelerations (schneiders and scarano, 2016). although vic+ and its variants are proven to be successfully increasing the spatial resolution of flow field information using scattered measurement data on uniformly structured computational grids, their applicability is restricted to purely fluidic domains. however, most practical engineering applications are influenced by dynamic aeroelastic behaviors which contain non-uniform solid boundaries that might deform unsteadily owing to their interaction with the fluid medium. thus, computation of fluid information in presence of curved walls or solid objects (stationary or moving) introduces significant drawbacks in terms of numerical accuracy and appropriate surface definition for implementation of adequate boundary conditions. without proper definition of those solid boundaries, the accuracy of determining the corresponding fluid behavior is further downgraded as the information transfer between fluid and solid domains strongly depend on the interface description where the surface loading exerted by the flow and the boundary shape are in an interactive relationship (dowell, 2004). more recently proposed methods for managing non-uniform solid intrusions, separate the computational domain in to multiple regions in which close surface locations are handled by varying the integration direction. although these methods provide accurate results in comparison with the extrapolation techniques, the improvements are associated with increased levels of complexity and computational cost. therefore the current study introduces two approaches for providing vic+ algorithm with the capability of performing data assimilation in presence of solid boundaries by implementing the well known computational fsi frameworks of arbitrary lagrangian-eulerian (noh, 1963) and immersed boundary treatment methods (peskin, 1982). 2 methodology two main approaches, named arbitrary lagrangian-eulerian vic+ (ale-vic+) and immersed boundary vic+ (imvic+), are proposed to handle the solid boundary effects for vic+ applications. boundary fitted coordinate systems and mesh adaption procedures are employed in ale-vic+ approach, whereas in imvic+ method the immersed boundary treatment is utilized to satisfy the appropriate boundary conditions while preserving uniform mesh formations. 2.1 arbitrary lagrangian-eulerian approach for vic+ in order to avoid the individual shortcomings of eulerian and lagrangian perspectives while leveraging from their respective advantages, a technique referred to as the arbitrary lagrangian-eulerian (ale) method is introduced by noh (1963), where both approaches are utilized in a coupled manner to handle both fluidic and structural domains. as the necessity of a coupled method emerges from the motion of boundaries enclosing the fluidic domain, the corresponding mesh structures are required be modified accordingly. hence, a natural approach can be considered as completely regenerating the grid structure at each time step. however, this process generally requires considerable user interaction and immense computational resources (luke et al., 2012). instead, grid deformation algorithms provide a valuable solution categorized under two main groups of physical analogy based (farhat et al., 1998; löhner and yang, 1996; helenbrook, 2003) and interpolation based schemes (wang and przekwas, 2012; jones and samareh-abolhassani, 2012; liu et al., 2006). utilizing these various methodologies, there exists multiple applications of the ale method for vortex simulations based on the vic model, for cost-effective high-fidelity numerical simulations of fluidstructure interaction (fsi) problems. in this regard, cottet and poncet (2004) performed conformal mapping of the fluidic domain for three dimensional direct numerical simulations of wall bounded flows where the grid structure in close proximity of a sphere was fitted to the surface of the solid object for application of a hybrid particle-mesh vortex method. furthermore, kudela and kozlowski (2009) employed a boundary fitted coordinate system for flow simulations around arbitrary shaped objects using the vic framework during which fourth order interpolation kernels used by cottet and koumoutsakos (2000); sagredo and tercero (2003) are modified for particle-mesh switching of vorticity distributions in the near wall regions. conformal mesh ptv measurements fluid -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.038 0.04 0.042 0.044 0.046 0.048 0.05 0.052 initial velocity -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.038 0.04 0.042 0.044 0.046 0.048 0.05 0.052 final velocity ptv measurements structure 𝒖" 𝐷𝒖" 𝐷𝑡 figure 1: ale-vic+ reconstruction framework. the ptv measurements for the structural component is provided (purple box). the rectangular structured computational grid is deformed for boundary fitted coordinate generation (black box). the ptv measurements for the flow is provided (green box). an initial velocity estimate is made (gray box), which is input into vic+ iterative procedure (blue boxes) to find the optimization variables that yield a velocity and material derivative distributions of minimum discrepancy with the ptv measurements (orange box). employment of boundary fitted coordinate systems and their deformations for treating unsteadily deforming domains for vic+ applications is composed of two main steps; a computational grid is generated according to the surface information and the flow governing equations within vic+ framework are solved over the generated mesh structure. the algorithm is initiated by generating a conformal grid structure from the boundary shape definitions either known a priori or captured by means of optical measurement methods. after an initial boundary fitted grid structure is generated, the mesh is deformed according to the boundary motion so that the exact interaction between the fluidic and solid domains can be expressed in a time-resolved manner. in order to achieve a continuous boundary conformation, the choice of deformation scheme is determined as rbf based mesh deformations (de boer et al., 2007) due to their superior characteristics of mesh deformation accuracy and cost-efficiency (smith et al., 2000; beckert and wendland, 2001). the formulations employed for rbf based mesh deformation method utilized are described by (de boer et al., 2007) where a comparitive study over many variants of rbfs was conducted using two different mesh quailty metrics based on mesh size preservation and mesh skewness. among 14 different rbfs with compact and global supports, thin plate spline (tps) and cp c2 rbfs stood out both in terms of keeping the size alterations and skewness to a minimum whilst not compromising mesh adaptation efficiency. according to the presented results, cp c2 rbf is utilized to update the computational grid due to a superior performance of mesh deformations especially in close proximity of the immersed boundary surface. then, the flow governing equations on the updated conformal grid are solved by performing a oneto-one mapping between the physical and computational coordinate systems. the mapping relates to the transformation variables necessary for accurate description of mathematical operators constructing the link between the two grids. the physical coordinate system is selected as a cartesian one since the flow field properties are obtained from the piv/ptv measurements are already defined on a cartesian coordinate system. hence, the computational grid locations in any mesh form can be expressed as functions of the physical coordinate system variables, xc = xc(xp,yp,zp) yc = yc(xp,yp,zp) zc = zc(xp,yp,zp) (1) where subscript c and p, refer to the physical and computational coordinates respectively. accordingly, the transformation variables defining the link between the two coordinate systems is represented by means of a jacobian matrix. therefore, the flow governing equations within vic+ method are described on the computational coordinates by transforming the vector variables utilizing the chain rule and the transformation matrix. jt = ∂(xc,yc,zc) ∂(xp,yp,zp) =  ∂xc ∂xp ∂xc ∂yp ∂xc ∂zp ∂yc ∂xp ∂yc ∂yp ∂yc ∂zp ∂zc ∂xp ∂zc ∂yp ∂zc ∂zp  (2) finally, as the orientation of velocity and acceleration vectors are preserved on the cartesian descriptions, the resultant flow properties of velocity and material acceleration values are linearly interpolated at the original particle locations for calculating the error between the dense flow field interpolation and the measurement data. following the exact procedure of adjoint gradient computation introduced for vic+, additional modifications are implemented to take into account the vector transformations between the physical and computational grid structures. hence, the gradients for the proceeding steps of the optimization are calculated and the optimization procedure is performed until a specified convergence criteria is achieved. 2.2 immersed boundary treatment approach for vic+ the vic framework introduced by christiansen (1973) allows the fast fourier transform (fft) based poisson solvers to be employed over a predefined computational grid (wu and jaja, 2013) allowing higher fidelity and resolution capabilities, while preserving the computational efficiency. as the fast poisson solvers are utilized to characterize the rotational component of velocity vectors, physical intrusions within the flow field are required to be handled employing additional velocity or forcing terms (peskin, 1982). therefore, the need for boundary fitted coordinate systems and introducing transformation operations between computational and physical coordinate systems is obliterated. accordingly, walther and morgenthal (2002) and cottet and poncet (2004) implemented integral boundary equations on the vic method in order to impose no-through and no-slip boundary conditions by means of surface singularities. however, defining no-through boundary condition over the penetrating velocity components results in an integral boundary equation which corresponds to an ill-posed fredholm integral equation of first kind. instead, the vortex sheet strengths are determined via the tangential velocity components yielding a fredholm integral equation of second kind (beale and greengard, 1994). furthermore, in order to obtain a unique solution for multiply connected regions, kelvins theorem of circulation conservation or kutta condition is introduced as an additional constraint (morgenthal and walther, 2007). implementation of the immersed boundary treatment for vic+ method is based on the theory of vector decomposition provided via the helmholtz theorem where the rotational component obtained from the vic method is superimposed with the potential flow component computed from the immersed boundary corrections. the numerical implementation of boundary integral equations for adequate description of boundary conditions over the interface surfaces is performed using the panel method introduced by hess and smith (1967). considering that the structural information is obtained by means of either one of the aforementioned approaches described for ale-vic+, the solid boundary surface is characterized by means of quadrilateral panels each equipped with singularity elements of sources and doublets to introduce a scalar potential influence of the physical intrusion. with singularity elements attached, the potential inductions of the quadrilateral panels are computed over the complete computational domain employing the formulations provided by katz and plotkin (2001). assignment of singularity elements ptv measurements fluid ptv measurements structure !! "!! "# calculate uw immersed boundary treatment for !! uh=uw+ !! figure 2: imvic+ reconstruction framework. the ptv measurements for the flow is provided (green box). an initial velocity estimate is made (gray box). the ptv measurements for the structural component is provided (purple box). surface elements are assigned with singularities (black box). the resultant velocity fields is used as an input into vic+ iterative procedure while velocity fields are corrected with immersed boundary treatment (blue boxes) to find the optimization variables that yield velocity and material derivative distributions of minimum discrepancy with the ptv measurements (orange box). initializing with a freestream velocity value, the corresponding vorticity strengths are utilized to compute the velocity distribution over the computational domain from the vic method. the calculated velocity field penetrates through the physical boundaries where the normal velocity components to each panel are equated to the relative source strengths (σi) of the corresponding panels in order to reduce the strengths of the dipoles (µi) for ensuring numerical uniqueness (tarafder et al., 2010). σi = ni ·vi (3) furthermore, since the self induced scalar potential should vanish at collocation points over a surface of singularities (lewis, 1991), the dipole strengths are calculated by constructing a linear system of equations that total sum of potential induction at the central locations of the quadrilateral panels equals to zero. n ∑ i=1 aiµi + n ∑ i=1 biσi = 0 (4) in order to establish a unique solution, the corresponding vortex rings (dipoles) are imposed to comply with the conversation of circulation while their strengths are being determined. the resultant overdetermined linear system is solved employing a least squares method (soifer, 2013). moreover, the scalar potential field induced by the surface singularities is differentiated in there dimensions to obtain the velocity vector components, uφ = 〈uφ,vφ,wφ〉= 〈 ∂φ ∂x , ∂φ ∂y , ∂φ ∂z 〉 (5) which are superimposed with the rotational velocity components to calculate the resultant velocity field distributions. u = uω +uφ (6) then, the corresponding velocity and vorticity fields are utilized to calculate the material derivative distributions over the computational domain in accordance to the inviscid navier-stokes formulation. finally, the cost function for the optimization procedure is determined over the error accumulation of velocity and material acceleration values at the original particle track locations in comparison to the measured data. for the optimization procedure, it is assumed, due to the dependence of the potential flow component to the rotational elements, that the errors directly relate to the vortex-in-cell base which is dictated by the vorticity distributions. hence, for each step of the optimization procedure, the gradient is calculated in terms of the vorticity strengths and the corresponding potential flow component is calculated to correct the velocity field distributions in order to satisfy the physical boundary condition of no penetration through the solid surfaces. 3 numerical assessment validation studies of the proposed methods are performed with a direct numerical simulation (dns) of flow over periodic hills (chen et al., 2014). the numerical simulations are performed with periodic boundary conditions connecting the inflow and outflow boundary conditions while the non-uniform surface contours of the hills are treated by means of an immersed boundary method to account for their influence over the fluidic domain. the inflow conditions are initiated with a non-dimensional uniform velocity distribution of u = 1 which corresponds to a hill height based reynolds number of reh = 10,595 as the non-dimensional kinematic viscosity is prescribed to be ν = 9.45× 10−5. u [-] 𝜀u [-] 0 1 2 3 x [-] 0 0.5 1 1.5 2 y [-] -0.5 0 0.5 1 1.5 u [-] a b a b a b a b a b figure 3: instantaneous non-dimensional streamwise velocity distribution over the z=0 plane with nondimensional streamwise vorticity isosurfaces of ωx = -10 (purple) and ωx = 10 (white) for the reference dns results (1st row). instantaneous non-dimensional streamwise velocity distribution over the z=0 plane with tri-linear interpolation, vic+, ale-vic+ and imvic+ (2nd row, from left to right). planar distributions of non-dimensional streamwise velocity reconstruction error magnitudes over the z=0 plane with tri-linear interpolation, vic+, ale-vic+ and imvic+ (3rd row, from left to right). in order to provide an accurate representation of scattered particle track information, the dns results are randomly downsampled with particle track concentrations of c=10 part/h3. the corresponding particle image density over the projected volumes obtained as np=0.012 ppp aiming slightly below the particle concentrations obtained during the experimental campaigns in section 4. stimulation of ptv data structure is achieved via a pseudo-particle tracking approach using a runge-kutta 4 time integration procedure (hwang et al., 2007). in accordance to the documented track lengths by schanz et al. (2016) for accurate extraction v [-] 𝜀v [-] w [-] 𝜀w [-] figure 4: instantaneous non-dimensional normal (left) and spanwise (right) velocity distribution over the z=0 plane for the reference dns results (1st row). instantaneous non-dimensional normal (1st column) and spanwise (3rd column) velocity distribution over the z=0 plane with tri-linear interpolation, vic+, ale-vic+ and imvic+ (2nd to 5th rows). planar distributions of non-dimensional normal (1st column) and spanwise (3rd column) velocity reconstruction error magnitudes over the z=0 plane with tri-linear interpolation, vic+, ale-vic+ and imvic+ (2nd to 5th rows). of velocity and acceleration values, the particle tracks are reconstructed with 7 particles. then a gaussian noise of 0.2 voxels in all three dimensions are artificially introduced to particle locations along the tracks to account for measurement and reconstruction errors. finally, the corresponding particle tracks are regularized with polynomials of order 2 to compute velocity and material acceleration properties. moreover, in order to model the scarcity of particles in the near wall region observed in experimental data sets, particle tracks within the close proximity of the wall are removed from the synthetic data (schneiders et al., 2017). to be able to demonstrate the improvements obtained with the proposed approaches over the state of the art of data assimilation, the standard vic+ method is also employed to perform the dense interpolation of the velocity and material accelerations. however, since the base algorithm of vic+ is not equipped with a capability of handling the non-uniform boundary, the grid locations corresponding to the solid domain are artificially modified to have zero velocity and material acceleration values to prevent numerical divergence of the optimization procedure. to start with the pure ptv approach where the agw is used to capture flow properties in close surroundings of each grid locations, the results failed to provide almost any fluidic information due to the lack of particles. hence, the corresponding need for an interpolation approach to reconstruct a coherent flow field description is addressed by linear interpolation, vic+, ale-vic+ and imvic+ approaches. the qualitative comparisons of velocity magnitude distributions reveals similar characteristics of overall coherence levels with the reference simulations in terms of identifying major flow structures (fig. 3, 2nd row). accordingly, the reconstructed streamwise velocity components using both linear interpolation and vic+ variants represent an accelerated flow behavior over the hill form (fig. 3, a) and a separation region with recirculating flow downstream (fig. 3, b). nevertheless, the detailed structures of local velocity magnitude variations are depicted with increased accuracy using vic+ variants as the separation effects are captured with greater agreement to the reference (fig. 3, a & b). furthermore, the major differences between the original vic+ and proposed variants are observed especially in close proximity of the hill surface. the peak fluctuation magnitudes are resolved with a greater agreement to the reference simulations by employing both ale-vic+ and imvic+ whereas the independency of vic+ from the relevant surface shape caused loss of accuracy close to the interaction interface that also propagated towards the regions away from the surface (fig. 3, 3rd row). 𝜀u [-] 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 figure 5: planar distributions of non-dimensional streamwise velocity reconstruction error magnitudes at 0.1h of the hill surface with tri-linear interpolation, vic+, ale-vic+ and imvic+ (from left to right). moreover, the superiority of vic+ variants over linear interpolation becomes even more apparent when the comparisons are performed over the secondary velocity components of normal and spanwise flow elements. in absence of a dominant flow behavior enforced by the immersed boundary form, reconstructions of secondary flow structures represent the ability of vic+ based approaches to resolve the fluidic behavior with greater detail by means of appropriate physical definitions (fig. 4, 1st and 3rd columns). the major differences between the original vic+ method and the proposed variants are again observed in close proximity of the hill surface. both ale-vic+ and imvic+ approaches provided reduction in reconstruction errors in comparison to reference data. however, the corrections due to immersed boundary treatment implemented by imvic+ have no influence on the spanwise velocity magnitudes (fig. 4, 3rd and 4th columns). considering the orientation of the surface elements designated for the hill form form, the fluid penetration through the hill surface is caused by the streamwise and normal velocity vector components. accordingly, the application imvic+ provides modifications to the flow properties within those directions to prevent unphysical flow peneration through the surface by ensuring the satisfaction of no-through boundary condition. hence, the resultant superposition of potential and rotational velocity fields does not impose any alterations on the spanwise velocity magnitudes which can be depicted when compared against the results of vic+. finally, the reduction in error levels gives further evidence of the improved accuracy with the application of ale-vic+ and imvic+, compared to both linear interpolation and the standard vic+. moreover, the dominant effect of the immersed boundary treatment is observed for the streamwise velocity components where decreased error levels in close proximity of the periodic hill surface refer to an elevated level of accuracy over the original vic+ application with the immersed boundary treatment (fig. 5). nonetheless, mitigation of error levels in close proximity of the hill surface denote improved accuracy of the dense flow field reconstructions as a result of the modifications implemented by imvic+. the observed modulations between the different methods tend to decrease significantly in regions away from the hill surface which is consistent with the theoretical formulations of surface singularities where the influence of singularity elements decay with the euclidean distance (fig. 3, 3rd row). 4 experimental assessment as a part of the holistic optical metrology for aero-elastic research (homer) european union h2020 project, the experimental setup employed in this work is designed to investigate fluid-structure kinematics of turbulent boundary layer-unsteady panel interactions where the experiments are conducted in a low-speed wind tunnel of tu delft high speed laboratory at a freestream velocity of 10m/s. the panel to be deformed is a square elastic membrane with sufficiently high moment of inertia to prevent any aeroelastic deformations and have full control over the membrane shape. a dc motor is connected to the center of the membrane by means of a gear and rod mechanism, and actuated at three different frequencies of 1 hz, 3 hz and 5 hz with an amplitude of 30 mm from valley to crest. the corresponding reduced frequencies obtained with the membrane motion of 1 hz and 3 hz are in the order of k ∼0.05 where a quasi-steady state can be assumed. however, the reduced frequency at 5 hz reaches to a level of k ≈0.1 and shall be considered within the unsteady aerodynamics regime (leishman, 2016). furthermore, a black foil with a regular grid of light-grey dots is applied to the upper face of the model to enable the structural displacement measurements by means of lagrangian particle tracking (lpt). a 120 cm long rigid plate with lego blocks located at 10cm from its leading edge is installed upstream of the model to ensure well-developed turbulent boundary conditions at the test section. the flow is seeded with hfsb tracers, which are inserted into the flow in the wind tunnel’s settling chamber via an in-house built seeding rake at rate of 2×106 bubbles/second. the image acquisiton is performed with three photron fastcam sa1.1 cmos cameras while the measurement volume is illuminated by means of three led light sources (lavision led-flashlight 300). finally, the experimental setup is equipped with two trustability board mount pressure sensors to provide reference static pressure values for comparisons against the results of non-intrusive surface pressure reconstruction algorithms. led blue light 𝑉! = 10𝑚/𝑠 𝑅𝑒 = 5×10" photron fastcam sa1.1 cmos figure 6: schematic representation (left) and photo (right) of the experimental setup for turbulent boundary layer interactions with unsteadily deforming elastic membrane. the acquired images are processed with the stb algorithm for lpt (schanz et al., 2016) using the commercial software package davis version 10.0.5 from lavision gmbh. then the particle tracks are reconstructed with a minimum length of 7 particles within consecutive images. for the computation of velocity and lagrangian acceleration information, a minimum number of 5 particles are selected for fitting a 3rd order polynomial for regularization of the particle motions in the temporal domain. as the membrane surface is equipped with tracer markers, surface markers possessed greater light intensities captured by the recording devices compared to the hfsb tracers of the fluid domain. therefore, sequential employment of low-pass and high-pass filters allowed the individual analysis of fluid and solid tracers respectively. the employed large-scale experimental setup resulted in a tracer particle concentration of c=100 par/δ99 where the thickness of the fully developed turbulent boundary layer just upstream of the membrane was recorded as δ99 =0.06 m. hence, with the corresponding image particle density of np=0.02 ppp, using the raw stb data becomes inadequate for capturing any relevant flow features. therefore, trilinear interpolation, vic+, ale-vic+ and imvic+ approaches are employed to increase the spatial resolution of fully time-resolved flow field information. furthermore, in order to enable a comparative analysis with the pressure tap readings, the pressure field over the densely interpolated flow field data is computed by relating the material accelerations to the static pressure distribution over the navier-stokes equation. the resulting pressure gradients are integrated by constructing a poisson equation while neglecting the viscous diffusion terms due to the low order of magnitude, o(10−5), of their influence for turbulent flow conditions. ∇ 2 p = ∇ · (∇p) = ∇ · ( −ρ du dt ) (7) then, the reconstruction of surface pressure over the non-uniformly deformed elastic membrane is performed utilizing two different approaches of an omni-directional integration procedure similar to the approach introduced by jux et al. (2020) and a reconstruction scheme with curvilinear transformations proposed by cakir (2020). the letter approach enabled direct computation of the surface pressure alongside the global pressure information without the need of external extrapolations. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t/t -40 -30 -20 -10 0 10 pr es su re [p a] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t/t -30 -20 -10 0 10 pr es su re [p a] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 t/t -40 -30 -20 -10 0 10 pr es su re [p a] 0 1 2 3 4 5 6 7 8 9 10 10 12 14 16 18 pressure tap linear interpolation vic+ ale-vic+ imvic+ figure 7: instantaneous pressure reconstruction of linear interpolation, vic+, ale-vic+ and imvic+ methods in comparison to the pressure tab measurements for 1hz (top), 3hz (middle) and 5hz (bottom) of unsteady membrane motion. comparing the surface pressure information reconstructed with four different approaches, the variations throughout the overall pressure profiles are observed to be relatively confined. nevertheless, both ale-vic+ and imvic+ enabled a greater agreement with the pressure tap measurements by minor improvements (fig. 7). three main reasons can be deduced for these minor variations in correlation with the validation studies. first of all, the spatial gradients of both velocity and pressure over the measurement domain are dominated by the controlled motion of the elastic membrane. hence, as motion frequencies of the membrane correspond to reduced frequencies of k < 0.1, these gradients can be reconstructed even with the linear interpolation without severe loss of accuracy. secondly, considering the assumption of zero pressure gradients within the turbulent boundary layers and the membrane motion, the dirichlet boundary condition dictates the high percentage of pressure variations in time. although there exists non-zero pressure gradients throughout the realistic boundary layers, these relate to pressure modulations in the order of 6∼8 pa while the absolute pressure difference captured at highest deformation state of the membrane is ∼30 pa. hence, the pressure variations aimed to be reconstructed with a superior accuracy by ale-vic+ and imvic+ correspond to ∼25% of the pressure modulation amplitude. lastly, the boundary conditions for vic+, ale-vic+ and imvic+ methods are determined via linearly interpolating the stb data over the corresponding boundaries. considering the close proximity of the dirichlet boundary condition of pressure reconstruction to the computational domain boundaries of vic+ variants, the differences between the various approaches in terms of the absolute pressure values are further alleviated. table 1: rms of instantaneous pressure reconstruction errors [pa] of linear interpolation, vic+, ale-vic+ and imvic+ for 1 hz, 3 hz and 5 hz of unsteady membrane motion. motion frequency 1hz 3hz 5hz linear interpolation 5.2 4.7 6.8 vic+ 4.9 5.1 5.3 ale-vic+ 2.1 2.1 4.1 imvic+ 2.1 2.1 3.6 nonetheless, there exits specific time instants where the differences between vic+ and the proposed variants are amplified with reconstruction errors up to∼70% of the pressure fluctuation amplitudes obtained using vic+. this is related to the extreme sensitivity of the standard vic+ method to the spatial distribution of the available particle tracking information. the absence of a proper boundary condition definition in close proximity of the elastic membrane, vic+ algorithm becomes strongly dependent on particles in the near wall regions to drive the optimization procedure towards an accurately solution which is a considerably rare situation in practical cases. therefore, ale-vic+ and imvic+ approaches provide the capability of accurately reconstructing the flow properties even in the cases of complete absence of particles in the near wall regions by providing a kinematic characterization of the solid boundary intrusions. the resultant accuracy improvements achieved by the implementation of ale-vic+ and imvic+ over linear interpolation and vic+ are also observed over the cumulative error levels over the pressure reconstruction profiles (tab. 1). 5 conclusions ptv techniques reveal scattered data structures that are required to be fitted on regular grids in order to analyze the measurement results. in case of large scale applications with the use of hfsb tracer particles, reduced particle concentration specifications further depletes the flow characterization capabilities of timeresolved data sets. however, the available governing equation based data assimilation techniques such as flowfit (gesemann et al., 2016) and vic+ schneiders and scarano (2016) enable dense volumetric interpolations of flowfield information for regions of uniform rectangular computational domains with sole fluid presence. in this regard, the introduced variants of ale-vic+ and imvic+ provide the standard vic+ algorithm with the capability of incorporating appropriate boundary condition definitions for dense flow field characterization in close proximity of solid objects with generic geometries. ale-vic+ method implements the ale method with an rbf based mesh deformation scheme to ensure the adaptability of the grid formations to the unsteady deformations of the fsi interface. on the other hand, imvic+ approach preserves fft based poisson solvers to increase computational efficiency using uniform predefined computational grids where immersed boundary treatments are utilized to satisfy the boundary conditions by means of additional flow components. the validation studies of the proposed methods are performed with a numerical test case of flow over periodic hills, where the dns data sets are manipulated to simulate realistic experimental conditions. even though both linear interpolation and vic+ variants resulted in coherent flow behaviors with the hill form, the local variations of velocity components favored the latter in terms of greater reconstruction accuracy. with the application of ale-vic+ and imvic+, reconstruction accuracy improvements over the standard vic+ method are achieved especially in close proximity of the hill surfaces in terms of streamwise and normal velocity components composing the surface flow penetrations. the modifications are observed to be confined to the close proximity of the solid boundaries where the particle tracking information is able to construct an accurate objective function for the optimization procedure. finally, both data assimilation approaches are applied to enable instantaneous flow field characterization for the measurements of turbulent boundary layer interactions with a dynamically deforming elastic membrane. the densely reconstructed flow field properties are then employed to compute the pressure distribution over membrane surface, revealing the time-resolved interaction between the flow structures and the membrane deformations. the superior accuracy specifications of ale-vic+ and imvic+ methods against trilinear interpolation and the standard vic+ method achieved by enabling the kinematic discretization of the unsteadily deforming membrane motion, provided a greater agreement with the pressure tap measurements by reducing surface pressure reconstruction errors by ∼50% for all three membrane motion frequencies. acknowledgements this work has been carried out in connection to the project homer (holistic optical metrology for aeroelastic research), which is funded by the european commission, program h2020 under grant no. 769237. also, the authors would like to thank prof. stefan hickel from delft university of technology for providing the periodic hill flow dns data set that is used for the numerical assessments. references agui jc and jimenez j (1987) on the performance of particle tracking. journal of fluid mechanics 185:447–468 beale jt and greengard c (1994) convergence of euler-stokes splitting of the navier-stokes equations. communications on pure and applied mathematics 47:1083–1115 beckert a and wendland h (2001) multivariate interpolation for fluid-structure-interaction problems using radial basis functions. aerospace science and technology 5:125 – 134 cakir bo (2020) bridging experimental simulations with computational frameworks for time-resolved characterization of fluid-structure interactions. master’s thesis. delft university of technology caridi gca, ragni d, sciacchitano a, and scarano f (2016) hfsb-seeding for large-scale tomographic piv in wind tunnels. experiments in fluids 57:190 casa ldc and krueger ps (2013) radial basis function interpolation of unstructured, three-dimensional, volumetric particle tracking velocimetry data. measurement science and technology 24:065304 chen zl, hickel s, devesa a, berland j, and adams na (2014) wall modeling for implicit large-eddy simulation and immersed-interface methods. theor comput fluid dyn 28:1–21 christiansen i (1973) numerical simulation of hydrodynamics by the method of point vortices. journal of computational physics 13:363 – 379 cottet gh and koumoutsakos pd (2000) hybrid methods. in vortex methods: theory and practice. page 237–260. cambridge university press cottet gh and poncet p (2004) advances in direct numerical simulations of 3d wall-bounded flows by vortex-in-cell methods. journal of computational physics 193:136 – 158 de boer a, van der schoot m, and bijl h (2007) mesh deformation based on radial basis function interpolation. computers & structures 85:784 – 795 dowell eh (2004) modeling of fluid-structure interaction. in a modern course in aeroelasticity. pages 491–539. springer netherlands elsinga g, scarano f, wieneke b, and oudheusden b (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 farhat c, degand c, koobus b, and lesoinne m (1998) torsional springs for two-dimensional dynamic unstructured fluid meshes. computer methods in applied mechanics and engineering 163:231 – 245 fukuchi y (2012) influence of number of cameras and preprocessing for thick volume tomographic piv. in 16th int. symp. on applications of laser techniques to fluid mechanics, july 9-12, 2012. lisbon, portugal gesemann s, huhn f, schanz d, and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on the application of laser and imaging techniques to fluid mechanics, july 4-7, 2016. lisbon, portugal helenbrook bt (2003) mesh deformation using the biharmonic operator. international journal for numerical methods in engineering 56:1007–1021 hess j and smith a (1967) calculation of potential flow about arbitrary bodies. progress in aerospace sciences 8:1 – 138 hwang t, doh d, jo h, tsubokura m, piao b, kuroda s, kobayashi t, tanaka k, and takei m (2007) analysis of fluid–elastic-structure interactions in an impinging jet with a dynamic 3d-ptv and noncontact 6d-motion tracking system. chemical engineering journal 130:153 – 164 jones w and samareh-abolhassani j (2012) a grid generation system for multi-disciplinary design optimization. in aiaa 12th computational fluid dynamics conference, june 19-22, 1995. san diego, ca, u.s.a. jux c, sciacchitano a, and scarano f (2020) flow pressure evaluation on generic surfaces by robotic volumetric ptv. measurement science and technology 31:104001 katz j and plotkin a (2001) low-speed aerodynamics. cambridge aerospace series. cambridge university press. 2nd edition kudela h and kozlowski t (2009) vortex in cell method for exterior problems. journal of theoretical and applied mechanics 47:779–796 leishman j (2016) principles of helicopter aerodynamics. cambridge aerospace series. cambridge university press lewis ri (1991) the basis of surface singularity modelling. in vortex element methods for fluid dynamic analysis of engineering systems. cambridge engine technology series. page 3–43. cambridge university press liu x, qin n, and xia h (2006) fast dynamic grid deformation based on delaunay graph mapping. journal of computational physics 211:405 – 423 löhner r and yang c (1996) improved ale mesh velocities for moving bodies. communications in numerical methods in engineering 12:599–608 luke e, collins e, and blades e (2012) a fast mesh deformation method using explicit interpolation. journal of computational physics 231:586 – 601 morgenthal g and walther j (2007) an immersed interface method for the vortex-in-cell algorithm. computers & structures 85:712–726 noh wf (1963) cel: a time-dependent, two-space dimensional, coupled eulerian-lagrange code. technical report ucrl-7463. lawrence radiation lab., univ. of california. livermore, ca, u.s.a peskin c (1982) the fluid dynamics of heart valves: experimental, theoretical, and computational methods. annual review of fluid mechanics 14:235–259 sagredo b and tercero jco (2003) z-splines: moment conserving cardinal spline interpolation of compact support for arbitrarily spaced data. research report / seminar für angewandte mathematik 2003-10 scarano f, ghaemi s, caridi gca, bosbach j, dierksheide u, and sciacchitano a (2015) on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments. experiments in fluids 56:42 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 schneiders j, azijli i, scarano f, and dwight r (2015) pouring time into space. in 11th international symposium on particle image velocimetry, september 14-16, 2015. santa barbara, ca, u.s.a. schneiders jfg and scarano f (2016) dense velocity reconstruction from tomographic ptv with material derivatives. experiments in fluids 57:139 schneiders jfg, scarano f, and elsinga ge (2017) resolving vorticity and dissipation in a turbulent boundary layer by tomographic ptv and vic+. experiments in fluids 58:27 smith mj, cesnik ces, and hodges dh (2000) evaluation of some data transfer algorithms for noncontiguous meshes. journal of aerospace engineering 13:52–58 soifer v (2013) main equations of diffraction theory. in computer design of diffractive optics. woodhead publishing series in electronic and optical materials. pages 1 – 24. woodhead publishing tarafder s, saha g, and sayeed t (2010) analysis of potential flow around 3-dimensional hydrofoils by combined source and dipole based panel method. journal of marine science and technology 18:376–384 tokarev mp, alekseenko mv, bilsky av, dulin vm, and markovich dm (2013) tomographic piv measurements in a swirling jet flow. in 10th international symposium on particle image velocimetry – piv13, july 2-4, 2013. delft, the netherlands walther jh and morgenthal g (2002) an immersed interface method for the vortex-in-cell algorithm. journal of turbulence 3:n39 wang z and przekwas a (2012) unsteady flow computation using moving grid with mesh enrichment. in aiaa 32nd aerospace sciences meeting and exhibit, january 10-13, 1994. rano, nv, u.s.a. wu j and jaja j (2013) high performance fft based poisson solver on a cpu-gpu heterogeneous platform. in ieee 27th international parallel and distributed processing symposium ipdps 2013, may 20-14, 2013. pages 115–125. boston, ma, u.s.a introduction methodology arbitrary lagrangian-eulerian approach for vic+ immersed boundary treatment approach for vic+ numerical assessment experimental assessment conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 characterization of non-linear internal waves using piv/plif techniques m. mohaghar1∗, d. r. webster1 1 georgia institute of technology, school of civil and environmental engineering, atlanta, usa ∗ mohaghar@gatech.edu abstract internal waves are ubiquitous in the ocean. they often form in regions of high temperature or salinity variability as the pycnocline oscillates to form the wave (phillips, 1966). they can be generated either from the interaction of tidal currents with submarine bathymetry (garrett and kunze, 2007) or by wind stress at the ocean surface (munk and wunsch, 1998). the current study addresses non-linear internal waves due to their importance in the mixing and dynamics of both atmospheric and oceanographic flows. due to the significance of this phenomena, numerous investigations have been conducted to obtain satisfactory theoretical solutions for internal waves in several types of fluid systems. the verification of these models requires precise and accurate experimental data. it should be noted that such models generally assume simple two-layer stratified system separated by a sharp interface. in reality, there is a gradient of density at the interface of the two layers, which can make both experimental and theoretical analysis more challenging. to date, most experimental studies for several types of internal waves have been performed using ultrasonic probes, conductivity probes, resistance-type wave gauges, or salinity-sensor-type wave gauges, as given by davis and acrivos (1967),koop and butler (1981),michallet and barthelemy (1998) and umeyama (2002). there is one recent study that used the particle image velocimetry (piv) technique to determine the eulerian velocity field of internal waves, but it lacks the detailed density measurements necessary to fully understand the flow (umeyama and matsuki, 2011). the current work aims to fully understand the dynamics of internal waves by measuring the density and velocity fields, and then comparing the experimental results with the theoretical non-linear wave solution. a laboratory-scale apparatus was created to replicate the flow characteristics of internal waves in a twolayer stratified system. an experimental configuration is presented with a density jump of 1.1 and 1.5 σt separately. experiments are conducted in the tank (2.438 m × 50 cm × 50 cm), which was constructed from clear acrylic sheets with thickness of 1.905 cm. the schematic of the internal wavemaker apparatus is shown in fig. 1(a) (mohaghar et al., 2020). a line diffuser (pvc) was installed along the middle of the tank floor to be used to fill the tank. a half-cylinder plunger-type wavemaker was used to create a perturbation at the pycnocline represented by the interface between the density layers. on each revolution of the drive mechanism, the switch sent a voltage signal to the external trigger port of a pulse generator. by precisely controlling the delay following the external trigger signal, the pulse generator sent a signal to the nd:yag laser and the camera to capture an image at a targeted phase of the wave cycle. images are recorded with a high resolution 29 mp ccd camera, (14-bits, 6600 × 4400 pixels). piv was used to measure the velocity field, and the fluids in both layers were seeded with neutrallybuoyant particles. the seeded particles were illuminated using a dual-cavity new wave research gemini piv laser at wavelength of 532 nm, which is diverged into a sheet. light entering the piv camera passed through a 532 nm bandpass filter. the image pairs were processed with insight 4gt m software using a 32 × 32 pixel final spot size with 50% overlap. a sample of piv vector field for the case of ∆ρ = 1.5σt is shown in fig. 1(b). in order to measure the density fields, the flow is visualized using the planar laser-induced fluorescence (plif) method for scalar visualization. a laser-fluorescing dye, rhodamine 6g, is mixed into the heavier layer and the light sheet is used to fluoresce the dye. following the procedures outlined by mohaghar (2019), the dye concentration is then inferred from the digital images. in order to capture only fluorescence emitted by rhodamine 6g, the camera is equipped with a notch filter blocking the 532 nm wavelength of light. a sample of a final processed plif image for the case of ∆ρ = 1.5σt is shown in fig. 1(c). 369 fig. 1. schematic of the boundary layer problem (blp) for a two-layer stratified internal wave. 370 371 372 fig. 2. schematic diagram of the internal wavemaker apparatus. 373 374 (a) (b) (c) figure 1: (a) schematic diagram of the internal wavemaker apparatus. (b) sample of piv vector field. (c) sample of processed plif image. the sample fields shown are at the same phase in the wave cycle. the interface location, density gradient, wave amplitude and period, velocity and vorticity fields, kinetic energy and shear strain rate are quantified by several phases in one wave cycle and subsequently compared with the corresponding predictions based on third-order stokes internal-wave theory. references davis re and acrivos a (1967) solitary internal waves in deep water. journal of fluid mechanics 29:593– 607 garrett c and kunze e (2007) internal tide generation in the deep ocean. annu rev fluid mech 39:57–87 koop cg and butler g (1981) an investigation of internal solitary waves in a two-fluid system. journal of fluid mechanics 112:225–251 michallet h and barthelemy e (1998) experimental study of interfacial solitary waves. journal of fluid mechanics 366:159–177 mohaghar m (2019) effects of initial conditions and mach number on turbulent mixing transition of shockdriven variable-density flow. ph.d. thesis. georgia institute of technology mohaghar m, jung s, haas ka, and webster dr (2020) copepod behavior responses around internal waves. frontiers in marine science 7:331 munk w and wunsch c (1998) abyssal recipes ii: energetics of tidal and wind mixing. deep sea research part i: oceanographic research papers 45:1977–2010 phillips om (1966) the dynamics of the upper ocean. cambridge university press umeyama m (2002) experimental and theoretical analyses of internal waves of finite amplitude. journal of waterway, port, coastal, and ocean engineering 128:133–141 umeyama m and matsuki s (2011) measurements of velocity and trajectory of water particle for internal waves in two density layers. geophysical research letters 38:l03612 validation of multi-frame piv image interrogation algorithms in the spectral domain steven j. beresh,1,* douglas r. neal,2 and andrea sciacchitano3 1 sandia national laboratories, albuquerque, nm, u.s.a. 2 lavision inc., ypsilanti, mi, u.s.a. 3 delft university of technology, delft, the netherlands * sjberes@sandia.gov abstract multi-frame correlation algorithms for time-resolved piv have been shown in previous studies to reduce noise and error levels in comparison with conventional two-frame correlations. however, none of these prior efforts tested the accuracy of the algorithms in spectral space. even should a multi-frame algorithm reduce the error of vector computations summed over an entire data set, this does not imply that these improvements are observed at all frequencies. the present study examines the accuracy of velocity spectra in comparison with simultaneous hot-wire data. results indicate that the high-frequency content of the spectrum is very sensitive to choice of the interrogation algorithm and may not return an accurate response. a top-hat-weighted sliding sum-of-correlation is contaminated by high-frequency ringing whereas gaussian weighting is indistinguishable from a low-pass filtering effect. some evidence suggests the pyramid correlation modestly increases bandwidth of the measurement at high frequencies. the apparent benefits of multi-frame interrogation algorithms may be limited in their ability to reveal additional spectral content of the flow. introduction conventional piv image interrogation cross-correlates two frames at a small time separation, an implementation that has been familiar since the advent of piv [1]. but the use of only two frames in a correlation places limits on the accuracy and the dynamic range of the velocity measurement (e.g., [2]). one means of improving this situation is to correlate over multiple frames. three or even four pulses may be recorded in rapid sequence and used to generate a more accurate correlation [2], which has been demonstrated by ding and adrian [3]. in this implementation, a tripleor quadruple-pulsed system would generate a single vector field, repeated at the repetition rate possible by the light source and camera framing rate. a threeor four-frame camera analogous to the two-frame interline-transfer ccd camera does not presently exist. the development of time-resolved piv (tr-piv) extends this concept by making long, continuous sequences of images available for interrogation algorithms. as tr-piv has become widespread, several different multi-frame correlation algorithms have emerged. one approach is to continue conventional twoframe correlation, but to optimize the temporal separation for each vector for maximum accuracy and dynamic range [4]. the most straightforward extrapolation from the tripleor quadruple-frame correlation is the sliding sum-of-correlation (soc) [5,6], which averages over some n images in correlation space to produce a more accurate correlation. the key difference from the tripleor quadruple-frame approach is that the latter produces a single vector field from the several exposures whereas soc “slides” over the continuous sequence of images to produce a similar continuous sequence of vector fields. a modification of the soc method adds gaussian weighting over the sliding window to improve the correlation accuracy, analogously to the use of such weighting spatially to mitigate the effects of discontinuities at the edges of interrogation windows [7,8]. even more sophisticated algorithms have been invented. the pyramid correlation from sciacchitano et al [8] offers greater flexibility and claims superior accuracy to soc. it operates similarly to soc but it varies the number of frames and the stride between them on a vector-by-vector basis to individually optimize the accuracy. lynch and scarano [9] follow the fluid trajectory to translate and rotate interrogation windows comprising the multi-frame correlation. the same concept of following the local trajectory has been found in additional algorithms for tr-piv [10,11], and these bear some resemblance to the class of lagrangian particle tracking algorithms such as shake-the-box employed in three-dimensional particle tracking velocimetry [12,13]. each advancement of multi-frame correlation analysis has rigorously examined the accuracy of the method in comparison to conventional two-frame correlation and documented the overall improvement in a statistical sense. distributions of accuracy and fluctuations summed over the entirety of all vectors in the data set show an improvement of each successive multi-frame interrogation algorithm. however, none of these prior studies is concerned with the accuracy of the algorithms in spectral space. this is unfortunate because a key attraction of tr-piv is its ability to return spectral content of the flowfield. just because these algorithms improve the accuracy and dynamic range of the statistical populations of measured vectors does not imply that these improvements are equally distributed across the frequency content of the tr-piv signal and therefore does not guarantee an improvement to the measured spectrum. tr-piv recently has shown application to the measurement of turbulence decay properties at high frequencies [14-20], whose interpretation may be sensitive to any dependence of interrogation accuracy upon frequency content. when beresh et al extended their 400 khz pulse-burst piv [18] to mhz rates [21], the intent was to employ multi-frame interrogation on the oversampled data to reduce measurement noise and thereby raise the effective frequency limits of the measurement of the turbulence spectrum. however, application of different multi-frame algorithms returned different high-frequency spectral content and it was ambiguous which should be considered most correct. this motivates the present investigation to examine the performance of accepted tr-piv multi-frame interrogation algorithms with regards to the spectral content they return. to accomplish this, the data set of neal et al [22] has been chosen because it includes simultaneous hot-wire anemometry (hwa) data to compare to its tr-piv measurements. though originally used to assess the efficacy of several uncertainty quantification techniques [23], it can be repurposed here to assess multi-frame image interrogation instead. the present effort is designed to answer whether multi-frame tr-piv image interrogations accurately measure spectral content. experimental configuration a brief description of the neal et al experiment is provided here, with the full details to be found in ref. [22]. measurements were acquired in a rectangular jet of dimensions width w=72.8 mm and height h=10.2 mm with exit velocity of u0=5 m/s. the jet is initially laminar then transitions and becomes fully turbulent in its far-field. the measurements used here are taken from two positions: a downstream position of x/h=19.0 and y/h=0.0 at which the flow is fully turbulent, and a nearer position of x/h=4.0 and y/h=0.0 at which the laminar jet is beginning to become unstable. an additional case was studied at x/h=4.0 and y/h=0.4 where large-scale vortex roll-up occurs at the edge of the jet, but these results were found to echo the unstable laminar position and therefore are omitted here. two tr-piv measurements were made simultaneously, both using a single-cavity nd:ylf laser as the light source with a maximum repetition rate of 10 khz. one was termed the measurement system, or pivms, and used a single lavision highspeedstar 5 cmos camera to image a wide field of view. this system produced noisy results and therefore may be more revealing of higher-accuracy analysis. the second trpiv system, termed the high dynamic range system, or piv-hdr, provided higher-quality results. this system used high magnification to view a smaller region of the jet and arranged two cmos cameras such that one was normal to the laser sheet and could be used for two-component piv analysis while the second was set at an angle to use as a stereo pair to the first. the present analysis uses only one camera in 2c mode. the data were acquired at 10 khz with 20,000 samples. the original data analysis of neal et al used four iterations of 32 × 32 pixel interrogation windows with 75% overlap for the hdr data and four iterations of 16 × 16 pixel windows with 75% overlap for the ms data. the same settings are used herein. power spectral density (psd) functions of the velocity fluctuations were computed using the welch periodogram method, segmented into blocks of 1000 vector fields with 50% overlap between segments. in addition, measurements from a hot-wire anemometer were acquired with the probe head positioned immediately downstream of the piv field of view, within 1-2 mm. the single-wire probe was aligned with the streamwise direction and had a sensitive region of 1 mm. data were acquired at 30 khz for a record length of 1,200,000 samples. results the psd’s of the piv-hdr data and the hotwire data in the fully turbulent region were given by neal et al in their fig. 20 [22]. it is reproduced here as fig. 1 with their original tr-piv spectrum labeled “mst” and overlaid with reprocessed data labeled “two-frame.” the latter have been interrogated using davis 8.4.1 and a conventional two-frame correlation stepped across the time series using the same four iterations of 32 × 32 pixel windows with 75% overlap as in the mst data. this serves as a baseline for subsequent comparisons. whereas the mst spectrum was derived from a single vector sequence, the newly analyzed data averaged spectra from a 6 vector by 7 vector block immediately upstream of the hot-wire probe to improve convergence, reducing the apparent “thickness” of the plotted spectrum. as will be seen in subsequent figures, this is necessary to identify more subtle differences between varied interrogation approaches. the flow characteristics change imperceptibly over the vectors within this block and therefore there is no significant loss of information by averaging across them. figure 1 demonstrates that the baseline image interrogation used in the present work correctly returns the same spectrum as the original analysis in neal et al. the agreement is near perfect for the hdr data set but the new interrogation returns a slightly elevated spectrum in comparison to the mst spectrum. the reason for this latter discrepancy has not been identified but it is not an impediment to any of the multi-frame analysis to follow because it all originates from this baseline. the first multi-frame algorithm to be tested is the sliding sum-of-correlation (soc) without any weighting of the selected images – that is, a top-hat filter is applied across the cross-correlation functions of the n images used. the resulting spectra are shown in fig. 2 alongside the baseline two-frame correlation of fig. 1 and the hot-wire spectrum. two sets of spectra are shown, one for the fully turbulent case and another for the unstable laminar case. while the noise floor of the two-frame correlation is reduced when using the soc, this alone does not guarantee that the multi-frame correlations lead to more accurate high-frequency spectra as judged by comparison with the hot-wire data. the n=3 soc spectrum for the hdr data falls nearest to the hot-wire spectrum in fig. 2a but still betrays a distortion near where the hot-wire begins to roll off to its noise floor (about 2-4 khz). as n is increased, the spectrum does not move towards closer agreement with the hotwire even though the correlation theoretically should become more accurate. in fact, the distortion becomes more prominent. it is speculated that this increasing distortion is a form of acceleration error, which is a known source of error in piv analysis [2,24]. if the flow experiences acceleration between successive frames, then the displacements between those frames will vary as well. as multiple correlations are summed, their peaks will not coincide and therefore correlation broadening or peak splitting will occur. this adds additional noise or even bias to the correlation, and this effect may increase with the use of fig. 1: comparison of spectra from neal et al [22] in the fully turbulent region, both hot-wire and trpiv, to a newly analyzed piv spectrum using conventional two-frame correlation. additional frames as the displacements become more diverse. in this manner, the distortion observed in the hdr data of fig. 2a worsens as n increases. the noise levels for the ms case in fig. 2a never come into agreement with the hot-wire data no matter how many images are used. the distortions to the hdr spectra of fig. 2a are not observed here, probably because the unstable laminar flow does not experience acceleration error as does the turbulent case. instead, the top-hat filter induces high-frequency undulations in the amplitude that clearly are non-physical. this effect is most clearly observed for larger values of n and is stronger for the unsteady laminar case in fig. 2b in which the noise floor extends for a larger portion of the spectrum. (note the y-axis in fig. 2b is expanded to fully reveal the high-frequency spectral undulations.) even for the hdr case, no continuation of the decay slope emerges from soc interrogation; instead, the noise floor is filtered and then begins ringing as in the ms case. these artifacts are similar to the response of a top-hat filter in digital signal processing [25] and observed spatially in iterative piv analysis with image deformations if appropriate weighting is not applied [26]. though the amplitude of the high-frequency noise is much reduced from the two-frame correlation, the true spectral character of the flow is not revealed. these spectra produced using (a) (b) fig. 3: comparison of two-frame spectra from fig. 1 to multi-frame correlation using a sliding sum-of-correlation (soc) of n images and a gaussian filter. (a) fully turbulent region; (b) unstable laminar region. the arrow in (b) is explained in the text. (a) (b) fig. 2: comparison of two-frame spectra from fig. 1 to multi-frame correlation using a sliding sum-of-correlation (soc) of n images and a top-hat filter. (a) fully turbulent region; (b) unstable laminar region. a top-hat filter indicate clearly that an appropriate weighting function is needed to prevent spectral distortions. when the sliding sum-of-correlation is weighted by a gaussian filter, strikingly different spectra emerge as shown in fig. 3. note that here n is provided as a symmetric range whereas n was absolute when considering the top-hat filter in fig. 2. here, as n is increased, the spectra roll off at earlier frequencies and show classic signs of low-pass filtering. this is easiest to identify for the hdr data. the n=±1 spectrum for the turbulent case in fig. 3a shows increased agreement with the hot-wire data but offers only a mild reduction in the noise floor (it actually appears to match the noise of the hot-wire, likely a coincidence). the laminar case in fig. 3b shows a similarly small reduction in noise but little evident improvement in the spectrum. as n is increased to ±2 and ±3, the hdr spectra in each plot lose highfrequency content and diverge from the hot-wire spectrum. figure 3b suggests a noise floor that is filtered by the soc algorithm to produce a spectral shape consistent with a low-pass filter rather than a continuation of the instability slope. the ms data are similar as the value of n is increased; the noise does diminish but the spectral shape simply suggests enhanced filtering. although the spectra slopes are much smoother and monotonic than those returned by the top-hat filter in fig. 2, it does not follow that they must be more physically realistic. the application of the gaussian weighting eliminates the instability of the top-hat filter but instead it acts as a strong low-pass filter on the data. this removes energy in the velocity fluctuations that should be present in the high-frequency range of the spectra. in particular, the high-frequency roll-off associated with turbulent dissipation (fig. 3a) or the growing instability (fig. 3b) is not better captured by the multi-frame interrogation. finally, the pyramid correlation was tested using five different configurations, varying the maximum number of images ni and the maximum number of pyramid levels nl. three are shown in fig. 4 for each case in which ni = nl; reducing ni without reducing nl did not meaningfully alter the results. the spectra are remarkably alike to those produced using the gaussian-weighted soc and similarly show signs of lowpass filtering. for both flow cases and both piv measurement systems, an increase in the number of images used corresponds to a reduction in the noise floor but also a characteristic roll off in the high-frequency region of the spectra. one exception is found, however, as the number of images and levels increases to ni = nl = 3 for the turbulent case in fig. 4a, the filtering effect tapers off and closely matches the ni = nl = 2 spectrum. this probably indicates that the optimization of the pyramid correlation reduces the number of images and levels that actually are used in the correlation despite the maximum permissible. both these (a) (b) fig. 4: comparison of two-frame spectra from fig. 1 to multi-frame correlation using the pyramid correlation. (a) fully turbulent region; (b) unstable laminar region. the arrow in (b) is explained in the text. spectra agree more closely with the hot-wire spectrum without displaying the characteristic sign of lowpass filtering increasing with number of images. a closer examination of the spectra in fig. 4 suggests that the implementation of the pyramid correlation may reveal a little more of the valid physics before the low-pass filtering effect manifests. this is easiest to recognize for the laminar case in fig. 4b. as the noise levels drop with increasing ni and nl, the falling slope of the instability appears to extend to modestly higher frequencies. the characteristic shape of lowpass filtering is applied to the high-frequency noise rather than the fluid dynamics. this is clearest for the hdr data in which the inherent noise is lesser and is indicated with the arrow in the frequency range of 450 – 550 hz. this contrasts with the gaussian-weighted soc in fig. 3b, in which the different cases branch off the spectrum at the same point, revealing no additional range of the instability slope (also indicated by an arrow). a similar extension of the high-frequency slope also may be visible for the turbulent case in fig. 4a as ni increases, but the expected slope is more difficult to judge than in the laminar case. nonetheless, there is reason to believe that as the pyramid correlation reduces the noise floor, some additional fluid dynamics are revealed without compromising the frequency response. the top hat and gaussian filters also can be applied in temporal space rather than correlation space. a sliding average with a kernel of n=3, 4, or 5 images (which is 2, 3, or 4 vector fields) to match that of the top hat soc was applied to the two-frame time-series vectors and then transformed into frequency spectra. these results are shown in fig. 5a for the unstable laminar flow, overlaid on the spectra from fig. 2b. no ringing is produced in this case but neither is any additional information added to the high-frequency slope of the instability peak; the correlation noise simply is filtered differently. therefore, while a sliding average reduces correlation noise, it does not reveal any additional frequency content. more informative is the gaussian time filter in fig. 5b. here, another sliding average is performed on the two-frame time series but now it is weighted by a gaussian in the same manner as the weighting in correlation space from fig. 3b. these spectra are overlaid on the gaussian soc spectra. some high-frequency ringing is observed in the time-filtered spectra but is removed for clarity in the plot. the overlay of the two analyses shows that the gaussian time filter produces very nearly the same spectra as the gaussian soc. since the time-filtering is simply a form of a low-pass filter and would not extract additional accuracy from a correlation, fig. 5b supports the observation from fig. 3 that the gaussian soc multi-frame correlation merely acts as a lowpass filter and not a means of improving spectral accuracy. the effect of the multi-frame correlation algorithms on the time-series data is shown in fig. 6. for this, only the unstable laminar case is examined as it is easier to distinguish flow fluctuations from noise (a) (b) fig. 5: comparison of sliding soc spectra to time-filtering of the two-frame time series in the unstable laminar region. (a) top hat soc and sliding time average; (b) gaussian weighted soc and sliding time average. fluctuations for non-turbulent conditions. only the pyramid correlation is shown as the gaussian-weighted soc is visibly indistinguishable from it in the time domain. (even the high-frequency undulations of the top-hat filter are too low in magnitude to be visible in the time series.) fig. 6a shows the performance of the hdr data and fig. 6b the ms data; both can be compared to the hot-wire traces. a large-scale deviation of both piv configurations from the hot-wire data is seen. it is not clear why the hot-wire did not return low-frequency characteristics in accordance with both piv systems but the midand high-frequencies of present interest match well. this also can be seen in the spectra for the unstable laminar case such as fig. 4b, in which the hot-wire spectrum shows a much larger magnitude than the piv spectra for frequencies below 10 hz. possible explanations include the small distance between the hot-wire probe position and the piv measurement location (though convection time has been accounted) and the differing spatial resolutions. the piv time traces in fig. 6 show reduced fluctuations when a larger number of images are used in the correlation. but it is difficult to evaluate whether the increased smoothness of time-traces in fig. 6 is a result of reduced noise for increased accuracy or simply a result of low-pass filtering of the signal content. (a) (b) fig. 7: probability density functions of the error of the piv data compared to the hot-wire data for the unstable laminar region. (a) hdr measurement system; (b) ms measurement system. (a) (b) fig. 6: time series of data calculated using the pyramid correlation for the unstable laminar region, compared to simultaneous hot-wire data. (a) hdr measurement system; (b) ms measurement system. another means to evaluate the multi-frame correlation accuracy is to histogram the error of the piv measurement via comparison with the simultaneous hot-wire data and look for reduced errors when using multi-frame algorithms. this is accomplished in fig. 7, in which the instantaneous differences between the piv data and the hot-wire data are formed into probability density functions. these provide the distribution of error when velocities are calculated by the various interrogation algorithms and then are compared to the hot-wire data as the true value (as in sciacchitano et al 2015 [23]). the error distributions in fig. 7a do not indicate any improvement in the accuracy for the hdr data set by using the pyramid correlation or increasing the number of images within it. the analogous distributions for the ms data set in fig. 7b show more variation between the different analysis algorithms but no evidence of a narrower distribution indicative of reduced error when the pyramid correlation is employed. perhaps this should not be surprising since the accuracy improvements sought in the spectra occur at relatively high frequencies at which the energy in the flow is substantially reduced. therefore, if such improvements occur, they would be inconsequential to the p.d.f.’s in fig. 7 that are found from the gross flow field behavior dominated by large-scale low-frequency motion. also note that the separation of each error distribution from a zero peak is due to the low-frequency discrepancy between the piv and the hot-wire data. this is not a concern to the present analysis since the focus is on higher frequency ranges. a better approach to assessing whether the multi-frame algorithms can reveal higher-frequency spectral content must focus on only the high-frequency fluctuations. this was accomplished by high-pass filtering the data before error analysis at a cutoff frequency of 300 hz, which can be seen in the spectra of the unstable laminar flow to be a reasonable separation between the large-scale motion that all analyses reproduce effectively and the higher frequency content that is subject to analysis artifacts. figure 8 shows the p.d.f.’s for both the hdr and ms systems and superposes results using both the gaussian-weighted soc and the pyramid correlation. as can be seen in fig. 8a, the noise levels of the hdr system are still too low to differentiate between analysis cases; differences with the hot-wire data remain dominant. differences in the spatial location of each measurement may allow too much evolution of the flow in this frequency range to draw an effective comparison. the ms system is more effective in revealing the decrease of error levels as more images are used in multi-frame algorithms. however, the difference between the gaussian-weighted soc and the pyramid correlation are secondary to the number of images used. nothing in this plot can be used to determine that one method is superior to the other or to differentiate whether reduced discrepancies with the hot-wire data are due to filtering of noise or actual improved physical accuracy. (a) (b) fig. 8: probability density functions of the error of the piv data compared to the hot-wire data for the unstable laminar region. data have been high-pass filtered at 300 hz to focus on the highfrequency region of the spectrum. gaussian-weighted soc and pyramid correlation analyses are compared. (a) hdr measurement system; (b) ms measurement system. discussion and future work the results provided here demonstrate that the variety of available multi-frame correlation algorithms do not return equivalent results. when the number of images used is large, it should be expected that a low-pass filtering of the velocity spectrum is created. but the differences go beyond this straightforward fact. in the presence of acceleration, an increase of the number of images used for interrogation can also increase the variability of the particle displacements. hence, when correlations are summed from varying displacements, the peaks become subject to broadening or splitting, thereby increasing correlation noise and/or bias. but more dominant is the impact of numerical factors in the multi-frame correlations. the sliding sumof-correlation using a top-hat weighting scheme (i.e., a simple sum of n correlations) induces a numerical instability that leads to strong high-frequency ringing. this is eliminated when instead using a gaussian weighting on correlation summation, but the results in frequency space are essentially indistinguishable from low-pass filtering of a two-frame time series. the sum of correlation reduces noise and increases overall precision, but this does not accurately reveal any spectral content at frequencies exceeding that of the two-frame correlation. stated differently, the noise is filtered but not independently from the signal. the pyramid correlation shows somewhat more promise for revealing high-frequency physics. while low-pass filtering of the noise spectrum is evident, some signal separation occurs as well. this reveals a modest improvement of the signal bandwidth in the mid-to-high-frequency range. the present results suggest that the multi-frame algorithms return results that are a mixture of low-pass filtering due to the increased number of images and the detection of spectral characteristics from the fluid dynamics. it is non-trivial to distinguish the filtering effects that arise from signal processing considerations from the legitimate physical content sought by these algorithms. efforts beyond the scope of the present paper are required before this fundamental question can be illuminated. comparisons of simultaneously acquired tr-piv and reference hot-wire data would, in principle, be helpful in this regard. the coherence function should reveal over which frequencies valid flow information may be separated from measurement noise by multi-frame interrogation. these have not been reported herein because challenges matching the two signals in the relevant mid-to-high-frequency range interfered with finding any significant distinguishing characteristics between multi-frame algorithms. unfortunately, the present work also has suggested limits of comparison between piv and hot-wire data owing to differences in spatial resolution and measurement location. valid comparisons may only be possible on a statistical basis rather than the instantaneous comparison required to provide a more definitive understanding of multi-frame correlation behavior. this paper represents the first known study of the accuracy of velocity frequency spectra when interrogated by multi-frame correlation methods. results establish that the high-frequency outcome of the velocity spectrum is very sensitive to choice of the interrogation algorithm and may not return an accurate response. a low-pass filtering effect due to use of more images may explain the apparent reduction in error rather than an increased precision of the measurement. the apparent benefits of multi-frame interrogation algorithms may be limited in their ability to reveal additional spectral content of the flow. additional study on this matter is intended in coming years. acknowledgements sandia national laboratories is a multi-mission laboratory managed and operated by national technology and engineering solutions of sandia, llc., a wholly owned subsidiary of honeywell international, inc., for the u.s. department of energy’s national nuclear security administration under contract de-na0003525. references [1] adrian, r. j., “twenty years of particle image velocimetry,” experiments in fluids, vol. 39, no. 2, 2005, pp. 159-169. [2] westerweel, j., elsinga, g. e., and adrian, r. j., “particle image velocimetry for complex and turbulent flows,” annual review of fluid mechanics, vol. 45, 2013, pp. 409-436. [3] ding, l., and adrian, r. j., “n-pulse particle image velocimetry-accelerometry for unsteady flow-structure interaction,” measurement science and technology, vol. 28, no. 1, 2017, pp. 014001. [4] hain, r., and kähler, c. j., “fundamentals of multiframe particle image velocimetry (piv)”, experiments in fluids, vol. 42, no. 4, 2007, pp. 575-587. [5] meinhart, c. d., wereley, s. t., and santiago, j. g., “a piv algorithm for estimating time-averaged velocity fields,” journal of fluids engineering, vol. 122, no. 2, 2000, pp. 285-289. [6] scarano, f., bryon, k., and violato, d., “time-resolved analysis of circular and chevron jets transition by tomo-piv”, 15th international symposium on applications of laser techniques to fluid mechanics, lisbon, portugal, 2010. [7] astarita, t., “analysis of weighting windows for image deformation methods in piv,” experiments in fluids, vol. 43, no. 6, 2007, pp. 859-872. [8] sciacchitano, a., scarano, f., and wieneke, b., “multi-frame pyramid correlation for time-resolved piv,” experiments in fluids, vol. 53, no. 4, 2012, pp. 1087-1105. [9] lynch, k., and scarano, f., “a high-order time-accurate interrogation method for time-resolved piv,” measurement science and technology, vol. 24, no. 3, 2013, pp. 035305. [10] jeon, y. j., chatellier, l., and david, l., “fluid trajectory evaluation based on an ensemble-averaged cross-correlation in time-resolved piv,” experiments in fluids, vol. 55, no. 7, 2014, pp. 1766. [11] yegavian, r., leclaire, b., champagnat, f., illoul, c., and losfeld, g., “lucas-kanade fluid trajectories for time-resolved piv,” measurement science and technology, vol. 27, no. 8, 2016, pp. 084004. [12] discetti, s., and coletti, f., “volumetric velocimetry for fluid flows,” measurement science and technology, vol. 29, no. 4, 2018, pp. 042001. [13] schanz, d., gesemann, s., and schroeder, a., “shake-the-box: lagrangian particle tracking at high particle image densities,” experiments in fluids, vol. 57, no. 5, 2016, pp. 70. [14] vetel, j., garon, a., and pelletier, d., “denoising methods for time-resolved piv measurements,” experiments in fluids, vol. 51, no. 4, 2011, pp. 893-916. [15] oxlade, a. r., valente, p. c., ganapathisubramani, b., and morrison, j. f., “denoising of time-resolved piv for accurate measurement of turbulence spectra and reduced error in derivatives,” experiments in fluids, vol. 53, no. 5, 2012, pp. 1561-1575. [16] galmiche, b., mazellier, n., halter, f., and foucher, f., “turbulence characterization of a high-pressure high-temperature fan-stirred combustion vessel using ldv, piv, and tr-piv measurements,” experiments in fluids, vol. 55, no. 1, 2014, pp. 1636. [17] miller, j. d., jiang, n., slipchenko, m. n., mance, j. g., meyer, t. r., roy, s., and gord, j. r., “spatiotemporal analysis of turbulent jets enabled by 100-khz, 100-ms burst-mode particle image velocimetry,” experiments in fluids, vol. 57, no. 12, 2016, pp. 192. [18] beresh, s. j., henfling, j. f., and spillers, r. w., “postage-stamp piv: small velocity fields at 400 khz for turbulence spectra measurements,” measurement science and technology, vol. 29, no. 3, 2018, pp. 034011. [19] willert, c. e., “’profile piv’ – more than just an optical hotwire: new potentials of piv in boundary layer research,” 18th international symposium on flow visualization, zurich, switzerland, june 26-29, 2018. [20] manovski, p., gulotta, p., giacobello, m., de silva, c., hutchins, n., and marusic, i., “velocity and pressure measurements of a turbulent boundary layer at 80 khz using 2d piv,” 3rd workshop on data assimilation and cfd processing for piv and lpt (virtual meeting), 2020. [21] beresh, s. j., spillers, r. w., soehnel, m. m., and spitzer, s. m., “extending the frequency limits of ‘postage-stamp piv’ to mhz rates,” aiaa paper 2020-1018. [22] neal, d. r., sciacchitano, a., smith, b. l., and scarano, f., “collaborative framework for piv uncertainty quantification: the experimental database,” measurement science and technology, vol. 26, no. 7, 2015, pp. 074003. [23] sciacchitano, a., neal, d. r., smith, b. l., warner, s. o., vlachos, p. p., wieneke, b., and scarano, f., “collaborative framework for piv uncertainty quantification: comparative assessment methods,” measurement science and technology, vol. 26, no. 7, 2015, pp. 074004. [24] boillot, a., and prasad, a. k., “optimization procedure for pulse separation in cross-correlation piv,” experiments in fluids, vol. 21, no. 2, 1996, pp. 87-93. [25] smith, s. w., the scientist and engineer’s guide to digital signal processing, 1997, http://www.dspguide.com/pdfbook.htm. [26] astarita, t., “analysis of weighting windows for image deformation methods in piv,” experiments in fluids, vol. 43, no. 6, 2007, pp. 859-872. http://www.dspguide.com/pdfbook.htm the 100 eyes tomographic piv yuki harada*, kazuto saiga, jun sakakibara department of mechanical engineering, meiji university higashimita 1-1-1, tamaku, kawasaki, 214-8571, japan abstract piv is one of the methods to measure velocity in a flow field, but its dynamic velocity range is narrower than other flow velocimeter. this disadvantage is particularly apparent in measurements of spectrum in turbulent boundary layers, where the higher wave number side of the spectrum cannot be measured with high accuracy. in this study, we captured images of the same particle in the flow field from many different direction simultaneously, and reduced the measurement error of the particle displacement by averaging the acquired particle positions, so called ‘multiple eye piv’ [maekawa, a., sakakibara, j., 2018, meas. sci. tech., 29, 064011]. we applied this method to obtain the energy spectrum in a turbulent pipe flow aiming for resolving higher wave number. particle images were captured by a single high-speed cmos camera (fastcam nova s6, 6000 fps, photron) through a mirror array consists of 110 flat mirrors arranged in the shape of an axisymmetric ellipsoid (fig.1), as shown in fig.2. the images were evaluated by tomographic piv method to resolve three-dimensional velocity field. fig.3 shows energy spectrum in a pipe measured by tomographic-piv with number of mirrors, n, up to 100 in addition to the 2d2c-piv with a single mirror. although the spectrum curve for the result of tomographic-piv begins to depart from the reference curve at wavenumber beyond 10-1, such wavenumber grows as n increases, and consequently the plateau of the curve appeared at lower energy. such a downward shift of the plateau is expected due to the improvement of the dynamic velocity range, which is approximately one order in energy, i.e. three times in velocity, found between n=4 and 100. note that the cases of n=4 and 40 loses the dynamic range against the 2c2d-piv case. from the above, we can summarize that the advantage of multiple eye piv over the 2c2d-piv is effective when the number of mirrors is more than 40. in this experiment, the issue is that particles images flickered. in order to resolve this issue, we tried to use fluorescent particles, and obtained a clear particle images in the following experiment. we are now analyzing whether the energy spectrum can be measured with higher accuracy due to improved resolution of the particles. figure 1 mirror array figure 2 state of using a mirror array figure 3 energy spectrum 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a grid-free least-squares method for pressure evaluation from lpt data m. bobrov1,2, m. hrebtov1,2, v. ivashchenko1, r. mullyadzhanov1,2, a. seredkin1,2, m. tokarev1,2, d. zaripov1,3,∗, v. dulin1,2, d. markovich1,2 1 institute of thermophysics sb ras, lavrentyev ave. 1, 630090 novosibirsk, russia 2 novosibirsk state university, pirogov str. 2, 630090 novosibirsk, russia 3 school of mechanical science and engineering, huazhong university of science and technology, 430074 luoyu road 1037, wuhan, china ∗zaripov.d.i@gmail.com lagrangian particle tracking shake-the-box (stb) method (schanz et al., 2016) acquires the 3d positions of tracer particles from the temporal sequences of their 2d projection images even for rather high seeding densities. approximation of tracks by analytical functions (gesemann, 2015) provides an accurate evaluation of tracers’ local velocity and acceleration. this data, which is obtained on non-regular grid, can be used to estimate local pressure fluctuations based on the navier–stokes equation. the present paper describes a grid-free least-squares method for the gradients and pressure evaluation based on irregularly scattered lpt data with random noise minimization. the performance of the employed method is assessed based on synthetic images of virtual particles seeded in a wall-bounded turbulent flow. the tracks are obtained from the direct numerical simulation (dns) of an initially laminar boundary layer flow around a hemi-sphere, mounted onto a flat wall. the reynolds number based on the sphere diameter and free stream velocity is 7000 corresponding to a fully turbulent wake (see figure 1). figure 1: location of the virtual cameras with respect to the coordinate system and a flow domain where particles were initially seeded (larger box) and roi (smaller box) with visualization of the vortex structures with instantaneous isosurface of λ2 =−5 colored by streamwise velocity magnitude in order to study the effect of particle image concentration (up to 0.2 ppp) on the overall accuracy, two hundred thousand inertial particles were randomly and uniformly seeded into a flow domain as illustrated in figure 1. we considered four concentrations, i.e. nppp = 0.005, 0.05, 0.12 and 0.2 ppp. to quantify the image noise effect, a random noise with different amplitude was added to the projection images for the moderate case of nppp = 0.05. the images were processed using an stb algorithm (similar to that of gesemann) enabling an accurate tracking of particles and evaluation of their velocity and acceleration. the firstand second-order gradients of the velocity and acceleration were evaluated using a grid-free least-squares method (mavriplis, 2003). afterwards the local values of pressure were computed employing a modified version of the method, where the pressure gradients were obtained directly from the navier-stokes equations (kuhnert and tiwari, 2004). besides, in order to reveal the effect of spatial resolution and performance of the employed algorithms, the original tracks from the dns were used to evaluate the same flow quantities. we refer to such case as hacker’s data. the examples of the results are presented in figures 2 and 3. particle image concentration nppp = 0.05 is shown in figure 2 for the comparison with the hacker’s data. the velocity and acceleration field are interpolated to the regular grid using the least-squares method, whereas the pressure is evaluated from the poison equation. the resolution is sufficient to recover large-scale flow structures and negative pressure regions in the wake. figure 2: the instantaneous distributions of the wall-normal velocity (left) and acceleration (middle) components and pressure (right) obtained for hacker’s and stb data figure 3: the root-mean-square deviations of the error between the exact and estimated velocities, velocity gradients, accelerations and pressure (from left to right) for different concentrations and image noise level for nppp = 0.05 the performance of the used stb algorithm is limited for the cases of high seeding density nppp = 0.12 and noise level of 10%. besides, the spatial resolution is not enough to approximate accurately the velocity gradients and particles acceleration on the regular grid. however, the least-squares method demonstrates a remarkable accuracy for the pressure evaluation from the exact particles’ locations, velocities and acceleration (see hacker’s data in figure 3), viz., even for nppp = 0.05 the pressure error is below 10%. acknowledgements this work was financially supported by the russian science foundation, grant number 19-79-30075. references gesemann s (2015) from particle tracks to velocity and acceleration fields using b-splines and penalties. arxiv preprint arxiv:151009034 kuhnert j and tiwari s (2004) grid free method for solving the poisson equation. wavelet analysis and applications pages 151–166 mavriplis d (2003) revisiting the least-squares procedure for gradient reconstruction on unstructured meshes. in 16th aiaa computational fluid dynamics conference, orlando, usa, june 23-26, 3986 1-13. schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 high speed piv measurements in water hammer r. capanna1∗, p. m. bardet1 1 the geroge washington university/ mechanical and aerospace department/ washington dc/ usa ∗ capanna@gwu.edu abstract an experimental study addressing the challenge to measure relaxation coefficient of very fast phenomena such as water hammers is presented. an acrylic projectile containing water is accelerated and impacts a metal wall creating a water hammer. state of the art laser measurements techniques will be deployed in order to achieve such goal. a compressed air custom built cannon is used to accelerate the projectile and create the impact leading to the water hammer. first experimental results for shadowgraphy and piv measurements are presented and discussed with focus on the future development for the presented facility. 1 introduction the relap-7 code is the next-generation nuclear reactor system safety analysis code being developed at idaho national laboratory (berry et al., 2013, 2018, 2015). in relap-7, the comprehensive sevenequation multiphase model is used to represent quasi-one-dimensional gas-liquid flows for problems with varying cross-sectional areas. for fast transients (such as water hammer or steam explosion) in water, the seven-equation model takes into account non-equilibrium processes through relaxation rate terms. due to the complex polar and tri-atomic nature of the h2o molecules, the relaxation rate terms in the seven-equation model rely on simplified models and limited data. there is therefore significant empiricism and knowledge gap in those terms that limits the application domain of relap-7 for fast transients. unfortunately, no analytical model describes h2o satisfactorily over the range of parameters considered here because of its complex geometry and polar nature. therefore, one must rely on a combination of experiments and molecular dynamic simulations (partly calibrated by experimental results) to estimate the relaxation times. to measure return to equilibrium, an experiment should therefore resolve independently rotational and vibrational temperatures, the relaxation time will be the time at which the two temperatures agree. therefore, the thermal and mechanical relaxation times will be determined experimentally. they depend on temperature and pressure and are on the order of tenth of microseconds or longer for the experimental cases that will be considered here. the work presented in this paper represents a first effort in the characterization of the water hammer realized in a new experimental facility by using laser measurements techniques. the facility is based on the rich pipe concept. however, instead of using a drop tower, a compressed air cannon has been constructed. it consists of a driver volume and a barrel. the projectile is a titanium pipe filled with water that will go water hammer when the pipe hits a solid obstacle. as a first step for the visualization of the water flow undergoing water hammer a shadowgraphy technique has been implemented. then a first of a kind very high-speed piv technique has been implemented allowing to reach more than 100 frame/s. this temporal resolution is required in order to resolve very fast transients involved in water hammer phenomena. important challenges were solved in order to perform high speed piv measurements on a moving target, and they will be illustrated in this paper. to the author knowledge the implementation of piv measurements at this temporal resolution represent a first of a kind. some work has been done on water hammer piv measurements, with focus in the spatial resolution, but at low time resolution (15 hz) as described in brito et al. (2014). first the experimental facility and its main characteristics will be presented, then the laser setup and the challenge due to the specific configuration will be illustrated. finally, main results obtained with both shadowgraphy and piv techniques will be illustrated. finally, discussion will be opened on the further steps for quantitative measurements of relaxation constants by using advanced techniques such as ultrafast absorption spectroscopy with femtosecond lasers. figure 1: schematic view of the compressed air cannon. 2 experimental facility as already mentioned above, the facility consists of a compressed air cannon. this design has been chosen in order to improve the repeatability of the experiments and to have the final velocity and direction of the projectile to be identical at each shot as much as possible. some modifications have been done on the piston and cylinder system in order to improve the repeatability and to maximize the discharge speed of the chambers. in other standard applications (rohrbach et al., 2012) we usually find a valve which brings the air into the barrel and which gives thus the trust force to the projectile. since, for our application we are in the conditions of chocked regime, this means the air mass flow rate (ṁ) directly depends on the diameter of the valve, as expressed by equation of the chocked regime: ṁ =cda √ ργ(p1 −patm) ( 2 γ+1 ) γ+1 γ−1 (1) where p1 is the pressure of the front chamber, patm is the atmospheric pressure at the outlet of the barrel, cd is a dimensionless discharge coefficient, ρ is the density of the gas and γ =cp/cv ratio of the gas and a is the cross section of the barrel (or of the valve in other situations). since commercial solenoid valves have by design a very narrow cross section, this means that the mass flow rate of the discharge chocked flow will be very limited, so meaning that the pressure differential that the projectile experience will be not the total pressure difference between the front chamber and the atmospheric pressure. in order to have a trust force the most efficient, we want the projectile to experience the whole pressure difference ideally instantaneously. we cannot achieve the instantaneity but increasing the cross sections we can increase the discharge flow rate. so, the maximum we can achieve, is when the front chamber directly discharges into the barrel. in order to achieve this goal, the piston rod has been modified (shortened) and a front plate is added to the piston rod (with an o’ ring for the sealing.). so now the cylinder has two chambers, the back chamber and the front chamber. the front chamber is the chamber where all the gas which will fire the projectile is stored, while the back chamber is needed to push the front plate of the cylinder rod towards the wall of the barrel for sealing the front chamber. for the same reasons, the outlet nozzle of the back chamber is much larger than the inlet nozzle, so the back chamber could be emptied as fast as possible. in order to minimize the time for the gas to flow from the back chamber, and also to maximize the volume of the front chamber, we want the volume of the back chamber to be as small as possible. after all these design considerations have been done, we were able to design the size of our system. a cylinder of 15.24 cm diameter with a 35.56 cm stroke has been used. the piston rod and the piston have a total length of 30.48 cm, which thus leaves a back chamber of 5.08 cm long and a front chamber of 25.4 cm figure 2: picture of the assembled air cannon. figure 3: frame of the projectile exiting the barrel. long. a very high precision barrel has been used with an inner diameter of 5.08762 cm+ 0.01778 cm− 0.000 cm and 2 m long. the maximum service pressure of the chambers is 1.7 mpa, which is thus capable of firing a projectile of about 2 kg at a velocity of about 70 m/s (at the outlet of the barrel). one can thus imagine that the pressure on the back chamber should be greater than the pressure in the front chamber in order to insure the sealing of the front chamber. one should remark that since the front plate also experiences a pressure gap, the active surface where the front chamber pushes is smaller than the surface of the back chamber, then this means that even without any pressure difference between the back and the front chamber we will have resultant force which pushes the front plate towards the wall. after a quick calculation, it results that at the service pressure of 1.7 mpa in both chambers, a net force of about 4000 n results in the direction of the barrel. this force is more than the double of the force needed to guarantee the sealing of the o’ ring. we can thus use the same pressure in both chamber, which allow to simplify the design of the piping and to use only one gas tank for feeding the whole system. the pressure inside the chamber is controlled with two pressure sensors which have an error less than 0.1% thus allowing to have a very accurate control of the initial conditions of our experiments, and thus to insure a good repeatability of the tests. finally, the compressed air cannon is mounted to a 10 inch i-beam, itself mounted on a frame to bring the barrel to the height of the laser. the i-beam was necessary to add mass to the overall assembly and minimize recoil of the system. also, it will serve as a support to mount a solid obstacle to intercept the projectile (see figure 2). to monitor the projectile speed exiting the barrel, a series of 3 fast photodiodes are positioned at the exit of the barrel. they have a rise time of less than 1 ns and will capture precisely the front of the projectile. they are connected an oscilloscope to measure the outlet velocity of the projectile. the photodiodes will serve as a trigger signal to start the acquisition of the instruments that will be deployed in the water hammer projectile. tests have been performed to assess the repeatability of the velocity between different shots with a dummy projectile made of teflon (as shown in figure 3). in figure 4 the measured velocity for 15 different tests performed at the same nominal conditions of 3bar in the front chamber and 3.2 bar on the back chamber are shown. with the current design we can obtain a precision of about 0.5% at 95% confidence. 0 2 4 6 8 10 12 14 16 test # 27.5 27.55 27.6 27.65 27.7 27.75 27.8 27.85 27.9 27.95 28 v e lo c it y [ m /s ] repeatability @ 3bar mean 68% confidence 99% confidence figure 4: frame of the projectile exiting the barrel. 3 piv and shadowgraphy setup first tests with shadowgraphy and piv measurements are performed by using a test projectile made of acrylic and filled with distilled water inside (as shown in figure 5). piv silver coated particles with a diameter of 2 µm have been used as a tracer for the flow. this projectile is used for the first tests because it is cheap and easy to build, but it can be destroyed during tests due to its fragility. the choice to use a cheap test projectile, is dictated to the elevated number of tests needed for synchronization and calibration of all the tools necessary for deploying piv in such a challenging environment. for final quantitative measurements a new titanium body projectile is designed in order to resist several shots without breaking. the first measurement technique implemented is the shadowgraphy which allows to visualize the dynamic of the projectile and the water flow inside it. the shadowgraphy technique is simple to implement and consists of a powerful led lamp placed in front of a camera and the trajectory of the moving target is placed in between the camera and the light. for our application the high-speed camera phantom v.710 is used with a resolution of 640× 256 pixels and an exposure time of 3 µs leading to an acquisition rate of 40000 fps. the physical resolution obtained by using a 200 mm nikon lens at 2 m from the target is 208µm/pixel resulting in a magnification of m = 0.096. the led lamp used is a veritas constellation model 120 giving 12000 lumen of light intensity, used in continuous mode (it could be used in strobe mode up to 100 khz) and placed about 1 m away from the target. later, a piv technique has been implemented in order to perform time resolved measurements of the flow field undergoing water hammer. the implementation of a piv technique in water hammer represents a big challenge due to the very fast involved phenomena, and to the authors knowledge time resolved piv in water hammer at very high frequencies have never been performed. a very powerful and fast laser was needed in order to have a repetition rate high enough to temporally resolve the transients involved in a water hammer. the spectral energies quasimodo pulse burst laser has been used for this setup, which allows a repetition rate up to 1 mhz with a pulse length of 1 ns at 532 nm. due to the high repetition rate, the laser can only work for 10 ms and needs a cooling time of about 10 s in between each burst. the energy of each burst is of 16 j/burst, giving thus an energy of 0.16 mj/pulse. this represented a synchronization challenge, meaning that the trigger of the laser must be perfectly synchronized with the impact of the projectile on the solid wall. the high-speed camera used for the piv measurements is an idt y7-s3 with a reduced resolution of 1920200 pixels allowing an acquisition rate of 100000 fps with an exposure time of 8 µs. a 60 mm figure 5: laser alignment on the impact area for piv measurements. nikon lens has been used with the camera placed at about 50 cm from the target resulting in a resolution of 24 µ/pixel and a magnification m = 0.29. a system of 3 mirrors and a cylindrical and a spherical lens has been used in order to bring the laser light into the impact point and to create a laser sheet of about 0.5 mm thickness (as shown in figure 5). the master clock of the laser system has been used for synchronizing the camera acquisition and exposure with the laser pulses, and a fast photodiode (thorlabs pda10a) with a laser pointer placed 5 cm form the impact area has been used to trigger both the laser and the camera. 4 results at this stage preliminary results are shown. in figure 6 the water hammer recorded with the shadowgraphy technique by the phantom camera at a 40000 fps is reported. the rarefaction wave produced cavitation bubble which are visible in 6 different frames, and this allows to have a rough estimation of the shock wave speed inside the projectile which about 900 m/s. this estimation agrees with the calculated value for the shock wave travelling in water inside an acrylic pipe which is of 980 m/s. the shadowgraphy measurements allowed for the first time (to the authors knowledge) do visualized the rarefication wave inside a transparent projectile undergoing water hammer, and also proved that the experimental facility and the available tools are suitable for the purpose non-intrusive measurements in a water hammer. however, due to the very high speed of the shock wave due to the water hammer, an acquisition rate of 40000 fps is not enough to completely resolve the flow field undergoing water hammer, thus a better high-speed camera has been chosen for the piv measurements (as discussed above). some of the piv raw images collected with the idt camera at 100000 fps are shown in figure 7. at this stage only some qualitative analysis has been performed on these images, but with the implemented piv technique we are able to visualize and follow the water flow field undergoing water hammer. the presence of some bubbles due to the rarefication wave is evident. some piv software could be used to compute the time resolved local flow velocities inside the projectile undergoing water hammer. 5 conclusions a new experimental facility that address the challenge to measure relaxation coefficient of very fast phenomena such as water hammers has been presented in this paper. a first of a kind very fast shadowgraphy and piv techniques have been deployed for the measurements of such fast phenomena. it has been demonstrated that the tools used for these measurements give useful results for the understanding of the flow fields figure 6: shadowgraphy images of water hammer: (a) frame 1; (b) frame 2; (c) frame 3; (d) frame 4; (e) frame 5; (f) frame 6. figure 7: piv raw images of water hammer: (a) frame 400; (b) frame 450; (c) frame 500; (d) frame 550; (e) frame 600; (f) frame 650; (g) frame 700. in a water hammer a represent a first step in the development of further techniques for the measurement of relaxation coefficients. several challenges have been overcome in order to trigger and synchronize in a very precise way all the tools used for the piv measurements. further piv measurements will be performed on a new projectile, which will allow to have several repetitions of the measurements, acquiring a statistic on the measurements. the new projectile has a titanium body to resist the strong impacts and a sapphire tube to resist the internal pressure and allow uv light to pass trough (needed for eventual absorption spectroscopy measurements). references berry r, zou l, zhao h, andrs d et al. (2013) relap-7: demonstrating seven-equation, two-phase. technical report. idaho national laboratory (inl) berry ra, peterson jw, zhang h, martineau rc, zhao h, zou l, andrs d, and hansel j (2018) relap-7 theory manual. technical report. idaho national lab.(inl), idaho falls, id (united states) berry ra, zou l, and andrs d (2015) relap-7 progress report. fy-2015 optimization activities summary. technical report. idaho national lab.(inl), idaho falls, id (united states) brito m, sanches p, ferreira rm, and covas di (2014) piv characterization of transient flow in pipe coils. procedia engineering 89:1358–1365 rohrbach z, buresh t, and madsen m (2012) modeling the exit velocity of a compressed air cannon. american journal of physics 80:24–26 introduction experimental facility piv and shadowgraphy setup results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 an infrared quantitative imaging technique (ir-qiv) for remote sensing of river flows edwin a. cowen1∗, seth a. schweitzer1 1 defrees hydraulics laboratory, school of civil & environmental engineering, cornell university, ithaca, ny ∗ eac20@cornell.edu stage and discharge are some of the oldest measurements in environmental fluid mechanics and are vital in forecasting water supply and flood safety. these measurements are traditionally manpower intensive, hence expensive, and dangerous under high flow conditions. considering climate change and the planet’s increasing population there is a critical need for better, more accurate, and frequent, in space and time, data for model and forecast guidance. this need spans monitoring small-scale turbulent processes to calibrating and nudging continental scale river dynamics models. driven by applications from river gaging networks to fish behavior modeling to flood and erosion forecasting, and more generally, the near-shore environment of lakes, estuaries and the coasts, remote sensing with quantitative imaging tools is a rapidly expanding field. such tools can be deployed from fixed platforms, drones, planes and satellites with valuable information contained within the visible to infrared spectral bands. figure 1: infrared image of the water surface of a river (sutter slough, california, usa). the infrared image is georeferenced and overlaid on an aerial image. detailed thermal patterns can be seen at the water surface. yellow and blue hues indicate thermal patterns at the water surface, purple and silver hues are from foliage on the river banks. the width of the river is approximately 50 m. distances are in meters on the utm grid. in this presentation we focus on using a remotely mounted infrared (ir) camera to monitor the mean and instantaneous surface velocity field of rivers and on how bathymetry, flow rate, and metrics of turbulence, can be inferred from the collected ir images. we provide details of our developed infrared quantitative image velocimetry (ir-qiv) method, which capable of measuring instantaneous velocity at high spatial and temporal resolution, over spatial domains with side length scales of order 10 m to 100 m (i.e., areas of 102 m2 to 104 m2) without the use of artificial flow seeding or illumination (schweitzer and cowen, under review). we present results from field measurements, made in collaboration with the united states geological survey (usgs) and the department of water resources (dwr), in the sacramento–san joaquin river delta, ca, usa, and the finger lakes region of new york, usa. we compare state-of-the-art acoustic approaches used by the usgs to measurements made by our ir-qiv technique. we describe key similarities and differences relative to current visible light based techniques (e.g., large scale particle image velocimetry, or lspiv), methods to minimize uncertainty in the measurements, and how to use the physics of open channel flows to calculate the bathymetry from remotely measured turbulent integral length scales of the flow (johnson and cowen, 2016) and leverage the measured surface mean velocity field to calculate the flow rate at a river cross-section. figure 2: five minute mean velocity field over several hundred m2 at the surface of a river, measured by ir-qiv. background color indicates the local temporally averaged velocity magnitude. arrows indicate the local mean velocity vector. we describe considerations related to acquisition of infrared images for ir-qiv (camera selection, effects of environmental conditions on image quality and suitability for velocimetry), and also aspects that are relevant to large-scale, image-based, velocimetry methods, regardless of the spectral range of the images (i.e., ir or visible-light), in particular for images acquired at oblique viewing angles. these include selection of an optimal algorithm for pattern tracking (e.g., cross-correlation, minimum quadratic difference, phase-only correlation), optimal subwindow size selection based on image dynamic range and parameters such as length scales apparent in the images, georeferencing needs, and methods of quantifying uncertainty in the measurements. figure 3: comparison of ten minutes of surface velocity records made by ir-qiv and an adv located at a depth of approximately 1 m and a horizontal distance of 1 m from the ir-qiv measurement location. acknowledgements funding for this work was provided by the california department of water resources (dwr). references johnson ed and cowen ea (2016) remote monitoring of volumetric discharge employing bathymetry determined from surface turbulence metrics. water resources research 52:2178–2193 schweitzer sa and cowen ea (under review) instantaneous river-wide water surface velocity field measurements at centimeter scales using infrared quantitative image velocimetry. water resources research 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 tomographic piv measurement of a re-entrant jet in a cavitating venturi udhav u. gawandalkar∗, christian poelma multiphase systems, process and energy, delft university of technology, the netherlands ∗u.u.gawandalkar@tudelft.nl, c.poelma@tudelft.nl abstract partial cavitation occurs when low-pressure regions caused by separated shear layers are filled with vapours. partial cavitation is inherently unsteady and leads to periodic cloud shedding. the periodically generated re-entrant jet travelling beneath the vapour cavity is considered as one of the mechanisms responsible for the periodic cloud shedding (callenaere et al. (2001)). however, the exact physical mechanism that drives the shedding remains unclear. the re-entrant flow exists as a thin liquid film wedged between the wall and the vapour cavity. the flow in this thin film is generally assumed to move with the same order of magnitude as the bulk flow, yet in the opposite direction. there have been several attempts to measure the velocity of the re-entrant flow to get insight into the physics of re-entrant flow and its contribution to cloud shedding. however, the flow topology of the re-entrant jet poses a major challenge to experimentally study it. the unsteady nature of the flow and the opacity of the cavitation cloud adds to the further complexity. in this work, we show that tomographic piv (elsinga et al. (2006)) can be extended to exploit the flow topology to accurately measure the velocity and thickness of the re-entrant flow. this in turn provides better insight into the role of re-entrant flow in periodic cloud shedding. figure 1: (a) experimental setup for tomographic piv. schematics of tomographic piv setup in (b) x′− z′ (inset shows zoomed-in view of re-entrant liquid film and vapour cavity in x− z plane) (c) y′− z′ plane. the experiments are performed in a cavitation loop described in detail in a previous study of jahangir et al. (2018) at a cavitation number (σ) of 0.97 and reynold number (rethroat) of 170034. the axisymmetry of re-entrant flow is exploited to gain optical access to the re-entrant jet as shown in figure 1 b, c. three highspeed cameras equipped with an objective lens of 105mm ( f # = 5.6) and high pass orange filter (λ >590nm) are arranged in a linear configuration (24◦,0◦, −24◦) as shown in figure 1 a, c. furthermore, scheimpflug adapters are used to align mid-planes of the illuminated area with the focal planes. such a configuration is chosen due to the cigar-shaped measurement volume, i.e. larger extent of axial direction (x) than other two directions (y,z) (see inset in figure 1 b). the liquid flow is seeded with fluorescent tracer particles which absorb incident green light and emit orange light such that spurious reflections (green light) resulting from the vapour cavity are suppressed. the volume illumination of particles is achieved by a nd:ylf (λ ∼ 527nm) laser source introduced from the front and diverged using a plano-concave lens. interestingly, the re-entrant flow is enclosed by the venturi wall and the vapour cavity. hence, the measurement volume is naturally formed by the vapour cavity blocking the incident light in z-direction (see figure 1 b) and venturi wall. thus, knife-edge filters are not required. the effective measurement volume spans over ∼ 24×3.2×2.8 mm3. the images are acquired at a rate of 17.9khz and are pre-processed to remove the background intensity. further, the particle intensities are reconstructed with an iterative mart algorithm using davis 8.4. the autocorrelation of particle images shows that re-constructed particles are slightly elongated in one direction spanning on an average over ∼6 pixels. the particle image intensity in x− z projections are used to visualise the re-entrant flow thickness while the time series of reconstructed particle intensities are cross-correlated to evaluate velocity vector fields. moreover, owing to the periodicity in cloud shedding, the projections and the velocity fields are phase-averaged conditioned on a given cavity length (lc = 9mm, 11mm, 13.4mm corresponding to t/t = 0.3, 0.38, 0.54, where t is the shedding time period) over 370 instances to study the dynamics of the cavity shedding process. the standard deviation in reconstructed particle image intensity (x− z projections) is then used to quantify the re-entrant liquid film thickness at each time instance (not shown here). figure 2: (a) phase-averaged re-entrant flow (colour indicates concentration of tracer particles i.e. dark blue patches indicates no particles while green/yellow indicates liquid flow), (b) phase-averaged axial velocity (ux) in x− z plane (see figure 1 b for axes) for three different time instances (t/t = 0.3,0.38,0.54) in a shedding cycle. the bulk flow is from left to the right. note that the velocity of extremely thin high shear region close to the venturi wall could not be resolved due to the limitation of measurement technique. the velocity vector fields show that the re-entrant flow is a consequence of the stagnation point and impinging jet flow at the cavity closure region driven upstream by the adverse pressure gradient (see figure 2 b). apparently, the re-entrant flow for the cavitating venturi is not periodically generated, but rather exists continually beneath the vapour cavity for 0.1 . t/t . 0.6, until cavity detachment commences at t/t ' 0.6. the measured thickness of re-entrant flow spans over 30-45 pixels corresponding to ∼ 1mm and shows a spatio-temporal variation i.e. it is thinner closer to the cavity closure while thicker near the throat. as the cavity grows in time (t/t ∼ 0.3 to 0.54), the re-entrant flow thickness also increases. during this time, the re-entrant flow front is seen to travel upstream (see figure 2 a). furthermore, maximum velocity of re-entrant jet is also seen to increase substantially from ∼ 0.24ut to ∼ 0.6ut (see figure 2 b). this suggests that as the cavity grows in time, re-entrant flow momentum increases progressively along with an increase in re-entrant flow thickness. thus re-entrant flow interacts with the vapour cavity and initiates its pinching followed by shedding. references callenaere m, franc jp, michel jm, and riondet m (2001) the cavitation instability induced by the development of a re-entrant jet. journal of fluid mechanics 444:223–256 elsinga ge, scarano f, wieneke b, and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 jahangir s, hogendoorn w, and poelma c (2018) dynamics of partial cavitation in an axisymmetric converging-diverging nozzle. international journal of multiphase flow 106:34–45 microsoft word ispiv2021_whtien_288f.docx 1 effects of particle properties on visualizing flows in a twostage electrostatic precipitator using particle image velocimetry gede suantara darma and wei-hsin tien1 1 department of mechanical engineering, national taiwan university of science and technology, taipei, taiwan whtien@mail.ntust.edu.tw abstract the amount of particulate matter (pm) in the environment has been confirmed to be health risks on human bodies[1, 2], and therefore removing suspended particles has become the research goal of many studies. electrostatic precipitator (esp) is one of the high-efficiency particle collection technologies[3-7]. particle image velocimetry (piv) has been an effective tool for visualizing the flow patterns in experimental fluid mechanics, and many studies adopted this technique to study flows in esp[8-10]. however, particles charged by the electric field can cause deviation in measurement results since it does not follow the ionized air flow which can be charged differently from the tracer particles. in this study, the observation of the effects of different particle properties on flow field in a two-stage esp is the objectives of this study. a two-stage esp was built and four different seeding particles, aluminum oxide (al2o3) particle, oil droplet particle, sodium chloride (nacl) particle, and titanium dioxide (tio2) particle, are tested in the current study. in this study, the streamwise velocity of the flows ranges from 2.36 m/s to 4.18 m/s, the voltage of the corona electrode varies from 8 kv to 12 kv with a positive polarity, and the voltage of the collector electrode is fixed at 16 kv. to investigate the 3-d flow patterns inside the channel, data at different planes were taken for comparison. the results show that by increasing charge voltage from 8 kv to 12 kv with a streamwise flow velocity the 2.36 m/s, the y-component velocity for al2o3 particle, oil droplet particle, nacl particle and tio2 particle increased by 50.6%, 76.0%, 33.5% and 51.9%, respectively. moreover, for the case of the 4.18 m/s primary flow, the y-component velocity for al2o3 particle, oil droplet particle, nacl particle and tio2 particle increase by 52.7%, 59.2%, 59.4% and 65.9% after the voltages increase from 8 kv to 12 kv. piv results for oil droplet particle shows slower y-component velocities, which can be due to the lower archimedes number of 3.12e-06 and the mobility number that is larger than 3. on the contrary, in most of results from tio2 particles show high y-component velocity, which is due to the highest archimedes number of 1.15e-03 of the seeding particles tested in this study. this result shows that the particle is less affected by buoyancy effect. the piv results of the middle plane also shows that the ycomponent of velocity from -2.6 m/s to -0.5 m/s, in contrast to -1.0 m/s to 1.0 m/s from the near wall observation plane. these results are consistent to simulation results of the electric field distribution, which shows unequal electric field strengths between the middle and near wall regions of the test section. only half of the cage shape distribution of the electric field can be observed, and primary flow influences the ionic wind to move to the downstream area. based on the results, the oil droplet and tio2 particles are more suitable for the role of tracer particles compared to aluminum oxide and sodium chloride particles. figure 1 schematic diagram two-stage esp 2 figure 2 piv results at 2.63 m/s primary flow with 8 kv charge and 16 kv collector: (a) velocity maps of four different particles, and (b) velocity profiles at four different locations: (a) x/dh = 0.25, (b) x/dh = 0.5, (c) x/dh = 0.75 and (d) x/dh=1.0 references [1] f. sánchez-soberón et al., "main components and human health risks assessment of pm10, pm2. 5, and pm1 in two areas influenced by cement plants," atmospheric environment, vol. 120, pp. 109-116, 2015. [2] j. t. zelikoff et al., "effects of inhaled ambient particulate matter on pulmonary antimicrobial immune defense," inhalation toxicology, vol. 15, no. 2, pp. 131-150, 2003. [3] h. j. white, industrial electrostatic precipitation. addison-wesley pub. co., 1963. [4] j. böhm, electrostatic precipitators. elsevier amsterdam, 1982. [5] s. masuda and s. hosokawa, "electrostatic precipitation," in handbook of electrostatic processes: marcel dekker new york, 1995, pp. 441-480. [6] a. mizuno, "electrostatic precipitation," ieee transactions on dielectrics and electrical insulation, vol. 7, no. 5, pp. 615-624, 2000. [7] z. he and e. m. dass, "correlation of design parameters with performance for electrostatic precipitator. part ii. design of experiment based on 3d fem simulation," applied mathematical modelling, vol. 57, pp. 656-669, 2018. [8] j. podliński, m. kocik, r. barbucha, a. niewulis, j. mizeraczyk, and a. mizuno, "3d piv measurements of the ehd flow patterns in a narrow lectrostatic precipitator with wire-plate or wireflocking electrodes," czechoslovak journal of physics, vol. 56, pp. b1009-b1016, 10/01 2006. [9] a. niewulis, j. podliński, m. kocik, r. barbucha, j. mizeraczyk, and a. mizuno, "ehd flow measured by 3d piv in a narrow electrostatic precipitator with longitudinal-to-flow wire electrode and smooth or flocking grounded plane electrode," journal of electrostatics, vol. 65, no. 12, pp. 728-734, 2007/11/01/ 2007. [10] c. wang, z. xie, b. xu, j. li, and x. zhou, "experimental study on ehd flow transition in a small scale wire-plate esp," measurement science review, vol. 16, 06/01 2016. (a) (b) 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 effect of gust wind on flow over a wall-mounted fence d. bhamitipadi suresh1, e. j. aju1, m. j. zaksek1, m. m. leffingwell1, y. jin1∗ 1 department of mechanical engineering, the university of texas at dallas, richardson, tx 75080, usa ∗ yaqing.jin@utdallas.edu abstract in this work, the characteristics of incoming and wake flows downstream of wall-mounted fences under wind gust were explored with wind tunnel experiments. a time-resolved particle image velocimetry was used to capture the flow dynamics across two different fence heights. the results show that during the gust period, the wake presents distinct meandering and strong flow mixing. the probability density function distribution of flow velocities indicates that the mixing effect increases with the streamwise distances. specifically, for locations above the fence top tip, the growth of streamwise distance decreases the footprint of wind gust. however, for locations lower than the fence top tip, the local wind flows exhibit stronger variations before and after wind gust with the growth of downstream distance. overall, at the same relative streamwise and spanwise locations downstream of fences within the wake region, the higher fence better suppresses the influence of gust wind. 1 introduction wall mounted fences (wmf) have been studied for more than five decades (plate, 1971) for their unique aerodynamic properties and applications. they have been shown to offer protection against damage caused by winds (dong et al., 2010), reducing the wake flow and thus enhancing the deposition of air borne particles such as sand or snow (alhajraf, 2004; basnet et al., 2015), and accelerating wind speed at high altitude to increase the wind power production (tobin et al., 2017), among others. in one of the earliest works on wmfs, raine and stevenson (1977) studied turbulent characteristics behind both solid and porous fences and they established empirical relationships between mean velocity and turbulence intensity in the wake. a wind tunnel study conducted by judd et al. (1996) together with a large-eddy simulation by patton et al. (1998) showed that the fluid flow accelerates in the region above the fence. tobin et al. (2017) illustrated that this phenomenon can be effectively captured by installing wmfs upstream of wind turbines to increase power production by at least 10%. kim and lee (2001) deployed particle tracking velocimetry to study turbulent shear flow upstream of wmf. their results show that the separation point detaches and moves upstream of fence surface causing the streamline curvature to increase near the fence. more recent experimental investigation by tobin and chamorro (2018) found that wakemoment coefficient of wmf appeared to depend strongly on surface roughness and change with the cosine of incident angle. it, however, did not appear to change with aspect ratios (fence span length/height) of 10 or higher. aside from normal flow conditions, sudden intermittent or persistent increases in velocities, also known as gusts, have long been known for altering the fluid wake and change aerodynamic loading of various structures (hayashi, 1992; gromke and ruck, 2018; letson et al., 2019). in natural environments, complex topographic terrain of earth acts as a precursor of local rapid increase in velocity in atmospheric boundary layer (abl) (wagenbrenner et al., 2016). hayashi (1992) investigated turbulent wind flow in abl and found that effective mixing of flow occurs at peak gust due to efficient transport of downward momentum and that momentum flux dictates gust development. study by gromke and ruck (2018) highlights the effects of gust on damage patterns in forest and it illustrates that downstream vortex behind a row of trees (can be thought of as a wmf) deflects high momentum fluid from above which increases wind loading on subsequent rows. recent experiments by letson et al. (2019) analyzed properties of gust wind using doppler lidar and sonic anemometer to best describe its behavior at wind turbine heights. their probability distributions of gust parameters had better agreement between the two modes of measurement for wind coherence functions on vertical displacements than on horizontal displacements. despite the efforts reviewed above, our understanding of how gust winds affect the wake flows of wmfs remains very limited. in this work, wind tunnel experiments with state-of-the-art particle image velocimetry (piv) were conducted to study the incoming and wake flows of wmfs of two heights impinged by wind gusts. this study reveals the wake mixing mechanisms for structures under rapid variation of incoming flow velocities, and highlights the heterogenous wake dynamics in response to the wind gusts across various streamwise and vertical locations. experiment set up details are discussed in sec. ii, results are illustrated in sec. iii, main conclusions and future scope are summarized in sec. iv. 2 experimental setup figure 1: a) schematic of the experimental setup; b) photograph of boundary layer roughness elements in blast. wake characteristics over two wmfs were studied in boundary layer and subsonic tunnel (blast) in the university of texas at dallas. blast has a testing section of 30 m length, 2.8 m width and 2.1 m height. the fences were mimicked by flat acrylic plates with heights h1 = h (hereafter as low fence) and h2 = 2h (hereafter as high fence), where h=10 cm, and shared the same span of 30 cm and thickness of 4 mm. both fences were vertically mounted on the bottom wall of blast. in this work, surface roughness with short circular cylinders of 1.5 cm diameter and 2.5 cm height every 0.25 m was placed along the test section to develop the turbulent boundary layer incoming flows (see figure 1b). before the wind gust was initiated, the time-averaged incoming flow velocity at the top-tip of low and high fences (utip) were 2.2 m/s and 2.3 m/s. details of the non-dimensional incoming velocities and turbulence intensity are detailed in figure 2. a wooden square lattice mesh which covers the span of wmf, as shown in figure 1a, was used to block the incoming flow before the occurrence of gust. the mesh is 0.4 m length and 0.4 m width and composed with 23 horizonal and vertical wooden sticks, resulting in a porosity of 63%. the lattice mesh was mounted on a computer-controlled servo motor from its base. after the incoming flow reached the state-steady with sufficient time, the motor was rotated 90◦ within 2s, where the mesh became parallel to the flow. this resulted in the sudden variation of local blockage and therefore produced wind gusts. the influence of gust wind can be clearly visualized in the streamwise velocity distributions shown in figure 2c-e, where the time-averaged incoming velocity increased ∼ 23% after the gust at both y = h and y = 2h. to well characterize the influence of gust wind on wake flows, a time-resolved planar piv system from tsi was implemented to measure the flow statistics. a phantom veo440 camera with 4 mp resolution was used to capture the flow at a frequency of 200 hz for 15s (3000 image pairs). the camera covered a field of view (fov) of 491 x 307 mm2, corresponding to x/h ∈ [−1.3,3.4] and y/h ∈ [0.35,2.9] (the origin of the coordinate was set at the base of the fence and fov was set on the center of span). the air flow was seeded with soap bubbles of mean diameter 15µm, and the fov was illuminated with a 1 mm thick laser sheet from a high-speed laser. the captured image pairs were then interrogated using insight 4g software from tsi. with a multi-pass image processing, the final interrogation window size was 24 × 24 pixels2 with 50% overlap, resulting in a final vector grid spacing of ∆x = ∆y = 2.3 mm. overall, the uncertainty for the identification of seeding particle locations was approximately 0.1 pixel, leading to the uncertainty of flow velocity measurement of∼ 1.4% considering the bulk particle displacement of∼ 7 pixels between two successive images. figure 2: a): time-averaged streamwise velocity profile of incoming boundary layer flow; b) is same as a) but for the turbulence intensity. c-e) are representative instantaneous velocity distributions within the fov before, during and after wind gust. figure 3: streamwise velocity distribution over low fence, (a) before gust, (c) during gust, (e) after gust. figures (b), (d), (f) are corresponding vorticity contours. 3 result and discussion the influences of wind gust on the wake flows of fences are first illustrated via the normalized streamwise velocity distribution and wake vorticity magnitude in figure 3. before the wind gust was initiated, the wake flow presents clear velocity shear near the top tip of the fence, which produces the distinctive kelvin–helmholtz instability (figure 3a,b). the occurrence of wind gust leads to strong disturbance to the flow. as illustrated in figure 3c, the velocity magnitude in both wake region (i.e., y/h < 1) and upper region (i.e. y/h > 1) increased during the wind gust. during this process, the wake flow also presented clear ‘meandering’ dynamics, where the kelvin–helmholtz instability no long concentrates along y/h≈ 1. it is worth pointing out that due to the sudden variation of local wind velocities, strong flow mixing occurred during the wind gust, where vortical structures across different scales are observed in the incoming flow and upper region (figure 3d). the characteristics of flow reached a new steady-state after the wind gust passed (figure 3e,f). although the velocity magnitude significantly increased compared to the instant before gust, the location of velocity shear remains similar as those observed in figure 3a. this resulted in the similar distribution of kelvin–helmholtz instability but with overall stronger magnitude compared to the instants before gust. these phenomena were also observed for the high fence illustrated in figure 4. the time series of wind figure 4: streamwise velocity distribution over high fence, (a) before gust, (c) during gust, (e) after gust. figures (b), (d), (f) are corresponding vorticity contours. velocities within the upper region across various streamwise locations are illustrated in figure 5a. overall, the wind velocities present sudden increase right after the occurrence of gust wind. to further highlight the variation of local flow velocities, the corresponding probability density function (pdf) distribution of wind velocities are presented in figure 5b-d. specifically, in the very near wake region (x/h = 1), the pdf presents two distinctive peaks, corresponding to the flow velocities before and after the wind gust (figure 5b). interestingly, the second peak representing the higher wind velocity after gust gradually weakened with the growth of streamwise distances (figure 5c, d). note that the height of wake region gradually expands figure 5: a) representative time series of streamwise velocity u/utip for low fence at y/h = 2.5. (b-d) are the corresponding pdf distribution of normalized streamwise velocities. figure 6: a) representative time series of streamwise velocity u/utip for low fence at x/h = 1. (b-d) are the corresponding pdf distribution of normalized streamwise velocities. along the streamwise distance (see figure 3); therefore, the wind velocities located further downstream experience stronger mixing effects with the wake flows. this results in broader local wind velocity distributions and suppresses the intensity of secondary peak initiated by wind gust. similar to the cases along streamwise direction, the wind gust also produces heterogeneous influences on local velocity fluctuations along the vertical direction. while wind velocities within the upper region present distinct variation after the gust with dual peaks in pdf distribution, this is not the case within the wake flow (figure 6); here, the pdf distribution of wind velocities presents a sole peak for y/h≤ 1. it is worth pointing out that the wake velocities exhibit much stronger fluctuations than those within the upper region. this results in a wide range of overlap between the wind velocities before and after the wind gust, thus suppresses the appearance of ‘dual peaks’ in the pdf distribution. finally, to highlight the influence of fence height on wake velocity variations during wind gust, the pdf distributions of streamwise flow velocity before and after wind gust at the same relative locations downstream of both fences are illustrated in figure 7 and 8. here, all locations are at the half fence height but with different streamwise distances. overall, the pdf distribution shifts towards the negative values of u/utip after the occurrence of wind gust, which is induced by the stronger backward flow (i.e., u < 0) as illustrated in figure 3 and 4. regardless of fence height, the gust wind produces little influence on wind velocities within the very near wake regions (figure 7a and 8a). in particular, the pdf distribution of wake velocities is nearly identical before and after wind gust for the high fence at x/h = 1. with the growth of streamwise distances, the flow mixing between wake and upper regions becomes stronger and more rapid, where more footprint of wind gust enters the wake region thus resulting in larger differences of flow velocities before and after gust. such differences are in general more distinctive for the lower fence, indicating that within the same turbulent boundary layer, the wake flows of structures with smaller size are more sensitive to the influence of wind gusts. figure 7: pdf distribution of normalized wake velocity downstream of low fence at y/h = 0.5 and a): x/h = 0.5; b): x/h = 1; c): x/h = 1.5. figure 8: pdf distribution of normalized wake velocity downstream of high fence at y/h = 1 and a): x/h = 1; b): x/h = 2; c): x/h = 3. 4 conclusions the occurrence of wind gust leads to distinctive flow mixing and wake meandering downstream of wallmounted fences. for locations above the fence height within the very near wake, the pdf distribution of wind velocities reveals two clear peaks corresponding to velocities before and after gust. however, this phenomenon is gradually diminishing with the growth of streamwise distances due to the stronger mixing effects, as well as the decrease of vertical distances due to the higher local flow fluctuations. in general, for both fences within the very near wake region, the local flow characteristics present little variations before and after wind gust. our future work will explore the influence of wind gust with various intensities, and its impact on more complex structures such as wind turbines and urban buildings. acknowledgements this work was supported by the department of mechanical engineering, the university of texas at dallas, as part of the start-up package of dr. y.j. references alhajraf s (2004) computational fluid dynamic modeling of drifting particles at porous fences. environmental modelling & software 19:163–170 basnet k, constantinescu g, muste m, and ho h (2015) method to assess efficiency and improve design of snow fences. journal of engineering mechanics 141:04014136 dong z, luo w, qian g, lu p, and wang h (2010) a wind tunnel simulation of the turbulence fields behind upright porous wind fences. journal of arid environments 74:193–207 gromke c and ruck b (2018) on wind forces in the forest-edge region during extreme-gust passages and their implications for damage patterns. boundary-layer meteorology 168:269–288 hayashi t (1992) gust and downward momentum transport in the atmospheric surface layer. boundarylayer meteorology 58:33–49 judd mj, raupach mr, and finnigan jj (1996) a wind tunnel study of turbulent flow around single and multiple windbreaks, part i: velocity fields. boundary-layer meteorology 80:127–165 kim hb and lee sj (2001) time-resolved velocity field measurements of separated flow in front of a vertical fence. experiments in fluids 31:249–257 letson f, barthelmie rj, hu w, and pryor sc (2019) characterizing wind gusts in complex terrain. atmospheric chemistry and physics 19:3797–3819 patton eg, shaw rh, judd mj, and raupach mr (1998) large-eddy simulation of windbreak flow. boundary-layer meteorology 87:275–307 plate ej (1971) the aerodynamics of shelter belts. agricultural meteorology 8:203–222 raine jk and stevenson dc (1977) wind protection by model fences in a simulated atmospheric boundary layer. journal of wind engineering and industrial aerodynamics 2:159–180 tobin n and chamorro lp (2018) wakes behind surface-mounted obstacles: impact of aspect ratio, incident angle, and surface roughness. physical review fluids 3:033801 tobin n, hamed am, and chamorro lp (2017) fractional flow speed-up from porous windbreaks for enhanced wind-turbine power. boundary-layer meteorology 163:253–271 wagenbrenner ns, forthofer jm, lamb bk, shannon ks, and butler bw (2016) downscaling surface wind predictions from numerical weather prediction models in complex terrain with windninja. atmospheric chemistry and physics 16:5229–5241 introduction experimental setup result and discussion conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 time-resolved sphere and fluid motions in turbulent boundary layers yi hui tee1∗, ellen k. longmire1 1 university of minnesota, aerospace engineering and mechanics, minneapolis, usa ∗ teexx010@umn.edu abstract this paper extends the study by tee et al. (2020) to investigate the effect of large coherent structures on motion of spheres with specific gravities of 1.006 (p1) and 1.152 (p3) at reτ = 670 and 1300 (d+ = 56 and 116). the sphere and fluid motions are tracked simultaneously via 3d particle tracking and stereoscopic particle image velocimetry over the streamwise-spanwise plane, respectively. with sufficient mean shear, sphere p1 lifts off of the wall upon release before descending back towards the wall at both reτ. it typically accelerates strongly over a streamwise distance of less than one boundary layer thickness before approaching an approximate terminal velocity. by contrast, the denser sphere p3 does not lift off upon release but mainly slides along the wall. at lower reτ where wall friction is stronger, this sphere translates with unsteady velocity, significantly lagging the local fluid. the streamwise velocities of both spheres correlate strongly with the fastand slow-moving zones that approach and move over them. in most runs, both spheres lag the local coherent structures and travel with either fastor slow-moving zones throughout the observed trajectories. vortex shedding, which is most prevalent for sphere p3 at reτ = 670, is also important. the sphere spanwise motion is prompted by wall friction, spanwise fluid motion, and/or meandering of the coherent structures, and spheres do not appear to migrate preferentially into slow-moving zones. 1 introduction in particle-laden flow, the transport of particles such as sand, dust, sediment, plankton, and pollutants in air, rivers, or oceans is complicated by the presence of particle-wall and particle-turbulence interactions. as these flows are turbulent in nature, coherent structures in the boundary layer can have significant effects on particle suspension, deposition, and transport. early studies examining particle wall-normal motion in turbulent open-channel flows include imaging experiments from sutherland (1967), francis (1973), and sumer and oguz (1978), to name a few. sutherland (1967) proposed an entrainment hypothesis whereby strong turbulent eddies could disrupt the viscous sublayer and lift grains off of an underlying sediment bed. later, kaftori et al. (1995), van hout (2013), and baker and coletti (2021), among others, incorporated direct visualization techniques to measure particle and fluid velocities. these studies concluded that particle resuspension and deposition events are strongly influenced by the coherent structures and intermittent fluid forces acting on the particle. research by rashidi et al. (1990), pedinotti et al. (1992), and niño and garcia (1996) on particle spanwise motion concluded that small inertial particles with diameter, d+ ∼o(1) tend to accumulate in low-speed streaks near the wall where ejection events are prominent. from here onward, the superscript + denotes quantities normalized by the friction velocity (uτ) and the kinematic viscosity (ν). particles of finite size can experience variations in shear and normal forces around their circumferences. in this context, the study by costa et al. (2020) comparing the results between interface-resolved and one-way-coupled point-particle direct numerical simulations (dns) demonstrated distinctive differences in particle behavior near the wall due to the absence of any shear-induced lift force in the point-particle model. this finding also highlights the importance of instantaneous fluid forces on the motion of discrete particles. zeng et al. (2008) quantified the fluid forces acting on a fixed sphere located at multiple distances above a smooth wall. the mean lift forces simulated for spheres with 1.78 ≤ d+/2 ≤ 12.47 centered at a wallnormal location y+ = 17.31 from the wall at friction reynolds number, reτ = 178.12 were negative in all cases. tomographic piv performed by van hout et al. (2018) at reτ = 352 downstream of a tethered sphere with d+/2 = 25 centered at y+ = 43 above the wall also suggested a negative lift contribution due to the sphere wake tilting away from the wall. by contrast, hall (1988), who measured the mean lift force acting on a stationary particle lying on the wall in a turbulent boundary layer using a force transducer, reported a positive lift contribution. the experimental data showed that for 3.6 < d+ < 140 and particle reynolds number, 6.5 < rep < 1250, the normalized mean lift forces are strongly positive and could be approximated by f+ l = (20.90± 1.57)(d+/2)2.31±0.02. these results imply that the net wall-normal force including lift related to the mean shear can vary significantly with the sphere position relative to the wall. all of these effects can significantly impact particle motion in wall-bounded turbulent flows, where the particles can either slide or roll along the bounding surface or lift off from and collide with the wall. aside from lift forces induced by mean shear and turbulence, magnus lift can play a role when solid body rotation is present. this effect remains relatively unstudied in particle-laden turbulent wall-bounded flow due to the challenges in reconstructing and modeling particle rotation. current experimental methods for reconstructing sphere orientation include printing specific patterns over the sphere surface (zimmermann et al., 2011; mathai et al., 2016) and embedding visible tracers into the interior of transparent spheres (bellani et al., 2012; klein et al., 2013). the former method compares the unique pattern captured by high-speed cameras with synthetic projections to extract the absolute sphere orientation; the latter method resolves tracer velocities within the solid body to obtain the rotation rate. barros et al. (2018) extended klein et al.’s (2013) methodology to include opaque spheres. small dots were marked all over the solid surface, and two cameras were employed to reconstruct the 3d rotation rate using kabsch’s (1976) algorithm. in the present study, we conduct simultaneous particle tracking and stereoscopic particle image velocimetry (spiv) to investigate the 3d motion of individual finite-size spheres and the surrounding fluid motion in turbulent boundary layers. multiple sphere densities and flow conditions are considered. to obtain both the translation and rotation of a sphere, barros et al.’s (2018) methodology is adapted to the requirements of the current experimental setup. a detailed discussion on sphere motion has been reported previously in tee et al. (2020). in this paper, we will focus on the new results that we have obtained on fluid motion surrounding a moving sphere to understand particle-turbulence and particle-wall interactions. 2 methodology the experiments were conducted in a recirculating water channel with a glass test section of 8 m length and 1.12 m width. a 3 mm cylindrical trip-wire located at the entrance of the test section triggered the development of a turbulent boundary layer along the bottom wall. we focus on reτ =670 and 1300 to investigate the effect of mean shear and turbulence on sphere motion. the water depths were maintained at 0.396 m and 0.392 m respectively. these correspond to free-stream velocities (u∞) of 0.205 and 0.464 m s-1, with boundary layer thicknesses (δ) of 0.076 and 0.073 m. the mean flow statistics of the unperturbed turbulent boundary layers were determined from planar piv measurements in streamwise wall-normal planes. hereafter x, y, and z define the streamwise, wall-normal, and spanwise directions respectively. to achieve a repeatable and controllable initial condition, magnetic spheres molded from a mixture of wax and iron oxide were used. the sphere surfaces were black, and white dots were painted at arbitrary locations using an oil-based pen to monitor both translation and rotation (see inset in figure 1b). we consider two spheres of diameter, d =6.35 mm with specific gravities (ρp/ρ f ) of 1.006 (p1) and 1.152 (p3), where ρp is the sphere density and ρ f is the fluid density. the sphere diameters are significantly larger than the kolmogorov length scale, with d+ of 56 and 116 respectively. meanwhile, the particle stokes numbers (st+, stδ) expressed as the ratio of particle response time, τp = (ρ f + 2ρp)d2/36νρ f (crowe, 2005) to the characteristic flow time scale based on viscous time scale (ν/u2 τ) and largest time scale (δ/u∞), range from 262 to 1230 and 9.1 to 23.5, respectively. the initial particle reynolds numbers defined as rep = ureld/ν are 730 and 1730, where urel is the difference between the mean fluid velocity and velocity of the particle center. for each run, a given sphere was held statically on the smooth wall in the boundary layer by a magnet placed flush with the outer wall of the channel. the sphere was positioned at a location 4.2 m downstream of the trip wire and 4δ away from the nearest sidewall. this location will be considered as the origin in x and z, with the bottom wall as y = 0. the magnet was then deactivated, releasing the sphere and allowing it to propagate with the incoming flow. a screen was located at the end of the test section to capture the sphere and prevent it from recirculating around the channel. for each case considered, up to j = 10 trajectories were captured using the same sphere. details of the experimental parameters are summarized in table 1. for sphere tracking, two pairs of phantom v210 high-speed cameras were arranged in stereoscopic configurations, looking from the side wall, to track the sphere in 3d space over a relatively long field of view (see figure 1a). two white led panels illuminated the domain considered. the particles were tracked over a streamwise distance up to x = 5δ. before computing the particle translation and rotation, the grayfigure 1: experimental setup. (a) top view: two pairs of high-speed cameras (s1 and s2) with infrared (ir) -block filters, aligned in stereoscopic configurations for capturing the trajectory and rotation of a marked sphere over a long field of view. (b) cross-section view: a pair of stereoscopic high-speed cameras with ir-pass filters, positioned under the channel for capturing the fluid motion illuminated by the infrared laser over the streamwise-spanwise plane. the sphere was held in place by a magnet connected to a solenoid (on). dashed line box illustrates the magnet position after turning off the power supply (solenoid off) to release the sphere. inset: example of sphere captured in gray-scale with diameter (d) spanning ∼ 43 pixels. table 1: summary of experimental parameters. |vs| represents sphere settling velocity magnitude in quiescent flow; fl ∗ = (fl−fb)/fb where fl and fb denote the mean wall-normal fluid-induced force based on hall’s (1988) expression and the net buoyancy force, respectively. reτ initial rep d+ sphere ρp/ρ f |vs|/u∞ st+ stδ initial fl ∗ 670 730 56 p1 1.006 0.083 262 9.10 11±2 p3 1.152 0.78 287 9.98 −0.77±0.04 1300 1730 116 p1 1.006 0.037 1120 21.4 61±10 p3 1.152 0.34 1230 23.5 0.24±0.2 scale images were pre-processed using a matlab circular hough transform routine to isolate the sphere from the background. the extracted sphere images were then imported to davis 8.4 and further processed with 3 x 3 gaussian smoothing and sharpening routines to increase the dot contrasts. subsequently, pixel intensity values that were less than the white dots were set to 0 to isolate the dots from the sphere image. after performing a volumetric calibration, a 3d-ptv routine was implemented to reconstruct the dot coordinates from both camera pairs. the data sets obtained from ptv were composed of the 3d coordinates of true and ghost markers and their corresponding 3d velocity vectors. hence, the filtering methodology proposed by barros et al. (2018) was employed to remove the ghost tracks. once the true markers were identified, the sphere centroid was determined by applying the equation of a sphere. then, a rotation matrix that best aligned the markers of consecutive images was obtained (barros et al., 2018). for fluid motion, a third pair of high-speed cameras (phantom m110) was arranged in stereoscopic configuration, looking from the bottom wall, to obtain the three components of fluid velocity within a x− z plane (see figure 1b). the flow was seeded with silver-coated hollow glass sphere tracers, with an average diameter and density of 13 µm and 1600 kg m-3, respectively. an oxford firefly infrared pulsed laser with a wavelength of 808 nm was used to illuminate the tracer particles. the laser sheet illuminated through the side wall at y = 0.7d had a thickness of 1 mm with field of view of 0.3 < x/δ < 1.7 and −0.5 < z/δ < 0.5. infrared-block and -pass optical filters were mounted to the lenses of the tracking and spiv cameras respectively to optimize the image quality. to capture both time-resolved sphere and fluid motions, all six cameras were triggered simultaneously with the infrared laser at 240 and 480 hz for reτ = 670 and 1300, respectively. stereoscopic self-calibration was carried out on top of the classic calibration using 200 image figure 2: sphere wall-normal trajectories (y) plotted based on the centroid positions at reτ = 670 (a) and reτ = 1300 (b), respectively. left axis: normalized by inner scaling; right axis: normalized by sphere diameter. pairs from unperturbed flow fields. prior to processing the spiv images in davis 10.1, the sphere, which appeared as a very bright spot, was removed using matlab. then, the spatial auto-mask function in davis 10.1 was implemented to mask out regions without tracer particles such as the shadow and area where the sphere had been extracted. sliding sum-of-correlation with a filter length of 2 images, and an overlap of 50% over initial interrogation window sizes of 64 by 64 pixels followed by three passes of 32 by 32 pixels was then employed to obtain the three-component velocity vectors (see sciacchitano et al., 2012). spurious vectors were removed based on the universal outlier detection criterion (westerweel and scarano, 2005). the spatial resolutions of the computed velocity vectors are 24 and 50 viscous units at reτ of 670 and 1300, equivalent to 2.73 mm. the mean unperturbed fluid velocities (u) at laser sheet heights of y+ = 40 and 80 are 0.124 and 0.287 m s-1, respectively. 3 results and discussion 3.1 sphere wall-normal motion figure 2 shows the sphere wall-normal (y) trajectories plotted against their streamwise distance traveled, with all particle runs superposed. note that these trajectories represent new data obtained from the current simultaneous sphere and fluid tracking experiments, using two out of the three spheres considered in tee et al. (2020). the sphere behavior was consistent with the previous runs. for completeness, we will provide a brief summary of the sphere motions here. readers are encouraged to refer to tee et al. (2020) for a more detailed analysis of three-dimensional sphere translation and rotation. for stationary spheres, the mean lift forces against the net buoyancy forces are computed using hall’s (1988) equation obtained for a fixed sphere in a turbulent boundary layer where fl = f+ l ν2ρ f , fb = (mp−m f )g and fl ∗ = (fl−fb)/fb (see table 1). here, mp is the mass of sphere, m f is the mass of fluid displaced and g is the gravitational acceleration. as all spheres are denser than water, the net buoyancy force will always act downward in the direction of gravity. thus, if fl ∗ > 0, the sphere is likely to lift off upon release, and vice versa. for the least dense sphere p1, at reτ = 670, fl ∗ = 11. increasing reτ to 1300 doubles d+ and thus the sphere mean lift force increases fivefold. these estimations agree very well with our observations where sphere p1 mostly lifts off of the wall once release at both reτ (plotted as black in figure 2). additionally, owing to the stronger resultant upward force, sphere p1 at reτ = 1300 lifts off higher than at reτ = 670. this shows that the initial lift-off height correlates strongly with the local mean shear. for the densest sphere p3, no initial lift-offs are observed (plotted as blue in figure 2). this sphere does not have sufficient lift force to overcome the downward force and translates along the wall upon release. here, the sphere slides but does not roll along the wall upon release, unlike what was observed by drake et al. (1988) and yousefi et al. (2020) for dense particles on rough beds. in general, most of our results on initial sphere lift-off agree well with the hall’s (1988) equation. by varying the initial turbulent conditions, yousefi et al. (2020) concluded also that the mean flow irrespective of the initial turbulent structures is responsible for the particle lift-offs. sphere p1, which always lifts off initially, always descends towards the wall after reaching a local maximum in height, typically undergoing multiple subsequent lift-off events. this sphere either contacts the wall and then lifts off again, or else reascends without returning to the wall, similar to what was reported by francis (1973), sumer and oguz (1978), van hout (2013), and yousefi et al. (2020). from our studies, we also noticed that even after touching and sliding along the wall, the sphere could ascend to greater heights than the initial maximum. at the lower reτ, the sphere lifts off more frequently and to lower maximum heights. the lift-off angles are less than 12◦ throughout all of the trajectories. for sphere p1, only minimal rotations are observed at both reτ throughout all trajectories. sphere p3, which does not generally lift off upon release, did experience repeated lift-off events further downstream, with magnitude of ≤ 0.1d. this behavior is observed frequently at both reτ after the sphere begins to roll forward, occurring consistently starting at x ≈ 2δ when reτ = 670. the rotational velocity is stronger at reτ = 670 than at reτ = 1300, thus indicating a stronger forward rolling to sliding tendency. 3.2 sphere streamwise velocity figures 3a and 4a illustrate the respective sphere p1 and p3 streamwise velocities (up) at reτ = 670 for all runs (left axis; solid lines). the sphere velocities are normalized by the mean unperturbed fluid velocities at the height of the sphere centroids (u(y)). in a uniform, steady, unbounded flow, an initially stationary sphere always accelerates to the local fluid velocity with zero relative velocity. in our studies, however, the presence of turbulence and the wall both modify the surrounding flow fields and sphere kinematics. due to the large initial drag, the spheres accelerate strongly upon release until they achieve an approximate terminal velocity. this acceleration occurs within x ≤ 1δ for all cases except p3 at reτ = 670. the approximate terminal velocity for sphere p1 is closer to the mean local fluid value than that for p3 at both reτ. even though sphere p1 has density fairly close to that of the fluid, it still lags behind the local fluid mean in most runs with infrequent occasions where it travels faster than the local fluid mean at both reτ. for this sphere, the streamwise velocity fluctuation also correlates positively with the respective y-trajectory as shown by the two sample runs (red and blue curves) in figure 3a. here, as sphere p1 ascends, it gains more momentum from the faster-moving fluid away from the wall and accelerates; as it descends, it loses momentum due to the slower-moving fluid near the wall and thus begins to decelerate. meanwhile, the velocity curves for sphere p3 at reτ = 670 initially fluctuate significantly with shorter wavelengths before increasing strongly near x > 1.5δ to an approximate terminal velocity. this delayed acceleration also corresponds with the times where the sphere transitions from forward sliding to rolling with small repeated lift-off events. as the small lift-off events (x > 2δ) occur at a much shorter wavelength than the corresponding streamwise velocity fluctuations in the same region, these variations appear decoupled as opposed to sphere p1. as sphere p3 interacts with the wall more often, its forward motion is strongly retarded by the friction force compared with sphere p1 which mostly translates above the wall. after attaining an approximate terminal velocity, velocity fluctuations of order ±0.2u∞ are observed in most runs for all cases. for sphere p1, as highlighted above, although the velocity fluctuation matches the sphere wall-normal position, the magnitude of the fluctuations is not directly proportional to the lift-off magnitude. here, within the same case, the velocity curves also spread over a wide range compared with mean sphere velocity. this suggests that the velocity gradient that changes with the wall-normal position is not the only reason behind the sphere streamwise velocity fluctuation. to understand the widespread variation of the sphere streamwise velocity, we look at the corresponding streamwise fluid velocity contour plots. within streamwise-spanwise planes of the logarithmic layer, long coherent structures that appear as alternating fastand slow-moving zones, or high and low momentum regions, are observed commonly as previously reported by researchers such as dennis and nickels (2011) and tan and longmire (2017). here, we notice that these structures have significant effects on the sphere streamwise velocity such that a sphere traveling in a low momentum region (figure 3b which corresponds to the blue up curve in figure 3a) accelerates less and lags the mean flow more than the same sphere traveling in a high momentum region (see up plotted in red in figure 3a and the corresponding fluid velocity in figure 3c). meanwhile, sphere p3 at the same reτ lags the fluid more significantly due to stronger wall friction. therefore, it is overtaken repeatedly by both low and high momentum regions as shown in figure 4b, causing its streamwise velocity to fluctuate more rapidly than that for sphere p1. as the spheres are significantly larger than the kolmogorov length scale (d = 25 and 44η), and st+ are significantly larger than stδ, the spheres are more likely to be accelerated and decelerated by the large scale motions in the logarithmic region than by smaller scale motions closer to figure 3: sphere p1 at reτ = 670. (a) left axis (solid lines): sphere streamwise velocity, up normalized by mean unperturbed fluid velocity at the sphere center location for all runs. right axis (dashed lines): sphere wall-normal trajectories. blue and red curves: p1 in low and high momentum regions, respectively. black dash-dot lines: spiv field of view. (b, c) samples of time-resolved fluctuating streamwise fluid velocity, u surrounding the sphere in low and high momentum regions (blue and red curves in (a)) respectively. u is mean unperturbed fluid velocity at the laser sheet height of y+ = 40 (y = 0.7d). grey region under the sphere represents sphere shadow. the wall as reported by ebrahimian et al. (2019). in addition, distinct wake features can be observed consistently downstream of sphere p3 within the spiv field of view as indicated by the regions with strong negative u in figure 4b. vortex shedding can be identified from the black and green contour lines which represent clockwise and counter-clockwise swirls. the swirling strength is computed from the imaginary part of the complex eigenvalue of the local velocitygradient tensor and normalized by its root mean square value (see wu and christensen, 2006). swirling regions including 4 or more grid points are then identified using a threshold of 0.5. in the measurement plane, these appear as pairs of counter-rotating vortices, which could be slices of hairpin-like loops as observed by van hout et al. (2018) using tomographic piv. in this region, the local particle reynolds numbers are ∼ o(500). as sphere p1 translates with velocity closer to the mean fluid value, its rep, after it accelerates steeply from rest, decreases from 730 and 1730 at reτ = 670 and 1300 to a range between 1 < rep < 300. if we consider sphere p1 in figure 3b, which translates relatively slower than the local fluid mean and where the instantaneous rep is about 220, then vortex shedding would be present occasionally based on zeng et al.’s (2008) conclusion for rep > 200. by contrast, for sphere p1 in figure 3c, which translates faster than the local mean fluid and has an instantaneous rep < 50, vortex shedding would typically be absent. here, the region of slow moving fluid upstream of and below the sphere is most likely the wake left behind as the sphere accelerates from rest and moves in the positive z direction. therefore, for a discrete particle with significant rep, vortex shedding can play an important role not only in affecting the instantaneous drag force but also in modifying the turbulence organization. for particles very close to the wall, the shedding also likely affects the instantaneous wall-normal force. to validate our findings on sphere velocity variation, we computed the two-point spatial correlation coefficients between the sphere and fluid velocities across all runs in both streamwise and spanwise directions within the spiv field of view at y = 0.7d using the following equation: rup,u f (x,z) = 1 j−1 j ∑ j=1 ( up(xo,zo)−up(xo,zo) σup )( u f (xo +∆x,zo +∆z)−u f (xo +∆x,zo +∆z) σu f ) (1) the over-line represents time-averaged quantity within the field of view in each run; subscript ‘o’ represents the origin for spatial correlation; σ represents the standard deviation. in most runs, even though the spheres move in the y−direction (especially p1), they do not rise completely above the laser sheet. in the correlations, we consider only results where the sphere intersects the laser sheet positioned at y= 0.7d (y+ = 40 and 80 for reτ = 670 and 1300, respectively) throughout the spiv field of view. the results for both p1 and p3 figure 4: sphere p3 at reτ = 670. (a) sphere streamwise velocity, up normalized by mean unperturbed fluid velocity at the sphere center location for all runs. blue line: sample run in (b). black dash-dot lines: spiv field of view. (b) sample of time-resolved fluctuating streamwise fluid velocity, u surrounding the sphere plotted as blue in (a). black and green contours in the bottom plot represent clockwise and counterclockwise swirls. figure 5: two-point spatial correlation coefficients between the sphere and fluid streamwise velocities at reτ = 670 for sphere p1 (a) and p3 (b). at reτ = 670 are plotted in figure 5 in the form of contour plots, with the origin (xo,zo) centered at the sphere centroid location. note that even though the number of runs is insufficient to achieve smooth statistical convergence over the entire domain shown, the results are nevertheless useful in highlighting the predominant trend for large-scale particle-turbulence interaction. the results demonstrate that the streamwise velocity of these spheres is positively correlated with the surrounding streamwise fluid velocity (rup,u f (x,z) > 0; red). specifically, the sphere velocity is strongly affected by the fastand slow-moving zones that move over the sphere in the form of long, relatively narrow structures. adjacent to the positively correlated region are long, narrow regions with negative correlation (blue) indicative of the surrounding fluid structures. here, the sphere velocity is positively correlated with both the upstream and downstream fluid. for sphere p1, the upstream and downstream patterns have similar strength and size. by contrast, for sphere p3, the downstream region remains positively correlated over a longer distance, likely a result of the stronger wakes present in this case. these results imply that for an initially stationary sphere with large rep, upon release, its forward motion, which is governed by the relative force between the drag and friction, is strongly dependent on the coherent structures that approach and move over the spheres as well as the vortex shedding. for sphere p1, its wall-normal force, which is a function of the wall-normal component of the fluid velocity and the surrounding shear and pressure fields, must also be affected by these fluid velocity variations. figure 6: (a) sphere spanwise positions plotted based on the centroid locations at reτ = 670 for sphere p1 (black) and p3 (blue). (b) sample trajectory for sphere p3 at reτ = 670. (c) sample of time-resolved spanwise fluid velocity, w surrounding sphere p1 at reτ = 670, plotted in red in figure 3a. the black curves superposed on top of the contours represent the sphere spanwise position along its trajectory. 3.3 sphere spanwise motion the spanwise trajectories of spheres p1 and p3 at reτ = 670 are plotted in figure 6a. once released, instead of propagating along z = 0, the spheres typically move sideways to some degree. then, they either continue to propagate in one direction or else reverse and travel in the opposite direction, with some crossings over the z = 0 plane. in all cases, the maximum spanwise distance traveled from z = 0 is approximately 12% of the corresponding streamwise distance traveled. for the wall-interacting sphere p3, most of the spanwise curves initially fluctuate at higher frequencies than in the other lifting cases. the range including the direction changes (when x < 2δ) corresponds directly with the region prior to the onset of forward rolling. if we assume that the displacement results from a pure rolling motion about the streamwise axis, then the spanwise displacement based would be zs = θxd/2. this result for one sample run is plotted in red in figure 6b and compared to the true spanwise position in blue. interestingly, the zs trajectory corresponds very well with the z-trajectory especially for x < 1.5δ. the small and growing deviation between the curves 1δ < x < 2δ suggests that the particle slid in the spanwise direction while rolling over this range. similar to this result, in most runs, the spanwise motion for sphere p3 often has a rolling component induced by a spanwise fluid torque and wall friction. while many previous studies concluded that particles with smaller st+ tend to migrate into low-speed streaks or zones, our results on larger particles show no preferential behavior of this sort. here, a particle that lags in a surrounding slow-moving region and is approached by a trailing fast-moving region will accelerate and travel with the high momentum fluid. similarly, a particle that lags in a surrounding fast-moving region could be overtaken by a trailing slow-moving region and then decelerate. the various runs observed do not reveal any obvious tendency of the spheres to migrate in the spanwise direction from highto low-speed zones. we do notice examples where a particle traveling within a long, slow-moving zone as shown in figure 3b, tends to meander with the coherent structure. also, in some other runs, the particle spanwise motion is strongly affected by the spanwise fluid motion. for example, in figure 3c, instead of moving towards the slow-moving zone in the +z direction, the sphere moves towards −z. by referring to the corresponding spanwise velocity contour plot shown in figure 6c, we note that this sphere changes direction because it becomes surrounded by fluid moving in the negative spanwise direction (blue). 4 conclusions simultaneous particle tracking and stereoscopic particle image velocimetry experiments were conducted to investigate the three-dimensional translation and rotation of spheres and their surrounding fluid motions at reτ = 670 and 1300. individual spheres with diameters of 56 and 116 viscous units and specific gravities of 1.006 (p1) and 1.152 (p3) were released from rest and tracked over a streamwise distance up to x ≈ 5δ. in this paper, the fluid motions surrounding the sphere within the field of view of 0.3 < x/δ < 1.7 and −0.5 < z/δ < 0.5 at y = 0.7d were discussed. upon release, when the mean shear lift force is larger than the net buoyancy force, the less dense sphere p1 lifts off from the wall in almost all runs. this sphere undergoes multiple lift-off events, including saltation and resuspension, with a stronger lift-off magnitude observed at higher reτ. although this sphere mostly travels above the wall, it nevertheless lags behind the mean fluid velocity even after attaining an approximate average terminal velocity. throughout its trajectory, the lifting sphere translates with very weak or minimal rotations about any axis. by contrast, upon release, the wall-interacting sphere p3 first slides along the wall with minimal rotation. at reτ = 670, the initial acceleration of this sphere is significantly retarded by the opposing friction force, in contrast to the cases where the sphere accelerates steeply over a streamwise distance of δ. after propagating downstream by ≈ 1.5δ, this sphere accelerates again as forward rolling (with slipping) and repeated small lift-off events of magnitude less than 0.1d begin to occur. hence, wall friction is important in impeding the acceleration of the denser sphere as well as in prompting the rolling motion. a detailed discussion on sphere motions can be found in tee et al. (2020). by correlating the sphere and fluid motions, the current results suggested that coherent structures in the boundary layers such as the high and low momentum regions, vortex shedding, as well as spanwise fluid motions, have important effects on sphere kinematics. for both spheres, the fluctuations in the sphere streamwise velocity are strongly affected by the large-scale coherent structures that approach and move over the sphere. for sphere p1, the fluctuations in the sphere streamwise velocity are also correlated with the sphere wall-normal positions. meanwhile, for sphere p3, the fluctuations are more correlated to the vortex shedding. in all cases, the spheres move significantly in the spanwise direction migrating up to 12% of the streamwise distance traveled. no preferential alignments with fluid structures are observed as the spheres are seen within both fastand slow-moving zones. for the denser sphere, due to the direct wall interactions, its spanwise motion is strongly correlated with rotation about the x-axis which must be induced by a fluid torque. the spanwise motion of the lifting sphere, which travels mostly above the wall, correlates with spanwise motion in the fluid. a sphere that travels within a long, slow-moving zone is affected by the meandering nature of that structure. as most spheres lag the local fluid velocity, the magnitude of the relative velocity plays an important role in determining whether the sphere travels a significant distance within one zone or whether it is overcome relatively rapidly by succeeding fastand slow-moving zones. acknowledgements the authors thank diogo c. barros, nicholas morse, ben hiltbrand and alessio gardi for their help with this project. this work was funded by the u.s. national science foundation (cbet-1510154). the first author is supported by the university of minnesota graduate school under the doctoral dissertation fellowship. references baker lj and coletti f (2021) particle–fluid–wall interaction of inertial spherical particles in a turbulent boundary layer. j fluid mech 908 barros d, hiltbrand b, and longmire ek (2018) measurement of the translation and rotation of a sphere in fluid flow. exp fluids 59:104 bellani g, byron ml, collignon ag, meyer cr, and variano ea (2012) shape effects on turbulent modulation by large nearly neutrally buoyant particles. j fluid mech 712:41–60 costa p, brandt l, and picano f (2020) interface-resolved simulations of small inertial particles in turbulent channel flow. j fluid mech 883 crowe ct (2005) multiphase flow handbook. crc press dennis dj and nickels tb (2011) experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. part 2. long structures. j fluid mech 673:218 drake tg, shreve rl, dietrich we, whiting pj, and leopold lb (1988) bedload transport of fine gravel observed by motion-picture photography. j fluid mech 192:193–217 ebrahimian m, sanders rs, and ghaemi s (2019) dynamics and wall collision of inertial particles in a solid-liquid turbulent channel flow. j fluid mech 881:872–905 francis j (1973) experiments on the motion of solitary grains along the bed of a water-stream. proceedings of the royal society of london a mathematical and physical sciences 332:443–471 hall d (1988) measurements of the mean force on a particle near a boundary in turbulent flow. j fluid mech 187:451–466 kabsch w (1976) a solution for the best rotation to relate two sets of vectors. acta crystallographica section a: crystal physics, diffraction, theoretical and general crystallography 32:922–923 kaftori d, hetsroni g, and banerjee s (1995) particle behavior in the turbulent boundary layer. i. motion, deposition, and entrainment. phys fluids 7:1095–1106 klein s, gibert m, bérut a, and bodenschatz e (2013) simultaneous 3d measurement of the translation and rotation of finite-size particles and the flow field in a fully developed turbulent water flow. measurement science and technology 24:024006 mathai v, neut mw, van der poel ep, and sun c (2016) translational and rotational dynamics of a large buoyant sphere in turbulence. exp fluids 57:51 niño y and garcia m (1996) experiments on particle–turbulence interactions in the near–wall region of an open channel flow: implications for sediment transport. j fluid mech 326:285–319 pedinotti s, mariotti g, and banerjee s (1992) direct numerical simulation of particle behaviour in the wall region of turbulent flows in horizontal channels. int j multiph flow 18:927–941 rashidi m, hetsroni g, and banerjee s (1990) particle-turbulence interaction in a boundary layer. int j multiph flow 16:935–949 sciacchitano a, scarano f, and wieneke b (2012) multi-frame pyramid correlation for time-resolved piv. exp fluids 53:1087–1105 sumer bm and oguz b (1978) particle motions near the bottom in turbulent flow in an open channel. j fluid mech 86:109–127 sutherland aj (1967) proposed mechanism for sediment entrainment by turbulent flows. j geophys res 72:6183–6194 tan ym and longmire ek (2017) recovery of vortex packet organization in perturbed turbulent boundary layers. phys rev fluids 2:104602 tee yh, barros dc, and longmire ek (2020) motion of finite-size spheres released in a turbulent boundary layer. int j multiph flow 133:103462 van hout r (2013) spatially and temporally resolved measurements of bead resuspension and saltation in a turbulent water channel flow. j fluid mech 715:389–423 van hout r, eisma j, elsinga ge, and westerweel j (2018) experimental study of the flow in the wake of a stationary sphere immersed in a turbulent boundary layer. phys rev fluids 3:024601 westerweel j and scarano f (2005) universal outlier detection for piv data. exp fluids 39:1096–1100 wu y and christensen k (2006) population trends of spanwise vortices in wall turbulence. j fluid mech 568:55–76 yousefi a, costa p, and brandt l (2020) single sediment dynamics in turbulent flow over a porous bedinsights from interface-resolved simulations. j fluid mech 893:a24, 1–28 zeng l, balachandar s, fischer p, and najjar f (2008) interactions of a stationary finite-sized particle with wall turbulence. j fluid mech 594:271–305 zimmermann r, gasteuil y, bourgoin m, volk r, pumir a, and pinton jf (2011) tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow. rev· sci· inst· 82:033906 introduction methodology results and discussion sphere wall-normal motion sphere streamwise velocity sphere spanwise motion conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 stereoscopic micro piv investigation of velocity boundary layer near piston top of a tumble enhanced si ic engine m. shimura1∗, e. yokoyama1, h. kosuda1, m. kamata2, o. nakabeppu2, t. yokomori3, m. tanahashi1 1 tokyo institute of technology, department of mechanical engineering, tokyo, japan 2 meiji university, graduate school of science and technology, kanagawa, japan 3 keio university, graduate school of science and technology, kanagawa, japan ∗ shimura.m.aa@m.titech.ac.jp abstract to develop higher efficiency and lower emission gasoline engines, ultra-lean burning under high reynolds number conditions is desired. it is believed that enhancement of tumble flow in the engine cylinder is effective for increase of turbulent intensity, resulting in improvement of characteristics of flame propagation and ignition under a strong discharge, while the enhancement of tumble flow might cause heat loss from the wall. investigations of characteristics of turbulence and distributions of wall and gas temperature in engine cylinders are still challenging due to transient and high pressure, and due to cycle-to-cycle variations. in the previous study (jainski et al., 2013), a micro particle image velocimetry (micro piv) measurements were conducted in an engine cylinder at up to 1100 rpm and the characteristics of velocity boundary layer around a cylinder head were investigated. the study has shown that the log-law does not properly present the measured velocity distributions near the wall. in our previous study (shimura et al., 2018), a micro piv was conducted in a motored engine cylinder to investigate velocity boundary layer characteristics near piston top before the top dead center (tdc) at a constant engine speed of 2000 rpm to deepen understanding characteristics of velocity boundary layer in engine cylinder with tumble flow. the velocity boundary layer was well fitted to the blasius theory at 30 cad before tdc and deviated from the theory at 15 cad before tdc. however, the obtained data was two components of velocity in the measurement plane, which means that effects of magnitude of velocity were not clear in the previous measurement. in this study, stereoscopic micro piv was conducted to elucidate the effects of magnitude and direction of velocity on the characteristics of velocity boundary layer near the piston top in the tumble enhanced si ic optical engine. the tumble enhanced si ic optical engine used in the previous study (shimura et al., 2018; matsuda et al., 2019) was used also in this study. the bore is 75 mm and the stroke is 112.5 mm. length of the connecting rod is 250 mm. the engine has two intake valves of the diameter 29 mm and two exhaust valves of the diameter 25 mm. the compression ratio is 13.0. the optical access is achieved through the quartz glass cylinder. a tumble enhancing intake port is used for the sake of improvement of ignition and flame propagation. the engine speed can be set up to 2000 rpm at the maximum. the overall flow fields taken by a preliminary piv experiment can be seen in the literatures (shimura et al., 2018; matsuda et al., 2019). the laser beams for piv are from two nd:yag lasers (lotis, ls-2131, 150 mj/pulse, 532 nm) are led to the same optical axis by a mirror and a polarizing beam splitter. the laser beam is formed into laser sheet of 180 µm thickness by laser sheet forming optics and led into the engine cylinder. the scattering light was collected by long distance microscope lenses (quester, szm100) and imaged onto ccd cameras (princeton technology, es4020) in the stereoscopic alignment with 18 degrees. to compensate for the difference in the focal length caused by the quartz engine liner, a cylindrical lens of 1000 mm focal length was placed in front of each long distance microscope lens. sio2 of 1 µm mean diameter was used for tracer particles. the micro piv was operated at about 6.6 hz to be synchronized with engine speed. the time separation of the successive particle images was 1.5 µs. the field of view of the micro piv was 3.5 mm × 3.5 mm on the piston top including central axis of the cylinder. here, x and y coordinates are set to the direction from the exhaust to the intake valves and the direction from the piston to the pent roof, respectively. z coordinates is perpendicular to x and y axes, and the orizin of the coordinates is set at the center of the piston top. the spatial resolution of piv, which is defined by the size of interrogation region, is 108.8 µm × 54.4 µm. vector spacing is 54.4 µm × 27.2 µm. the first vector position is about 27.2 µm away from the wall. the measurements were conducted at 345 cad. the engine was motored at 2000 rpm and operated for three intake valve open timings of -30 cad. the operation condition of the engine tested contain strong cycle-to-cycle variations, which results in the large root-mean-square values of velocity fluctuation near the center of the piston top (shimura et al., 2018). to evaluate flow characteristics in the cycle-to-cycle variations, conditional averaging based on magnitude of fluid velocity is used in this study. figure 1(a) shows a histogram of the magnitude of combined velocity of u and w. the magnitude of velocity can be considered as momentum of fluid because few fluctuation of density is considered and temperature boundary layer is enough thin compared to the velocity boundary layer. the large variations in the momentum can be observed in fig. 1(a). the large variations are considered to be caused by the variations of tumble core locations. the fraction of the large momentum here, the momentum are classified into c1 to c4 based on fractions (c1: 54.4%, c2: 19.5%, c3: 19.5%, c4: 6.6%). figure 1(b) and (c) shows mean velocity distribution classified into c1 and c4 in fig. 1(a). the distribution is fitted to the log-law velocity profile of developed wall turbulence. the mean velocity profile for c1 shows large discrepancy from that of general turbulent boundary layers, while that for c4 show relatively close to that of general turbulent boundary layer. c2 and c3, which are not shown here, have trend between the c1 and c4 profiles. these results show that the velocity profiles which can be assumed to be the developed turbulent boudary layer in the targeted condition is less than half of cycles, which means partial applicability of conventional cfd models for prediction of boundary layer of the engine condition. acknowledgements this work is the result of a collaborative research program with the research association of automotive internal combustion engines (aice) for fiscal year 2020. the authors gratefully acknowledge the concerned personnel. references jainski c, lu l, dreizler a, and sick v (2013) high-speed micro particle image velocimetry studies of boundary-layer flows in a direct-injection engine. international journal of engine research 14:247–259 matsuda m, yokomori t, minamoto y, shimura m, tanahashi m, and iida n (2019) a cycle-to-cycle variation extraction method for flow field analysis in si ic engines based on turbulence scales. in sae technical papers. january shimura m, yoshida s, osawa k, minamoto y, yokomori t, iwamoto k, tanahashi m, and kosaka h (2018) micro particle image velocimetry investigation of near-wall behaviors of tumble enhanced flow in an internal combustion engine. international journal of engine research page 1468087418774710 (a) (b) (c) figure 1: (a) histogram of momentum. mean velocity distribution classified based on the magnitude of momentum for (b) c1, (c) c4 in the histrgram. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 piv measurement of turbulence over a streamwise preferential porous medium m. morimoto 1∗, y. okazaki 1, y. kuwata 1 and k. suga 1 1 osaka prefecture university, dep. of mechanical engineering, sakai, osaka, japan ∗ morimoto@htlab.me.osakafu-u.ac.jp abstract this study examines the possibility of orthotropic porous medium whose streamwise permeability is larger than the wall-normal permeability to reduce turbulent friction inspired by recent numerical studies of rosti et al. (2018); gómez-de segura and garcı́a-mayoral (2019). because gómez-de segura and garcı́a-mayoral (2019) used brinkman equation to approximate the flow in the porous media, it is uncertain that such porous media really reduce the friction. we make a layered porous medium, which satisfies the drag reducing condition suggested by gómez-de segura and garcı́a-mayoral (2019), and carry out particle image velocimetry measurements of turbulent square duct flows over it and examine the drag reduction probability. from the analyses of the obtained data, it is found that the friction on the porous-wall is nearly the same as that of the smooth-wall at reb < 10000 and tends to increase at reb > 10000. 1 introduction understanding the turbulent flow physics over permeable porous media is of great importance from the engineering view point. many researchers hence have dedicated to elucidate the characteristics of such flows (e.g. lovera and kennedy, 1969; zippe and graf, 1983; breugem et al., 2006; pokrajac and manes, 2009; manes et al., 2009; suga et al., 2010, 2011, 2017; manes et al., 2011; suga, 2016). from those studies, it is well known that the wall permeability usually increases near-wall turbulence. rosti et al. (2018); gómez-de segura and garcı́a-mayoral (2019), however, reported numerical studies which indicated turbulent dragreduction over anisotropic porous media with a high streamwise permeability. since the flows inside porous media of those numerical studies were not exactly treated but modelled by the brinkman equation (gómezde segura and garcı́a-mayoral, 2019) or were not solved by using idealized surface boundary conditions (rosti et al., 2018), the realizability of their proposed drag reducing conditions has never been fully convinced yet. therefore, we have performed piv experiments of turbulent square duct flows over a porous medium at the bulk reynolds numbers of 3000-15000. the flow facility is the same as that used in the previous study (suga et al., 2020) of our group. to satisfy the proposed drag reducing conditions, we have designed the structure of the porous medium. the porosity of the medium is 0.9 and the ratio of the square roots of the streamwise to wall-normal permeabilities is 4.3. this ratio well satisfies the drag reduction condition suggested by rosti et al. (2018); gómez-de segura and garcı́a-mayoral (2019). from the analyses of the obtained experimental data, which cover the drag reduction range of the wall-normal permeability reynolds number suggested by gómez-de segura and garcı́a-mayoral (2019), we have discussed whether the porous medium has the drag-reducing ability. 2 experimental method figure 1(a) illustrates the experimental flow facility. the working fluid is tap water and the flow is conditioned in a conditioning tank and fully developed in a 3 m long drive section. then the flow enters a 1 m long test section whose cross-sectional view is shown in figure 1(b). the test section, whose cross-section is 50 mm (height, h) × 50 mm (width), consists of solid smooth acrylic top and side walls and a porous bottom wall of 10mm thickness. (a) flow facility (b) cross-sectional view (c) size of the mesh (d) structure of the porous medium figure 1: schematics of the experimental facility and the details of the porous medium. the porous medium is made of stainless-steel woven-wire-mesh-sheets whose mesh spacing and wire diameter are g = 0.15 mm and d = 0.1 mm, respectively, as illustrated in figure 1(c). the porous structure looks like a cardboard structure: corrugated mesh-sheets are sandwiched by flat mesh-sheets as illustrated in figure 1(d). the characteristics of the porous medium are listed in table 1. the porosity ϕ is obtained by measuring the weight and the mass of the porous medium. the diagonal component of the permeability tensor kαα, is measured from the relation between the pressure drops and the flow rates through the porous medium stuffed into the horizontal duct flow facility. the permeability ratio parameter is defined as ψαβ =√ kαα/kββ. table 1: characteristics of the porous medium. ϕ ψxy ψzy kxx [mm2] kyy [mm2] kzz[mm2] 0.9 4.3 1.7 0.0269 0.00145 0.00426 the piv measurements are carried out at the symmetry plane of the test section. the measured bulk reynolds numbers reb =ubh/ν, where ub is the bulk mean velocity and ν is the kinematic viscosity of the fluid, are 3000,5000,7500,10000 and 15000. 3 results and discussions 3.1 streamwise velocities as shown in figure 2, the distribution profiles of the streamwise mean velocities look almost symmetrical. this indicates that the effects of the porous medium are not significant and almost the same as those of the smooth wall. note that y/h = 0 and 1.0 correspond to the porous-bottom and solidsmooth-top surface locations, respectively. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 re b =15000 re b =10000 re b =7500 re b =5000 re b =3000 u /u b y/h figure 2: streamwise mean velocity distributions. to investigate the difference between the porous and the solid wall sides in more detail, profiles are compared in the semi-logarithmic chart. since the present study does not measure the wall friction, the streamwise friction velocity uτ is calculated by the correlation proposed by gavrilakis (2019) referring to the dns results for rectangular ducts. for the fully developed straight square duct, the darcy–weisbach friction factor f may be written as f = 8u2 τ u2 m . (1) note that uτ represents the averaged friction velocity. the simulation data of fully developed duct flows by gavrilakis (2019) collapse to the power law f = 0.281re−1/4.13 m . (2) using eqs.(1) and (2), uτ is calculated to normalize the present data. figure 3 shows the mean velocity u+(= u uτ ) profiles normalized by uτ as a function of the normalized wall-normal distance y+ = yuτ ν . the dashed lines and the two-dot chain lines express the dns data by pirozzoli et al. (2018) for reference purposes and the solid lines in figure 3 express the logarithmic law of the velocity u+ = 1 κ lny++5.5 (3) where κ is the von kármán constant of 0.41. figure 3 indicates that the present data at reb = 7500 are well accord with the dns data at reb = 7000. this implies that the estimated friction by eq.(2) reasonably represents the present measurements. as can be seen in figure 3, the u+ distributions of the porous and the solid wall sides are almost identical at reb = 3000− 7500, while that of the porous wall side is obviously below that of the solid wall side at reb = 15000. it is also recognized that the profile of the porous wall side seems slightly below that of the solid wall side at reb = 10000. note that the downward shift of the mean velocity (in the semi-logarithmic chart) corresponds to the increase of the wall friction. from this trend, it 0 5 10 15 20 25 30 35 40 45 50 55 60 65 1 10 100 1000 5 5 5 25 20 15 10 5 0 0 0 0 re b =15000 re b =10000 re b =7500 re b =3000 re b =5000 porous wall side solid wall side log law pirozolli et al. re b =7000 re b =4410 y+ u + figure 3: comparison of the streamwise mean velocities. can be expected that when reb . 10000, the porous wall friction is comparable to that of the smooth surface, and it gradually increases with the reynolds number at reb > 10000. gómez-de segura and garcı́a-mayoral (2019) argued whether the porous media reduced the turbulent drag depending on the wall-normal permeability reynolds number √ k+ yy = uτ √ kyy ν . they simulated that the maximum drag reduction occurred at √ k+ yy ≈ 0.38 for ψxy = 3.6 and 5.5 while the drag reduction effect became extinct at √ k+ yy > 0.6. the values of √ k+ yy at reb ≤ 10000 in the present study are in the range of the drag reduction suggested by gómez-de segura and garcı́a-mayoral (2019) as shown in table 2 while at reb = 15000 the value of √ k+ yy does not satisfy the condition of the drag reduction. when √ k+ yy satisfies the drag reduction condition, the effect of the present streamwise preferential porous medium can be expected to be similar to that of a smooth wall, and it does not drastically reduce the turbulent skin friction as gómez-de segura and garcı́a-mayoral (2019) predicted. in case that √ k+ yy does not satisfy the condition, the friction increases as predicted. table 2: permeability reynolds numbers. reb 3000 5000 7500 10000 15000√ k+ yy 0.16 0.26 0.36 0.48 0.69 3.2 turbulence quantities figure 4 presents the root mean square (r.m.s.) velocities and the reynolds shear stress distributions. the profile at each reynolds number looks quite symmetry. this tendency is similar to that of the aforementioned streamwise velocities. 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 v rms u rms re b =15000 re b =10000 re b =7500 re b =5000 re b =3000 u i r m s/u b y/h (a) r.m.s velocities 0.0 0.2 0.4 0.6 0.8 1.0 -0.0045 -0.0030 -0.0015 0.0000 0.0015 0.0030 0.0045 re b =15000 re b =10000 re b =7500 re b =5000 re b =3000 uv /u b2 y/h (b) reynolds shear stresses figure 4: turbulence quantity distributions. to see the difference of the r.m.s. velocities between the porous and solid wall sides, figure 5 compares the r.m.s. velocities: urms and vrms, at reb = 5000 and 15000. at reb = 5000, as shown in figure 5(a), the observed tendency is the same as that suggested by the velocity distribution, i.e., there is no increase of turbulence on the porous wall side. at reb = 15000, as shown in figure 5(b), r.m.s. velocities of the porous side are larger than that of the solid side and this trend is also the same as that of the velocity distribution. 0.0 0.1 0.2 0.3 0.4 0.5 0.00 0.05 0.10 0.15 0.20 0.25 porous wall side solid wall side u i r m s/u b y/h (a) reb = 5000 0.0 0.1 0.2 0.3 0.4 0.5 0.00 0.05 0.10 0.15 0.20 0.25 porous wall side solid wall side u i r m s/u b y/h (b) reb = 15000 figure 5: comparison of the r.m.s. velocities between the porous and solid wall sides. as for the reynolds shear stresses shown in figure 6, at reb = 5000 both profiles of porous and solid wall sides are at the same level while at reb = 15000 the reynolds shear stress of the porous wall side is higher than that of the solid wall side. these trends are consistent with those observed in the r.m.s. velocities. the trend at reb = 15000 is consistent with the fact that the semi-logarithmic velocity over the porous wall profile is lower than that on the solid wall side. we assume that this difference may come from the development of the secondary flows which we will investigate in due course. 0.0 0.1 0.2 0.3 0.4 0.5 0.000 0.001 0.002 0.003 0.004 porous wall side solid wall side |u v| /u b2 y/h (a) reb = 5000 0.0 0.1 0.2 0.3 0.4 0.5 0.000 0.001 0.002 0.003 0.004 porous wall side solid wall side |u v| /u b2 y/h (b) reb = 15000 figure 6: comparison of the reynolds shear stresses between the porous and solid wall sides. in order to discuss bursts which contribute to the formation of turbulent flow energy and the reynolds stress, fig.7 compares the decomposed reynolds shear stress profiles at reb = 5000 and 15000 using the quadrant analysis method of willmarth and lu (1972): qm = 1 n ∑(u′v′)m (4) where subscript m(= 1−4) corresponds to the quadrant event. it is seen that the contributions of the second quadrant(q2): ejections, are significantly larger on the porous wall side than those on the solid wall side, both at reb = 5000 and reb = 15000. it is thus considered that the vortex structure near the porous wall is different from that near the solid wall. furthermore, it is interesting that the third quadrant(q3): inward interactions, clearly dominates over the first quadrant(q1): outward interactions, on the porous wall side at reb = 15000. we assume that these trends may relate to the secondary flows, and hence we plan to perform piv measurements at different spanwise sections to confirm this. 10 100 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 q m / uv q1 q2 q3 q4 y+ (a) porous wall side at reb = 5000 10 100 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 q m / uv q1 q2 q3 q4 y+ (b) solid wall side at reb = 5000 10 100 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 q1 q2 q3 q4 q m / uv y+ (c) porous wall side at reb = 15000 10 100 -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 q1 q2 q3 q4 q m / uv y+ (d) solid wall side at reb = 15000 figure 7: quadrant analyses of the reynolds shear stress distribution at reb = 5000 and reb = 15000. the reason why the present porous wall behaves like a smooth wall at reb < 10000 is assumed that the normalized mesh size g+ = uτg ν and the normalized wire diameter d+ = uτd ν are sufficiently small enough to be negligible. (it is known that when the roughness height is of the same order or smaller than 5, the wall roughness hardly affects turbulence.) as shown in table 3, g+ and d+ are small enough to be ignored. at reb = 15000, it is considered that the flow through porous medium affects turbulence generation even though g+ and d+ are smaller than 5. table 3: normalized mesh size and wire diameter. reb 3000 5000 7500 10000 15000 g+ 0.653 1.05 1.47 1.93 2.79 d+ 0.424 0.679 0.957 1.25 1.81 4 concluding remarks to understand the turbulence characteristics of a streamwise-preferential porous medium, piv measurements have been carried out. fully developed turbulent square duct flows over a porous medium whose permeability ratio of the wall-normal to streamwise permeabilities is ψxy = 4.3 are discussed at reb = 3000,5000,7500,10000 and 15000. the presently obtained major remarks are: i. at reb < 10000, the mean velocity profiles suggest that the wall friction on the present porous wall is nearly the same as the smooth wall friction while at reb > 10000 the porous wall friction tends to be larger than the smooth wall friction. ii. at reb = 5000, the r.m.s. velocity and the reynolds stress distributions of the porous and solid wall sides are almost the same, while at reb = 15000, both distributions of the porous side are larger than those of the solid wall side. the turbulence trend at reb = 15000 indicates the increase of the wall wall friction on the porous side, which is consistent with the trend of the semi-logarithmic velocity distributions. iii. in the range of all measured reynolds numbers, even at reb = 15000 where the friction increases on the porous side, the normalized mesh size and the normalized wire diameter are considered to be small enough to be ignored. this trend suggests that the turbulence is affected by the flow through the porous medium. although gómez-de segura and garcı́a-mayoral (2019) showed drastic drag reduction by streamwise preferential porous media in their simulation, it is not observed in the present experiments. it was found that in their drag reducing condition, the present streamwise-preferential porous medium produces the friction as much as the smooth surface does. acknowledgements a part of this study was financially supported by the research grant (no. 19h02069) of the jsps. the authors thank dr. kaneda for supporting the experiments. references breugem wp, boersma bj, and uittenbogaard re (2006) the influence of wall permeability on turbulent channel flow”. j fluid mech 562:35–72 gavrilakis s (2019) post-transitional periodic flow in a straight square duct. j fluid mech 859:731–753 gómez-de segura g and garcı́a-mayoral r (2019) turbulent drag reduction by anisotropic permeable substrates – analysis and direct numerical simulations. j fluid mech 875:124–172 lovera f and kennedy jf (1969) friction factors for flat bed flows in sand channels. j hydr div, asce 95:1227–1234 manes c, poggi d, and ridol l (2011) turbulent boundary layers over permeable walls: scaling and nearwall structure. j fluid mech 687:141–170 manes c, pokrajac d, mcewan i, and nikora v (2009) turbulence structure of open channel flows over permeable and impermeable beds: a comparative study. phys fluids 21:125109 pirozzoli s, modesti d, orlandi p, and grasso f (2018) turbulence and secondary motions in square duct flow. j fluid mech 840:631–655 pokrajac d and manes c (2009) velocity measurements of a free-surface turbulent flow penetrating a porous medium composed of uniform-size spheres. transp porous media 78:367–383 rosti me, brandt l, and pinelli a (2018) turbulent channel flow over an anisotropic porous wall–drag increase and reduction. j fluid mech 842:381–394 suga k (2016) understanding and modelling turbulence over and inside porous media. flow turb combust 96:717–756 suga k, matsumura y, ashitaka y, tominaga s, and kaneda m (2010) effects of wall permeability on turbulence”. int j heat fluid flow 31:974–984 suga k, mori m, and kaneda m (2011) vortex structure of turbulence over permeable walls. int j heat fluid flow 32:586–595 suga k, nakagawa y, and kaneda m (2017) spanwise turbulence structure over permeable walls. j fluid mech 822:186–201 suga k, okazaki y, and kuwata y (2020) characteristics of turbulent square duct flows over porous media. j fluid mech 884. a7 willmarth ww and lu ss (1972) structure of the reynolds stress near the wall. j fluid mech 55:65–92 zippe hj and graf wh (1983) turbulent boundary-layer flow over permeable and non-permeable rough surfaces. j hydraul res 21:51–65 bf5f413db4cc055d6b5e0890ee101ab90b7acd0461ab14d5b822fd1642ec7333.pdf introduction experimental method results and discussions turbulence quantities concluding remarks bf5f413db4cc055d6b5e0890ee101ab90b7acd0461ab14d5b822fd1642ec7333.pdf bf5f413db4cc055d6b5e0890ee101ab90b7acd0461ab14d5b822fd1642ec7333.pdf 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 three-dimensional density measurements of a heated jet using laser-speckle tomographic background-oriented schlieren s. amjad∗, j. soria, c. atkinson 1 laboratory for turbulence research in aerospace and combustion, department of mechanical and aerospace engineering, monash university, clayton, victoria, australia ∗ shoaib.amjad@monash.edu abstract (a) (b) figure 1: a) fifteen-camera experimental rig, b) schematic of laser expansion. optical axis of camera 1 is aligned with the global z-axis, and x is the jet axis. three-dimensional density field measurement techniques can be used to understand the complex heat transfer and mixing processes that occur in turbulent flows. tomographic background-oriented schlieren (bos) is an optical technique that can be used to measure the instantaneous three-dimensional density field in turbulent flows. light rays propagating through the flow are deflected from their ambient path due to variations in refractive index related to the spatial density gradients. in bos, a camera is placed looking through the flow at a reference image, which captures path-integrated information on the refractive index gradients in the form of apparent image displacements richard and raffel (2001). the displacements recorded simultaneously from many cameras placed around the flow form the basis of a tomographic reconstruction of the three-dimensional refractive index gradients goldhahn and seume (2007), from which the density field is obtained through integration of the gradients and application of the gladstone-dale relation. most tbos experiments to date have used printed background patterns and strobe lighting to record deflections. the lighting systems often result in temporal integration on the order of many hundreds of flow time scales to achieve adequate image exposures, which prevents the observation of instantaneous turbulence structures such vortex roll-up. defocus blurring must also be carefully managed, as the sensitivity figure 2: longitudinal slice through reconstructed density field ρ (kg/m3) at one time-step at y/d = 0. flow is from left to right. domain length is 0.3 < x/d < 4.6. to displacements is increased by focussing further away from the object. our proposed experimental set-up shown in figure 1 uses a pulsed laser beam for both short-duration illumination and the creation of a suitable background pattern in the form of laser speckle patterns meier and roesgen (2013). the beam is spread to illuminate a surface that is observed by fifteen cameras that are evenly-spaced circumferentially around the flow. we present a methodolgy for selecting the optimal focal length, focus distance, and aperture by considering the compromise between displacement sensitivity, defocus blurring and speckle size. using an optimised iterative tomographic reconstruction method amjad et al. (2020), we demonstrate the suitability of tomographic laser-speckle bos for the collection of turbulent density field statistics using a heated air jet. the 3d reconstructions of the density field of a heated jet show excellent reproduction of turbulence structures with spatial resolution of 840 µm (0.084d) per voxel. acknowledgements the support of australian research council (arc) for this work through a discovery grant is gratefully acknowledged. this research was supported by an australian government research training program (rtp) scholarship. the research benefited from computational resources provided through the national computational merit allocation scheme (ncmas), supported by the arc. this work was supported by the massive hpc facility (www.massive.org.au). references amjad s, karami s, soria j, and atkinson c (2020) assessment of three-dimensional density measurements from tomographic background-oriented schlieren (bos). measurement science and technology 31:114002 goldhahn e and seume j (2007) the background oriented schlieren technique: sensitivity, accuracy, resolution and application to a three-dimensional density field. experiments in fluids 43:241–249 meier a and roesgen t (2013) improved background oriented schlieren imaging using laser speckle illumination. experiments in fluids 54:1549 richard h and raffel m (2001) principle and applications of the background oriented schlieren (bos) method. measurement science and technology 12:1576 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 an experimental study of unsteady heat transfer and phase changing process upon impacting of ice crystals onto heated surfaces pertinent to aero-engine icing phenomena haiyang hu, linchuan tian, hui hu* department of aerospace engineering, iowa state university, ames, iowa 50014, usa *corresponding authors: huhui@iastate.edu extend abstract ice accretion on exposed surfaces of aero-engine components has been widely recognized as a significant hazard to aviation safety in cold weathers. icing process due to the impingement of the supercooled water droplets suspended in the cloud onto the cold surfaces of inlet components of aeroengines have been studied extensively for decades. since ice particles were believed to simply bounce off from the exposed surfaces of aero-engine components, ice crystals in the clouds were initially considered not to pose a threat to aviation safety. therefore, the ice accretion process due to the impacting of ice crystals onto the surfaces of hot engine componentes has not been studied until recently. it has been found recently that, tiny ice particles in the cloud may be partial/full melting upon impacting onto the hot surfaces of aero-engine components, such as heated inlet guide vanes (igv) and various probes. the partially/fully melted ice crystals were found to stick onto the hot surfaces and form thin water film, which would intercept more oncoming ice particles and lead to significant ice accretion over the surfaces of the hot engine components. the ice crystal induced ice accumulation on the critical aero-engine components has been found to cause significant engine performance loss and erroneous data being read from the probes. in the present study, a series of experimental investigations were conducted to elucidate the underlying physics of the dynamic ice accretion process pertinent to ice crystal icing phenomena. a novel ice crystal icing test rig with the capacity of generating controllable amount of ice crystals and flying speed up to 100 m/s was developed in a temperature-controllable environment chamber for the ice crystal icing studies. by using a high-speed imaging system, a digital particle image velocimetry(piv), and an infrared (ir) thermal imaging system, a comprehensive experimental campaign was performed to characterize the transient impacting process of ice crystals, dynamic ice accretion and unsteady heat transfer process associated with the impacting of ice crystals onto heated surfaces, in comparison to those due to the impingement of supercooled water droplets. by using an ultra-sensitive force sensor and a high-speed image system, a comparative study is conducted to examine the differences in the transient impinging dynamics of single water droplets, supercooled water droplets, and ice crystals onto solid surfaces with different wettability and stiffness. by upgrading the unique icing research tunnel of iowa state university (i.e., isu-irt) with additional ice crystal icing capability, a set of explorative studies are also conducted to examine the characteristics of the dynamic ice accretion processes over the heated surfaces of an aero-engine inlet guide vane (igv) model under both ice crystal icing and supercooled droplet icing conditions. the anti-/de-icing performance of a novel hybrid strategy by integrating icephobic coatings and minimized surface heating are also evaluated under both supercooled water droplet icing and ice crystal icing conditions. the new findings derived from the present studies are very helpful to gain further insights into the ice crystal icing phenomena for the development of more effective and robust anti-/de-icing strategies to ensure safer and more efficient aircraft/aero-engine operations in cold weathers. mailto:huhui@iastate.edu fig. 1: schematic of the isu ice crystal icing test rig fig. 2. comparison of the impacting of supercooled water droplets and ice crystals onto a frozen-cold test plate and heated test plate fig.3. effects of the temperature of the heated test plate on the ice critical icing process utilization of direct forcing immersed boundary methods for the optimization of inertial focusing microfluidics patrick giolando1, hui ma2, barrett davis2, tamara kinzer-ursem2, steve wereley1 1 school of mechanical engineering, purdue university 2 weldon school of biomedical engineering, purdue university 1. introduction inertial focusing microfluidics have gained significant momentum in the last decade for their ability to separate and filter mixtures of particles and cells based on size [1-3]. however, the most important feature is that the separation is passive, without the need for external forces. at the heart of inertial focusing is the balance between counteracting lift forces: shear and wallinduced lift. shear-induced lift is a product of the curvature of the fluid flow and the rotation of the particle in the flow, while wall-induced lift is generated by the disturbance of the fluid by the particle near a wall. this phenomenon was first observed by segre and silberberg for the focusing of particles in a pipe, and was later extended to the focusing of cells and particle in rectangular channels [4]. taking advantage of inertial focusing we explore particle capture utilizing an expanded channel microfluidics chip design. by expanding a small region of the straight channel microvortices form in the well, which allows for size selective trapping of particles [1, 2]. modeling the two-way coupled with traditional finite volume method (fvm) or finite element method (fem) can prove costly as with each time step the body-fitted grid would have to be remeshed [5, 6]. immersed boundary methods (ibm) offer a cost effective solution, rather than solving the fluid equations on a body fitted grid they are solved on a regular cartesian grid and the boundary conditions are imposed on the fluid domain by the addition of a forcing term. the navier-stokes equations are solved for on this eulerian grid, while the newton-euler equations that govern the motion of the particle are solved for on the lagrangian grid that defines the surface of the particle. the direct forcing ibm accounts for the force and torque acting on the particle by the requirement of the predict fluid velocity to be the local velocity of the particle on the surface of particle [7, 8]. interpolations are required to find the velocity of the fluid on the lagrangian nodes, and then a spreading function to return the force on the lagrangian nodes back to the eulerian grid [9]. 2. methods 2.1 experimental methods 2.1.1 design and fabrication of microfluidics chips for this study, two chip designs were produced to evaluate the inertial focusing properties of particles. the first chip design is a straight channel microfluidics chip fabricated in polydimethylsiloxane (pdms, sylgard184 silicone elastomer kit) using a master mold developed with standard photolithography. a silicon wafer with dry resist film (permx 3050 series, dupont electronic technologies) was used to develop the mold and cast the pdms, which was then bound to a glass slide (sigma aldrich) and baked for 45 minutes at 95 ֯c. a second series of chip designs were produced with an expanded channel to produce microvortices for particle retention. these microfluidics chips were designed by cutting pressure sensitive adhesive (psa, arseal 90880, adhesive research, cyclic olefin copolymer (coc, zeon zeonor zf14-188) with a laser cutter (universal laser systems, vsl350). 2.1.2 particle imaging experimental data for the motion of buoyant polystyrene microparticles of size 1 and 7.32 µm in diameter, and acrylic particles of size 20 µm in diameter (fisher scientific) were captured using a fluorescence microscope (axio observer, zeiss). shutter speeds were varied from 1/10 to 1/10000 s, allowing for both particle image velocimetry (piv) data analysis and the observation of complete pathlines. the 1, 7.32, and 20 µm particles were mixed with deionized water at a concentration of 5x107 , 2.5x105 , and 6x104 particles per ml, respectively. particles were collected in a syringe (bd syringe, 1ml) and pumped through peek tubing (idex, 1569) utilizing a syringe pump (kd scientific inc) to vary flow conditions (0.1 ≤ re ≤ 500). 2.1.3 image analysis the expanded well design produced two separate fluid domains with dramatically different reynolds numbers (re), which required separate in-house algorithms for the quantification of particle velocities. for regions of slow fluid motion, particle motion was captured in image pairs that produced a strong cross-correlation, which is ideal for piv analysis. however, in regions of high reynolds flow the particles became faint streaks, and cross-correlation procedures became nonviable. particle streak velocimetry (psv) was employed to find and quantify the length of the streaks to determine the particles velocity. the first few image pairs were used to segment the images into regions of large and small re flow to be quantified by either piv or psv, respectively. the first image pair from the stack was split into interrogation window and evaluated with a fft cross-correlation algorithm to evaluate the strength of cross-correlation for each window. windows that produced cross-correlation resembling a dirac function were quantified with piv for the entire image stack. regions with a cross-correlation domains of lowered and wider peaks in the cross-correlation domain were segmented with a morphological operator to look for streaks. if streaks were identified of significant size psv was used to quantify the particle motion in the window for the entire stack. if there were no significant streaks in the window, then the particle velocity of that window was set to zero to avoid extraneous velocity vectors. this allowed for rapid and accurate quantification of the particle motion in the entire fluid domain within the microfluidics chip. figure 1. piv/psv algorithm. (a) image pair used to produce mask to separate windows for piv or psv analysis. (b) cross-correlation of a window in the image pair. (c) segmentation of images to identify streaks. (d) final quantification of particle velocities in the entire system. regions quantified with piv/psv are red/blue, respectively. 2.2 numerical methods 2.2.1 governing equations particle motion was governed by newton-euler equations, while the fluid motion was governed by the navier-stokes equations. the incompressible, newtonian navier-stokes equations: 𝜕𝑢𝑖 𝜕𝑡 + 𝜕 𝜕𝑥𝑗 𝑢𝑖𝑢𝑗 = − 𝜕𝑝𝑖 𝜕𝑥𝑖 + 1 𝑅𝑒 𝜕 𝜕𝑥𝑗 𝜕𝑢𝑖 𝜕𝑥𝑗 (1) 𝜕𝑢𝑖 𝜕𝑥𝑖 = 0 (2) where 𝑢𝑖 is the ith component of the fluid velocity, 𝑥𝑗 is the jth dimension, and 𝑝𝑖 is the ith component of pressure. notable this system was 2d flow and gravity was negligible in this system for small buoyant particles. re is defined as re = 𝜌ful 𝜇 (3) where 𝜌f is the density, 𝜇 is the dynamic viscosity, u is the characteristic velocity, and l is the characteristic length of the fluid. the particle was modeled by a string of interconnected nodes, the motion of which includes both translational and rotational velocity: 𝑢𝑝𝑛 = 𝑢𝑝 +𝜔𝑝 𝑥 𝑟 (4) where 𝑢𝑝𝑛 is the velocity of the particle node, 𝑢𝑝 is the velocity of the particle, 𝜔𝑝 is the angular velocity of the particle, and r is the radial arm from the position of the node to the center of mass of the particle. assuming buoyancy the newton-euler equations became: 𝜌𝑝𝑉𝑝 𝜕𝑢𝑝 𝜕𝑡 = ∮ 𝜏 ∗ 𝑛𝑑𝑎 𝜕𝑉 + 𝐹𝑐 (5) 𝐼𝑝 𝜕𝜔𝑐 𝜕𝑡 = ∮ 𝑟 𝑥 (𝜏 ∗ 𝑛)𝑑𝑎 𝜕𝑉 + 𝑇𝑐 (6) where 𝜌𝑝 is the density of the particle 𝑉𝑝 is the volume of the particle, 𝐹𝑐 is the force introduced by a collision, 𝐼𝑝 is the moment of inertia of the particle, 𝑇𝑐 is the torque introduced by a collision, and 𝜏 is the total stress tensor acting on the particle. finally, eq 1 is modified to include the forcing term: 𝜕𝑢𝑖 𝜕𝑡 + 𝜕 𝜕𝑥𝑗 𝑢𝑖𝑢𝑗 = − 𝜕𝑝𝑖 𝜕𝑥𝑖 + 1 𝑅𝑒 𝜕 𝜕𝑥𝑗 𝜕𝑢𝑖 𝜕𝑥𝑗 + 𝑓𝑖 (7) where the forcing term f is zero everywhere except in the vicinity of the particle. 2.2.2 numerical methods the navier-stokes equations are handled with pressure-correction scheme, which is highly compatible with the direct forcing ibm [5, 10]. the numerical method is semi-implicit second order difference method, where operator splitting was used to handle the linear terms with the 2nd order backward difference formula (bdf-2) and the nonlinear terms with the 2nd order adams-bashforth (ab-2) explicit method. spatially the viscous terms were approximated with the 2nd order central difference (cd-2) method, an adaptive upwind-downwind scheme is used to approximate the convective terms, and the laplacian in the poisson problem is approximated with a 9-point scheme (∝= 1/3) [11]. the velocity and pressure components are solved for on a fully staggered grid, also known as a marker and cell (mac) scheme, fig 1 bc. the first step of chorin’s projection method is to solve for the intermediate fluid velocity without the added forcing term: 𝑢𝑖 ∗−𝑢𝑖 𝑛 ∆𝑡 = 1 𝑅𝑒 𝜕2𝑢𝑖 𝑛 𝜕𝑥𝑗𝜕𝑥𝑗 − 𝜕(𝑢𝑖𝑢𝑗) 𝑛 𝜕𝑥𝑗 (8) where 𝑢𝑖 ∗ is the intermediate fluid velocity, and is notably not divergence free. as mentioned previously this is solved in two steps: linear and nonlinear terms. the second step is to solve for the forcing term, which done by first interpolating the intermediate fluid velocity onto the lagrangian nodes: 𝑈𝑙 ∗ = ∑ 𝑢𝑖𝑗 ∗ 𝛿𝑑(𝑥𝑖𝑗 − 𝑋𝑙 𝑛)∆𝑥∆𝑦𝑖𝑗 (9) where capital letters represent values on the lagrangian grid, and 𝛿𝑑 is the dirac delta function, fig 2a,b. the forcing term on the lagrangian nodes is then computed: 𝐹𝑙 𝑛+1/2 = 𝑈𝑝(𝑋𝑙 𝑛)−𝑈𝑙 ∗ ∆𝑡 (10) where 𝑈𝑝(𝑋𝑙 𝑛) is the velocity of the particle node, which includes both translational and rotational velocity. equ 10 handles both the no slip and no penetration boundary conditions. finally, the forcing term is interpolated back onto the cartesian grid: 𝑓𝑖𝑗 𝑛+1/2 = ∑ 𝐹𝑙 𝑛+1/2 𝛿𝑑(𝑥𝑖𝑗 − 𝑋𝑙 𝑛)∆𝑉𝑙𝑙 (11) where ∆𝑉𝑙 is the volume of the lagrangian grid cells, fig 2c. the third step is to update the intermediate velocity to account for the forcing term: 𝑢𝑖 ∗∗−𝑢𝑖 ∗ ∆𝑡 = 𝑓𝑛+1/2 (12) figure 2. interpolation between eulerian and lagrangian grid. the immersed boundary method utilized two independent grids to resolve the fluid-surface interface. a method for interpolating between the fully staggered eulerian grid and the lagrangian grid is achieved utilizing ibm. (a) the 4-point dirac delta function the kernel is used to interpolate between the grids. (b) the interpolation of the intermediate fluid velocity onto the lagrangian nodes. dark blue triangles are the intermediate u-velocity nodes, which are known and used to find the intermediate fluid uvelocity at the lagrangian node (large black dot), equ 9. the lagrangian forcing term is then found to impose the noslip boundary conditions, equ 10. (c) the spreading of the forcing term from the lagrangian nodes onto the eulerian nodes. the forcing term from each of the neighboring lagrangian nodes (large black nodes) are interpolated onto the eulerian node (dark blue triangle), equ 11. each node has a discrete volume, δv, associated with it such that the collection of nodes form a thin shell around the particle. in the fourth step, the projection function is solved: − 𝜕2𝑝𝑛+1 𝜕𝑥𝑗𝜕𝑥𝑗 = ( 𝜕𝑢𝑗 ∗ 𝜕𝑥𝑗 ) 1 ∆𝑡 (13) in the final step, the approximated pressure is used to update the divergence free velocity at the n+1 step: 𝑢𝑖 𝑛+1−𝑢𝑖 ∗∗ ∆𝑡 = − 𝜕𝑝𝑛+1 𝜕𝑥𝑖 (14) after solving for the velocity and pressure of the fluid domain at the next time point, the position of the particle needs to be updated. equs 5 and 6 are modified: (𝜌𝑝-𝜌f)𝑉𝑝 𝑑𝑢𝑝 𝑑𝑡 = −𝜌𝑓 ∑ 𝐹𝑙 𝑛+1/2 ∆𝑉𝑙 𝑁𝑙 𝑙=1 + 𝐹𝑐 𝑛+1/2 (15) 𝐼𝑝 𝑑𝜔𝑐 𝑑𝑡 = −𝜌𝑓 ∑ 𝑟𝑙 𝑛 𝑥 𝐹𝑙 𝑛+1/2 ∆𝑉𝑙 𝑁𝑙 𝑙=1 + 𝑇𝑐 𝑛+1/2 (16) collisions were modeled using a short ranged repulsive force, based on the work of glowinski et. al [12, 13]. 𝐹𝑐,𝑃1 𝑛+1/2 { 0 𝑖𝑓 |�⃗�𝑃1,2| > 2𝑅𝑃 + ∆𝑟𝑐 , 𝜅𝑐 ( 2𝑅+∆𝑟𝑐−�⃗⃗⃗�𝑃1,2 ∆𝑟𝑐 ) 2 �⃗⃗⃗�𝑃1,2 |�⃗⃗⃗�𝑃1,2| 𝑖𝑓 2𝑅𝑃 < |�⃗�𝑃1,2| < 2𝑅𝑃 + ∆𝑟𝑐 , 𝜅𝑐 ( 2𝑅+∆𝑟𝑐−�⃗⃗⃗�𝑃1,2 ∆𝑟𝑐 ) 4 �⃗⃗⃗�𝑃1,2 |�⃗⃗⃗�𝑃1,2| 𝑖𝑓 |�⃗�𝑃1,2| < 2𝑅𝑃 (17) where �⃗�𝑃1,2 = �⃗�𝑃1 − �⃗�𝑃2, ∆𝑟𝑐 is the threshold distance for the repulsive force, and 𝜅𝑐 = 𝜌𝑝𝑉𝑝|𝑔|. 3. results 3.1 model verification to verify the accuracy of the computational model, the model was compared to experimental data of increasing complexity. the accuracy of the numerical scheme solving for the navierstokes equation was first verified by comparing the model to experimental data for the lid driven flow in a square cavity for reynolds number of 100, 400, and 1000, fig 3a. cross-sections of fluid velocity predicted by the model were compared to ghia et. al [14] resulting in an average relative error of 0.802%. the accuracy of the ibm was then evaluated by comparing the model to another classical problem in fluid mechanics, flow past a stationary cylinder modeled with ibm mesh, fig 3b. for mid-range re, from 10 to 100, steady vortices downstream of the cylinder were formed. experimental data for the structure of the steady vortices were compared to model predictions with an average relative error of 4.139%. these steady vortices become unsteady at higher re which transitioned to unsteady von karmann vortices for higher re. the vortex shedding creates oscillations in lift and drag forces on the cylinder, fig 3c. finally, the coefficient of drag for the cylinder was compared to experimental data over varying re. the model predicted the coefficient of drag on a cylinder for re = 0.1, 1, 10, 30, 120, and 1000 with an average relative error of 3.016%, fig 3d (red dots). figure 3. model verification. (a) results from ghia et. al [14] (black dots) are compared to the model predicted for fluid velocity across mid-sections (grey lines) for the lid driven cavity flow. normalized velocity magnitude is plotted as a contour plot. (b) pseudo streamlines for the flow over a cylinder with re=30 and definitions of structural parameters of the steady vortices. (c) comparison of experimental data [15] for the flow over a cylinder with predicted values from the model. (d) coefficient of lift and drag for the flow over a cylinder at a re of 100. (e) comparison of experimental data to model predicted values for the coefficient of drag for varying re. 3.2 inertial focusing with both the accuracy of numerical methods for solving the acceleration of the fluid and solid phase verified, the model was used to predict the inertial focusing of particles. experimental data was collected for the migration of 7.32 µm particles, in a straight 50 µm wide pdms channel (blockage ratio of 0.146), into two beams of particles off the side of the walls. images were collected every 500 µm downstream of the inlet with short and long exposure to monitor the distribution of particles along the width of the channel (w), as well as their velocities, fig 4a,b. cross sections of the channel were analyzed to quantify the radial distribution of particles across the width of the channel, fig 4c. model predictions for the distribution of particles along the width of the channel were compared to the experimental data. the model predicted the final equilibrium position of the particles at 0.120 y/w from the wall, fig 4d. experimental data found the particles migrating to 0.1255 y/w, which is in agreement with previously measured equilibrium position of 0.125 y/w [16]. the relative error in the model prediction of 4%, or 0.025 µm which is well within in the standard deviation of the experimental data, 2.5 µm. fig 4. particle migration across streamlines. (a) light microscope image of 50 µm channel with 7.32 µm beads. (b) fluorescents of the 7.32 µm beads at a re of 20 and an exposure of 1/10 s. (c) averaged cross section of fluorescence normalized to fwhm. (d) experimental data (black dots) for the average radial position of particles downstream of the inlet compared to predicted results from ibm simulations (navy line). 3.3 particle capture experimental data for motion of 1, 7.32, and 20 µm beads was collected for varying re to quantify the size selective capture of particles as a function of well geometry and re. the 1 µm fluorescent beads were used to evaluate the re dependent development of the microvortices within the wells (not included). fig 5. particle capture in microvortices. (a) long exposure images of 7.32 µm beads for re = 1, and (b) re = 100. (c) short exposure images were then used to collect piv data for re =1 and (d) re = 100. (e) comparison of uvelocity of mid-slice of piv/psv data (black dots) and model predictions (blue line) for re = 1 and (f) re = 100. notably the difference between the data point circled in red and the model predictions for the fluid is the inertia of the particle that keeps the particle moving quickly as it enters the well before it decelerates. 4.1 error in piv/psv algorithm the algorithm for quantifying the velocity of particles within the fluid performed well for the motion of particles in small and mid-range re flow. the algorithm accurately quantified the motion of particles in the entire system for re = 1, fig 5. however, for re = 100 and 300 the algorithm could only accurately quantify the velocity of particles within and entering the well, fig 5. inside the channel (re = 100 and 300) the particle velocity was to great for the particle streaks to be captured over the background noise, fig 5. 4.2 microfluidics device fabrication the current method of fabrication for the expanded chip design relies on a laser cutter to etch the design. this not only produces rough boundaries that will likely affect the inertial focusing of the particles, but also limits the channel size to >150µm which is too large to observe inertial focusing of 7.32µm which limits the chip design to either capturing 7.32µm beads with a larger well or only capturing 20µm beads. to increase the resolution of the well microfluidics chip, the design will be fabricated using standard photolithography in the same way the straight chip design was fabricated. 4.3 microfluidics device optimization with the model able to predict the inertial focusing of the particles, as well as the development of microvortices at varying re, the model will be used to aid in the design and optimization of the well microfluidics devices. utilizing ibm any type of well geometry can be modeled as well as allow for the modeling of elastic, deformable cells. these simulations can be used to evaluate the rate of particle drift, which is directly related to their size and deformability. the opening of the well can then be modified to increase or decrease the amount of time the particles spend moving past the opening, thus allowing or preventing a size specific particle from drifting into the well and becoming captured. the shape of the well can also be modified to modulate the strength of the vortices to aid in particle retention. 4.4 biomedical engineering applications size selective capturing has numerous applications for filtering biological samples. the filtration of cancerous cells out of the blood stream for analysis is a practical use of these chip designs as the larger cancerous cells will experience a larger shear force and become captured in the wells much more readily than red blood cells [2]. inertial focusing is also greatly influenced by deformability of the particle; increased deformability shifts the focusing of the particle towards the centerline. this could be taken advantage of by filtering out malaria infected red blood cells, which become rigid during the incubation of the viral infection. 5. conclusion utilizing continuous and direct forcing immersed boundary methods we developed a model that accurately simulates the inertial focusing of particles. the model was then expanded to model the expansion of the channel with ibm and simulate the capture of 7.32 µm particles within the wells. future work will aim at utilizing the developed ibm model to optimize the geometry to enhance size selectivity and efficiency of the particle capture. the model will also be expanded to account for deformable and rigid cells. references [1] j. zhou, s. kasper, and i. papautsky, "enhanced size-dependent trapping of particles using microvortices," microfluid nanofluidics, vol. 15, no. 5, pp. 611-623, 2013, doi: 10.1007/s10404-013-1176-y. [2] s. c. hur, a. j. mach, and d. di carlo, "high-throughput size-based rare cell enrichment using microscale vortices," biomicrofluidics, vol. 5, no. 2, pp. 022206-022206-10, 2011, doi: 10.1063/1.3576780. [3] a. j. mach and d. di carlo, "continuous scalable blood filtration device using inertial microfluidics," biotechnol. bioeng, vol. 107, no. 2, pp. 302-311, 2010, doi: 10.1002/bit.22833. [4] g. segré and a. silberberg, "radial particle displacements in poiseuille flow of suspensions," nature (london), vol. 189, no. 4760, pp. 209-210, 1961, doi: 10.1038/189209a0. [5] w.-p. breugem, "a second-order accurate immersed boundary method for fully resolved simulations of particle-laden flows," journal of computational physics, vol. 231, no. 13, pp. 4469-4498, 2012, doi: 10.1016/j.jcp.2012.02.026. [6] j. lee and d. you, "an implicit ghost-cell immersed boundary method for simulations of moving body problems with control of spurious force oscillations," journal of computational physics, vol. 233, pp. 295-314, 2013, doi: 10.1016/j.jcp.2012.08.044. [7] a. gronskis and g. artana, "a simple and efficient direct forcing immersed boundary method combined with a high order compact scheme for simulating flows with moving rigid boundaries," computers & fluids, vol. 124, pp. 86-104, 2016, doi: 10.1016/j.compfluid.2015.10.016. [8] j. yang and f. stern, "a simple and efficient direct forcing immersed boundary framework for fluid–structure interactions," journal of computational physics, vol. 231, no. 15, pp. 5029-5061, 2012, doi: 10.1016/j.jcp.2012.04.012. [9] a. m. roma, c. s. peskin, and m. j. berger, "an adaptive version of the immersed boundary method," journal of computational physics, vol. 153, no. 2, pp. 509-534, 1999, doi: 10.1006/jcph.1999.6293. [10] m. uhlmann, "an immersed boundary method with direct forcing for the simulation of particulate flows," journal of computational physics, vol. 209, no. 2, pp. 448-476, 2005, doi: 10.1016/j.jcp.2005.03.017. [11] r. lynch, "fundamental solutions of 9-point discrete laplacians; derivationand tables," ed. purdue e-pubs, 1992. [12] r. glowinski, t. w. pan, t. i. hesla, d. d. joseph, and j. périaux, "a fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow," journal of computational physics, vol. 169, no. 2, pp. 363-426, 2001, doi: 10.1006/jcph.2000.6542. [13] m. h. abdol azis, f. evrard, and b. van wachem, "an immersed boundary method for flows with dense particle suspensions," acta mechanica, vol. 230, no. 2, pp. 485-515, 2019, doi: 10.1007/s00707-018-2296-y. [14] u. ghia, k. n. ghia, and c. t. shin, "high-re solutions for incompressible flow using the navier-stokes equations and a multigrid method," journal of computational physics, vol. 48, no. 3, pp. 387-411, 1982, doi: 10.1016/00219991(82)90058-4. [15] m. coutanceau and r. bouard, "experimental determination of the main features of the viscous flow in the wake of a circular cylinder in uniform translation. part 2. unsteady flow," j. fluid mech, vol. 79, no. 2, pp. 257-272, 1977, doi: 10.1017/s0022112077000147. [16] j. zhou and i. papautsky, "fundamentals of inertial focusing in microchannels," lab chip, vol. 13, no. 6, pp. 1121-1132, 2013, doi: 10.1039/c2lc41248a. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 particle pair statistics of inertial particles at small separation using stereoscopic particle tracking d. w. hoffman∗, j. k. eaton stanford university, department of mechanical engineering, stanford, usa ∗ dwhoff@stanford.edu abstract particle pair statistics of inertial particles having average stokes numbers of 2.1 and 14 are measured in isotropic turbulence at a reynolds number of reλ = 240. the radial distribution function (rdf) and mean relative approach velocity are obtained at small separation distances using 2-frame stereoscopic particle tracking velocimetry (stereo-ptv). at small separation distance, the rdf varies by an order of magnitude in the range of stokes numbers investigated. however, the mean relative approach velocity is found to have a weak dependence on stokes number. the results are shown to have high accuracy when compared to analogous mono-ptv datasets, and can be used to provide a more reliable estimate of the inter-particle collision rate. the main limitation of the measurement is observed at separation distances less than the laser sheet thickness, where the technique tended to underestimate the mean relative approach velocity. 1 introduction the agglomeration of inertial particles in turbulent flows takes place in a wide variety of settings, including rain formation, flocculation in water filtration, and volcanic ash dispersion. agglomerate growth through inter-particle collisions can have a large impact on the transport of the particle phase, particularly when gravity acts to enhance sedimentation. the rate of aggregate growth is directly proportional to the particle collision frequency, which depends in part on the underlying carrier flow turbulence, particle time scale, and particle concentration. if the particle stokes number based on the kolmogorov time scale is moderate, the turbulence enhances the collision rate through the mechanism of preferential concentration (eaton and fessler, 1994). sundaram and collins (1997) were first to link the effects of preferential concentration to the volumetric collision rate nc for spherical monodisperse particles with the following expression, nc = 4πn2d2 pg(dp)〈wr〉(−) (dp), (1) where n is the particle number density, dp is the particle diameter, g(r) is the radial distribution function (rdf), and 〈wr〉(−) (r) is the mean relative approach velocity. conventional 2d optical techniques can be used to measure g(r) and 〈wr〉(−) (r) directly for r > δ z, where δ z is the characteristic optical depth (eg. laser sheet thickness). however, it remains a challenge to obtain high accuracy for dp ≤ r ≤ δ z due to projection errors (holtzer and collins, 2002). several studies have attempted to overcome these challenges using high resolution 3d particle tracking techniques. de jong et al. (2010) used holographic imaging to obtain 3d particle coordinates and velocities, but the resulting mean approach velocity was heavily skewed by erroneous tails in the relative velocity distributions. dou et al. (2018) extracted particle velocities with greater fidelity using 4-frame stereo particle tracking velocimetry (ptv). however, the extra optical components, instrumentation, and setup required to obtain meaningful results makes the method less attractive for numerous applications. the focus of this paper is to evaluate a simpler 3d technique, 2-frame stereo-ptv, for the measurement of particle pair statistics at small separation in isotropic turbulence. we present the main limitations of the approach as well as recommendations for future improvements. 2 experimental methods particle tracking measurements of inertial particles are carried out in a nearly isotropic turbulent flow. particle coordinates and velocities are recorded as they undergo gravitational settling through the turbulence. the 2d and 3d coordinates are captured using a pair of stereoscopic cameras and a separate monoscopic camera respectively. two types of particles are used, which exhibit different degrees of preferential concentration. 2.1 apparatus a turbulence tower, depicted in fig. 1, is used to generate nearly isotropic turbulence in the absence of a net flow. synthetic jets, powered by 4 inch acoustic woofers, are arranged along the walls of the tower, which has the shape of an octagonal prism. a thorough characterization of the turbulence statistics at the central axis of the tower is provided by hoffman and eaton (2021). the power used to actuate all synthetic jets combined is 29 w, corresponding to a root-mean-square (rms) velocity of u′ = 0.73 m/s, a dissipation rate of ε = 10.1 m2/s3, and a reynolds number of reλ = 240. a list of turbulence quantities is given in table 1, including the integral length scale l, taylor microscale λ f , kolmogorov length scale η , and the kolmogorov time scale τη . 0.68 m top view ccd cameras nd:yag laser optics 1.00 m side view stereo cam 1 mono cam stereo cam 2 particle inlet optical windows x2 x1 x3 x1 figure 1: turbulence tower used to generate nearly isotropic turbulence. particles are introduced from the top and are illuminated on a plane passing through the central axis of the tower. particle coordinates are recorded by independent mono and stereo camera setups. table 1: list of quantities characterizing the gas phase turbulence. rms velocity u′ 0.73 m/s integral length scale l 71.9 mm taylor microscale λ f 4.9 mm reynolds number reλ = u′λ f /ν 240 dissipation rate ε 10.1 m2/s3 kolmogorov length scale η 135 µm kolmogorov time scale τη 1.2 ms particles are introduced into the turbulence tower from above. the particle feeding system (not shown in fig. 1) consists of a hopper and a stack of dispersing sieves located above the tower. at the start of each experiment, particles are gravity fed through a small opening at the bottom of the hopper, dispersed through the sieves, and enter the tower. the turbulence fully disperses them throughout the test section. due to the basset history force, particles that enter the imaged volume from outside of the isotropic region can complicate the overall particle kinematics. since the isotropic region extends above and below the measurement volume by about 0.5 m, the history effects are likely small for particles with fast settling rates (i.e. on the order of the rms velocity fluctuations). 2.2 particle characterization two types of glass microspheres, one solid and the other hollow, are studied. to obtain the size distribution, the solid glass particles are prepared in an electrolytic particle slurry and then measured with a coulter counter. the resulting distribution of particle diameters is plotted in solid black in fig. 2. the distribution is nearly monodisperse with a mean diameter of 53 µm and a standard deviation of 4.0 µm. 50 100 150 200 0 0.02 0.04 0.06 0.08 0.1 p d f solid glass (coulter counter) solid glass (optical) hollow glass (optical) hollow glass (corrected) figure 2: distribution of particle diameters as measured by coulter counter and high-resolution imaging. the hollow glass particles cannot be submerged in the electrolytic solution, because their average specific gravity is less than one, so the coulter counter is a poor choice for sizing these particles. alternatively, we use high-resolution static imaging of the particles on a diffuse back-lit surface to obtain a mean diameter of 98 µm and a standard deviation of 26 µm. the bias of the optical size distribution measurement is evaluated by also imaging the solid glass particles and comparing with the corresponding coulter counter data. the pdfs of the solid glass particles are found to have similar shapes, but the optical measurement yields a pdf that is offset toward larger particle diameters by about 6 µm. this is likely due to the point spread function and other sources of aberration from the camera lens, which tend to enlarge the shadow boundary of the particles in the images. the final hollow glass size distribution after applying a 6 µm offset correction is plotted in solid blue in fig. 2, resulting in a mean diameter of 92 µm. the particle densities ρp are measured using the liquid pycnometry method. by mixing a known mass of particles with water and measuring the total slurry volume and mass, the average particle density is inferred. the densities of the solid and hollow glass particles are found to be 2450 kg/m3 and 136 kg/m3 respectively. the particle response time τp relative to the fluid time scale τf is quantified by the stokes number st ≡ τp/τf and governs the behavior of the dispersed phase. when τη is used as the fluid time scale, the degree of preferential concentration reaches a maximum around st ≈ 1. the schiller-naumann drag correlation is used in eq. 2 for defining the particle time response, τp = ρpd2 p 18µ 1 1+0.150re0.687 p , (2) where µ is the fluid dynamic viscosity and rep = u′dp/ν is the particle reynolds number. the particle settling velocity ut is less than u′, so u′ is the most appropriate choice of velocity scale in the particle reynolds number definition. a summary of the important average quantities for each set of particles is given in table 2. table 2: average particle properties. dp (µm) ρp (kg/m3) ut (m/s) rep st solid glass 53 2450 0.19 2.6 14 hollow glass 92 136 0.035 4.5 2.1 2.3 particle tracking the particles are tracked over two consecutive frames using both monoscopic and stereoscopic camera setups. for the mono-ptv experiments, particle images are recorded on a single tsi model 630094 ccd camera with a 6600×4400 pixel array. an af micro-nikkor 200 mm lens with f/8 aperture setting results in an image magnification of 0.74. for the stereo-ptv experiments, a pair of tsi model 630159 cameras, each with a 2048× 2048 pixel array, are used. the stereo cameras are configured at a 76◦ opening angle and are equipped with 135 mm lenses at a 15◦ tilt angle to achieve coplanar focus. table 3 gives a complete summary of the ptv parameters. the particles are illuminated by a new wave solo iii-15 dual-pulse nd:yag laser with a wavelength of 532 nm. the beam passes through a set of lenses to produce a laser sheet of constant height. the 1/e2 laser sheet thickness is found to be 1.2 mm using the knife-edge traverse method, with ±6.5% spatial deviation across the field-of-view. variation in the laser intensity in space can cause a non-uniformity in the number of particles detected and bias the resulting particle statistics. to better quantify the degree of laser uniformity, we compute the particle concentration field, in particles per unit area, as recorded on the mono camera. the average concentration of solid glass particles is found to be 14.7 cm−2, with maximum spatial deviation of ±10%. the inter-frame time δ t is set to 100 µs for the mono-ptv experiment and 300 µs for the stereo-ptv experiment, which results in an average particle displacement of about 8 pixels. at least 2000 image pairs are collected in each experiment to achieve statistical convergence. particle coordinates are determined by thresholding the background subtracted images and extracting the centroid of each identified region. in the stereo-ptv experiments, the image plane coordinates are mapped to physical space using the calibration procedure outlined in machicoane et al. (2019). briefly, each centroid detected on a camera corresponds to a ray path that passes through the measurement volume. stereo pairing is achieved when the minimum distance between two ray paths from unique cameras falls below a chosen threshold. the corresponding particle coordinate is then identified as the midpoint of the line that is normal to both ray paths. a given ray path is allowed to have more than one stereo pairing, in order to reduce the effect of particle overlap in either of the stereo camera views. although entirely possible, it is unlikely that table 3: list of ptv parameters for mono and stereo experiments. mono-ptv stereo-ptv laser sheet thickness, δ z 1.2 mm 1.2 mm inter-frame time, δ t 100 µs 300 µs repetition time 0.69 s 0.69 s lens focal length 200 mm 135 mm lens aperture f/8 f/8 camera resolution 7.4 µm/pixel ≈ 21 µm/pixel field of view 49.1 × 32.7 mm 50.0 × 37.5 mm image pairs acquired 2350 2000 overlapping would occur for a single particle in both camera views simultaneously, given the large camera opening angle. once particle coordinates are identified, particles are linked between frame pairs using the nearest neighbor approach described in ouellette et al. (2006). conflicting links can arise when a particle in the second frame is the nearest neighbor for more than one particle in the first frame. when this is the case, the links are chosen such that the sum of all particle displacements is minimized. 3 results 3.1 radial distribution function the rdf g(r) is the first statistical quantity needed to compute the collision rate using eq. 1. it quantifies the likelihood of finding a particle a distance between r and r + dr from any reference particle relative to the case of uniform random particle distribution. when a measurement of the rdf is carried out, it is important to distinguish the three-dimensional rdf g3(r) = g(r) from lower-dimensional rdfs, such as the two-dimensional rdf g2(r), which deviates from g(r) when r < δ z. we follow the algorithmic procedure for computing the n-dimensional rdf described by larsen and shaw (2018), which is reflected by gn(r) = np ∑ i=1 pi(r)/δvi(r) (np−1)np/v . (3) in eq. 3, pi(r) is the number of particle pairs separated from the ith particle by a distance r and r+dr, δvi(r) is the shell volume in n-dimensions between radii r and r+ dr, np is the total number of particles, and v is the total measurement volume. for the st = 14 particles, g2(r) is computed directly from the mono-ptv data. although a separate mono-ptv experiment was not conducted for the st = 2.1 particles, g2(r) is emulated by projecting the stereoscopic particle coordinates onto the x1-x2 plane and then computing eq. 3. 10 0 10 1 10 2 10 0 10 1 10 2 10 0 10 1 (a) 10 0 10 1 10 2 10 0 10 1 10 2 1 1.2 1.4 1.6 1.8 2 2.2 2.4 (b) figure 3: radial distribution function gn(r) computed from two-dimensional (n = 2) and three-dimensional (n = 3) particle coordinates for (a) st = 2.1 and (b) st = 14. in fig. 3, g2(r) and g3(r) are plotted for st = 2.1 (left) and st = 14 (right). to the right of r = δ z, indicated by the vertical dashed line, g2(r) and g3(r) collapse to a single curve. for r < δ z, g2(r) deviates significantly from the true rdf. the attenuation of g2(r) stems from the fact that particle separation distances are aliased from larger to smaller values when projected onto a plane from a 3d volume, as described by holtzer and collins (2002). this bias increases as particles move closer together. because eq. 1 depends on the rdf at particle contact g(dp), and δ z� dp, the two-dimensional rdf provides an underestimate of nc. the stereo-ptv experiments provide 3d particle coordinates, so the plots of g3(r) in fig. 3 are free from projection errors and are the appropriate values to use in predicting nc. however, the rdf could only be measured accurately for r & 2dp, due to diffraction effects when imaging the particles, so a functional form is required for extrapolation to r = dp. reade and collins (2000) proposed a power-law fit for small r, given by eq. 4, which showed good agreement with rdfs attained from point particle simulations in the range 0≤ st ≤ 4. g(r) = c0 ( η r )c1 (4) in the st = 2.1 experiments, power-law behavior is observed for r/η < 3. in the st = 14 experiments, power-law behavior appears to persist toward larger values, up to r/η ≈ 8. the coefficients c0 and c1 are obtained for both g2(r) and g3(r) by fitting eq. 4 over the applicable range of r and are listed in table 4. table 4: power-law fitting parameters describing the measured rdfs for small r. st = 2.1 st = 14 c0 c1 g(dp) c0 c1 g(dp) g3(r) 11.92 1.25 19.3 1.93 0.18 2.28 g2(r) 8.52 1.06 12.8 1.40 0.03 1.44 holtzer & collins fit 29.29 1.81 58.6 1.47 0.05 1.54 for comparison, an alternate approach commonly used to estimate g(dp) is to compute g2(r) from monoptv data and apply a fitting procedure proposed by holtzer and collins (2002). their correction results in two coefficients identical to those used in eq. 4 in order to recover the true unattenuated rdf. the method relies on the assumption that g2(r) derives from a power-law rdf (at small r), which is confirmed here by examination of the stereo-ptv data. holtzer and collins showed that the correction recovers the power-law coefficients of the true rdf to within 10% when δ z/η < 4.90. however, in our experiments, δ z/η = 8.9, so the errors are expected to exceed 10%. the coefficients obtained using their fit are listed in table 4. while the coefficients are adjusted in the right direction when compared to those obtained from the direct fits to g2(r), they are overpredicted for st = 2.1 and underpredicted for st = 14 when compared to the coefficients obtained from the direct fits to g3(r). it appears that for a large degree of preferential concentration and δ z/η ∼ 10, the holtzer and collins fitting procedure performs worse than a direct power-law fit to g2(r). 3.2 relative velocity distribution the second statistic needed to compute the collision rate from eq. 1 is the mean approach velocity, defined by 〈wr,n〉(−) (r) = 0∫ −∞ −wr,np(wr,n|r)dwr,n, (5) where p(wr,n|r) is the pdf of radial relative velocity computed in n-dimensions conditioned on particle separation distance r. the two-dimensional velocity wr,2 and the three-dimensional velocity wr,3 are sampled from more than half a million particle pairs in the mono and stereo-ptv datasets respectively. a single sample is extracted from each particle pair by first projecting the pair of lab-frame velocities onto the radial line that connects their centroids and then taking the difference. finally, the samples are binned according to the particle pair separation distance. the pdfs of wr,n are plotted in fig. 4 at two chosen separation distances, r/η = 5.8 and r/η = 23. the pdf for st = 0 particles is also given as a reference, which are extracted from the instantaneous piv velocity -30 -20 -10 0 10 20 30 10 -3 10 -2 10 -1 10 0 10 1 p d f (a) -30 -20 -10 0 10 20 30 10 -3 10 -2 10 -1 10 0 10 1 p d f (b) figure 4: pdfs of normalized radial relative velocity wr,n/uη from two-dimensional (n = 2) and threedimensional (n = 3) measurements for (a) r/η = 5.8 and (b) r/η = 23. fields obtained using tracer particles in the experiments conducted by hoffman and eaton (2021). the distribution for the inertial particles is wider than the st = 0 distribution at r/η = 5.8 but somewhat narrower in the center of the distribution at r/η = 23. this demonstrates the ”sling” effect (falkovich and pumir, 2007), or caustics, which occurs at small scales of separation, and the filtering effect (ayyalasomayajula et al., 2008), which occurs at larger scales of separation. the distribution of velocities for st = 14 appears to be independent of the measurement type, since the mono and stereo-ptv results are nearly identical, ignoring statistical noise. however, deviations can be expected in the distributions for r < δ z. at these small separations, projection errors in the mono-ptv measurement can cause small relative velocities to alias toward larger velocities, resulting in heavier tails in the distribution. however, there are too few particle pairs contained in the smaller radial bins to display meaningful pdfs. the relative velocity distribution for the st = 2.1 particles more closely resemble st = 0 particles near the center of the distribution. however, the distribution tails are significantly thicker than expected, and could be a result of frame-pair mismatching introduced by the nearest neighbor tracking algorithm. 0 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 figure 5: nearest neighbor yield parameter γ as a function of r/η from the stereo-ptv experiments. a potential source of bias in the radial relative velocity measurement is quantified by comparing the number of particles identified in the first frame of all ptv frame pairs with the number of particles that are successfully matched after applying the nearest neighbor algorithm between frame pairs. in practice, there is always some loss of particles in the second frame due to the finite laser sheet thickness and strong out-of-plane motion. it is useful then to define a yield parameter, γ(r) = n(1) p ∑ i=1 p(1) i (r) n(1−2) p ∑ i=1 p(1−2) i (r) , (6) where n(1) p is the total number of particles identified in the first frame of the image pairs, p(1) i (r) is the number of particle pairs in the first frame separated from the ith particle by a distance r and r+ dr, n(1−2) p is the total number of particles that are successfully matched using the nearest neighbors algorithm, and p(1−2) i (r) is the number of successfully matched particle pairs separated from the ith particle by a distance r and r + dr. to summarize, γ quantifies the fraction of particles in the first frame that are successfully matched in the second frame conditioned on r. in fig. 5, γ is plotted against the normalized separation distance r/η . it appears that γ is not a function of r when r/η > 10, reaching a plateau of 0.65 for st = 2.1 and 0.76 for st = 14. the lower yield for the st = 2.1 particles overall is likely due to greater out-of-plane motion, since the particle rms velocity is larger. particles within a region of strong preferential concentration are generally more difficult to track with high fidelity, which partly explains the decline in yield for nearby particles. more importantly, the laser sheet thickness is δ z/η = 8.9, which corresponds to the point at which γ falls off. this suggests that overlap of nearby particles in the images is quite common. if two nearby particles are identified in the first frame, there is some probability that their images will overlap in at least one camera view of the second frame. if the particle pair has an inward radial relative velocity, then the likelihood of overlap is further increased. if this is the case, fewer samples are collected when wr,3 is negative, causing a skew in the relative velocity distribution toward positive values at small r. 0 10 20 30 40 50 0 5 10 15 20 25 30 (a) 0 10 20 30 40 50 -0.4 -0.2 0 0.2 0.4 0.6 0.8 (b) figure 6: (a) normalized variance and (b) skewness of the relative velocity distributions as a function of particle separation for st− 2.1 and st = 14 as measured by stereo-ptv. the st = 0 data is taken from 2d piv data. the shape of the relative velocity distributions can be better understood over all separation distances by plotting the normalized variance 〈 w2 r,n 〉 /u2 η and the skewness 〈 w3 r,n 〉 / 〈 w2 r,n 〉3/2 as functions of r. the variance, given in fig. 6a, highlights the steady decrease in the correlation of particle motion as the distance separating them increases. the distribution skewness, shown in fig. 6b, takes mostly negative values and exhibits minor deviations from the st = 0 trend computed from the piv fields. it is important to point out that two-point relative velocity statistics in turbulent flows are inherently asymmetric, as reported by tavoularis et al. (1978). particles can have more asymmetric relative velocity distributions than the underlying flow, due to their inertia, with the skewness reaching its most negative value for st ≈ 1 (ray and collins, 2011). for this reason, skewness has often been linked to preferential concentration. from fig. 6a, we observe that the skewness increases slightly with r for st = 2.1 and decreases with r for st = 14. these trends were also observed in the numerical study of ray and collins (2011), although the magnitude of skewness reported there was several times higher. two possible explanations for this could be the higher reλ in our experiments and the effect of polydispersity. the positive skewness observed on the left-most side of fig. 6 is an artifact of the nearest neighbor algorithm, and is only shown here to indicate the limitation of the measurement in capturing the radial relative velocity statistics. to obtain the mean approach velocity 〈wr,n〉(−) (r), all radial relative velocity samples in each radial bin that are less than zero are averaged together. in fig. 7, the mean approach velocity is plotted as a function of particle separation for both particle stokes numbers. the solid black line indicates the mean approach velocity for st = 0 particles, which is computed from the instantaneous piv velocity fields (hoffman and eaton, 2021). as expected, the mean approach velocity increases monotonically with r. 0 10 20 30 40 50 60 70 0 10 20 30 40 50 0 1 2 3 4 5 (a) 0 20 40 60 80 100 120 0 10 20 30 40 50 0 1 2 3 4 5 (b) figure 7: mean approach velocity computed from two-dimensional (n = 2) and three-dimensional (n = 3) data for (a) st = 2.1 and (b) st = 14. to the right of the vertical dashed line, which indicates the laser sheet thickness r = δ z, the results are the same regardless of whether two or three-dimensional velocities are used. for r < δ z, the mean approach velocity computed from the two-dimensional data is augmented relative to the three-dimensional data due to the projection errors. the smallest separation at which 〈wr,n〉(−) (r) can be reliably obtained from the three-dimensional measurement is r/η ≈ 5. this limiting value arises from the artificial positive skewness of the relative velocity distribution seen in fig. 6b, which occurs for r/η . 5. because the two and threedimensional measurements align closely above this lower limit, stereo-ptv offers little additional advantage over mono-ptv in estimating the mean approach velocity at particle contact. 4 conclusions two important particle pair statistics relevant for inter-particle collisions, the rdf and the mean approach velocity, are measured for two types of particles having an average stokes number of 2.1 and 14, and diameters of 0.68η and 0.39η respectively. stereo-ptv is used to estimate these quantities at separations near particle contact. the rdfs, which are obtained down to r ≈ η , exhibit power-law behavior at small separations, even for the higher stokes number. at small separation, the rdf varies by nearly an order of magnitude over the range of st measured. the advantage of using stereo-ptv over a two-dimensional technique is clear, given that the rdfs at particle contact are underpredicted by about a factor of 2 when mono-ptv data is used. thus, a three-dimensional measurement technique like stereo-ptv is necessary to obtain accurate estimates of the volumetric collision rate. adding a third or fourth camera view can incrementally boost the accuracy of the rdf measurement, with the cost of additional complexity in calibration, measurement synchronization, and data analysis. for applications where a two-dimensional particle detection technique must be used, the holtzer and collins power-law fitting procedure may not be reliable when the dimensionless laser sheet thickness δ z/η is greater than 4.9. the mean approach velocity is also obtained at small particle separation, but is found to be reliable only down to r/η ≈ 5. this limiting value for r is based on the location of nonuniformity in the yield parameter γ(r) as well as the anomalous skewness in the radial relative velocity distributions. two additional approaches could be used in the future to overcome these limitations: (1) counteract particle overlap in images through additional stereo camera views, and (2) improve position and velocity certainty over the particle tracks through continuous (high-speed) particle tracking. acknowledgements this material is based upon work supported by the national science foundation under grant ear-1756068. the code used to generate links defining the particle tracks was generously provided by n. ouellette. references ayyalasomayajula s, warhaft z, and collins lr (2008) modeling inertial particle acceleration statistics in isotropic turbulence. physics of fluids 20:095104 de jong j, salazar jp, woodward sh, collins lr, and meng h (2010) measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging. international journal of multiphase flow 36:324–332 dou z, ireland pj, bragg ad, liang z, collins lr, and meng h (2018) particle-pair relative velocity measurement in high-reynolds-number homogeneous and isotropic turbulence using 4-frame particle tracking velocimetry. experiments in fluids 59:30 eaton jk and fessler jr (1994) preferential concentration of particles by turbulence. international journal of multiphase flow 20:169–209 falkovich g and pumir a (2007) sling effect in collisions of water droplets in turbulent clouds. journal of the atmospheric sciences 64:4497–4505 hoffman dw and eaton jk (2021) isotropic turbulence apparatus with a large vertical extent. manuscript submitted for publication holtzer gl and collins lr (2002) relationship between the intrinsic radial distribution function for an isotropic field of particles and lower-dimensional measurements. journal of fluid mechanics 459:93–102 larsen ml and shaw ra (2018) a method for computing the three-dimensional radial distribution function of cloud particles from holographic images. atmospheric measurement techniques 11:4261–4272 machicoane n, aliseda a, volk r, and bourgoin m (2019) a simplified and versatile calibration method for multi-camera optical systems in 3d particle imaging. review of scientific instruments 90:35112 ouellette nt, xu h, and bodenschatz e (2006) a quantitative study of three-dimensional lagrangian particle tracking algorithms. experiments in fluids 40:301–313 ray b and collins lr (2011) preferential concentration and relative velocity statistics of inertial particles in navier–stokes turbulence with and without filtering. journal of fluid mechanics 680:488–510 reade wc and collins lr (2000) effect of preferential concentration on turbulent collision rates. physics of fluids 12:2530–2540 sundaram s and collins lr (1997) collision statistics in an isotropic particle-laden turbulent suspension. part 1. direct numerical simulations. journal of fluid mechanics 335:75–109 tavoularis s, bennett jc, and corrsin s (1978) velocity-derivative skewness in small reynolds number, nearly isotropic turbulence. journal of fluid mechanics 88:63–69 introduction experimental methods apparatus particle characterization particle tracking results radial distribution function relative velocity distribution conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 design of experiments: a statistical tool for piv uncertainty quantification s. adatrao1*, a. sciacchitano1, s. van der velden1, m. j. van der meulen2, m. cruellas bordes3 1 department of aerospace engineering, delft university of technology, delft, the netherlands 2 royal netherlands aerospace center (nlr), marknesse, the netherlands 3 german-dutch wind tunnels (dnw), marknesse, the netherlands * s.adatrao@tudelft.nl abstract a statistical tool called design of experiments (doe) is introduced for uncertainty quantification in particle image velocimetry (piv). doe allows to quantify the total uncertainty as well as the systematic uncertainties arising from various experimental factors. the approach is based on measuring a quantity (e.g. time-averaged velocity from piv) several times by varying the levels of the experimental factors which are known to affect the value of the measured quantity. in this way, using analysis of variances (anova), the total variance in the measured quantity can be computed and hence the total uncertainty. moreover, the analysis provides the individual variances for each of the experimental factors leading to the estimation of the systematic uncertainties from each factor and their contribution to the total uncertainty. the methodology is assessed for an experimental test case of the flow at the outlet of a ducted boundary layer ingesting (bli) propulsor to quantify the total uncertainty in time-averaged velocity from stereoscopic piv measurements as well as the constituent systematic uncertainties due to the experimental factors, namely, camera aperture, inter-frame time separation, interrogation window size and stereoscopic camera angle. 1 introduction despite the quantification of piv uncertainty being the key to discern measurement errors from the true flow physics, piv uncertainty quantification (uq) is often hindered by the complexity of the measurement chain, which introduces errors from various sources such as particles, illumination, imaging and processing. several approaches have been proposed for piv uncertainty quantification. however, they mostly focused on quantifying the uncertainty from random errors and were limited in the quantification of the systematic uncertainty (sciacchitano 2019). moreover, the main results of the 4th international piv challenge (kähler et al. 2016) showed that, even for the same set of image recordings, large differences in the piv results occurred among the participants due to the selection of the different processing parameters. the systematic error sources in piv are not only significant in the processing stage, but also during the data acquisition (sciacchitano 2019, among others). thus, it is necessary to quantify the constituent uncertainties arising from various systematic error sources while calculating the total uncertainty in piv measurements. design of experiments (doe) is a statistical tool used in many fields of science and engineering to evaluate the systematic effect of input factors on the measurement output. it was first employed for wind tunnel measurements by deloach (2000) and was shown to be effective for quantifying the systematic errors in experiment (deloach et al. 2012). smith and oberkampf (2014) stated doe to be an alternative tool to 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 overcome the limitations of the traditional uq methods. beresh (2009) and debonis et al. (2012) made use of doe to quantify the uncertainty of their piv measurements in a transonic and supersonic flow, respectively. however, their uq analysis was conducted only at the intersection points of two measurement planes. in this work, a piv-uq approach based on doe and analysis of variances (anova) is introduced and demonstrated for stereoscopic piv measurements at the outlet of a ducted boundary layer ingesting (bli) propulsor. 2 methodology doe refers to the process of planning the experiment in order to collect appropriate data that can be analysed by statistical methods resulting in valid and objective conclusions (montgomery 2013). in any experiment, some of the experimental parameters directly affect the output value and are called design factors; in piv measurements, those are for instance the inter-frame time separation, interrogation window size, camera aperture, stereoscopic camera angle, etc. additionally, some of the parameters, which affect the output directly or indirectly (in combination with the design factors) but are uncontrollable (or only partly controllable) during the measurements, are called nuisance factors; for piv, those include variations of the fluid properties during a measurement, seeding density and its distribution, etc. different measurements of a constant (ideally) quantity with varying levels of the design and/or nuisance factors show variations in the measured quantity. a proper data acquisition model and statistical analysis can be used to quantify the variance in the output quantity due to the variations in the levels of input factors (and their combinations). the present work employs the statistical tools doe and anova to quantify the total uncertainty in time-averaged piv measurements and the contribution of the design and nuisance factors to the total uncertainty. following montgomery (2013), a randomized complete block design (rcbd) is considered for data acquisition, as blocking is necessary for tackling the effect of the nuisance factors. in such experimental design, measurements are carried out in two or more blocks (of the nuisance factor), where the levels of the blocking factor are fixed in each block and the levels of the design factors are varied randomly in each block. let us take an example of experiment with two design factors a and b with a and b number of levels, respectively, and one blocking factor with n number of levels. following montgomery (2013), a linear statistical model for this design is:  ijk i j k ijkij y a b ab block       (1) where, yijk is the observed response at the ith level of factor a and jth level of factor b in kth block, μ is the overall mean effect, ai is the effect of the ith level of factor a, bj is the effect of the jth level of factor b, (ab)ij is the effect of the interaction between ai and bj, blockk is the effect of the kth level of the blocking factor, and εijk is an error component consisting of random error and the effect of unknown factors (i.e. their first order and higher order main and interaction effects) in the measurements. for this model, we are interested in checking whether the effects ai, bj, (ab)ij and blockk are zero (null hypothesis) or non-zero (alternative hypothesis). this can be achieved by the factorial anova (montgomery 2013) as shown in table 1, where yi.. denotes the total of all observations under the ith level of factor a, y.j. denotes the total of all observations under the jth level of factor b, yij. denotes the total of all observations under the ith level of factor a and jth level of factor b, y..k denotes the total of all observations under the kth level of blocking factor, and y... denotes the grand total of all the observations. from the anova table 1, the significance of the factor effects is determined by performing the f-test with desired confidence level, where the mean squares (ms) of the effects are compared with that of the error mean square (msε). therefore, it is possible to segregate the contribution of every factor in the total variance of the measurement. the total uncertainty (utotal) and constituent systematic uncertainties (ux) in the response variable are calculated as: 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 2 2 2 2 2 1 total total a b ab block ss u u u u u u abn        (2) 1 x x ss u abn   and x a,b,ab,block,  (3) where, ss is the sum of squares and represents the variability in the response variable as shown in the table 1. table 1: analysis of variances (anova) table for two-factor randomized complete block design (rcbd) source sum of squares degrees of freedom mean squares f0 a 2 21 ... a i.. i y ss y bn abn   1a  1 a a ss ms a   0 ams f ms  b 2 21 ... b . j . j y ss y an abn   1b 1 b b ss ms b   0 bms f ms  ab 2 21 ... ab ij . a b i j y ss y ss ss n abn       1 1a b    1 1 ab ab ss ms a b    0 abms f ms  block 2 21 ... block ..k k y ss y ab abn   1n  1 block block ss ms n   0 blockms f ms  ε total a b ab blockss ss ss ss ss ss        1 1ab n    1 1 ss ms ab n      total 2 2 ... total ijk i j k y ss y abn   1abn 1 total total ss ms abn   3 experimental assessment the methodology was applied on a wind tunnel experiment of a ducted boundary layer ingesting (bli) propulsor. the experiment was conducted in the low-speed tunnel (lst) operated by the german-dutch wind tunnels (dnw). this atmospheric, closed circuit wind tunnel has a test section of 3.0 m × 2.25 m cross section and length of 8.75 m. the operating range of this wind tunnel is up to 80 m/s. the measurements were performed at a mach number of 0.174 and a body length-based reynolds number of 6 × 106 corresponding to a freestream velocity of 60 m/s. an axisymmetric body is placed upstream of the propulsor as shown in fig. 1. the axisymmetric body has a length of 1.5 m and a maximum cross-sectional area of 0.0491 m2. the distance between the trailing edge of the body and the inlet of the propulsor is 0.15 m. stereoscopic piv measurements were performed in a cross plane 0.08 m downstream from the outlet of the propulsor. the aim of this experimental assessment is to employ the statistical tools doe and anova to quantify the total uncertainty in time-averaged piv measurements and the contribution of the design and nuisance factors to the total uncertainty. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 figure 1: schematic experimental setup of stereoscopic piv measurements at the outlet of the ducted boundary layer ingesting (bli) propulsor various factors during the acquisition and processing stages contribute to the total uncertainty. however, only some of the most significant ones are considered for the analysis. following sciacchitano (2019) and bhattacharya et al (2016), among others, four factors, namely camera aperture (f#), inter-frame time separation (∆t), interrogation window size (di) and stereoscopic camera angle (𝛼) were considered to be significant. therefore, for the analysis three design factorsf#, ∆t, di (assigned with a, b, c, respectively) and a blocking factor (𝛼) with two levels of each were selected. the two levels of the factors were: 4 and 5.6 for f#, 16 and 20 μs for δt, 16 and 32 pixels for di, and 44 and 54 degrees for 𝛼. following the 2n rule, n being the number of design factors, a total of 16 measurements were performed (23 = 8 in each block). figure 2: time-averaged contour plots of the streamwise velocity u and vector plots of the in-plane (y-z plane) velocity of the stereoscopic piv measurement 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) magnitude of local in-plane velocity gradient for streamwise velocity (b) rms of velocity fluctuations in streamwise velocity normalized by freestream velocity figure 3: contour plots of (a) magnitude of local in-plane velocity gradient for streamwise velocity and (b) rms of velocity fluctuations in the streamwise velocity normalized by the freestream velocity (the detailed results of anova are shown for the four regions which are selected based on the magnitude of velocity gradient and flow fluctuations: 1 = low velocity gradient and low flow fluctuations, 2 = low velocity gradient and high flow fluctuations, 3 = high velocity gradient and low flow fluctuations, and 4 = high velocity gradient and high flow fluctuations). three lavision imager scmos cameras were used to perform the measurements with two different stereoscopic angles (i.e. in two blocks). the cameras 1 and 2 formed the stereoscopic angle (𝛼12) of 44° and were considered to be the block i, whereas the cameras 1 and 3 formed the stereoscopic angle (𝛼13) of 54° and 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 were considered to be the block ii. it is to be noted that the stereoscopic angles were limited by the limited optical accessibility due to the wind tunnel wall and the position of the propulsor itself. the cameras have a sensor resolution of 2560 × 2160 pixels and a pixel size of 6.5 μm. the cameras were mounted with objective lenses of 135 mm focal length and scheimpflug adapter. the field of view (fov) obtained was 460 mm × 220 mm and the magnification factors for the cameras 1, 2 and 3 were 0.067, 0.073 and 0.069, respectively. the flow was seeded by an aerosol seeding generator, which produces dehs droplets of 1 μm mean diameter. the particles were illuminated by a quantel evergreen 200 laser (nd:yag, pulse energy of 200 mj per pulse, wavelength of 532 nm) forming a sheet of 4 mm thickness. the images were recorded and processed using the lavision davis 10.1.2 software. the data set at each run consisted of 2000 double-frame images and a total of 8 runs per block (stereoscopic camera angle) were performed in a random order. each measurement run was unique corresponding to the combination of one of the two levels of the three design factors. the processing was done using gaussian interrogation windows of 64 × 64 pixels with 50% overlap for the initial passes and 16 × 16 pixels or 32 × 32 pixels with 50% overlap for the final passes. the estimated time-averaged streamwise velocity component u and in-plane (y-z plane) velocity vectors are shown in fig. 2. the wake region can be seen in the centre of the measurement domain, whereas the outer region represents potential flow with streamwise velocity of 60 m/s. the flow is retarded at the periphery of the propulsor and the discontinuities in the mean streamwise velocity field due to the stator ring can be seen at the periphery. moreover, the in-plane velocity vectors are shown in fig. 2 which represent the magnitude and direction of y and z-velocity components v and w, respectively. the counter-clockwise rotation of the flow in the wake of the propulsor can be easily seen due to the direction of the vectors, where the magnitudes of v and w velocity components are larger than those in the outer potential flow region. moreover, contour plots of magnitude of local in-plane velocity gradient for streamwise velocity and rms of fluctuations in the streamwise velocity normalized by the freestream velocity (u∞) are shown in fig. 3(a) and (b), respectively. it is clear that the flow has varying degrees of velocity gradients and velocity fluctuations. therefore, the measured flow field is a suitable case to implement and assess the feasibility of the proposed approach in a range of flow conditions encountered in typical piv measurements. the analysis was performed for the whole fov to quantify the total uncertainty in the time-averaged velocity and the contribution of the individual factors to the total uncertainty. however, for simplicity, four regions were chosen based on the amount of velocity gradient and flow fluctuations, as shown in fig. 3(a) and (b), to explain the contribution of the factors to the total uncertainty. the results at these selected regions are explained in detail in section 4. 4 results the application of the proposed methodology to the flow at the outlet of the bli propulsor resulted into the quantification of the total uncertainty in the time-averaged velocity components. the contour plot of the total uncertainty (uu) of the mean streamwise velocity component u is shown in fig. 4. as expected, the total uncertainty of the mean velocity closely resembles the fluctuations root-mean-square, because it is equal to 𝜎 √𝑁𝑠⁄ (σ being the standard deviation and ns the number of samples), as discussed by sciacchitano and wieneke (2016). moreover, larger total uncertainty is retrieved in the regions of high velocity gradients, as reported by scarano (2002), which are mainly encountered at the outer edge of the propulsor slipstream. following these observations, four small regions in the flow field were selected to evaluate the results for the constituent systematic uncertainties based on the amount of velocity gradient and flow fluctuations as shown in fig. 3(a) and (b). the regions 1, 2, 3 and 4 correspond to the regions of low velocity gradient and low flow fluctuations, low velocity gradient and high flow fluctuations, high velocity gradient and low flow fluctuations, and high velocity gradient and high flow fluctuations, respectively, as shown in the table 2. the anova results in the four regions are obtained in the form of tables like the table 1, where the f0 values corresponding to the main and interaction effects of the design and blocking factors are calculated as shown in 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 the last column in the table 1. the f-test is then performed to estimate whether the effects are statistically significant or not, which is done by comparing the f0 values with the critical value fc which is 5.3 for 95% confidence level (for 1 degree of freedom of numerator and 8 degrees of freedom of denominator) in the present experimental case. if the f0 value is greater than fc, then the corresponding effect is statistically significant with the desired level of confidence. for example, in the region 3 in the measurement domain, the main effect of factor b (i.e. ∆t) is statistically significant as it shows f0 value of 11.5. the reader is advised to refer any standard book of statistics for a detailed explanation of the f-test (for example, montgomery 2013). the constituent uncertainties due to the main and interaction effects of the factors are calculated by equation (3) and their contributions to the total uncertainty in the streamwise velocity u are shown in the form of pie charts in fig. 5. the pie charts represent the percentage contribution of the systematic uncertainties to the total uncertainty. the sub-figures (a), (b), (c) and (d) are for the regions 1, 2, 3 and 4, respectively, which are marked in fig. 3(a) and (b). the mean streamwise velocity (u) components in these regions are 59.20 m/s, 59.75 m/s, 52.28 m/s and 64.17 m/s, respectively. the corresponding total uncertainties are 0.37 m/s, 0.51 m/s, 1.56 m/s and 1.60 m/s, which are shown in the centre of the pie charts in fig. 5. figure 4: total uncertainty in time-averaged streamwise velocity u calculated by the proposed methodology table 2: magnitude of local in-plane velocity gradient for streamwise velocity and rms of velocity fluctuations in the streamwise velocity (u’rms) normalized by the freestream velocity (u∞) at the four regions of analysis marked in fig. 3(a) and (b) regions velocity gradient (1/ms) u’rms / u∞ 1 0.00 – 0.02 0.00 – 0.01 2 0.70 – 0.80 0.18 – 0.22 3 2.70 – 3.90 0.06 – 0.08 4 2.70 – 3.30 0.14 – 0.16 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) region 1 (b) region 2 (low velocity gradient and low flow fluctuations) (low velocity gradient and high flow fluctuations) (c) region 3 (d) region 4 (high velocity gradient and low flow fluctuations) (high velocity gradient and high flow fluctuations) figure 5: contribution of systematic uncertainties to the total uncertainty in time-averaged streamwise velocity for the regions marked in fig. 3(a) and (b), due to main and interaction effects of the factorsa (camera aperture f#), b (inter-frame time separation ∆t), c (interrogation window size di) and block of stereoscopic camera angle it is clear that the total uncertainty increases with increase in the velocity gradient and the flow fluctuations, which agrees with the observation in the contour plot of total uncertainty in fig 4. the analysis shows that, in 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 most of the measurement domain, the main effects of the factors f# (factor a), ∆t (factor b) and stereoscopic camera angle (block) are statistically significant, whereas the main effect of the factor di (factor c) and all the two-way interaction effects are found to be insignificant. the blocking factorstereoscopic camera angle is the most significant factor in all of the four regions. it is due to the slight misalignment of the two measurement planes of the two blocks of the measurements (viz. the two stereoscopic systems). however, this uncertainty corresponding to the stereoscopic camera angles can be easily reduced by implementing a proper self-calibration (wieneke 2005), which has not been applied in this study. nevertheless, the stereoscopic camera angle is highly influential in stereoscopic piv measurements (prasad 2000) and should be selected optimally to minimize the related errors. the factor ∆t corresponds to the out-of-plane motion of the particles and it has significant contribution to the total uncertainty of the time-averaged streamwise velocity component in the regions of high velocity gradients and high fluctuations (regions 2, 3 and 4). however, the analysis for y and z velocity components show that the factor ∆t is significant also in the regions of low flow fluctuations (the results are not shown for conciseness). in that case, the factor ∆t corresponds to peak-locking error and, as observed by adatrao et al. (2021), the regions of low flow fluctuations are those where the mean velocity is affected by peak-locking errors the most. additionally, the factor f# is associated with errors due to out-offocus particles caused by imperfect camera focussing. analysing the image recordings, it was realized that, at the low level of the f#, the particle images in the potential flow in the top-left region of measurement domain for the camera 2 were out of focus, thus yielding larger uncertainty. for the flow regions of low flow fluctuations, i.e. regions 1 and 3, the blocking factor (i.e. the stereoscopic camera angle) contributes the most (97% and 84%, respectively) to the total uncertainty in the time-averaged velocity. however, for the flow regions of high flow fluctuations, i.e. the regions 2 and 4, the random error (factors not directly considered in the analysis, e.g. limited statistical convergence, image noise, variations of seeding concentration, etc.) has the biggest contribution of 71% and 57% to the total uncertainty in the mean streamwise velocity, as shown in fig. 5(b) and (d), respectively. this is due to the flow fluctuations in these regions being high which, owed to the limited statistical convergence of the measurements, makes it difficult to segregate the contribution of individual systematic uncertainties. it is to be noted that the error uncertainty from the anova represents the random uncertainty in the measurements plus the uncertainty due to the unknown experimental factors (i.e. the factors not considered as design or blocking factors). 5 conclusions a piv uncertainty quantification (uq) approach is proposed based on a statistical tool called design of experiments (doe). the basic principle of the approach is to measure a constant (ideally) quantity for the different levels of experimental factors and to compute total variance and individual variances arising from the different levels of each of the factors. the statistical analysis is performed using analysis of variances (anova). the proposed methodology is assessed considering the stereoscopic piv measurements of a flow at the outlet of a boundary layer ingesting (bli) propulsor to quantify the uncertainty of the time-averaged velocity. three design factors, namely camera aperture (f#), inter-frame time separation (∆t) and interrogation window size (di), and a blocking factor (the stereoscopic camera angle 𝛼) are considered for the analysis. the three design factors and the blocking factor are set at two different levels (low and high) each, resulting in a total of 16 measurements (23 = 8 in each block, following the 2n rule, n being the number of design factors) which are performed in a random order. the analysis results in the estimation of total uncertainty in the timeaveraged velocity as well as constituent systematic uncertainties due to the design and blocking factors. overall, it can be concluded that the stereoscopic camera angle has the largest contribution to the uncertainty of the measured time-averaged velocity (without self-calibration). the random errors due to the unknown experimental factors and limited statistical convergence are significant especially in regions of high fluctuations. of the design factors considered in this study, the inter-frame time separation t is highly significant especially in the regions of high flow fluctuations for the streamwise velocity component, whereas 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 it is significant for the velocity components v and w in the regions of high velocity gradients. a marginal role is played by the f#, due to the presence of out-of-plane particles in a region of camera 2. the contribution of the window size and of the interactions among factors to the uncertainty of the time-averaged velocity is found not to be statistically significant. the present work is thus able to segregate the systematic uncertainties due to the experimental factors considered for the analysis. moreover, knowing these constituent uncertainties, it will be possible to optimize the experiment in order to reduce the total uncertainty. the proposed methodology is successfully used for the time-averaged velocity. however, it can also be applied to the higher order statistics, e.g. reynolds stresses, to quantify the total and constituent systematic uncertainties in those quantities. moreover, the approach can easily be implemented for 3d measurements for uncertainty quantification. the future work will focus on validating and comparing the proposed approach with the conventional piv-uq approaches. additionally, a comparison between the 2n and 3n models (two and three levels of the design factors, respectively) will be performed. it is also planned to perform the self-calibration before applying the proposed methodology for the stereoscopic piv measurements. acknowledgements the research is partly funded by the dutch research organization nwo domain applied and engineering sciences, veni grant 15854 deploying uncertainty quantification in particle image velocimetry. references adatrao s, bertone m and sciacchitano a (2021) multi-δt approach for peak-locking error correction and uncertainty quantification in piv. meas. sci. technol. 32:054003 beresh sj (2009) comparison of piv data using multiple configurations and processing techniques. experiments in fluids 47:883–896 bhattacharya s, charonko jj and vlachos pp (2016) stereoscopic-particle image velocimetry uncertainty quantification. meas. sci. technol. 28:015301 debonis jr, oberkampf wl, wolf rt, orkwis pd, turner mgbh and benek ja (2012) assessment of computational fluid dynamics and experimental data for shock boundary-layer interactions. aiaa journal 50:891–903 deloach r (2000) the modern design of experiments: a technical and marketing framework. in 21st aiaa advanced measurement technology and ground testing conference, denver, co, usa, june 19-22 deloach r, obara cj and goodman w (2012) a practical methodology for quantifying the random and systematic components of unexplained variance in a wind tunnel. in 50th aiaa aerospace sciences meeting and exhibit, nashville, tennessee, usa, january 9-12 kähler cj, astarita t, vlachos pp, sakakibara j, hain r, discetti s, foy r and cierpka c (2016) main results of the 4th international piv challenge. experiments in fluids 57:1–71 montgomery dc (2013) design and analysis of experiments. 8th edition, john wiley & sons, new york prasad ak (2000) stereoscopic particle image velocimetry. experiments in fluids 29:103–116 scarano f (2002) iterative image deformation methods in piv. meas. sci. technol. 13:r1-r19 sciacchitano a (2019) uncertainty quantification in particle image velocimetry. meas. sci. technol. 30:092001 sciacchitano a and wieneke b (2016) piv uncertainty propagation. meas. sci. technol. 27:084006 smith bl and oberkampf wl (2014) limitations of and alternatives to traditional uncertainty quantification for measurements. in the asme 2014 fluids engineering summer meeting, chicago, il, usa, august 3-7 wieneke b (2005) stereoscopic-piv using self-calibration on particle images. experiments in fluids 39:267–280 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 ultrasound piv uncertainty quantification r. derakhshandeh1∗, s. bhattacharya1, b. a. meyers1, p. p. vlachos1 1 school of mechanical engineering, purdue university, west lafayette indiana, 47907, usa ∗ rderakhs@purdue.edu abstract ultrasound particle image velocimetry (upiv) is a non-invasive flow measurement technique where acousticopaque flow tracers are injected into a working fluid and ensonified to create ultrasound images. these images are processed using piv cross-correlation based algorithms to measure the velocity field (kim et al., 2004). upiv is useful for opaque flows, primarily where complex flows exist, accordingly, it is used in many industrial and clinical research applications such as studying intracardiac flow (crase et al., 2007). furthermore, the measurement provides suitable temporal and spatial resolutions for improved diagnostic metrics. mentioned applications and the sensitive diagnostic industrial and clinical decisions made based on these measurements intensifies the importance of characterizing the upiv measurement accuracy and associated uncertainty. however, quantifying upiv measurement uncertainty is non-trivial due to the complexity of possible uncertainty sources, their combination, and propagation through the measurement chain. the formation of a particle image by ultrasound significantly differs from optical imaging, introducing unique aspects to image quality that must be considered. particle images are formed across several ultrasound scan lines, yielding an elliptical particle image shape. furthermore, the particle’s reflected pressure wave is converted to a digital signal that undergoes signal modulation, and this process forms a non-gaussian point spread function (psf) along the scan line direction. additionally, clusters of tracers produce a single, bright image intensity and speckle image pattern. compared to conventional piv images, upiv incurs significantly higher image noise due to lack of filtration for the ultrasound reflection of the non-tracer obstacles. (a) (b) figure 1: comparison of a conventional piv image(a), and an echo piv image(b)(crase et al., 2007) although existing 2d piv uncertainty methods can potentially be applied to upiv, the image formation aspects introduced above must be taken into account to quantify upiv measurement uncertainty. therefore, in this work, we modified the methodology of three direct uncertainty estimation methods, image matching (im) (sciacchitano et al., 2013)moment of correlation (mc) (bhattacharya et al., 2018), and correlation statistics (cs) (wieneke, 2015), in order to increase their sensitivity to error sources specific to upiv. in the following paragraphs, these improvements are explained in detail. in the im method, the standard uncertainty is defined as the standard deviation of the disparity error histogram. the disparity error relates to the residual mismatch between paired particle image positions. in regular piv, the position is estimated using a 3-point gaussian fit. however, upiv scans lead to significantly stretched elliptical particle image patterns with aspect ratios 1 to 4, causing similar pixel intensities in the 3point neighborhood of the center. thus, a 3-point fit often fails or is inaccurate. to overcome this limitation, we instead use a least-square elliptic gaussian fit for particle image position estimation and disparity values to calculate the im uncertainty. for the mc method, the uncertainty is estimated directly from the cross-correlation plane by extracting the probability density function (pdf) of the displacements. the standard algorithm assumes a gaussian pdf exists and convolves it with another circular gaussian kernel to broaden the peak region. this leads to a more reliable pdf standard deviation estimate. the mc uncertainty calculation uses the sum of the covariance matrices for gaussian convolution, which simplifies to the sum of the variance terms for a circular gaussian kernel, expressed as px = √ c2 x −d2 and py = √ c2 y −d2. here, px and py are the pdf’s major and minor axis, cx and cy are the convolved pdf peak diameters, and d is the circular gaussian kernel diameter. the kernel diameter is dynamically estimated from the cross-correlation peak’s width. since in a upiv measurement, the cross-correlation peak is non-circular, the convolution kernel is also defined as a non-circular gaussian function. thus, a theoretical framework for a generically rotated elliptic gaussian kernel convolution is deduced. accordingly, the elliptical gaussian kernel major axis (dx), the minor axis (dy), and the orientation angle (α) are calculated by equations (1), (2), and (3) respectively. p2 x = (c2 x +c2 y )− (d2 x +d2 y)+ √ (c2 x −c2 y ) 2 − (d2 x −d2 y) 2 −2(c2 x −c2 y )(d2 x −d2 y)cosα 2 (1) p2 x = (c2 x +c2 y )− (d2 x +d2 y)− √ (c2 x −c2 y ) 2 − (d2 x −d2 y) 2 −2(c2 x −c2 y )(d2 x −d2 y)cosα 2 (2) α = (c2 x cos2(β)+c2 y sin2(β)−d2 x)− (py/px) 2(c2 x sin2(β)+c2 y cos2(β)−d2 y) p2 x − (p4 y /p2 x ) (3) in equation (3), β is the orientation of convolved pdf peak obtained from the least square fitting. the cs method models the uncertainty through the cross-correlation peak’s asymmetry attributed to the covariance sum of the pixel-wise intensity difference between two matching interrogation windows. in general, this sum is computed over a neighborhood region proportional to the particle image size. for upiv measurements, the cs uncertainty calculation is modified to dynamically set the covariance sum region in each direction proportional to the estimated autocorrelation diameter. the performance of the modified im, mc, and cs methods are tested using synthetic ultrasound images (meunier and bertrand, 1995) that represent a range of error sources, including particle image diameter, noise, seeding density, displacement, and flow shear rate. for the baseline condition, 512× 512 images with 3× 9 pixel diameter particles are generated with a seeding density of 0.03 particles per pixel with multiplicative (σ2 = 0.01) and additive (σ2 = 0.01,µ = 0) noise and constant displacements of 2.15 pixels in both the xand y-directions. also, to consider for the ghost particles, random particles has been added to the images; the number of these random particles is 5% of the total particles. the relevant parameters for the monte carlo image simulations are presented in the table 1. the parameters were varied independently to test each method’s sensitivity to different error sources. table 1: monte carlo test matrix diameter y-direction 3 pixels diameter x-direction 3:1:12 pixels displacement y-direction 0:0.05:3 pixels displacement x-direction same as it is in y-direction shear y-direction 0 shear x-direction 0:0.05:015 pixels/frame/pixel density 0.01:0.005:0.05 additive noise 0:0.01:0.1 multiplicative noise 0:0.01:0.1 figure 2 shows the rms error and the rms of the predicted uncertainty for each method as a function of particle image aspect ratio (ar). the particle image aspect ratio varies from 1 to 4 by varying the x-direction image diameter from 3 to 12 pixels, and the y-direction image diameter is kept constant at 3 pixels. each point in the plot represents the rms value over 12800 measurements. for ideal prediction, the rms of the error distribution should match the rms of the uncertainty distribution (sciacchitano et al., 2015). the current results show close agreement between the predicted and expected im uncertainty values for up to 1.5 ar. mc uncertainty predictions are within 10% of the rms error between ar values 1 and 2. all three methods’ performance deteriorates for ar values greater than 3, signifying further development may be required to account for the specific particle image characteristics in upiv. further development and validation will be done to improve each method’s performance to the different error sources. figure 2: comparison of the uncertainty methods results over different particle aspect ratio references bhattacharya s, charonko jj, and vlachos pp (2018) particle image velocimetry (piv) uncertainty quantification using moment of correlation (mc) plane. measurement science and technology 29:115301 crase sj, hockaday c, and mccarville pc (2007) brief report: perceptions of positive and negative support: do they differ for pregnant/parenting adolescents and nonpregnant, nonparenting adolescents?. journal of adolescence 30:505–512 kim hb, hertzberg jr, and shandas r (2004) development and validation of echo piv. experiments in fluids 36:455–462 meunier j and bertrand m (1995) echographic image mean gray level changes with tissue dynamics: a system-based model study. ieee transactions on biomedical engineering 42:403–410 sciacchitano a, neal dr, smith bl, warner so, vlachos pp, wieneke b, and scarano f (2015) collaborative framework for piv uncertainty quantification: comparative assessment of methods. measurement science and technology 26:074004 sciacchitano a, wieneke b, and scarano f (2013) piv uncertainty quantification by image matching. measurement science and technology 24:045302 wieneke b (2015) piv uncertainty quantification from correlation statistics. measurement science and technology 26:074002 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 evaluation of velocity fields in horizontal gas-liquid intermittent flows using stereoscopic-piv and instantaneous masking procedure l. s. fernandes1, r. s. n. de mesquita1, f. j. w. a. martins1,2, l. f. a. azevedo1,∗ 1 mechanical engineering department, pontifical catholic university of rio de janeiro, brazil 2 current address: institute for combustion and gas dynamics tomography group, university of duisburg-essen, germany ∗ correspondent author: lfaa@puc-rio.br abstract the main goal of this work was to obtain well-converged liquid velocity profiles for intermittent gas-liquid flows in a horizontal pipe. to this end, air and water with superficial velocities of jg = 0.5 m/s and jl = 0.3, 0.4 and 0.5 m/s, respectively, were driven into a 18-m acrylic test section with an inner diameter of 40 mm. all three-components of the velocity vectors were measured in a pipe cross-section using a highfrequency stereoscopic piv system, together with the laser induced fluorescence technique. photogates were used to measure the unit cell translational velocity, as well as to trigger data acquisition, allowing the calculation of ensemble-averaged velocity fields at specific positions, referenced to the gas-bubble nose tip position. an instantaneous image masking procedure was implemented, allowing the determination of non-dimensional ensemble-averaged velocity profile in the liquid film, referenced to gas-bubble boundary. the high-frequency system employed allowed the determination of the influence of the faster-moving gas bubble on the liquid velocity field in the plug region. the data presented are relevant to the validation and improvement of one-dimensional two-phase numerical models, as well as to better understand this complex flow. 1 introduction two-phase gas-liquid flows can be found in many engineering applications, ranging from oil and gas transport and production lines to nuclear reactor cooling systems. in fact, the continuously search for new oil reservoirs at deeper offshore locations has led to an increase in the distance from oil pre-processing facilities to well-heads (hua et al., 2012), increasing temperature and pressure variation along the production lines and enhancing, therefore, the possibility of occurrence of different gas-liquid flow patterns. there are two main reasons why intermittent flow in a horizontal pipe might occur. first, due to accumulation of liquid at lower parts of pipelines through hilly terrains, what is called severe slugging (al-safran et al., 2005). second, due to the natural growth of waves, due to kelvin-helmotz instability phenomenon in a stratified flow (taitel and dukler, 1976). in fact, an analysis of classical gas-liquid flow pattern maps (baker, 1953; brennen, 2005) clearly shows that the intermittent flow regime (elongated bubble flow and slug flow) occupies a large area in the maps, i.e., it is the dominant flow pattern for a considerable combination of gas and liquid flow rates, justifying the study of this gas-liquid flow pattern. the horizontal intermittent flow is usually characterized by a succession of unit cells, each one being composed of two regions, namely, liquid plug and liquid film. in the liquid film region, gas flows at a higher velocity at the upper part of the pipe, while slower liquid flows at the bottom part. differently, in the liquid plug region, the liquid phase occupies the whole pipe cross section. the presence of dispersed bubbles in the liquid plug is a condition used by many authors to distinguish between the elongated-bubble flow and the slug-flow regimes. in the present work, such differentiation will not be considered. the transient intrinsic characteristic of the intermittent flow described above causes abrupt and large variation in the fluid density at a specific location, what can generate severe damage to both equipments or structures (fabre et al., 1990). a good understanding and modelling of the intermittent flow is, therefore, fundamental to the proper operation and design of the flow systems. this work provides well-converged velocity profiles at different locations of the unit cell that can be used not only to improve and validate numerical simulations, but also to help elucidate the physic mechanisms governing this complex phenomenon. 2 experiment and data evaluation figure 1 shows a schematic view of the test section. it consisted of a 18-m long acrylic pipe with an internal diameter d of 40 mm. air and water were driven into the test section by 2 centrifugal compressors assembled in series and by a progressive cavity pump, respectively. this specific pump was used because it provides a flow rate independent of the outlet pressure, eliminating possible liquid flow rate variations due to pressure oscillations. both fluids entered the test section through a y-junction. the flow developed through a pipe length of 14.8 m (370 d) upstream of the measurement region, which was located 6.4 m downstream of a 180◦ horizontal curve and 3.6 m (90 d) upstream of the end of the horizontal pipe. water and air calibrated rotameters were used to measure the liquid and gas flow rates. figure 1: schematic view of the test section, highlighting the measurement station a stereoscopic-piv system (spiv) was used to measure all three-components of the velocity vector in a pipe cross-sectional plane. a 2-mm-thick laser light sheet was provided by a litron ldy304 pulsed laser (2x30 mj @ 400hz), while two high-speed cmos phantom m340 cameras (1280x1280 pixels @ 400hz) were symmetrically mounted at opposite sides of the pipe, in a horizontal arrangement, as indicated in figure 1. the cameras were placed downstream the laser light sheet, in order to reduce gas-bubble obstruction of the film region (fernandes et al., 2018). the 105-mm nikon-nikkor lenses with f# = 11 aperture were tilted in relation to the camera sensor using scheimpflug adaptors. a visualization box, filled with water, was used to minimize optical distortions due to the pipe curvature. also, in order to mitigate optical distortions, the pipe wall thickness at the measurement region was machined down to 1 mm. both cameras and laser were controlled by a tsi model 610036 synchronizer. a set of three equally-spaced infra-red photogates were positioned upstream of the measurement region. the differences in the refraction indexes of water and air deviated the infra-red beam away from the photogate detector when water was present, allowing the determination of the phase flowing in the upper part of the pipe. the first two photogates were used to measure the translational velocity of the gas-bubble, which was assumed to be the translational velocity of the unit cell. the third photogate was used to trigger the image acquisition. the same photogate system was used with success in previous works of the group (de oliveira et al., 2015; fernandes et al., 2018). in gas-liquid piv measurements, the interface is often a critical region. the light scattered at the interface can not only obscure particles near those regions, but also damage the camera sensors due to excess of light. a common practice to avoid such problem is to use the laser-induced fluorescence technique (lif) (lindken and merzkirch, 2002). in this work, polystyrene fluorescent particles impregnated with rhodamine 6g, with diameter ranging from 1 to 20 µm and density of 1.19 g/cm3 were used as seeding material. highpass optical filters were installed in front of the camera lenses, in order to transmite the light emitted by the particles and block the laser light scattered at the interface. 2.1 camera calibration the cameras were calibrated using a specially designed calibration rig. it consisted of a matrix of 140 equally-spaced points which was printed on a transparent sheet and glued on the surface of a propylene disk, as can be seen in figure 2(a). the disk was connected by a rod to a micrometer head, with a resolution of 10 µm, allowing the axial translation of the target, as shown in figure 2(b). the rod passed through an aperture in a cylindrical sleeve with rubber o-rings, which fitted the external part of the acrylic pipe, properly sealing it. (a) (b) figure 2: different views of the calibration target. during the calibration procedure, the pipe downstream of the visualization box was removed, the target inserted into the measurement region and the upstream pipe filled with water. a total of three calibration images of the planar target, equally-spaced of 0.5 mm along the pipe axis and centered at the laser light sheet position were acquired for each camera. a calibration polynomial of third order in x and y (inplane coordinates) and second order in z (out of plane coordinate) was generated based on the target points positions. a self-calibration procedure (wieneke, 2005) using low-density particle images was employed to refine the calibration polynomia that were used both to dewarp the acquired images and later to reconstruct the three-component velocity vectors. 2.2 experimental procedure the infrared photogate system described in section 2 was used to trigger the image acquisition. when the third photogate detected the passage of the gas bubble-nose, it automatically started the acquisition of 220 image pairs, for each camera, at a frequency of 400 hz, covering the passage of the gas-bubble nose through the measurement region. small manual adjustments were performed to determinate in which image of the set of time-series data, the bubble nose was located. whenever there were at least 80 image pairs registering the liquid film and the liquid plug (i.e., gas bubble nose tip between images 81 and 140 of the time-series), the run was validated. this procedure was repeated 1500 times, and image pairs were separated according to the time-distance from the gas-bubble nose (images captured at 2.5 ms, 5.0 ms, etc after or before the passage of the bubble-nose). the measured bubble-translational velocity, here considered as the unit cell translational velocity, was used to transform the time between consecutive image samples into spatial distance, following the same procedure of fernandes et al. (2018). three different cases were measured, with gas and liquid superficial velocities of jg = 0.5 m/s and jl = 0.3, 0.4 and 0.5 m/s respectively, as summarized in table 1. the mixture reynolds number was calculated based on the mixture superficial velocity and pipe diameter. table 1: summary of the cases measured case jl (m/s) jg (m/s) jm (m/s) reynolds (mixture) 1 0.3 0.5 0.8 32000 2 0.4 0.5 0.9 36000 3 0.5 0.5 1.0 40000 images were pre-processed by subtracting the average image intensity, in order to minimize the influence of the background during images processing. cross-correlation was performed on the dewarped images, using a recursive grid with final interrogation window of 32 x 32 pixels, with 50% overlap. the final measured velocity vector field had over 3700 vectors, in the liquid phase, equally spaced of 0.6 mm. all image pairs were processed using the software insight 4g, by tsi. 2.3 masking procedure piv evaluation relies on the measurement of the motion of tracer particles that are seeded in the flow. in the present work, the water was seeded, but not the gas, so the piv processing was restricted to liquid regions containing particles. fernandes et al. (2018) applied algorithmic masks based on the maximum and minimum pixel intensities of the particle images of the left and right cameras for each cross-sectional position, in relation to the bubble nose tip. the same local algorithmic mask was used for all piv evaluations at a particular cross-sectional location. this was possible because the gas-bubbles were relatively wellbehaved, due to the laminar characteristic of the liquid flow composed of a high-viscosity water-glycerin solution. in the present work, however, water was used as the liquid phase, leading to a turbulent intermittent flow with stochastic gas-bubble shapes (de oliveira et al., 2015). the region occupied by the gas phase, in the same pipe cross section relative to the detected nose position tip, varied significantly when comparing different instantaneous particle images, although the gas bubbles were always in the upper part of the pipe. this effect was more pronounced for images in the close vicinity of the bubble nose. the regions containing particles were automatically determined for each instantaneous image pair in each cross-sectional location, employing instantaneous algorithmic masks. the algorithmic masks were created based on the information of the presence, or lack, of particles within the interrogation windows as follows. first, instantaneous dewarped particle images from the first and second laser pulses, after background subtraction, were combined to artificially increase the particle concentration. as a second step, a sliding standard deviation filter with a window of 11x11 pixels was applied to detect particles. this procedure is robust against possible shot-to-shot fluctuations of the laser. next, instantaneous binary masks were created by thresholding those filtered images from each camera. threshold values for the left and right camera images were selected based on the average intensity level outside the pipe (dark region). the binarized images were composed of regions of ”ones”, related to mediumand high-intensity particles, and others of ”zeros”, mostly related to noise and low-intensity particles. as a fourth step, the binary mask was divided into 32x32 pixel regions with centers coinciding with those that would form the final vector grid. if a particular region contained any bright particle, the entire 32x32 pixel region was set to ”one”, otherwise the region was set to zero. following, dilate and erode binary operations (gonzales and woods, 2008) were used to fill up possible holes and to connect regions. this was necessary due to the conservative higher threshold levels employed that did not detect the low-intensity particles. the instantaneous masks for the left and right cameras correctly represented the seeded regions (non-obstructed liquid phase) what was verified by visual inspection of several image samples. finally, the final instantaneous mask at each cross-section was obtained from the minimum between the left and right masks (”and” logical operator). it is important to mention that the mask regions with ones were always equal or smaller than the liquid regions due to possible viewing obstruction caused by the bubble nose passage, as explained in fernandes et al. (2018). figure 3 shows a typical instantaneous masking procedure, combining the image obtained from the left an the right cameras, at an specific position relative to the gas bubble nose tip. additionally, instantaneous binary masks representing the gas phase at each cross-section were estimated based on the maximum between the left and right masks (”or” logical operator), following fernandes et al. (2018). figure 3: masking procedure for a specific instantaneous image in the liquid film. the merged image represents the instantaneous algorithmic mask for piv processing at this particular cross-section, and it was generated by the minimum between the binary masks of the left and right camera images. the ensemble-averaged velocity fields were computed only from valid instantaneous vectors. that means, vectors within the instantaneous masks and within 3 local standard deviation from their neighbours (westerweel and scarano, 2005). the final ensembled mask at each cross section, representing the nonobstructed liquid phase, was composed by the grid positions where at least 68.3% of the total amount of vectors available for the determination of the the ensemble-average (1500 samples) were not masked out by the instantaneous masks. this represents a conservative approach corresponding to a coverage of one standard deviation for a normal distribution. 3 results 3.1 velocity profiles in the liquid plug region figure 4 presents the measured streamwise velocity profiles in the liquid plug region for the three cases investigated. the profiles were extracted from the measured ensemble averaged velocity fields at a vertical line along the pipe diameter. also shown in the figure is a schematic view of the slug flow unit cell, indicating the positions of the vertical profiles in relation to the gas-bubble nose. as can be seen, the faster-moving gas-bubble deforms the velocity profiles at positions close to the bubble-nose (figures 4a and b), creating two local maximum points, located at approximately y/r = -0.1 and y/r = 0.5 and a local minimum point, located at y/r =0.1. the maximum velocity is located just downstream of the gas-bubble nose tip, approximately at y/r = 0.5. this effect is more evident at higher superficial velocities (case 3), where a higher translational velocity of the gas bubble prevails (hurlburt and hanratty, 2002). at farther positions inside the liquid plug (figures 4c and d), the velocity profile resembles the format of a fully-developed turbulent velocity profile in a straight pipe. the vertical profiles are, however, not entirely symmetric, what can be associated to the presence of small dispersed bubbles at the upper part of the pipe. the similarity between the streamwise velocity profiles at 2.35 d and 6.2 d inside the liquid plug raises a question whether there is a distance downstream to the gas-bubble nose where the velocity fields no longer change. to answer this question, the root mean square deviation (rmsd) between the velocity field located at 6.2 d downstream of the gas-bubble nose tip (figure 4d) and velocity fields at closer locations to the gas-bubble nose tip was calculated and presented in figure 5. as can be observed, after a distance of figure 4: streamwise velocity profiles at different locations inside the liquid plug for all 3 measured cases approximately 0.8 d from the gas-bubble nose, there are only minor variations in the streamwise velocity fields. the most significant changes happen less than 1 diameter downstream of the gas bubble nose. figure 5: normalized root mean square deviation between averaged streamwise velocity fields at different locations inside the liquid plug and the streamwise velocity field at 6.2 d from the gas-bubble nose tip. during the experiment, the superficial velocities of gas and liquid for each case remained constant. however, small oscillations in pressure can cause variations in the inlet flow rate of gas, given the fact that it was supplied by centrifugal compressors. a verification test can be made by calculating the mixture velocity. for incompressible flow, continuity dictates that the total flow rate and, therefore, the mixture velocity remains constant at any cross-section in the unit cell (woods and hanratty, 1999). table 2 present the mixture velocity calculated by integrating the measured streamwise velocity fields in the liquid plug, for each case. the maximum deviation observed was of 3.6 %, for case 3. 3.2 velocity fields in the bubble-nose region in this section, the behaviour of velocity fields of the averaged streamwise velocity in the bubble-nose region are evaluated. the averaged mask described above was used to separate gas regions, where seeding particles table 2: comparison of expected and measured mixture velocity for each case. case expected mixture velocity (m/s) measured mixture velocity (m/s) error (%) 1 0.8 0.81 1.65% 2 0.9 0.90 0.22% 3 1.0 0.96 3.6% were not presented, from the liquid regions, where piv evaluation was performed. figure 6 present vertical liquid velocity profiles obtained from case 2. it clearly shows the influence of the faster-moving gas-bubble, deforming the velocity profile at the upper part of the pipe, for positions downstream of the bubble nose tip, as already mentioned. an interesting feature presented here is the change in the velocity profile at positions around y/r = 0.4 from the position just upstream of the gas-bubble nose (0.08 d) to positions deeper inside the liquid film (0.39 d and 0.62 d). it seems that the gas-liquid interface moves at a lower velocity than that of the gas-bubble, causing a reduction on the streamwise velocity profile due to the non-slip condition on the gas-liquid interface. this issue will be better addressed in the next section. figure 6: averaged streamwise velocity profiles at different locations in the near region of the bubble nose for case 2 (jg = 0.5 m/s and jl = 0.4 m/s). figure 7 presents a schematic view of the slug unit cell, showing the averaged velocity vector fields in the vicinity of the gas bubble nose. colormaps represent the streamwise component, while in-plane velocity is represented by vector arrows. as one can see, the faster-moving gas bubble not only pushes forward the downstream liquid (revisit figure 6), but it also pushes the liquid downwards (figure 7a and b). this is the shedding mechanism, in which, for a frame of reference moving with the unit cell, liquid from the liquid plug is picked up by the film close to the gas-bubble nose tip, compensating the liquid lost by the film near the gas bubble tail, to the upstream liquid plug. for the first measurement planes just upstream of the gas-bubble nose (figure 7c and d), a circular motion around the gas-bubble is formed, where liquid is pushed away from regions that will be occupied by the gas bubble. further inside the liquid film, the downwards movement dominates the in-plane motion, what result in the formation of two counter-rotating vortices, as seen in figure 7d. figure 7: averaged velocity fields at different locations in the region near the bubble nose for case 2 (jg = 0.5 m/s and jl = 0.4 m/s). colormaps represent the averaged streamwise velocity component, while in-plane components are represented by vector arrows. 3.3 liquid film region figure 8 presents vertical profiles of the streamwise velocity at different positions inside the liquid film region. as expected, the mean velocity increases from case 1 to case 3, given the increase in the mixture velocity. another interesting effect is the decrease in the mean velocity when moving farther into the liquid film, far from the bubble nose. the same behaviour was also observed for laminar intermittent flows by fernandes et al. (2018). the velocity profiles were computed from the averaged streamwise velocity fields using the mean liquid mask from the non-obstructed liquid regions described in section 2.3. an analysis of figure 8 indicates that the upper part of the liquid film is moving at a smaller velocity than the liquid mean velocity (i.e., there is a concavity in the liquid velocity profile). this is an interesting observation, given the known fact that gas-liquid bubble moves at a higher velocity than the liquid film. there are two possible explanations for this phenomenon. it could be a measurement bias effect caused by the averaging procedure due to variations on the stochastic position of the gas-liquid interface, or it could be caused by the fact that the interface is translating at a lower velocity than the gas-bubble. the no-slip condition at the gas-liquid interface would, therefore, decrease the velocity at the upper part of the liquid film. to help answering this question, a different averaging procedure of the velocity profiles was implemented. this one was not based on the averaged velocity fields and the mean mask, but on the average of instantaneous velocity profiles obtained from the 1500 masked velocity fields. to account for variations on figure 8: averaged streamwise velocity profiles inside the liquid film at different positions upstream of the bubble nose tip. the instantaneous positions of the gas-liquid interface and liquid flow rates, the velocity profiles were non dimensionalized by the film height (distance between the gas-liquid interface and the pipe bottom wall) and by the maximum streamwise velocity. figure 9 presents the non-dimensional velocity profiles for different cross-sectional positions in the liquid film. not only the same reduction of the liquid velocity close to the interface is observed, but all velocity profiles appear to be represented by a single self-similar curve. the result seems to validate the hypothesis that the gas-liquid interface translates at a smaller velocity than the gas bubble. further investigation of the gas flow is needed to confirm this finding. figure 9: self-similar vertical profiles of the averaged streamwise velocity, made non-dimensional by the interface height and the maximum streamwise velocity. 4 conclusions we analyzed, in the present work, averaged velocity fields and profiles at various cross-sectional positions for intermittent gas-liquid flows in a horizontal pipe using the gas-bubble nose tip as reference. to this end, a high-frequency stereoscopic-piv system, together with the laser-induced fluorescence technique and photogate triggering were used. for the liquid plug, it is clear that significant variations on the streamwise velocity profile occur up to 0.8 d downstream of the gas-bubble nose, while at farther positions, the profile displays a shape similar to that of a fully-developed turbulent pipe flow. a slightly asymmetry on the velocity profile at the upper part of the pipe occurs due to the presence of dispersed bubbles. the influence of the faster-moving gas-bubble on the velocity fields in the vicinity of the bubble nose tip was evaluated using mean algorithmic masks. the bubble nose pushes the downstream liquid forwards and downwards, forming a pair of counter-rotating streamwise vortices, in the liquid film. for the liquid film, the instantaneous masking procedure used allowed the determination of nondimensional profiles, that seem to converge into a single self-similar curve, independent of the axial distance from the gas-bubble nose tip. the velocity profiles obtained seem to indicate that the reduction observed in the velocity close to the gas-liquid interface is a physical phenomenon associated to the motion of the interface at a lower velocity than the gas bubble. acknowledgements we would like to acknowledge the continuous financial support of petrobras, capes an agency for the brazilian ministry of education and cnpq, the ministry of science and technology research council. references al-safran e, sarica c, zhang hq, and brill j (2005) investigation of slug flow characteristics in the valley of a hilly-terrain pipeline. international journal of multiphase flow 31:337–357 baker o (1953) design of pipelines for the simultaneous flow of oil and gas. in fall meeting of the petroleum branch of aime. society of petroleum engineers brennen ce (2005) fundamentals of multiphase flow de oliveira wr, de paula ib, martins fjwa, farias psc, and azevedo lfa (2015) bubble characterization in horizontal air–water intermittent flow. international journal of multiphase flow 69:18–30 fabre j, peresson ll, corteville j, odello r, and bourgeois t (1990) severe slugging in pipeline/riser systems. spe production engineering 5:299–305 fernandes ls, martins fjwa, and azevedo lfa (2018) a technique for measuring ensemble-averaged, three-component liquid velocity fields in two-phase, gas–liquid, intermittent pipe flows. experiments in fluids 59:1–18 gonzales rc and woods re (2008) digital image processing, 3rd ed hua g, falcone g, teodoriu c, and morrison g (2012) comparison of multiphase pumping technologies for subsea and downhole applications. oil and gas facilities 1:36–46 hurlburt e and hanratty t (2002) prediction of the transition from stratified to slug and plug flow for long pipes. international journal of multiphase flow 28:707–729 lindken r and merzkirch w (2002) a novel piv technique for measurements in multiphase flows and its application to two-phase bubbly flows. experiments in fluids 33:814–825 taitel y and dukler ae (1976) a model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow. aiche journal 22:47–55 westerweel j and scarano f (2005) universal outlier detection for piv data. experiments in fluids 39:1096– 1100 wieneke b (2005) stereo-piv using self-calibration on particle images. experiments in fluids 39:267–280 woods bd and hanratty tj (1999) influence of froude number on physical processes determining frequency of slugging in horizontal gas–liquid flows. international journal of multiphase flow 25:1195–1223 introduction experiment and data evaluation camera calibration experimental procedure masking procedure results velocity profiles in the liquid plug region velocity fields in the bubble-nose region liquid film conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 effect of the boundary conditions, temporal, and spatial resolution on the pressure from piv for an oscillating flow n. sakib1∗, a. mychkovsky2, j. wiswall2, r. samaroo2, b. l. smith1 1 utah state university, department of mechanical and aerospace engineering, logan-ut, usa 2 naval nuclear laboratory, west mifflin-pa and schenectady-ny, usa ∗ nazmus.sakib@usu.edu abstract the pressure field of an impinging synthetic jet has been computed from time-resolved, three-dimensional, three-component (3d-3c) particle image velocimetry (piv) velocity field data using a poisson equationbased pressure solver. the pressure solver used in this work can take advantage of the temporal derivative of the pressure to enhance the temporal coherence of the calculated pressure field for time-resolved velocity data. the reconstructed pressure field shows sensitivity to the implementation of the boundary conditions, as well as to the spatial and temporal resolution of the piv data. the pressure from a 3d poisson solver that does not consider the temporal derivative of the pressure shows high random error. invoking the temporal derivative of the pressure eliminates this high-frequency noise, however, the calculated pressure exhibits an unphysical temporal drift. this temporal drift is affected by both the temporal resolution of the piv data and the spatial resolution of the piv vector field, which was systematically evaluated by downsampling the instantaneous data and increasing the interrogation window size. it was observed that decreasing the temporal resolution increased the drift, while decreasing the spatial resolution decreased the drift. 1 introduction the pressure field in a flowing fluid is an important dynamic property as this quantity can be used to analyze surface loads and other hydrodynamic conditions. traditionally, pressure measurements have been limited to surface pressure measurements, where conventional taps or microphone transducers are used to measure the static or fluctuating values, respectively (van oudheusden, 2013). acquiring pressure measurements within the flow field is considerably more difficult than collecting surface pressure measurements by traditional means. physical pressure probes are intrusive, must be oriented properly with respect to the unknown flow direction, and can only provide local point measurements. the use of physical sensors limits the ability to capture the dynamic aspects of the flow as pressure field information is limited to either coarse, instantaneous measurements provided by a probe array or ensemble-mean statistics provided by a traversing probe (tsuji et al., 2007). piv is an established, non-intrusive flow field measurement technique. with advancements in imaging technology and data processing methods, the accuracy and resolution of piv has evolved to the level where calculation of derived flow quantities, such as vorticity or divergence, are possible. volumetric piv techniques, such as tomographic (tomo-) piv (elsinga et al., 2006) and shake-the-box (stb) (schanz et al., 2016), have been developed to enable time-resolved three-dimensional, three-component (3d-3c) measurements to fully characterize the fluid velocity field. reconstruction of a pressure field from piv data was first investigated by jensen et al. (2001). the method has since been applied to obtain measurements of pressure fluctuations in a turbulent boundary layer (ghaemi et al., 2012), pressure on an airfoil (violato et al., 2011), and pressure loads on wind turbine blades (villegas and diez, 2014; lignarolo et al., 2014). piv-based pressure reconstruction has also been used for biological fluid dynamics problems, including embryonic heart (bark et al., 2017) and glottal channel studies (oren et al., 2015). though piv-based pressure reconstruction is now considered to be a quantitative measurement technique, assessments of the uncertainty and its dependence on various experimental and numerical parameters, namely the spatial and temporal resolution and the boundary conditions, have been limited. it has been shown theoretically that for a 2d pressure poisson solver, the propagation of gaussian errors from the velocity field to the pressure field is affected by the shape and area to volume ratio of the flow domain, boundary conditions, and the velocity error level in the field and in the boundary (pan et al., 2016). the work by pan et al. (2018) also shows that for poisson equation based pressure solvers, the numerical truncation error is dominant in coarse spatial resolution and the experimental error is dominant in fine spatial resolution. temporal resolution must also be considered for poisson equation based pressure solvers that use lagrangian tracking to estimate the material acceleration of the fluid. a recent poisson equation based pressure solver (jeon et al., 2017) uses the convection velocity of the flow structures to calculate the temporal derivative of pressure and then compute the pressure fields from time resolved piv data. the pressure solver uses boundary conditions of pressure at specific boundary points or as an average pressure in a specified volume in the measurement domain. except for the locations of the specific pressure, neumann type boundary conditions are used for all other boundary points. the boundary conditions can be provided either at the beginning of the time series or as constant across every time step. in this work, time-resolved tomo-piv measurements of an impinging synthetic jet in a water filled tank are used to calculate the pressure field using a poisson equation based pressure solver. the periodic nature of the synthetic jet velocity field makes it an ideal case for studying piv-based pressure reconstruction results as one can expect the pressure at any location to repeat each cycle. the effect of different implementations of the boundary conditions is evaluated by directly comparing the pressure calculated from piv at a particular surface location with that obtained from a pressure sensor at the same location. in addition, the effect of temporal and spatial resolution (relative to the major flow scale) on the calculated pressure field is examined by varying the frequency and the displacement amplitude of the synthetic jet. 2 pressure from piv a common method for calculating a pressure field from piv data is summarized in (van oudheusden, 2013). this technique uses measured velocity fields to calculate the pressure gradient within the flow. the pressure field is then calculated from the pressure gradient with the appropriate boundary conditions. section 2.1 explains the general approach for computing a fluid pressure field from a measured velocity field while section 2.2 describes the pressure solver algorithms used in this study. 2.1 fluid pressure from a measured velocity field the relationship between velocity and pressure in a flow field is described by the navier-stokes momentum equation, ∇p =−ρ du dt +µ∇ 2u, (1) where p, u, t, ρ, and µ denote pressure, velocity, time, density, and dynamic viscosity of the fluid, respectively. the material acceleration, du dt can be expressed in an eulerian frame of reference as du dt = ∂u ∂t +(u ·∇)u. (2) the pressure field can be obtained by spatial integration of the pressure gradient (equation 1) (liu and katz, 2004). however there are numerical challenges associated with this approach. this study focuses on the more common poisson equation based pressure solver. the pressure poisson equation is derived by applying the divergence operator to equation 1 and substituting equation 2 for the material acceleration to yield ∇ 2 p =−∇ · ((u ·∇)u) . (3) both the viscous and temporal terms are eliminated with continuity for an incompressible flow (∇ ·u = 0), and the pressure field can be calculated from the velocity field using pressure boundary conditions. in practice, it can be challenging to determine the pressure boundary conditions to calculate the pressure field using equation 3. pressure measurements can be used to determine dirichlet (pressure as a function of time at a spatial location) boundary conditions; however, in general, instantaneous measurements synchronized with the instantaneous velocity fields must be obtained at multiple spatial locations, and in many cases it is not feasible to determine the pressure boundary conditions using only pressure measurements. to address the problem of determining pressure boundary conditions, additional information can be determined from the measured velocity fields. specifically, if the material derivative can be determined from several instantaneous velocity fields, a neumann boundary condition (pressure gradient as a function of time at a spatial location) can be calculated using the navier-stokes equation, and the pressure field can be calculated using a combination of dirichlet and neumann boundary conditions. when using the velocity field data to calculate pressure boundary conditions, both the spatial derivative terms of the velocities within the domain using equation 3 and the pressure gradients at the boundary conditions using equation 1 are calculated. because the material acceleration is calculated, the pressure solver may first calculate the pressure gradient throughout the entire measurement domain from the navierstokes equation using the material acceleration term, and then use the following identity to spatially integrate the pressure gradient ∇ 2 p = ∇ · (∇p) . (4) 2.2 pressure solver algorithms used in this study the pressure solver in lavision davis 10.2 was used in this work. this software employs iterative pseudolagrangian tracking to calculate the material acceleration (liu and katz, 2006). the position of the same group of tracer particles located at the grid points are tracked over multiple vector fields to compute the velocity and material acceleration using a polynomial trajectory model. the computation cost of material acceleration calculation increases with the number of velocity fields considered. in this study 5 velocity fields were used to estimate the velocity and material acceleration. the calculated material acceleration is then optimized in a least squares manner. there are several other methods to calculate the material acceleration from piv velocity fields such as the eulerian approach (baur and kongeter, 1999), taylor’s hypothesis approach (de kat and ganapathisubramani, 2013; laskari et al., 2016) and the instantaneous vortex-in-cell (vic) method (schneiders et al., 2016). the iterative pseudo-lagrangian approach and the eulerian approach are purely numeric and therefore require time-resolved data with at least two subsequent velocity fields as an input to calculate the material acceleration while the taylor hypothesis approach and the vic method incorporate physical flow models so that a single, instantaneous velocity field is sufficient. once the material acceleration is calculated the pressure gradient is obtained by adding the viscous terms from equation 1, and is integrated with a pressure poisson solver to obtain the pressure field. the lavision solver used in this study uses a modified operator (equation 5) that includes the time derivative of pressure to calculate the pressure fields from time-resolved piv velocity fields. ∇ ′2 p = ∂2 p ∂x2 + ∂2 p ∂y2 + ∂2 p ∂z2 +ξ ∂2 p ∂t2 |c, (5) where ∇′ 2 is a modified operator and ξ is the weighting factor between the temporal and spatial derivative of the pressure. this approach eliminates the requirement of at least one dirichlet boundary condition per each time-step except the very first time-step. the time derivative of pressure is estimated by making the assumption that the pressure does not change on the convective frame which provides the following expression for the temporal derivative of the pressure (jeon et al., 2017) ∂p ∂t |c≈ 1 ∆t ∫ x x+uc∆t ∇pdx, (6) where uc is the estimated convection velocity of the vortical structures. additionally, the solver allows the temporal derivative term in equation (5) to be omitted by setting ξ to a small value. in this case, the convection velocity of the flow structure is not calculated and is equivalent to computing the pressure field separately for each of the instantaneous velocity fields. taking the time derivative of pressure to be zero is similar to computing the pressure field separately for each of the velocity fields. the weighting factor ξ allows studying the effect of the enforcement of strong or weak temporal coherence on the calculated pressure. considering the modified operator, equation 4 takes the following form ∇ ′2 p = fexp, (7) where the fexp term is calculated from the experimental velocity field. 3 experiment the experimental facility used in this work is described in section 3.1 and the experimental parameter space is outlined in section 3.2. 3.1 experimental facility and measurement figure 1 shows a schematic diagram of the experimental facility, which consists of a synthetic jet impinging on a circular plate contained in a hexagonal water-filled tank. the hexagonal sides of the aquarium act as water prisms to improve the camera viewing angles. an electromagnetic shaker oscillates a piston inside of a cylinder and pushes water through an orifice in the bottom surface of the tank, producing a synthetic jet, which generates vortex rings that travel upwards through the stagnant water in the tank towards the impingement surface. the impingement plate is fitted with three pressure sensors to provide capability for both dirichlet boundary conditions and validation measurements for the pressure calculated from piv as shown in figure 1. in the initial experimental arrangement, the jet was positioned near the right edge of the measurement volume. however, this setup allows the vortices to cross the boundary of the measurement volume as it propagates upwards which subsequently intensifies the temporal drift that is discussed below in section 4.1. to avoid the high temporal drift of the calculated pressure, the setup was modified to place the jet near the center of the measurement volume. figure 1: schematic diagram of the experimental facility. the thickness of the measurement volume is 20 mm. s1, s2 and s3 are the locations of the pressure sensors. the s1 pressure sensor is at the impingement point. frame-straddled, time-resolved images of the flow field were captured with four high-speed cmos (complementary metal-oxide-semiconductor) cameras. the flow was seeded with neutrally buoyant phosphorescent micro plastic particles of 50 µm diameter. a measurement volume of 60mm× 55mm× 22mm was illuminated by a dual-cavity nd:ylf (neodymium-doped yttrium lithium fluoride) laser. the raw images from the four cameras were processed by a multi-pass, 3d cross-correlation algorithm with a final interrogation volume of 32× 32× 32 voxels. a 75% interrogation volume overlap resulted in a vector spacing of 0.41 mm. the temporal resolution of the piv data is 1 ms. the velocity field obtained with tomographic piv is well resolved to capture the flow features of the synthetic jet propagation and impingement. (a) (b) figure 2: the velocity field obtained by tomographic piv. the synthetic jet has a displacement amplitude of 40 mm. (a) slice of the vector field at the mid xy-plane. the background colors represent the out of plane vorticity with red and blue denoting the counter clockwise and the clockwise motion respectively. (b) iso surfaces of the streamwise velocity in 3d. 3.2 experimental parameter space the test facility was operated to produce three synthetic jets with similar velocities and therefore similar pressure, but unique frequencies and displacement amplitudes, l0 (the distance traveled by a fluid particle during the forward stroke of the cycle). this enabled the effective temporal resolution of the piv measurements relative to the flow scale to be varied while maintaining constant data acquisition parameters and a similar pressure at the impingement location. table 1 summarizes the specifications of the jets. table 1: parameter space of the experiment umax (m/s) frequency, f (1/s) displacement dynamic pressure orifice diameter, amplitude change (pa) l0 (mm) d0 (mm) 2 2.5 80 750 4 2 5 40 750 4 2 10 20 750 4 4 results and discussion 4.1 effect of the boundary condition implementation to evaluate boundary condition options for each jet, the pressure field was computed by providing the pressure from the s2 sensor at the initial time step only and also by providing the time-averaged pressure from the s2 sensor at every time step, which is reasonably steady (table 2). the former results in pure neumann type boundary condition for every time step subsequent to the initial time step and the latter results in mixed boundary conditions for all the time steps. for both conditions, the pressure is calculated with convection velocity estimation turned on and off. this results in four experimental cases which are summarized in table 3. table 2: mean and standard deviation of s2 sensor pressure data for different jets jet displacement mean pressure (pa) standard deviation of pressure (pa) amplitude (mm) 80 0 93 40 0 95 20 0 84 table 3: experimental cases case s2 boundary condition convection estimation boundary condition type line color 1 constant off mixed red 2 constant on mixed green 3 initial off neumann orange 4 initial on neumann black the pressure data from the s1 sensor and pressure calculated from piv at the impingement location for each jet using these different boundary conditions are plotted in figure 3. it can be observed that when the convection velocity estimation is turned on, both case 2 and case 4 show a temporal drift. the pressure calculated without the convection velocity estimate (case 1 and case 3) does not show any temporal drift, however the computed pressure at the impingement location exhibits more random error. also the constant s2 boundary condition case (mixed type boundary condition) with convection velocity estimate turned on shows a drift similar to the initial s2 boundary condition (pure neumann condition) case with convection velocity estimate turned on. furthermore, the temporal drift increase with decreasing displacement amplitude of the jet. (a) (b) (c) figure 3: pressure from piv for a synthetic jet for three different displacement amplitudes and frequencies but similar dynamic pressure change. a) l0 = 80 mm, f = 2.5 hz, b) l0 = 40 mm, f = 5 hz, c) l0 = 20 mm, f = 10 hz. the impingement pressure is 750 pa for all three cases. the numeric value of ξ for convection velocity estimate on cases and convection velocity estimate off cases are 1 and 0.0001 respectively. 4.2 pressure from piv and temporal resolution figure 3 also shows that when the convection velocity is used, the temporal drift increases with increasing displacement amplitude of the synthetic jet. since these data were obtained at the same acquisition rate, this trend indicates that the calculated pressure field is related to the effective temporal resolution of the piv data. to systematically investigate this trend, the pressure field was recalculated in a way so that all three jets have the same number of velocity fields per cycle. this reduces the temporal resolution of the l0 = 80 and l0 = 40 jets by a fourth and a half, respectively, yielding an equivalent relative temporal resolution for all three jets. figure 4 shows the pressure at the impingement location from the s1 sensor and from piv for all three jets. the reduced temporal resolution in the l0 = 80 and l0 = 40 jets results in a higher temporal drift. however, even with the same effective temporal resolution, the temporal drift still increases with decreasing displacement amplitude. 4.3 effect of spatial resolution in order to investigate the effect of spatial resolution on the calculated pressure field, the piv images were reprocessed with a larger final pass interrogation window size of 40× 40× 40 voxels which results in a coarser spatial resolution. figure 5 shows the pressure from piv for reduced spatial resolution for all three jets. it can be observed that the reduced spatial resolution lowers the temporal drift. (a) (b) (c) figure 4: effect of temporal resolution on the pressure calculated from piv with 98 vector fields for each case. a) l0 = 80 mm, f = 2.5 hz, b) l0 = 40 mm, f = 5, c) l0 = 20 mm, f = 10 hz. (a) (b) (c) figure 5: effect of reduced spatial resolution on the pressure from piv. a) l0 = 80 mm, f = 2.5 hz, b) l0 = 40 mm, f = 5, c) l0 = 20 mm, f = 10 hz 5 conclusion and future work in this study, the pressure field for an impinging synthetic jet is reconstructed from piv velocity fields using a poisson equation-based pressure solver. the solver has the option to estimate the temporal derivative of the pressure for time resolved piv data via estimation of the convection velocity of flow structures. the pressure solver can also reconstruct the pressure field from individual velocity fields without considering the time derivative of the pressure which is similar to traditional 3d poisson solvers. the reconstructed pressure with the estimation of the time derivative of the pressure demonstrates a temporal drift. while the pressure without the temporal derivative estimation does not show any drift, it exhibits much larger random errors. the reconstructed pressure also shows sensitivity to the temporal resolution of the piv data and the spatial resolution of the piv processing. this current study shows that the temporal drift in the reconstructed pressure is lower for a coarse spatial resolution. future work will include the extension of the parameter space to identify any optimal spatial resolution for the pressure reconstruction as described in pan et al. (2018). pressure field reconstruction from the velocity field obtained by cutting edge particle tracking methods, such as shake the box, (stb) (schanz et al., 2016) and the study of the relevant parameters on the pressure field will be included in future studies. furthermore, as the uncertainty quantification of the stb velocity field becomes available, the propagation of velocity field uncertainty into the pressure field and quantify the uncertainty in the reconstructed pressure field will become possible. acknowledgements notice: this report was prepared as an account of work sponsored by an agency of the united states government. neither the united states government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third partys use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the united states government or any agency thereof or its contractors or subcontractors. the views and opinions of authors expressed herein do not necessarily state or reflect those of the united states government or any agency thereof. the authors would like to thank dr. young jin jeon of lavision gmbh for his assistance in understanding the equations that are solved within davis. references bark dl, johnson b, garrity d, and dasi lp (2017) valveless pumping mechanics of the embryonic heart during cardiac looping: pressure and flow through micro-piv. journal of biomechanics 50:50–55 baur t and kongeter j (1999) piv with high temporal resolution for the determination of local pressure reductions from coherent turbulence phenomena. in 3rd international workshop on particle image velocimetry. santa barbara, ca, usa de kat r and ganapathisubramani b (2013) pressure from particle image velocimetry for convective flows: a taylor’s hypothesis approach. measurement science and technology 24 elsinga ge, scarano f, wieneke b, and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 ghaemi s, ragni d, and scarano f (2012) piv-based pressure fluctuations in the turbulent boundary layer. experiments in fluids 53:1823–1840 jensen a, sveen jk, grue j, richon jb, and gray c (2001) accelerations in water waves by extended particle image velocimetry. experiments in fluids 30:500–510 jeon yj, michaelis d, and wieneke b (2017) estimation of flow structure transport in tr-piv data and its application to pressure field evaluation. in 2nd workshop on data assimilation and cfd processing for piv and lagrangian particle tracking. delft, the netherlands laskari a, de kat r, and ganapathisubramani b (2016) full-field pressure from snapshot and time-resolved volumetric piv. experiments in fluids 57:1–14 lignarolo le, ragni d, krishnaswami c, chen q, simão ferreira cj, and van bussel gj (2014) experimental analysis of the wake of a horizontal-axis wind-turbine model. renewable energy 70:31–46 liu x and katz j (2004) measurements of pressure distribution in a cavity flow by integrating the material acceleration. proceedings of the asme heat transfer/fluids engineering summer conference 2004, ht/fed 2004 3:621–631 liu x and katz j (2006) instantaneous pressure and material acceleration measurements using a fourexposure piv system. experiments in fluids 41:227–240 oren l, gutmark e, and khosla s (2015) intraglottal velocity and pressure measurements in a hemilarynx model. the journal of the acoustical society of america 137:935–943 pan z, whitehead j, thomson s, and truscott t (2016) error propagation dynamics of piv-based pressure field calculations: how well does the pressure poisson solver perform inherently?. measurement science and technology 27 pan z, whitehead jp, richards g, truscott tt, and smith bl (2018) error propagation dynamics of pivbased pressure field calculation (3): what is the minimum resolvable pressure in a reconstructed field?. arxiv pages 1–23 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 schneiders jf, pröbsting s, dwight rp, van oudheusden bw, and scarano f (2016) pressure estimation from single-snapshot tomographic piv in a turbulent boundary layer. experiments in fluids 57:1–14 tsuji y, fransson jhm, alfredsson ph, and johansson av (2007) pressure statistics and their scaling in high-reynolds-number turbulent boundary layers. journal of fluid mechanics 585:1–40 van oudheusden bw (2013) piv-based pressure measurement. measurement science and technology 24 villegas a and diez fj (2014) on the quasi-instantaneous aerodynamic load and pressure field measurements on turbines by non-intrusive piv. renewable energy 63:181–193 violato d, moore p, and scarano f (2011) lagrangian and eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic piv. experiments in fluids 50:1057–1070 introduction pressure from piv fluid pressure from a measured velocity field pressure solver algorithms used in this study experiment experimental facility and measurement experimental parameter space results and discussion effect of the boundary condition implementation pressure from piv and temporal resolution effect of spatial resolution conclusion and future work 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 an experimental investigation on the wind-driven runback motion of water droplets over solid surfaces with different wettabilities liqun ma, zichen zhang, hui hu* department of aerospace engineering, iowa state university, ames, iowa 50014, usa *corresponding authors: huhui@iastate.edu extend abstract aircraft icing is widely recognized as one of the most serious weather hazards to flight safety. specially designed hydro-/ice-phobic coatings are currently undergoing development for aircraft icing mitigation. it was found that hydro-/icephobic coatings would delay the ice accretion iover airframe surfaces so that the impacted supercooled water droplets could be blown away by the airflow from the airframe surface before being frozen into ice. it is of fundamental importance to understand the wind-driven runback behavior of water droplets over surfaces treated with different coatings, since the corresponding knowledge would be very helpful and essential to develop more efficient anti-/de-icing systems for aircraft icing protection. with the rapid development of surface engineering, a series of specially designed surface coatings succeed in icing mitigation using airflow to remove the remained water. while various hydro-/ice-phobic coatings/surfaces have been developed in recent years, the “state-of-the-art” icephobic coatings/surfaces can be generally divided into three categories, i.e., 1). lotus-leaf-inspired superhydrophobic surfaces (shs) with micro-/nano-scale surface textures to achieve very high contact angles (typically > 150°); 2). pitcherplant-inspired slippery liquid infused porous surfaces (slips) with a layer of liquid lubricant (which is immiscible with water) being sandwiched between ice and solid substrate materials; and 3). icephobic elastic materials/surfaces with deformable structures/surfaces. shs has a water droplet contact angle (ca) larger than 150° and a sliding angle (sa) less than 10° . shs always has a hierarchical structure which is similar to the lotus leaf, and water droplets on shs appear as water beads which can easily roll off the surface by wind or gravity before frozen. another strategy to reduce ice adhesion strength to a solid surface is to use a layer of liquid lubricant, which is immiscible with water, between ice and the solid surface. the use of such lubricated surfaces was investigated as early as 1960s, and has gained increasing attentions again recently with the introduction of a concept called slippery liquid-infused porous surfaces (slips). slips concept is inspired by the nepenthes pitcher plants, which have evolved highly slippery, liquidinfused micro-textured rim to capture insects. slips surfaces were not only found to be able to suppress ice/frost accretion by effectively removing condensed moisture even in high humidity conditions, but also exhibit at least an order of magnitude lower ice adhesion than most shs coatings. more recently, elastic materials/surfaces, such as polydimethylsiloxane or pdms in short, which would be structurally deformed/altered dynamically upon applying extra mechanical stress, have also been suggested for icing mitigation. elastic materials display ultra-low adhesion to ice due to their low work of adhesion and liquidlike deformability, while maintaining good mechanical durability due to their solid-like rigidity. it is found that water droplets would not only be more readily rebounding away from the surface after impingement, but also be able to roll away before frozen due to the hydrophobicity of pdms. considering the differences in wettabilities and mechanisms of water repellency, it is necessary to have a systematic understanding of how efficient the surfaces are when the aerodynamic force is applied to remove the adhered water droplets. mailto:huhui@iastate.edu in the present study, a comprehensive experimental campaign was conducted to characterize the transient runback behaviors of wind-driven water droplets over the surfaces of test plates coated with different hydro-/icephobic coatings (i.e., shs, slips and pdms). a high-resolution particle image velocimetry (piv) system was used to achieve quantitative measurements of the velocity field of the airflow around the wind-driven water droplets on the test surfaces with different wettabilities. with the detailed piv measurements of the airflow field around the runback water droplets and the droplet profiles, the aerodynamic forces and the adhesion forces acting on the water droplets were estimated. while fig. 1 shows the experimental setup used in the present study, fig. 2 to fig. 3 given some of the typical measurement results. more measurement results and comprehensive analysis and discussions will be provided in the full version of this research paper. fig. 1: experimental setup of piv measurements to characterize wind-driven runback of water droplets. fig. 2. piv measurements of wind-driven water droplets over test plates coated with different coatings. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 ghost particle reduction in 3d particle streak velocimetry c. tsalicoglou1∗, t. roesgen1 1 eth zürich, institute of fluid dynamics, zurich, switzerland ∗ ctsalico@ethz.ch abstract ghost particles are ambiguities in the process of the 3d-reconstruction of seeding particles detected in short-exposure imaging for volumetric flow velocimetry. 3d particle streak velocimetry (3d-psv) relies on long-exposure images, where the pathlines of the seeding particles are imaged as streaks. in this work, we demonstrate the inherent suitability of 3d-psv for ghost particle rejection by calculating the probability of ghost streak generation in different scenarios and comparing our results to simulations. 1 introduction volumetric velocimetry techniques for fluid flows, such as 3d particle tracking velocimetry (3d-ptv) and tomographic particle image velocimetry (tomo-piv), use the identified discrete locations of tracer particles in two or more camera views to reconstruct the tracers’ positions in 3d space, track them over time and retrieve the flow velocity. the reconstruction of the particles in 3d space can result in so-called “ghost particles”, which are reconstructed tracer particles for which it remains uncertain whether they are real or artifacts of the reconstruction process. more camera views, tracking, smoothness criteria, and intensitybased procedures are used to improve the reconstruction quality under increasingly demanding requirements for temporal and spatial resolution (e.g., schanz et al. (2016), novara et al. (2019)). in contrast to 3d-ptv, which relies on the reconstruction of points that represent “frozen” particles, 3d particle streak velocimetry (3d-psv) (e.g., rosenstiel and grigat (2010)) uses long-exposure images, where the signature of each particle is its pathline over the exposure time, allowing for the triangulation of pathline segments, or “streaks”. the streaks can be treated as linear segments when only the information about the connectivity of their endpoints is used or as curved segments when considering the shape of the connecting curve. we show here that already the use of the endpoint connectivity alone, employed in the reconstruction of linear streaks, allows for a significant reduction in ghost particle generation, without the need to consider additional time-steps or to perform particle tracking over the exposure time. 2 methods and results maas (1992) described the probability of generating ghost particles from images of randomly distributed particles as a function of the particles per pixel, volume depth, and relative position of the cameras. for n imaged particles, the expected number of ambiguous particles np in a search window f for an image of size f , was estimated as np = (n2 −n) f/f . the estimates were based on considerations in epipolar geometry, with the necessary condition for ghost particle generation being that, given one particle on an epipolar line, an ambiguity occurs as soon as there is at least one more particle on the same epipolar line. in streak images, twice the number of points must be considered, as the signature of each of the n particles is a line segment with both its endpoints in the same image, and we assume that all particles remain within the field of view during the exposure time. we consider a stereo setup where the cameras have co-planar image planes and parallel axes, as this setup results in parallel epipolar lines, which simplifies the subsequent considerations (fig. 1(a)). two scenarios are examined to calculate the probabilities of ghost streak generation: random displacements of the particles within the images and random displacements (a) 0 1000 3000 5000 7000 n, number of particles 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 n p / s , n um be r o f g ho st p ar tic le s / s tre ak s ambiguities vs. number of particles particles streaks, random displ. streaks, r= 10px streaks, r= 20px streaks, r= 40px streaks, r= 80px streaks, r= 160px (b) figure 1: (a) ghost streak generation in a two-camera setup and (b) number of reconstructed ghost particles and ghost streaks for different particle displacement scenarios, from estimates (lines) and simulations (dots) within a given maximum allowable radius, within a distance of [0,r]. for the case of random displacements, the expected number of ghost streak generations is np = 2(n2 −n)( f/f)2, while for a displacement within r we identify three mechanisms of ghost streak generation and derive the relevant probabilities. 3d reconstruction of the points and streaks is then performed using two methods: (a) the start and end points are reconstructed independently of each other, as in a time-resolved 3d-ptv setup, and (b) the endpoints are matched and reconstructed jointly. in the second case, while knowledge of the endpoint connectivity is maintained, the knowledge of the directionality of the streak is lost. therefore, each of the 2n points in one image can be matched to any of the 2n points in the second image. for these simulations, the maximum allowable tolerance for the epipolar constraint is set to 1 px, while 1 mpx images are used, and we do not constrain the reconstruction volume. the tests are performed with 100 datasets containing 1’000 to 7’000 particles each. for the streaks, matches are accepted when both endpoints of a streak in one image can be matched to both endpoints of a streak in the second image. the resulting number of ghost streaks, compared to that of ghost particles, demonstrates the advantage of reconstructing line segments (streaks) instead of points (particles) and validates our probability analysis (fig. 1(b)). 3 conclusions with long-exposure particle imaging in 3d-psv, particle pathlines are obtained, instead of frozen particle positions as in conventional 3d-ptv and tomo-piv. we show that the knowledge of the endpoint connectivity in streak imaging presents advantages in ghost particle elimination by reducing the requirements for the number of cameras, particle tracking and high-speed aqcuisition. streak reconstruction already results in lower numbers of ghost reconstructions in a two-camera setup, while the number of ghost streaks depends on the distribution of streak lengths, seeding density, epipolar constraint/reprojection error tolerance and camera configuration. references maas hg (1992) complexity analysis for the establishment of image correspondences of dense spatial target fields. international archives of photogrammetry and remote sensing 29:102–107 novara m, schanz d, geisler r, gesemann s, voss c, and schröder a (2019) multi-exposed recordings for 3d lagrangian particle tracking with multi-pulse shake-the-box. experiments in fluids 60:1–19 rosenstiel m and grigat rr (2010) segmentation and classification of streaks in a large-scale particle streak tracking system. flow measurement and instrumentation 21:1–7 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 introduction methods and results conclusions 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 1 piv investigation of cavitating flows around circular cylinders with hydrophobic coatings k. dobroselsky, a. lebedev, a. safonov, s. starinskiy, v. dulin* 1 kutateladze institute of thermophysics, novosibirsk, russia *corresponding author: vmd@itp.nsc.ru the treatment of the hydrophobic properties of solid surfaces is considered as a passive method to reduce the drag in water flows (rothstein, 2010) and to potentially affect the flow separation and vortex shedding (sooraj et al., 2020). the manufacturing of surfaces with microand nano-scale roughness allows to extend the hydrophobicity towards superhydrophobicity with the contact angle close to 180°. in such conditions the solid surface is not wetted completely and the air-water interphase partially remains on the surface texture. this results in so-called flow slip effect. therefore, a local phase transition during the flow cavitation or gas effervescence in near-wall low-pressure regions may additionally affect the slip effect for hydrophobic surfaces. the present work is focused on the comparison between cavitating and noncavitating flows around circular cylinders with lateral sectors with hydrophobic and non-hydrophobic coatings. the experiments are performed in a water tunnel, which consists of a water outgassing and cooling/heating section, honeycomb, contraction section, test section and diffuser. the water flow is driven by an electric pump, providing a bulk velocity up to 10 m/s in the transparent test section with 1 m length and 80×150 mm2 rectangular cross-section. the facility is equipped with an ultrasonic flowmeter, temperature and pressure sensors. besides, the static pressure inside the water tunnel can be varied by using a special shaft section. the measurements are performed by using high-repetition and low-repetition piv systems. the former is used for the analysis of large-scale flow dynamics in the wake region, whereas the latter one is used for high-resolution measurements in near-wall regions by using a long-distance microscope. the reynolds number based on the bulk velocity of the flow, diameter of the cylinders (d = 26 mm) and kinematic viscosity of the water is varied up to 2×105. the used cylinders were made of stainless steel and covered by fluoropolymer to alter hydrophobic properties by using a hot wire chemical vapor deposition method (see safonov et al., 2018). to cover the cylinders with an uniform coating layer with the thickness of approximately 500 nm, they were mounted on a rotating holder inside a vacuum deposition chamber with the pressure of 0.5 torr. the hexafluoropropylene oxide c3f6o served as a precursor gas for the fluoropolymer film. the precursor was activated by nichrome wires at temperature of 640 °c. during the deposition, the substrate temperature was about 30 °c. the contact angle for the water droplets on the coated surface was 124° as measured by a dsa-100 kruss device (see figure 1). afterwards the fluoropolymer coating on the cylinders was locally removed to obtain lateral sectors with non-hydrophobic properties (with the contact angle of 88°). it was done by ablating the fluoropolymer coating by using the second harmonic (532 nm) of a pulsed nd:yag laser. the laser radiation was focused on the cylinder surface with the effective spot of 0.9 mm2 (e2 criterion). the laser fluence of the translated spot was 0.3 j/cm2. the flow around four kinds of cylinders with the diameter of 26 mm were studied, viz., the stainless-steel cylinders, entirely coated by the fluoropolymer and without the coating. for the other two the fluoropolymer coating at the lateral surface of 180° and 90° sectors was removed (see figure 1). figure 1 a) the scheme of nanosecond laser removal of fluoropolymer coating from stainless steel cylinder surface. b) the image of treated cylinder. c) the measurements of contact angles. d) photo of the experimental setup (d) camera camera laser mirror mailto:vmd@itp.nsc.ru 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 2 the velocity field measurements were taken by using two independent piv systems. a low-speed piv system consisted of a pulsed dual-head nd:yag laser polis (50 mj pulses with the repetition rate of 7 hz) and a ccd camera (bobcat imperx with the images of 2048×2048 pixels). a high-repetition system consisted of a pulsed nd:yag laser photonics dm and two high-speed cameras photron nova s12 with different field of views (figure 2). the laser provided 8 mj pulses with repetition rate of 10 khz. at this acquisition rate the high-speed cameras provided 1024×1024 pixel images. these cameras were also used for the high-speed visualization of the cavitating flows. the laser beams were converted into laser sheets by using cylindrical and spherical lenses. the laser sheet thickness for the low-repetition piv system was less than 0.8 mm. the lasers and cameras were synchronized by ttl signals. the piv images were processed by using an in-house software actualflow. for the low-speed piv an adaptive cross-correlation algorithm was used with the final interrogation area size of 32×32 pixels and 50% spatial overlap rate. for the high-repetition piv measurements a multi-frame adaptive piv algorithm, similar to that by sciacchitano et al. (2012), was used. figure 3 shows the example of the time averaged velocity field and visualisation of the flow separation for the cylinder with different orientation of the 180° sector coating. the coating delays the flow separation and affects the shape of the wake. figure 2 the photographs of the test section during the piv measurements and the example of the piv images by two cameras with different fields of view figure 3 the examples of time-averaged velocity field and visualization of flow separation for a cylinder with superhydrophobic coating from the top and bottom for the reynolds number of 2×105 (without cavitation) the work was supported by russian government project 075-15-2019-1888 (supervised by prof. c. markides). references rothstein jp (2010) slip on superhydrophobic surfaces. annual review of fluid mechanics 42, 89-109 sooraj p, ramagya ms, khan mh, sharma a and agrawal a (2020) effect of superhydrophobicity on the flow past a circular cylinder in various flow regimes journal of fluid mechanics 897, a21 safonov ai, sulyaeva vs, gatapova ey, starinskiy sv, timoshenko ni and kabov oa (2018) deposition features and wettability behavior of fluoropolymer coatings from hexafluoropropylene oxide activated by nicr wire thin solid films 653, 165-172 sciacchitano a, scarano f, wieneke b (2012) multi-frame pyramid correlation for time-resolved piv. experiments in fluids 53, 1087-1105 1 0 -1 -1.5 -1 -0.5 0 0.5 1 1.5 -2.5 -2 -1.5 -1 -0.5-2.5 -2 -1.5 -1 -0.5 0.04 0 -0.04 -2.5 -2 -1.5 -1 -0.5-2.5 -2 -1.5 -1 -0.5 y/d xvymax x/d top bottom top bottom flow field around the badminton shuttlecock during flipping motion y. sakurai1, k. nakagawa2 and h. hasegawa1 1 graduate school of utsunomiya university, utsunomiya, japan 2 utsunomiya university, utsunomiya, japan abstract badminton is one of the most popular sports in the world. the shuttlecock is used in badminton game has the unique shape. the shuttlecock is truncated cone-shaped and consists of a cork, gaps and a skirt portion. the shuttlecock has aerodynamic properties which differ from the ball used in other racquet sports. as an example of unique aerodynamic property, the shuttlecock shows high deceleration. it is known that the initial velocity immediately after smashing may reach up to 137m/s (493 km/h) at maximum. the velocities of the shuttlecock are reduced from the initial velocity of 67 m/s to the terminal velocity of approximately 7 m/s for approximately 0.6 s (hubbard et al. 1997). in addition, turnover refers to the flipping experienced by a shuttlecock when undergoing heading change from nose pointing against the flight path at the moment of impact and a shuttlecock indicates the aerodynamically stable feature for the flip movement just after impact (cohen et al. 2015). the turnover stability of a series of feather and synthetic shuttlecocks was measured to compare the performance of synthetic shuttlecocks to that of feather shuttlecocks (calvin et al. 2013). the turnover stability of the shuttlecock is investigated through experiment and simulation, and the angular response of the shuttlecock in turnover was modelled and studied (calvin et al. 2015). furthermore, it was reported that the aerodynamic stability of the shuttlecock during flip movement was affected by gaps of the shuttlecock skirt in a previous study (nakagawa et al. 2017). however, the mechanism of turnover stability of the shuttlecock has not been fully understood. the purpose of this study is to investigate the unsteady flow field around the shuttlecock during flip movements. in the present, we simulated the flipping motion by wind tunnel experiments and visualized the flow field around the shuttlecock by a piv technique. figure 1 shows the schematic diagram of experimental apparatus and the experimental setup for the flow visualization system. the test section’s dimensions were 0.7 m ×0.7 m and the freestream turbulence intensity was less than 1 % within the operation range. the origin of the coordinate system is defined as the center of mass of the shuttlecock. the velocity is denoted by the components (u, v, w) in the directions (x, y, z). the test model is yonex feather shuttlecock (new oficial, no4, yonex co. ltd.), which is the official choice for the world’s leading international tournaments. the piv system in this experiment mainly consists of a high-speed camera (memrecam hx-6, nac image technology inc.) and a yaglaser (ldp-100mqg). the wind speed was set at 10 m/s corresponding to the reynolds number re based on the shuttlecock skirt diameter of 4.3 ×104. the angle of attack α = 0° indicates the state that the cork of the shuttlecock was set in the upstream direction in this experiment. figure 1: an overview of the experimental set up -50 0 50 100 150 200 0 0.1 0.2 0.3 α [d eg ] t[s] figure 2: angular response of shuttlecock in turnover process o.s. angle 0 10 velocity[m/s] (b) α = -24.4° t = 0.081 s (c) α = -32.8° t = 0.088 s (a) α = 0° t = 0.069 s x y flow figure 3: flow vectors around the shuttlecock in the turnover process the angles of attack of the shuttlecock versus elapse time during flip movements is shown in figure 2. the shuttlecock’s angle of attack is estimated by the high-speed camera. the initial angle of attack in the flipping experiments was set as α= 145°. the shuttlecock flips in the counter clockwise rotation beyond α=0° and changes to rotational direction (clockwise) at overshoot angle α = -38.5°. to eliminate any discrepancies arising from externalities, each shuttlecock was tested 5 times, and the same tendency as the experimental result was confirmed. figure 3 shows the unsteady flow fields around the shuttlecock in the turnover process. the results are phase-averaged by synchronizing the angle of attack of the shuttlecock over four measurements. at α = 0°, the flow through the shuttlecock gap is observed in the near-wake region of the shuttlecock skirt, and the flow vectors tilt to the right. at α = -24.4°, the flow through the gap is divided into two streams, one that merges into the velocity shear layer behind the right side of the shuttlecock skirt and the other that flows to the rearward of the shuttlecock, and this flow produces a counterclockwise flow field behind the shuttlecock skirt at α = -32.8° (circle in figure3(c)). the image of the flow transition after the overshoot is depicted in figure 4. the flow through the gap which generates the vortex is related to the turnover stability. reference hubbard m. and alison j. cooke., spin dynamics of the badminton shuttlecock. 6th international symposium on computer simulation in biomechanics. 1997, pp. 42–43. nakagawa k., hasegawa h., murakami m., and obayashi s., aerodynamic stability of a badminton shuttlecock. transactions of the jsme (in japanese), vol.83, no856, 2017. calvin s.h. lin., c. k. chua and j. h. yeo, turnover stability of shuttlecocks – transient angular response and impact deformation of feather and synthetic shuttlecocks. procedia engineering, 60, 2013, pp. 106– 111. cohen c., texier b.d., quere d. and clanet c., the physics of badminton, 2015, new journal of physics, 17, 063001. calvin s.h. lin., ck chua. and jh yeo., badminton shuttlecock stability: modelling and simulating the angular response of the turnover, 2015, proc. imeche part p: j sports engineering and technology, pp. 1–10. (b) α = -24.4° (c) α = -32.8° (a) α = 0° figure 4: the cartoon depicting of flow field around the shuttlecock during flip movement flow 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 the stereo-piv investigation of the unsteady flow in the draft tube of a model hydro turbine i. litvinov1,2∗, d. sharaborin1,2, s. shtork1,2, v. dulin1,2, s. alekseenko1,2, and kilian oberleithner 3 1 kutateladze institute of thermophysics, novosibirsk, russia 2 novosibirsk state university, novosibirsk, russia 3 technische universität berlin, berlin, germany ∗ litvinov@itp.nsc.ru abstract varying the generator load of a hydro turbine results in short-term changes in the rotation frequency of the runner, leading inevitably to flow instability and strong flow swirling behind the turbine. this may lead to the formation of unsteady flow regimes featured by vortex instability of the swirling flow behind the runner, known as the precessing vortex core (pvc) dörfler et al. (2012). this effect causes dangerous periodic pressure pulsations that propagate throughout the water column in the draft tube. the present study reports on stereo piv measurements of the air flow field inside a transparent draft tube of a model hydro turbine for a wide range of operation conditions. the research is focused on the time-averaged flow properties (mean velocity field and the second-order moments of velocity fluctuations), pressure pulsations and coherent flow structures in the velocity field. a detailed description of the aerodynamic test rig, used in these experiments, is presented in litvinov et al. (2018). the test section consists of a scaled-down geometric model of the francis-99 draft tube cervantes et al. (2015) with an inlet diameter d = 100 mm. the air flow inside the model is investigated. to generate the required flow distribution at the inlet to the cone, a pair of swirlers is used: a stationary swirler, acting as guide vanes, and a rotary swirler, representing an analogue of the turbine runner litvinov et al. (2018). the pair of swirlers is designed for the optimal operating conditions (the best efficiency point – bep) corresponding to a volumetric flow rate qc = 48.5 l/s and a runner rotation speed nc = 40.5 hz. the experimental setup includes a computer for controlling the airflow and rotation frequency of the rotor with an uncertainty of 1.5% and 0.5%, respectively. the flow is studied for the operating parameters of the flow rate in the range from 0.5qc to qc to replicate the off-design and the bep operation conditions of the hydro turbine. figure 1 shows the used piv equipment and a sketch of the test section. a laskin nozzle aerosol generator was used to seed the jet flow with seed oil droplets. a double-head nd:yag laser (quantel, evergreen) illuminated the tracer particles. the laser beam was converted into a laser sheet with a thickness of less than 1 mm by using a system of cylindrical and spherical lenses. on average, the pulses energy was 70 mj before the laser sheet optics (measured by a power meter coherent labmax). particles images were captured by a pair of ccd cameras (bobcat imperx). the piv images (4904x3280 pixels is size) were processed by using an in-house software actualflow. time separation between two piv laser pulses was 30µs. the images were preprocessed to remove background (minimal intensity for each pixel). during four iterations of an adaptive cross-correlation algorithm the interrogation area size was reduced from 64×64 to 16×16 pixels. the spatial overlap rate between the interrogation areas was 50%, and the resulting spatial resolution was 0.5 mm four behringer ecm8000 microphones were used to record the pressure pulsations on the draft tube walls in the cross-section a-a as shown in figure 1. microphone signals were digitized by an adc and amplified using behringer preamplifiers. the pvc frequency was identified via time-resolved pressure signals at a sampling rate of 20 khz. the microphone signals were decomposed into azimuthal spatial and time fourier domains. figure 2 shows an example of the power spectral density of the asynchronous part of the pressure pulsations pas,i(t) = pi(t)−(1/4)∑ 4 i=1 pi(t) for the cases of flow rates 0.5qc (off-design) and qc (bep regime). as shown, the most energetic peak in the spectra occurs for the case of 0.5qc. this dominant #4 #3 #1 #2 microphones cone piv domain a-a swirler system z cross-section a-a connection with the draft tube elbow x 1 10 100 1000 0.0 5.0x10 -4 1.0x10 -3 1.5x10 -3 2.0x10 -3 3 fpvc 2 fpvc ps d [a rb . u n. ] f [hz] 0.5qc qc fpvc figure 1: 2d sketch of the test section (left) and photo of the piv configuration (right) figure 2: spectra of the asynchronous part of the pressure pulsation of four acoustic sensors (the vertical axis in relative units) for a set of flow rates 0.5qc (off-design) and qc (bep regime) peak is considered to be associated with the pvc. figure 3 shows the mean velocity field for the flow rates 0.5qc (off-design) and qc (bep regime). for the regime with 0.5qc, when the flow dynamics is related to strong pulsations due to the pvc, the time-averaged velocity field is characterized by a compact recirculation zone with the length of 0.2d. for the bep regime with qc is characterized by a smaller recirculation region (0.1d), which is associated with the flow past the centrebody. it is noteworthy that this flow is featured by the flow core rotation in the opposite direction to the sense of the main flow swirl. further analysis is focused on the phase-averaged velocity fields and on the results of proper orthogonal decomposition (pod). figure 3: mean velocity fields for the 0.5qc case, the off-design condition with pvc (left) and the bep regime, qc (right), (u0 is a bulk velocity, a solid line indicates recirculation region border) acknowledgements the research is supported by russian foundation for basic research (grant no. 20-58-12012). i. litvinov acknowledges support of the grant of the president of the russian federation (project no. mk-1504.2021.4, in the part of pressure signal analysis). the funding of the german research foundation (grant no. 429772199) is acknowledged. references cervantes m, trivedi c, dahlhaug og, and nielsen t (2015) francis-99 workshop 1: steady operation of francis turbines. in j. phys.: conf. ser. volume 579. page 011001 dörfler p, sick m, and coutu a (2012) flow-induced pulsation and vibration in hydroelectric machinery: engineer’s guidebook for planning, design and troubleshooting. springer science & business media litvinov i, shtork s, gorelikov e, mitryakov a, and hanjalic k (2018) unsteady regimes and pressure pulsations in draft tube of a model hydro turbine in a range of off-design conditions. experimental thermal and fluid science 91:410–422 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 piv measurements of the wake formation from a rough flat plate s. lawrence∗, c. atkinson, j. soria laboratory for turbulence research in aerospace and combustion (ltrac) department of mechanical & aerospace engineering, monash university, clayton, australia1 ∗ sean.lawrence2@monash.edu abstract wake flows are prevalent in a wide range of engineering applications and their behaviour can significantly impact engineering design and performance. a considerable body of work exists on smooth body wake structures and flows over rough bodies, however, there is a lack of fundamental physical understanding of the amalgamation of the two fields. two-component two-dimension particle image velocimetry (2c-2d piv) is used to investigate the effect of surface roughness on the formation of large scale structures in the near wake of a thin flat plate. both high-speed and low-speed, high-resolution piv setups have been used to investigate the effect of surface roughness on the boundary layer and the near wake of the plate to gain insight into the underlying physical connection between these regions. 1 introduction wake flows are prevalent in a wide range of engineering applications including turbomachinery, airfoil, and naval vessel design and performance. wakes form behind any body submerged in a fluid with appreciable free steam velocity. the flow around the body and its behaviour in the wake greatly dictates the induced lift and drag. therefore, there is significant engineering interest in understand and optimising these flows. the presence of surface roughness introduces additional complexity to what is already a complex turbulent flow. a significant body of work exists on the impacts of surface roughness on the turbulent boundary layer (tbl), however, the effects of surface roughness on wake development have received little attention. surface roughness on symmetric airfoils has been found to increase wake width, mean velocity deficits and turbulence intensity levels across the wake width, along with reducing the vortex shedding frequency (zhang et al. (2004)). the underlying physical mechanism by which the modifications surface roughness makes to the tbl affect the subsequent formation of near wake structures is currently unknown. this investigation studies the flow over smooth and two-dimensional (2d) rough surfaces using 2c-2d piv measurements taken in the boundary layer upstream of the trailing edge and the near wake of a thin, flat plate with a blunt trailing edge. 2 methodology experiments were performed on a series of rough acrylic plates mounted vertically on a joined aluminium spine in the ltrac large horizontal water tunnel facility at monash university. the roughness geometry, figure 1, consists of 2d spanwise square bars whose height increases linearly and was selected based on its elicitation of a self-preserving response in the turbulent boundary layer (kameda et al. (2008) and talluru et al. (2016)). for consistency, and to allow comparison with existing literature, the streamwise wavelength and relative roughness height were selected to be λx = 4 and k/δ = 0.052, respectively. the streamwise growth rate of the roughness, dk/dx = 0.0013, was selected using reynolds number matching of the growth rate used by kameda et al. (2008) with preliminary mean velocity measurements over a smooth plate. 2c2d piv measurements were obtained using a 4 mp pco dimax high-speed camera and a 29 mp imperx b6640 high-resolution camera. ε δ y x k figure 1: 2d roughness from kameda et al. (2008). 101 102 103 y+ 5 10 15 20 25 u + smooth 2d rough figure 2: mean boundary layer velocity 200 mm upstream of the trailing edge (xsmooth/δ99 = −3.6 and xrough/δ99 =−2). −4 −2 0 2 4 y/t 0.0 0.2 0.4 0.6 0.8 1.0 u /u ∞ smooth 2d rough figure 3: near wake streamwise velocity at 4 plate thicknessess downstream (x/t = 4). −4 −2 0 2 4 y/t −0.010 −0.005 0.000 0.005 0.010 u ‘ v ‘ smooth 2d rough figure 4: near wake reynolds stress at 4 plate thicknessess downstream (x/t = 4). 3 results mean boundary layer profiles and wake profiles for the streamwise velocity and reynolds stress are shown in figure 2, figure 3 and figure 4. these and additional results will be presented and discussed. acknowledgements financial support for this project has been provided by the maritime division of the defence science and technology group. the authors acknowledge the support provided by the arc and ncmas. references kameda t, mochizuki s, osaka h, and higaki k (2008) realization of the turbulent boundary layer over the rough wall satisfied the conditions of complete similarity and its mean flow quantities. journal of fluid science and technology 3:31–42 soria j, cater j, and kostas j (1999) high resolution multigrid cross-correlation digital piv measurements of a turbulent starting jet using half frame image shift film recording. optics & laser technology 31:3–12 talluru km, djenidi l, kamruzzaman m, and antonia ra (2016) self-preservation in a zero pressure gradient rough-wall turbulent boundary layer. journal of fluid mechanics 788:57–69 zhang q, lee sw, and ligrani pm (2004) effects of surface roughness and freestream turbulence on the wake turbulence structure of a symmetric airfoil. physics of fluids 16:2044–2053 introduction methodology results 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 enhanced data assimilation of 4d lpt with physics informed neural networks jengmin han1∗, dong kim1, hyungmin shin1, kyung chun kim1 1 pusan national university, school of mechanical engineering, busan, south korea ∗ hoon8674@pusan.ac.kr abstract according to recent trend of explosive growth of computation power and accumulated data, demand for the deep learning application in various research fields is increasing. as following this trend, remarkable achievements are presented in the experimental fluid mechanics field. one of the most outstanding research is physics informed neural networks (pinn) raissi et al. (2020). physical knowledge, which has been accumulated by humans, is imposed on the neural networks. pinn was used the automatic differentiation for implementing the governing equations as a physical constraint. by utilizing this concept, physical constraints make neural networks finding physical meaning of phenomena instead of simply fitting to the label data. kim et al. (2021) conducted velocity field measurements of flow past the side mirror model by 4d lagrangian ptv (particle tracking velocimetry) and implemented the anfis (adaptive neuro-fuzzy inference system) data assimilation (da) to increase the spatial and temporal resolution. although the da results are successful, while no physical constraint is imposed. in this study, incompressible continuity equation governed mass conservation constraint is implemented by using automatic differentiation. da is accomplished with the pinn for enhancing resolutions of the flow past the side mirror model. the increased spatial resolution of 3d velocity and vorticity fields with the trained pinn is compared with the anfis result. the simplified architecture of both models is shown in figure 1. (a) anfis (b) pinn figure 1: basic architecture of the (a) anfis and (b) pinn network. as shown in figure 2, the blunt side mirror model is placed in front of the analysis volume where marked by a red box. the flow condition is reh = 85,752(h = 0.1m,ν = 0.00001516m2/s), upstream flow velocity is 13 m/s. the helium filled soap bubbles (hfsb) was used for tracking particles, universal ur5 robotic arm and quantronix darwin-duo nd ylf laser (21v, 10a), four cmos cameras were used to measure time-resolved 3d velocity fields. the frame rate was 856 fps. detail description about experimental method and further results of the measurement are available from kim et al. (2021). the input data of anfis is obtained at 0 ¡ x/h ¡ 1.5, -0.7 ¡ y/h ¡ 0.7, 0 ¡ z/h ¡ 1.3 region and nodes of that are 30, 28 and 26, respectively. total nodes are 21,840 and the u/u∞, v/u∞, w/u∞ are used to labels. we shuffle all data before separate the data. 70% of inputs and labels are training data and remaining 30% are test data. sugeno-type fuzzy inference which suggested by jang (1993) is implemented and 6 generalized bell functions are used to input membership function. total train epochs are 20,000. same inputs and labels are applied to pinn training. the first and last layer have 3 neural and the other 10 layers have 250 neural. total training epochs are 30,000. anfis and pinn are trained on a single nvidia rtx 3080 gpu card and it took 2 hours and 4 hours for whole training, respectively. (a) anfis (b) pinn (c) pinn figure 2: average streamwise vorticity by (a) raw and step size x 4 (b) anfis, (c) pinn anfis and pinn model’s test root mean squared error (rmse) regarding to streamwise velocity are 0.013 and 0.0128, respectively. also, the second-order continuity equation is calculated to compare the raw data, anfis and pinn on the step size x1, and the result is 1.56, 3.92 and 0.65, respectively. this result demonstrates the role of physical constraint, which restricts the model diverge from the physics and complies with the physical law. the vortex are calculated using predicted velocity. figure 2(b) and 2(c) show the clear vortex structures than obtained by raw data and show the connected horseshoe vortex. in addition, figure 2(c) has more intense vortex region behind the obstacle than the others. comparison between pinn and anfis based da is following. both of them have just 0.013 and 0.0128 rmse. so, they have great potential for data assimilation to increase the spatial resolution. but, pinn method has smaller error in mass conservation (continuity equation) which means the using pinn is more desirable for physical meaning informed da. therefore, pinn can be considered to have more remarkable potential on the data assimilation of experimental fluid mechanics. acknowledgements this work was supported by the national research foundation of korea (nrf) grant, which is funded by the korean government (msit) (no. 2020r1a5a8018822). references jang js (1993) anfis: adaptive-network-based fuzzy inference system. ieee transactions on systems, man, and cybernetics 23:665–685 kim d, safdari a, and kim kc (2021) sound pressure level spectrum analysis by combination of 4d ptv and anfis method around automotive side-view mirror models. scientific reports 11 raissi m, yazdani a, and karniadakis ge (2020) hidden fluid mechanics: learning velocity and pressure fields from flow visualizations. science 367:1026–1030 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 simultaneous particle tracking and temperature measurements during additive manufacturing using a high-speed spectral plenoptic camera dustin kelly1, ralf fischer2, ari goldman1, sarah morris1, bart prorok2, and brian thurow1 1 auburn university, advanced flow diagnostics laboratory, auburn, al usa 2 auburn university, materials research and education center, auburn, al usa in this work, a high-speed spectral plenoptic camera was used for three-dimensional (3d) simultaneous particle tracking and pyrometry measurements of hot spatter particles ejected during the metal additive manufacturing process. additive manufacturing (am) has an increasing role in the aerospace, energy, medical and automotive industry (debroy et al., 2018). while this new technology enables the production of highly advanced parts, research on the fundamental mechanisms governing the laser-matter interactions are an ongoing challenge because of the spatial and temporal resolution inherent to the am process. one challenge is the characterization of spatter particles ejected from the melt pool, as these particles can be incorporated into the final part affecting the mechanical properties (deng et al., 2020). one potential solution for simultaneously measuring velocity and temperature of the spatter particles is the spectral plenoptic camera. figure 1: (left) a simple schematic of a three color spectral plenoptic camera showing how a single microlens captures an image of the aperture plan, and (right) the band pass filter array layout for these experiments where 800 nm is red, 600 nm is orange, and 532 nm is green. the plenoptic camera is a type of light-field camera, which provides the ability to instantaneously capture both angular and spatial information with one sensor. adelson and wang (1992) developed the modern design of a plenoptic camera, which is composed of a microlens array placed in front of a relay lens that images the microlens array onto a traditional sensor. each microlens of the array images the aperture plane, where each pixel discretizes the aperture, capturing the angular information as shown in figure 1. a convenient way to parameterize plenoptic images is through two-plane parameterization as described by levoy (2006), where the u-v and s-t planes correspond to the aperture and microlens planes, respectively. plenoptic imaging provides the ability to generate perspective images of the scene by adjusting the (u,v) coordinate. a recent modification of the plenoptic camera, first introduced by danehy et al. (2017), adds spectral filters at the aperture plane of the main lens. each microlens captures sub-images of the spectral filters as shown in figure 1. the spectral plenoptic camera provides the ability to individually select spectral filters, where each filter possesses limited angular information. increasing the number of different spectral filters decreases the overall angular information for a particular wavelength/spectrum. the current implementation of the spectral module and the high-speed plenoptic camera has a maximum of seven filters as shown in figure 1, in which there were three different spectral 10 nm band-pass filters as indicated by the filter layout image. the camera used was a phantom veo4k high-speed camera capable of 1000 hz at a resolution of (2048x2048) with a microlens array (471x362) placed in front of a relay lens that relays the microlens images to the sensor. the spectral module is composed of two lenses designed for a working distance/magnification and to f-match the microlens array as described by fahringer et al. (2018), where a magnification of 0.6 was chosen for these experiments. the first step of the ptv algorithm is locating the particles in the volume for each frame using plenoptic ray bundling, first described by clifford et al. (2019). ray bundling takes advantage of the two plane parameterization, where perspective images are first generated and particle locations are found through applying a minimum threshold. the perspective is the (u,v) coordinate and the location on the image is the (s,t) coordinate of the rays found during thresholding. every ray is then traced between the two planes, where the particle locations correspond to the point where the rays of different perspectives converge. this corresponds to a 3d location in the image space, which is converted to the object space. velocity measurements were made using a central finite time difference particle tracking technique, wherein particles’ 3d locations were matched in the images. ray bundling was conducted with the (i) 600 nm filter perspectives, (ii) 800 nm filter perspectives, and (iii) all perspectives to determine the uncertainty. dual-wavelength pyrometry was used to estimate the particle temperatures, where temperature is determined by the ratio of the average intensity between 600 nm and 800 nm filters for each microlens (r = i600nm/i800nm). temperature measurements are limited to the focal plane of the camera due to the assumption that the spectral information captured by one microlens originates from one particle, which only occurs at the focal plane of the camera. further improvements to the pyrometry algorithm could remove this limitation. the temperature calibration was performed in a lindberg/blue m tube furnace. an inconel 625 shim with a thermocouple attached to it was placed in the center of the furnace and temperature calibration images were captured at temperatures ranging between 950◦c and 1250◦c at intervals of 50◦c. the am experiment was performed on a customized am machine at auburn university’s materials research and education center. the laser source was an ipg ylr-400ac continuous wave ytterbium fiber laser with a wavelength of 1070 nm and a maximum output power of 400 w. an ipg mid-power scanner with a 250 mm f-theta lens was used to deliver the beam onto a 10x10 mm inconel 625 substrate. an inconel 625 powder layer of about 30 µm was spread onto the substrate. the laser scan path was a single continuous line scan with 800 mm/s scan velocity and 250 w laser power, and the laser traversed the z=0 plane of the volume from right to left in figure 2. the 8.5 mm long scan was performed below the scan head and perpendicular to the direction of view of the plenoptic camera. the single line scan was performed under ambient conditions for the demonstration of the capabilities of the plenoptic camera. figure 2: (a) spectral plenoptic image with a zoomed image with a blue circle corresponding to a single microlens that images a particle, (b) particle locations with the color corresponding to temperature with velocity vectors (mm/ms). figure 2(a) shows a spectral plenoptic image of a high temperature particle field generated by the additive manufacturing process. figure 2(b) shows particle locations along the x-y plane calculated using ray bundling where the particle color corresponds to the temperature. the velocity vector size is scaled with velocity (mm/ms). particle velocities ranged between 0.3 m/s to 7 m/s, where the faster particles originated in the first 5 ms, which agrees with the velocities found by guo et al. (2018). traditionally with single plenoptic reconstructions, the uncertainty in the z-direction is 6 to 10 times larger than in the x and y directions. this is on a similar order even with the reduced angular information per wavelength. the majority of particle temperatures ranged between 1000◦c to 1600◦c. with a melting temperature of approximately 1300◦c, the inconel 625 particles were present in both liquid and solid states. for particles along the focal plane, a general cooling trend of approximately 150◦c/ms was observed. the measurement uncertainty for both particle location and temperature are still a current topic of investigation. acknowledgements this work was sponsored by the united states national institute of standards and technology under contracts nist-70nanb16h272 and nist-70nanb18h220. the authors gratefully acknowledge the support of mr. steven moore and mr. emre kayali at auburn university’s materials research and education center. references adelson e and wang j (1992) single lens stereo with a plenoptic camera. ieee transactions on pattern analysis and machine intelligence 14:99–106 clifford c, tan z, hall e, and thurow b (2019) particle matching and triangulation using light-field ray bundling. 13th international symposium on particle image velocimetry danehy pm, hutchins wd, fahringer tw, and thurow bs (2017) a plenoptic multi-color imaging pyrometer. 55th aiaa aerospace sciences meeting pages 1–7 debroy t, wei h, zuback j, mukherjee t, elmer j, milewski j, beese a, wilson-heid a, de a, and zhang w (2018) additive manufacturing of metallic components – process, structure and properties. progress in materials science 92:112–224 deng p, karadge m, rebak rb, gupta vk, prorok bc, and lou x (2020) the origin and formation of oxygen inclusions in austenitic stainless steels manufactured by laser powder bed fusion. additive manufacturing 35:101334 fahringer tw, danehy pm, and hutchins wd (2018) design of a multi-color plenoptic camera for snapshot hyperspectral imaging. 2018 aerodynamic measurement technology and ground testing conference pages 1–9 guo q, zhao c, escano li, young z, xiong l, fezzaa k, everhart w, brown b, sun t, chen l, and et al (2018) transient dynamics of powder spattering in laser powder bed fusion additive manufacturing process revealed by in-situ high-speed high-energy x-ray imaging. acta materialia 151:169–180 levoy m (2006) light fields and computational imaging. computer 39:46–55 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 trackfit: uncertainty quantification, optimal filtering and interpolation of tracks for time-resolved lagrangian particle tracking s. gesemann1∗ 1 dlr (german aerospace center), institute of aerodynamics and flow technology, department of experimental methods, göttingen, germany ∗ sebastian.gesemann@dlr.de abstract advanced lagrangian particle tracking methods (such as the stb algorithm (schanz et al. 2016)) are a very useful tool for uncovering properties of flow. as a measurement technique, the results of such methods are perturbed by different sources of errors and noise. this work addresses the problem of optimal filtering of particle tracks as well as estimating uncertainties of derived quantities such as location, velocity and acceleration of observed particles. the behavior and performance of this new filtering method (“trackfit”), first introduced at gesemann et al. (2016) is analyzed and compared to the savitzky–golay filter (savitzky and golay (1964)) which is commonly used for these purposes. the optimal choice of parameters of this filtering method as well as the uncertainty quantification of the reconstructed tracks can be extracted from a spectral analysis of the recorded raw particle tracking data. this is in contrast to a savitzky–golay filter where the choice of parameters might often be driven by experience and gut feeling. estimating the power spectral density (psd) of the particle trajectory signals for the purpose of optimal filtering parameter selection represents a challenge due to possibly short trajectory signals. in the following work we will present a method for psd estimation that is applicable in this scenario. in addition, we show that regardless of the choice of savitzky–golay filter parameters, the resulting filter will not approximate the ideal noise reduction filter well unlike the “trackfit” described in this work. 1 introduction in the interest of optimal noise reduction filtering and interpolation for derived quantities such as velocity and acceleration and their uncertainty estimation, knowledge about the spectral properties of the position-overtime signals is important. we expect the low frequencies of such signals to have a lot of energy and a high signal-to-noise ratio while for higher frequencies we expect a low signal-to-noise ratio due to mostly white measurement noise. further, we expect the measurement noise to be additive and statistically uncorrelated to the true positional signals. in such a case the optimal filter (optimal with respect to minimizing the sum of squared errors) would reduce to a simplified wiener filter that ignores cross correlations between signal and noise. such a filter’s response can be expressed as follows: h( f ) = snr( f ) 1+snr( f ) (1) in equation 1 snr( f ) refers to the local signal power to noise power ratio close to the frequency f . for a high signal-to-noise ratio the filter gain will approach 1 while for a low signal-to-noise ratio the gain will approach zero to suppress the noise. two challenges arise in the context of lagrangian particle tracking (ltp). the particle trajectories may span only a small number of time steps (order of 30). in order to estimate the ideal filter transfer function, an accurate estimate of the power spectral densities of the true signal and the additive noise is necessary. but for such short signals, spectral estimation requires special attention. the possibly short nature of particle trajectories also poses a problem during the application of a filter especially at the borders of the signal (the beginning and ending of a trajectory) because the filter would require samples outside of the recorded domain. the remainder of this paper is structured as follows: section 2 will cover the problem of spectral analysis for this kind of filtering problem. section 3 will show the results of our spectral estimation method when applied to a known data set from the 1st lpt and da challenge for testing whether the method results in a reasonable power spectrum estimate but also to verify that our assumptions about what such a spectrum may look like are true. section 4 will describe the trackfit filtering method (see also (gesemann et al. (2016)) with its properties. in section 5 the trackfit and savitzky–golay (savitzky and golay (1964)) filter methods are analyzed and compared. section 7 closes with a summary and conclusion. 2 spectral estimation for our case with potentially short tracks which have strong low-frequency components we have developed an appropriate spectral estimation method. the method can be summarized with the following steps: 1. prefilter (fir) the position-over-time data 2. compute autocorrelation of the result 3. apply levinson-durbin recursion for auto-regressive model on autocorrelation data 4. compensate for prefiltering in auto-regressive model 2.1 prefilter a prefilter can be used for spectral analysis as a first stage to flatten the signal spectrum. the spectrum of the resulting intermediate signal would be estimated instead to derive the original spectrum by compensating for the prefilter’s response. this approach can be preferable to directly estimating the original signal’s spectrum. in particular, an fft-based estimation tends to suffer from spectral leakage due to the use of finite windows. spectral leakage manifests in the form of a broader main lobe and the presence of side lobes for a single frequency that is present in the signal. these artefacts will be less noticeable if the signal already has a flat shape. for spectral estimation based on the auto-regressive model, prefiltering also has benefits. the effect of different prefilters is shown in section 2.2. apart from flattening the spectrum, such a prefilter should also have a short impulse response, e.g. two or three samples. this becomes obvious when the filter has to be applied to potentially short signals. suppose a short signal with 25 particle locations is available. after applying a prefilter with an impulse response of three samples only 23 samples of the result can be used for estimating autocorrelation coefficients. the longer the filter’s impulse response, the shorter the intermediate signals will get. the prefilters we chose are first and second order digital fir filters with the following transfer functions hp1 and hp2: hp1(z) = 1− z−1 hp2(z) = 1−1.9z−1 +0.9z−2 (2) these filters attenuate the low frequencies and amplify the higher frequencies. 2.2 spectral estimation via auto-regressive model the auto-regressive model (ar) basically describes a random process as filtered white noise using an allpole iir filter for coloring the noise. with the help of the levinson-durbin recursion the filter coefficients can be extracted from autocorrelation coefficients. this allows another form of spectral estimation in that the filter represents the spectral shape (with an average response of 0 db over a linear frequency axis) and the noise power represents an overall offset for the power spectral density. see listing 1 for a gnu octave script that shows this process. % let acf be a vector with the autocorrelations % for lags zero to p (inclusive) % auto-regressive model ar(p) computed from acf using % levinson-durbin recursion [a,v] = levinson(acf); % a = order p all-pole filter coefficients % v = variance of white noise % power spectral density estimate by evaluating the % filter's transfer function and scaling with variance [h,f] = freqz(1,a); % transfer function p = abs(h).ˆ2 * v; % power spectral density estimate loglog(f(2:end), p(2:end)); listing 1: gnu octave example script for estimating the power spectral density based on autocorrelation coefficients via an auto-regressive model of order p. 2.3 test and comparison of spectral estimation methods to test the various spectral estimation methods a ground truth spectrum has been chosen that is believed to be representative of typical particle tracks including measurement noise, see figure 1. the lower frequency part is dominated by true particle locations while the higher frequency part is dominated by flat white measurement noise. the ground truth is the sum of two power spectra: signal (psds) and noise (psdn). on a normalized frequency axis (ranging from zero to one for the nyquist frequency) they are defined as follows: psds( f ) = 1 (3.77 f )2 +(641.52 f 2)2 +(17363.515 f 3)2 (3) psdn( f ) = 0.00592 (4) based on the chosen ground truth spectrum and the transfer function of the prefilter autocorrelation coefficients can be computed directly using a fourier transform. only 21 autocorrelation coefficients have been selected (for lags 0 to 20 inclusive) to test how the spectral estimation methods perform. the fft-based method extends the 21 coefficients for lags 0 to 20 to 41 coefficients for lags -21 to 21 by mirroring and zero-padding and applies a hann window to the result. the windowed autocorrelation function is then used as input to a zero-padded fft. the resulting magnitudes are squared and plotted against their frequency. the ar-based method applies the computations shown in listing 1 of section 2.2 with p = 20. as can be seen in figure 1, fft-based methods struggle to deal with such a spectrum given only a small symmetric window of 41 autocorrelation coefficients. we can clearly see the side lobes of lower frequencies that dominate the estimation of the power spectrum estimates for higher frequencies. the prefilters help reduce the damage by amplifying the higher frequencies and attenuating them again after the estimation. but the most important feature of the spectrum for the purpose of noise reduction is the frequency region in which the power spectrum flattens again because this is where the signal-to-noise ratio crosses the 0 db level and the point at which a noise reduction filter should start to attenuate the high frequencies. unfortunately, the fft-based methods fail to resolve this reliably in this case even with the prefilters enabled (k > 0). the auto-regressive approach tracks the true spectrum more closely in comparison. most errors of the estimates are below 1% and only rise with the lower frequencies to about 6%. the estimated curves oscillate around the ground truth which is not surprising given that they are expressed using an order 20 polynomial. between different prefilters the curves look similar. but the equation systems to compute the filter coefficients are very different in their ”numerical difficulty”, see table 1. high condition numbers can make the method unreliable in the light of finite precision arithmetic and rounding errors. the use of appropriate prefilters can lower the condition number and thus improve numerical stability of the method. in fact, the condition number can be seen as a measure of how well the prefilter is able to ”whiten” the signal. 10 -3 10 -2 10 -1 10 0 10 -10 10 -09 10 -08 10 -07 10 -06 10 -05 10 -04 10 -03 10 -02 10 -01 10 00 10 01 10 02 10 03 10 04 10 05 10 06 10 07 frequency p o w e r sp e c tr a l d e n si ty fft-based spectral estimation 10 -3 10 -2 10 -1 10 0 10 -10 10 -09 10 -08 10 -07 10 -06 10 -05 10 -04 10 -03 10 -02 10 -01 10 00 10 01 10 02 10 03 10 04 10 05 10 06 10 07 frequency p o w e r sp e c tr a l d e n si ty ar-based spectral estimation true error (fft, k=0) error (fft, k=1) error (fft, k=2) true error (ar, k=0) error (ar, k=1) error (ar, k=2) figure 1: power spectral density estimation method comparison for a synthetically generated case. the black curve represents the true signal spectrum. for the spectrum estimates only the errors to the ground truth are shown. k refers to the prefilter order with k = 0 meaning no prefilter. k = 0 k = 1 k = 2 condition number 2.6 ·108 3.3 ·103 8.1 ·101 table 1: condition numbers for different prefilter orders 3 spectral estimation test on fluid simulation data the question arises whether the black curve in figure 1 for a hypothetical power spectrum is representative of measured particle motion in a fluid. therefore, we applied our spectral estimation method on a known data set of the first data assimilation challenge (sciacchitano et al. (2021a)). this data set covers particle locations for 25 time steps based on a fluid simulation and simulated white measurement noise. figure 2 shows the power spectral density estimate of the simulated particle data for the particles’ z coordinates which closely matches the spectrum assumption from the previous section. in particular, we have the same slope of about -6 in the log-log plot right before the measurement noise becomes dominant and the curve flattens. we have observed this slope to be typical in these sorts of fluid experiments. 4 filtering with trackfit instead of low-pass filtering by direct convolution, a filtering effect can also be achieved by posing and solving an overdetermined linear equation system in the least squares sense such as the one in equation 5: 10 -3 10 -2 10 -1 10 0 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 normalized frequency p o w e r sp e c tr a l d e n si ty figure 2: power spectral density estimation of particle data of 1st da challenge (0.160 ppp case).  w w w . . . w w −1 1 −1 1 −1 1 . . . . . . −1 1  s′ = ( w · s 0 ) (5) here, s refers to the raw unfiltered signal, s′ refers to the filtered signal that needs to be solved for and w is a scalar weighting factor for the identity portion of the equation system. the lower part of the equation system sets finite differences of the first order to zero. higher order differences can also be used. this approach sidesteps the problem of missing samples at the signal’s beginning and end and is thus easily applicable without special treatment at the borders. solving this kind of equation system has the effect of a low-pass filter where the weight w controls the cutoff frequency and the finite difference order controls the steepness of the low-pass filter’s transition band. the choice for w given a finite difference order k and a normalized cutoff frequency fcuto f f between 0 and 1 roughly follows the following relation: w≈ (π · fcuto f f ) k (6) this filtering approach can be modified so that instead of solving for a filtered signal we solve for scale factors for a set of smooth and compact basis functions for the purpose of interpolation. with the cubic b-spline base function as basis β3(x) =  2 3 − x2 ( 1− 1 2 |x| ) for 0 <= |x|< 1 1 6 (2−|x|) 3 for 1 <= |x|< 2 0 for 2 <= |x| (7) which evaluates to 1 6 , 4 6 and 1 6 at points −1, 0 and 1 and the use of third order finite differences of the b-spline coefficients which correspond to the actual third order derivative at the midpoints of the b-spline curve between two neighboring knots, the modified equation system looks as follows:  1w 4w 1w 1w 4w 1w 1w 4w 1w . . . . . . . . . 1w 4w 1w 1w 4w 1w −1 3 −3 1 −1 3 −3 1 −1 3 −3 1 . . . . . . . . . . . . −1 3 −3 1  c = ( 6w · s 0 ) (8) here, the solution c is a set of scale factors which control the contribution of the various shifted b-spline base functions to the trajectory. given a signal s with n samples, n+2 scaling coefficients will be computed to cover every interval with four cubic base splines. the choice of regularizing with the third order derivative is motivated by the slope of estimated frequency spectra of position-over-time signals in simulations as well as real stb experiments. a derivative order of k will approximate the response of the ideal wiener filter for a signal slope of −2k in a log-log plot right before the power spectral density curve starts to flatten. using this modification a continuous curve is reconstructed instead of a discrete signal. thus, the curve can be evaluated at any point in time including its temporal derivatives for velocity and acceleration. 5 analysis and comparison 10 -2 10 -1 10 0 10 -4 10 -3 10 -2 10 -1 10 0 ideal wiener filter savitzky-golay, n=19, k=4 savitzky-golay, n=13, k=3 trackfit w=0.213 figure 3: comparison of ideal filter gain with savitzky-golay (window size n and polynomial order k) filters and trackfit (cutoff frequency parameter w). based on the assumed ground truth spectrum that is the sum of the true signal and white noise the ideal filter transfer can be determined according to equation 1 and compared to the response of the real filter realizations of the savitzky-golay filter and trackfit, see figure 3. for the savitzky-golay filter the window lengths n were selected for polynomial order k = 3 and k = 4 so that the filter’s response would approximate the ideal filter response. but these filters tend to have a poor suppression of high frequencies which would retain more of the measurement noise than necessary. the trackfit approximates the ideal wiener filter very well for this type of spectrum. it retains the necessary low frequency information and rejects the high frequency measurement noise just as the wiener filter would. 6 uncertainty estimation each b-spline coefficient computed with trackfit for a particle trajectory can be represented as a weighted sum of the raw particle location data with the help of the equation system’s pseudo-inverse. in addition, each derived quantity from the b-spline curve (such as location, velocity or acceleration) is also a weighted sum of the b-spline coefficients. the concatenation of two linear mappings is itself linear. therefore, any of these derived quantities can be written as a weighted sum of the raw unfiltered particle location data, for example, the velocity of a particular particle at time instant t based on the noisy particle location samples s j: v(t) = ∑ j α j(t) · s j (9) under the assumption of uncorrelated white measurement noise with a power level σ2 le that can be extracted from the flat high frequency portion of the power spectral density estimates, it is possible to perform gaussian error propagation. assuming the variance of the location error in s j is estimated to be σ2 le then the variance of the error of velocity σ2 ve can be written as σ 2 ve(t) = σ 2 le ∑ j α 2 j(t) (10) this gives us uncertainty estimates of any quantity based on the spectral power density estimates of the measurement data and the noise reduction/interpolation approach which effectively controls the α scale factors that weight each individual particle location measurement. 7 summary and conclusion in this work we have presented a method to perform spectral analyses on possibly short particle trajectories which is tailored to strong low frequency content and fast decay using a compensating prefilter. the resulting spectral information allows approaching the ideal noise reduction filter. further, the benefits of trackfit (gesemann et al. (2016)) have been highlighted. specifically, it performs a joint noise reduction approximating the ideal wiener filter with an interpolation that offers consistent temporal derivatives for velocity and acceleration. in addition, it was shown how gaussian error propagation can be applied based on the estimated level of the measurement noise floor from the spectra and the filtering coefficients α. we have applied these methods in various experiments as well as both the first lpt challenge (sciacchitano et al. (2021b)) and the first da challenge (sciacchitano et al. (2021a)) with good results. acknowledgements the project leading to this contribution has received funding in the frame of the project homer from the european union’s horizon 2020 research and innovation program under grant agreement no. 769237. references gesemann s, huhn f, schanz d, and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser and imaging techniques to fluid mechanics, lisbon, portugal. pages 4–7 savitzky a and golay mje (1964) smoothing and differentiation of data by simplified least squares procedures.. analytical chemistry 36:1627–1639 sciacchitano a, leclaire b, and schröder a (2021a) main results of the first data assimilation challenge. in 14th international symposium on particle image velocimetry sciacchitano a, leclaire b, and schröder a (2021b) main results of the first lagrangian particle tracking challenge. in 14th international symposium on particle image velocimetry introduction spectral estimation prefilter spectral estimation via auto-regressive model test and comparison of spectral estimation methods spectral estimation test on fluid simulation data filtering with trackfit analysis and comparison uncertainty estimation summary and conclusion 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 large-scale structures of scalar and velocity in a turbulent jet flow jesse reijtenbagh∗, jerry westerweel, willem van de water laboratory for aero and hydrodynamics, delft university of technology and j.m. burgers centre for fluid dynamics, 2628 cd delft, the netherlands ∗ j.reijtenbagh@tudelft.nl we study the relation between large-scale structures in the concentration field with those in the velocity field in a dye-seeded turbulent jet. the scalar concentration in a plane is measured using laser-induced fluorescence. uniform concentration zones of an advected scalar are identified using cluster analysis. we simultaneously measure the two-dimensional velocity field using particle image velocimetry. the structures in the velocity field are characterized by finite-time lyapunov exponents. the measurement of the scalarand velocity fields moves with the mean flow. in this moving frame, turbulent structures remain in focus long enough to observe well-defined ridges of the finite-time lyapunov field. this field gauges the rate of point separation along lagrangian trajectories; it was measured both for future and past times since the instant of observation. the edges of uniform concentration zones are correlated with the ridges of the past-time lyapunov field, but not with those of the future-time lyapunov field. u = 0.04 m/sc x y (a) (b) d jet figure 1: the experimental setup. (a) schematic view of the arrangement of cameras,traversing system and jet (not to scale). (b) schematic view of the turbulent jet and sketch of the co-moving observation window (not to scale). in each run a total of 210 piv frames and 101 lif frames is acquired at a rate of 10 hz. the coordinates within a comoving frame are (x,y),the distance of its right edge to the orifice is d. the experiments involve a turbulent jet which contains a fluorescent dye (rhodamine b) and is seeded with piv-particles. in a laboratory fixed frame (eulerian frame), the observation of lagrangian dynamics is limited by the passage of flow structures through the observation window. therefore, an experiment was designed where the measuring equipment moves with the mean flow, by using a traverse mechanism driven by a stepper motor, as demonstrated in figure 1. separate cameras were used for particle image velocimetry and laser induced fluorescence to measure the velocityand concentration field in a thin slice of the evolving turbulent jet. the piv-camera is equipped with a shortpass filter (fes0550, thorlabs, < 550 nm) with a transmission ratio in the rejection region of 0.01 % and a 105 mm lens, while the lif camera has a longpass filter (fel0550, thorlabs, > 550 nm) with a transmission ratio in the rejection region of 0.01 %, and also a 105 mm lens. both the pivand lif-measurements are done using a double-pulsed nd:yag laser (spectra physics quanta ray). the velocities are found from the images of the piv-camera using davis, while the scalar concentration from the lif-images is found using a third-order calibration function based on the image intensity and the position of this scalar. this calibration function is determined by performing lif-measurements on a container with known dye concentrations that covers the entire measurement range. in snapshots of the concentration field we identify regions with more-or-less uniform concentration, using the methods of cluster analysis, recently introduced in turbulence by fan et al. (2019) (figure 2). these uniform concentration zones are reminiscent of uniform momentum zones that are found in turbulent shear flows (de silva et al., 2016; eisma et al., 2015; adrian et al., 2000). we find the edges of these regions, which we link to structures of the velocity field. these structures are defined by the spreading rate of two nearby fluid parcels, quantified by the finite-time lyapunov exponent (ftle). local maxima of this lyapunov exponent are possible candidates of lagrangian coherent structures (lcs), which form transfer barriers in the flow (shadden et al., 2005). lyapunov exponents can be found by looking at the spreading rate of two fluid parcels in both forward an backward in time, which results in past ftle and future ftle, respectively. by moving our measurement equipment along with the flow, we greatly increase the time fluid parcels can be observed, which results in a more detailed ftle-field. x (m) y (m ) 0 0.02 0.04 0.06 0 0.02 0.04 0.4 0.6 0 0.02 0.04 0.06 x (m) x (m) 0 0.02 0.04 0.06 0 1 2 (c) (b)(a) figure 2: (a) snapshot of tracer concentration c(x, t), taken at d = 0.83m from the jet orifice. (b) field of (a), coarsened into 4 uniform concentration zones. (c) past finite-time lyapunov exponent in the same field as (a) and (b). the large-scale filamentous structure of λ−t (x,y) roughly corresponds to the large-scale structure of the edges of the uniform concentration zones (suggested by arrows). comparing both the past and future ftle-field with the edges of the uniform concentration zones shows similar structures in the concentration-field and the past ftle-field (figure 2). these similarities are not found between the future ftle and the uniform concentration zones. although the structure of the past ftle-field resembles that of the edges of concentration zones, they do not coincide exactly. the normalized correlation between edges of concentration zones and the past ftle-field is small (≈ 0.02), and the conditional averages of the ftle-fields on lines perpendicular to zone edges only show a small peak of the past ftle on the edge of a uniform concentration zone. references adrian rj, meinhart cd, and tomkins cd (2000) vortex organization in the outer region of the turbulent boundary layer. j fluid mech 422:1–54 de silva cm, hutchins n, and marusic i (2016) uniform momentum zones in turbulent boundary layers. j fluid mech 786:309–331 eisma j, westerweel j, ooms g, and elsinga ge (2015) interfaces and internal layers in a turbulent boundary layer. phys fluids 27 fan ds, xu jl, yao mx, and hickey jp (2019) on the detection of internal interfacial layers in turbulent flows. journal of fluid mechanics 872:198–217 shadden sc, lekien f, and marsden je (2005) definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensional aperiodic flows. phys d nonlinear phenom 212:271–304 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 piv measurements in a turbulent boundary layer overlying a spanwise heterogeneous roughness r. yao1, k. t. christensen1,2 1 university of notre dame, department of aerospace and mechanical engineering, notre dame, in, 46556, usa 2 illinois institute of technology, department of mechanical, materials and aerospace engineering & civil, architectural and environmental engineering, chicago, il, 60616, usa 1 introduction in nature and engineering applications, wall-bounded flow often encounter a heterogeneous surface condition, such as the atmosphere boundary layer at the urban boundary and flow over riveted aircraft surfaces. in a particular scenario, when the surface heterogeneity is predominantly in the spanwise direction of the flow, this roughness heterogeneity can generate secondary flow in cross flow plane which is very different from smooth-wall or homogeneous rough-wall boundary layers. figure 1: (a) important parameters of the ridge-type roughness: h, ridge height; s, the spacing of the ridges; w , ridge width. (b) surface models used in these experiments (the ri of the clear one is matched with that of the working fluid during experiments). (c) planar piv setup for streamwise–wall-normal measurements. a number of experimental (barros and christensen, 2014; vanderwel and ganapathisubramani, 2015; zampiron et al., 2020) and numerical (anderson et al., 2015; hwang and lee, 2018; castro et al., 2021) studies have shown features associated with the secondary flow including: streamwise oriented alternating lowand high-momentum pathways (lmp, hmp); downwash and upwash flow at hmp and lmp, respectively; counter-rotating streamwise vortices formed across an lmp and hmp. the secondary flow mechanism is explained based on prandtl’s secondary flow of the second kind according to anderson et al. (2015). with this current understanding, this work uses piv to document the spatio-temporal information of this special flow in x− y and y− z planes over a ridged spanwise heterogeneous rough surface. the results present here mainly focus on the mean and turbulence statistics measured in a flow facility at moderate reynolds number. 2 methods the roughness models used in the current experiments are derived from an idealized ridge-type roughness, wherein the roughness topography is constructed from equally spaced bars of square cross-section (fig 1a). in the design of the roughness model, the size and spacing of the ridge elements were selected to ensure the generation of strong secondary flows for ridged roughness (vanderwel and ganapathisubramani, 2015; medjnoun et al., 2018). piv measurements are performed in a refractive-index-matched (rim) flow facility (fig. 1c) wherein the refractive index of the working fluid (aqueous nai) matches that of solid models of the roughness so that reflections and aberrations in the piv illumination and imaging are minimized and flow in the immediate vicinity of the roughness can be interrogated by piv. figure 1(b) shows the roughness tiles for rim and the overall roughness arrangement in the test section. figure 2: (a) ensemble-averaged streamwise velocity field between at the center between spanwiseseparated ridges. (b,c) ensemble and streamwise-averaged streamwise and wall-normal velocity profiles positioned on top of a ridge and between two ridges. 3 results initial results showing the time-averaged and time and streamwise-averaged velocities from x−y plane piv measurements are shown in fig. 2. figure 2a shows the time-averaged streamwise component velocity in the position between two ridges from wall to the free stream. in this case the data below y = 3.8 mm is behind the ridges and therefore demonstrates the applicability of rim in this case. figure 2a also verifies the streamwise homogeneity of the mean flow. the ensembleand streamwise-averaged velocity profiles are calculated and shown in figs. 2b,c. the profiles confirm that the hmp and downwash region is located in between the ridges while the lmp and upwash is observed above the ridges which is consistent with observations in the literature (vanderwel and ganapathisubramani, 2015; medjnoun et al., 2018; castro et al., 2021). the ongoing progress of this work includes: stereo-piv measurements in the cross-plane, frequency analysis, and quantification of inner–outer interactions in this flow scenario. follow-on research will focus on aligning these same ridges obliquely to the mean flow to understand the persistence of these secondary flows relative to the spanwise heterogeneity of the topography. references anderson w, barros jm, christensen kt, and awasthi a (2015) numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness. journal of fluid mechanics 768:316–347 barros jm and christensen kt (2014) observations of turbulent secondary flows in a rough-wall boundary layer. journal of fluid mechanics 748 castro ip, kim j, stroh a, and lim hc (2021) channel flow with large longitudinal ribs. journal of fluid mechanics 915 hwang hg and lee jh (2018) secondary flows in turbulent boundary layers over longitudinal surface roughness. physical review fluids 3:014608 medjnoun t, vanderwel c, and ganapathisubramani b (2018) characteristics of turbulent boundary layers over smooth surfaces with spanwise heterogeneities. journal of fluid mechanics 838:516–543 vanderwel c and ganapathisubramani b (2015) effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers. journal of fluid mechanics 774 zampiron a, cameron s, and nikora v (2020) secondary currents and very-large-scale motions in openchannel flow over streamwise ridges. journal of fluid mechanics 887 introduction methods results 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 tracking particles in poiseuille flow for several pipe diameters in three dimensions s. sridharan, c. poelma department of mechanical, maritime & materials engineering, delft university of technology, delft, the netherlands abstract a setup is devised to track suspended particles in a pipe in three-dimensional space using the shadowgraphyptv technique. this system consists of a single camera and a mirror, and is used to track particles for over 20 pipe diameters at three downstream locations. pipe to particle diameter ratios (d/d) of 18, 9, and 6 are investigated. the bulk reynolds number is varied between reb = 300-1250. as expected, particles are observed to migrate radially to a location corresponding to the segré-silberberg annulus. in addition, we observe particles also moving in the azimuthal direction (clockwise or counter-clockwise), with some particles moving as much as 180◦ during their passage through the field of view. this helical motion persists throughout the pipe (600d long) and the azimuthal velocity increases with the reynolds number (reb). the effect of particle size and the reynolds number on this previously undocumented, three-dimensional motion is studied. 1 introduction particles suspended in poiseuille flow undergo inertial migration to a particular radial equilibrium position, commonly referred to as the segré-silberberg annulus. the dominant contribution to this effect is the lift force due to shear around a particle, following from the parabolic velocity profile (asmolov, 1999). matas et al. (2004) showed that increase in size and/or reynolds number results in accumulation of particles at an additional radial location, more towards the pipe centre . the long-term stability of this ‘inner annulus’ is not clear, as the theory (which neglects finite-size effects) predicts that the particles should migrate even closer to the wall as reb increases. however, a larger fraction of particles are observed to reach the inner annulus at higher reynolds numbers 1000d away from the entrance (morita et al. (2017)). recent experimental work from nakayama et al. (2019) show that there is a critical reynolds number above which the inner annulus is more stable. it should be noted that previous experiments are based on stochastic analysis of particle radial locations, i.e. only based on locations in a cross-sectional plane at various streamwise locations. modelling this effect is challenging even at single particle level when inertia becomes significant, especially when the particle size is very high (d/d < 15) (hood et al. (2015). in order to investigate these phenomena in more detail, we track particles over several pipe diameters in three dimensions with a measurement technique based on shadowgraphy and particle tracking velocimetry. the flow is imaged along two perpendicular directions, and particles are detected by their shadows. the 3d position is reconstructed from the two projections by matching the downstream coordinate of each particle. the magnification is adjusted based on the particle size to ensure consistent detection, allowing larger field of views (l/d ≈ 20). this is preferable as we intend to locate large particles slowly migrating over a long distance: typically cross-stream velocities are less than 5% of its streamwise velocity. based on our observations, particles are observed to accumulate at two radial locations (≈ 0.8r and 0.6r from pipe axis) at higher reynolds numbers (reb > 700), with larger particles (d/d = 6) preferably staying at the inner location. this persists even 500 pipe diameters away from the entrance. further, particles with d/d = 6 and 9 exhibit peculiar spiralling behavior, i.e. they also have an azimuthal velocity if their radial location is more than 0.4r from the center. 2 experimental setup a flow loop consisting of a 6.5 m long pipe with 0.01 m diameter (d) is constructed, see fig. 1 for a schematic representation. the flow is driven by a constant head maintained by an overflow tank. the suspension enters the pipe through an inlet chamber containing a flow conditioner, followed by a smooth contraction. the outflow of the suspension from the pipe is collected in a reservoir and pumped back to the overflow tank using a peristaltic pump, forming a closed loop. the bulk reynolds number (reb=ubd/ν) is maintained between 300-1250. a neutrally buoyant solution is prepared by adding sodium sulfate to the water to match the density of the polystyrene particles (ρp = 1035 kg/m3). particles with a mean diameter of 0.515 mm, 1.12 mm, and 1.67 mm were used, corresponding to d/d ratios of 20,9 and 6 respectively.the particle reynolds number (rep ≡ reb(d/d)2) varies from 1.2-35. the particle concentration is kept below 0.05%, typical spacing between the particles for d/d = 20, 9, 6 are 0.6d, 1.5d, and 10d respectively. at these concentrations, the suspension kinematic viscosity is very close to that of pure water (ν = 1.1 × 10−6 m2/s, at 20 oc). figure 1: schematic diagram of the optical system used to reconstruct the three-dimensional position of a particle in the pipe in the cross-sectional (x− y) plane. the particles are tracked in three field of views: fov 1, fov 2, and fov 3 corresponding to 35-70d, 300-350d, and 510-550d from the pipe entrance, respectively. a typical raw image is shown with top view and front view of the pipe. the imaging system consists of a camera and a planar mirror positioned at 45◦ to the object plane (y-z plane, fig-1). a water-filled container with calculated width is used to compensate for the optical path difference between the reflected and direct paths. the system is arranged such that the planes along the perpendicular views intersect at the axis of the pipe. this allows reconstruction of any point inside the pipe into a 3d space. an imager scmos camera (lavision gmbh) with 50 mm lens is used, along with two led panels placed perpendicular to the (x-y) plane. a mirror is placed at 45o with the horizontal (x axis) above a rectangular pmma section enclosing the pipe. a typical image contains two perpendicular views of the pipe in the (y-z) and the (x-z) planes with the z axis as the epipolar line. the field of view is varied depending on the particle (image) size, covering 10d, 20d, and 45d of pipe length for d/d = 18,9 and 6 respectively. the images are captured at three downstream locations: 35d-70d, 300d-320d, and 500-510d from the entrance. the images have a spatial resolution of 0.22 mm and a temporal resolution of 0.02 s. particles are tracked separately in individual views and the tracks are reconstructed in 3d space by matching their streamwise locations. occlusions/ghost particles are rare occasions at the concentration studied. also, the relatively linear behaviour facilitates tracking in each view and allows matching based on first order estimates (i.e. constant displacement for each particle across frames). there is a small mismatch in streamwise locations between the two views because of the difference in their optical path (∆s) away from the image centre as the correction is only valid at the image centre. this introduces a linear deviation in streamwise locations between the views with a difference of ∆s tanθ, where θ is the viewing angle (along z, see fig. 1). further, there is an additional difference in depth of particle between the views due to its location in 3d space. from our results, their mismatch varies linearly with z, with a maximum of 40 px towards the end of the image, corresponding to 2.6 mm. the mismatch error is corrected by a self-calibration function based on the cross stream positions of multiple particles tracked in both views at very low concentration (fig. 2). this function is used to correct the streamwise position of particle images in the top view and are further matched with the images in the front view to reconstruct their 3d trajectories (fig. 8). figure 2: mismatch in streamwise (z) coordinates of particles between both views (left), where t and f subscripts represent top view and front view respectively. the slope of the linear mismatch (right) is a function of the cross stream positions. 3 results the particle cross stream positions are used to generate radial probability density functions, p(r), and the trajectories are used to determine the particle velocity. the results for the pdfs are shown in fig.3. particles with d/d = 20 accumulate, as expected, in a stable annulus at approximately 0.8r from the centre of the pipe for reb = 350 the ‘segré-silberberg’ annulus. for higher reynolds numbers, particles accumulated preferentially at two radial locations: 0.8r and 0.6r from the pipe centre. the latter is referred to as the ‘inner annulus’. from 300d to 500d downstream, the percentage of particles in this inner annulus decreases, as more and more particle migrate to the equilibrium position. the migration of particles to the equilibrium location slows down with increase in reynolds number; the lowest reb case (blue curve) is closest to the equilibrium, while the highest case would require an even longer pipe to fully reach this equilibrium. fig.3 also confirms that the equilibrium position shifts outward with increasing reb (asmolov, 1999). this will be discussed in detail later. figure 3: probability density function p(r) for particles with d/d = 20. (left) at 300d from the entrance. (right) 500d from the entrance. the color represents pdfs for different reynolds numbers with reb = 350(blue), reb = 500 (green), reb = 800 (red), reb = 1000 (magenta), reb = 1250 (black). 0 0.2 0.4 0.6 0.8 1 r/r 0 2 4 6 8 p (r ) d/d = 9, l/d = 300 0 0.2 0.4 0.6 0.8 1 r/r 0 2 4 6 8 p (r ) d/d = 9, l/d = 500 figure 4: probability density function p(r) for particles with d/d = 9. (left) at 300d from the entrance. (right) 500d from the entrance. (color: fig 3). the situation is different for the larger particles (d/d = 6, 9), where the preferential location appears to depend on the reynolds number. the particles preferentially appear in the inner annulus at higher reynolds numbers: at the lowest reynolds number measured (reb = 350), they accumulate at 0.8r. for higher reynolds numbers(reb > 700), they accumulate at 0.6r (fig. 4). the pdfs for particles with d/d = 9 shows a gradual decrease in the accumulation of particles towards the centre as reb increases and distributes around one peak. the particles with d/d = 6 show a similar behaviour but accumulate at two preferred locations. the peak positions for different particles at different reb is shown in figure 5, along with data from literature. figure 5: preferential radial locations of particle accumulation as a function of reynolds number (reb). from the reconstructed trajectories, the streamwise velocity of particles match the local fluid velocity with 2% error margin, rising upto 5 % near wall. particles at reb = 350 are observed to travel mostly parallel to the pipe centreline, with a few particles migrating slowly in the radial direction. at higher reynolds numbers, particles with d/d = 6 and 9 are found to be moving in the azimuthal direction, in addition to radial migration. these motions are observed at 0.55-0.85r from the tube axis, where the azimuthal velocity is higher for particles away from the axis. statistically, there is no preferred azimuthal direction (clockwise vs. anticlockwise). the azimuthal velocity increases with the reynolds number and the particle size, with a magnitude less than 5% of its streamwise velocity (uθ,p/uz,p <0.05). at reb = 1250, most particles (85 %) with d/d = 9 are observed to move azimuthally 300d away from the entrance (fig. 6). the maximum observed magnitude of the azimuthal velocity of particles is 0.7 mm/s. at this reynolds number, particles with d/d = 6 (fig 7) have a maximum azimuthal velocity of 3 mm/s, where they are observed to move over 270◦ in 40d (i.e. throughout the full field of view). visual inspection confirms that azimuthal motion persists over the entire length of the pipe. this azimuthal (or spiralling) behaviour has been observed before (shao et al., 2008), but little is known about the physical mechanisms behind it. figure 6: azimuthal velocity of particles with d/d = 9 (uθ) as a function of their radial locations. reb = 500, 750, 1000, 1250; rep = 6.2, 8.6, 12.3, 15.4 (left-right). figure 7: cross-stream migration observed for particles with d/d = 6 for different reynolds numbers (in columns). the top row shows the normalized radial probability density functions, p(r). the bottom row shows the azimuthal velocity (uθ) of particles along the radial location of the particles. rep = 12.5,19.4, 23.6, and 29.1(left to right). 4 conclusion and outlook suspended particles are tracked along several diameters (up to 45d) in three dimensions to study their migration. the reconstruction of 3d trajectories over a narrow and long field of view is demonstrated. the mirror optics contributes to an addition linear mismatch which can be corrected given the angle of view is small (<15◦). 310 0.5 315 0.5 320 l /d 325 y 0 x 330 0 -0.5 -0.5 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 u /u c 310 0.5 320 330 0.5 l /d 340 y 350 0 x 360 0 -0.5 -0.5 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 u /u c figure 8: particle trajectories reconstructed in three-dimensional space at reb = 600. the flow direction is from bottom to top. the colormap denotes the azimuthal velocity (uθ) of the particle normalized with the centreline velocity (uc). the circle indicates the flow domain and the gray line represents the projection of tracks in the (x− y) plane. the pdfs of radial location constructed are consistent with the literature (matas et al. (2004); nakayama et al. (2019); morita et al. (2017)). the radial displacements are very low, typically under 10 pixels over 20d. for the particles with d/d = 20, the percentage of particles in the inner annulus decrease downstream. this suggests that the particles would eventually reach the stabe annulus around 0.8r. large neutrally buoyant particles (d/d = 6 and 9) migrate radially to a stable annulus as expected (either the inner or outer, depending on the reynolds number). however, they also move along the azimuthal direction, in contrast to particles of d/d = 20. the azimuthal velocity of the particles increases with the bulk reynolds number and the particle size. further, there are also few particles moving inward towards the tube at 300d downstream but the percentage decreases downstream. such consistent motion of particles show migration patterns that do not agree with theoretical understanding asmolov (1999). the particle reynolds number is more than 8 (rep > 8) for azimuthally moving particles. although there is no experimental evidence in the literature, there are two numerical studies (shao et al., 2008; yu et al., 2013) that hint at secondary flow patterns. they postulate that the large size of particles leads to azimuthal motion. note that our results are still not consistent with their work, but the migration patterns at higher rep does indicate flow reversal around a large particle. the observation of the azimuthal motion that we report is a result of the fact that we document 3d particles tracks with high fidelity. previous studies generall relied on planar concentration information (matas et al. (2004), morita et al. (2017)). in ongoing studies, we are investigating the physical background of the peculiar azimuthal motion. references asmolov es (1999) the inertial lift on a spherical particle in a plane poiseuille flow at large channel reynolds number. journal of fluid mechanics 381:63–87 hood k, lee s, and roper m (2015) inertial migration of a rigid sphere in three-dimensional poiseuille flow. journal of fluid mechanics 765:452–479 matas jp, morris jf, and guazzelli é (2004) inertial migration of rigid spherical particles in poiseuille flow. journal of fluid mechanics 515:171–195 morita y, itano t, and sugihara-seki m (2017) equilibrium radial positions of neutrally buoyant spherical particles over the circular cross-section in poiseuille flow. journal of fluid mechanics 813:750 nakayama s, yamashita h, yabu t, itano t, and sugihara-seki m (2019) three regimes of inertial focusing for spherical particles suspended in circular tube flows. journal of fluid mechanics 871:952–969 shao x, yu z, and sun b (2008) inertial migration of spherical particles in circular poiseuille flow at moderately high reynolds numbers. physics of fluids 20:103307 yu z, wu t, shao x, and lin j (2013) numerical studies of the effects of large neutrally buoyant particles on the flow instability and transition to turbulence in pipe flow. physics of fluids 25:043305 introduction experimental setup results conclusion and outlook 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 measurements of intracrater flow dynamics utilizing a mound-bearing crater in a refractive index matched environment d. g. gundersen1, k. t. christensen1,2, g. blois1 1 university of notre dame, department of aerospace and mechanical engineering, notre dame, usa 2 illinois institute of technology, depts. of mechanical, materials & aerospace engineering and civil, architectural & environmental engineering, chicago, usa 1 introduction the processes controlling crater mound formation are the subject of ongoing research (bennett and bell iii, 2016). several theories exist on the formation of a central mound, with those pointing to wind processes as the predominant driving mechanisms being among the most compelling (kite et al., 2013; day et al., 2016; anderson and day, 2017). few experimental studies have been conducted to uncover impact crater driven flow dynamics. as such, direct and experimental flow measurements that could be used to validate previously developed fluid-topography interaction theories are not yet available. the objective of this study is to elucidate the intraand extra-crater circulation induced by unidirectional winds using experimentation on scaled models coupled with high spatial and temporal resolution flow measurements. 2 experiments piv measurements were performed on both an idealized crater shape and a model sourced from a digital elevation map (dem) of gale crater. laboratory experiments were performed on these physical models in the refractive index-matched (rim) flow facility at notre dame leveraging an aqueous solution of sodium iodide (nai) as the working fluid and cast acrylic crater models. the rim technique renders the solid model effectively invisible and thus allows unobstructed and unaberrated optical access to all regions of the flow produced by the crater. slight optical mismatches between the solid and fluid ris were minimized by fine tuning the fluid temperature. the models included both a synthetic crater shape based upon a mathematical model that served as a proxy of real craters, and a digital elevation map (dem) of gale crater, sourced from the hrsc experiment on mars express (jaumann et al., 2007). a low-pass filter was applied to the dem and the vertical scale was exaggerated by a factor of three in order to adhere to constraints of the facility. planar particle image velocimetry (piv) measurements were performed at two streamwise–wall-normal (x− y) plane positions and three wall-parallel (x− z) planes. measurements were also performed at four freestream velocities for each measurement plane to examine potential reynolds number effects, yielding a total of 20 independent datasets. 3 results statistical analysis was performed in order to reconstruct the spatial behavior of the underlying turbulence. here, an example of results is included in order to provide an overview of the measurements obtained in this study. figure 1 presents contours of the streamwise and wall-normal reynolds normal stresses, normalized by the square of the freestream velocity u∞, in both of the streamwise–wall-normal measurement planes. the measurement plane corresponding to fig. 1(a,c) is positioned at the spanwise plane of symmetry, while in fig. 1(b,d) the measurement plane is offset in the spanwise direction by 1.3h, where h is the crater rim height. the contrast between the flow maps of the turbulent stresses in the two different planes provides a qualitative measure of the three-dimensionality of the flow. a shear layer forms at the upstream rim of the crater and undergoes a series of shear–obstacle interactions. in the centerline plane (fig. 1(a,c,e)) the shear layer interacts with the mound, forming a merged shear layer that then impinges into the interior of the downstream rim. vertical profiles of turbulent stresses in the crater wake show imprints from the upstream shear layer dynamics, as they contain two maxima in turbulent figure 1: contours of normalized (a,b) streamwise turbulence stress, 〈u′u′〉, (c,d) wall-normal turbulence stress, 〈v′v′〉, and (e,f) turbulence shear stress, 〈−u′v′〉, in the wall-normal centerline plane (left) and the spanwise offset wall-normal plane (right). stresses. measurements show regions of elevated turbulence in the intracrater space below the rim, particularly for the offset plane (fig. 1b,d,f). the shear layers, populated by energetic coherent structures, are presumably linked to elevated transport of sediment and could account for some of the erosion/deposition processes hypothesized by previous studies. experiments on the gale crater model highlight similar areas of elevated turbulent stresses. these measurements could be used to support observational studies based on the interpretation of surface features in areas targeted by current missions. details of this study, published in gundersen et al. (2021), will be provided in the presentation. 4 conclusions the results presented herein demonstrate the effectiveness of the rim technique to image the flow within complex topographies, as well as some of its limitations. the measurements near the surface and within the intracrater space would not have been possible without utilizing a rim approach. experiments were performed on a gale crater model in addition to the idealized crater model. the results for the gale crater model shows flow features similar to the results on the idealized model. this gives evidence that the idealized geometry can be used as an analogue to geometries based on real impact craters. references anderson w and day m (2017) turbulent flow over craters on mars: vorticity dynamics reveal aeolian excavation mechanism. phys rev e 96:76–128 bennett ka and bell iii jf (2016) a global survey of martian central mounds: central mounds as remnants of previously more extensive large-scale sedimentary deposits. icarus 264:331–341 day m, anderson w, kocurek g, and mohrig d (2016) carving intracrater layered deposits with wind on mars. geophys res lett 43:2473–2479 gundersen d, blois g, and christensen kt (2021) flow past mound-bearing impact craters: an experimental study. fluids 6:216 jaumann r, neukum g, behnke t, duxbury tc, eichentopf k, flohrer j, gasselt s, giese b, gwinner k, hauber e et al. (2007) the high-resolution stereo camera (hrsc) experiment on mars express: instrument aspects and experiment conduct from interplanetary cruise through the nominal mission. planet space sci 55:928–952 kite es, lewis kw, lamb mp, newman ce, and richardson mi (2013) growth and form of the mound in gale crater, mars: slope wind enhanced erosion and transport. geology 41:543–546 introduction experiments results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 reynolds stress tensor and pressure-related turbulence transport terms measured by time-resolved tomographic-piv j.r. moreto1, x. liu1∗ 1 san diego state university, department of aerospace engineering, san diego, california, usa ∗ xiaofeng.liu@sdsu.edu abstract turbulence is inherently a three-dimensional and time dependent flow phenomenon (pope, 2001). because of the ubiquitous existence of turbulent flows in nature, accurate characterization of turbulent flows, either through experimental measurements or through direct numerical simulations, is of paramount importance for modeling turbulence (liu and katz, 2018). since its inception in 1984 (adrian, 1984), particle image velocimetry (piv), among several other conventional techniques used for turbulence measurements, has been a valuable tool for providing reliable experimental data for turbulence research. several advancements in hardware such as high-speed cameras, together with innovative algorithms and procedures, have extended the scope of piv to a variety of applications. westerweel et al. (2013) point out in a recent review article that one of the main advantages of the piv measurement is its unique ability in measuring quantitatively spatial derivatives of the flow field. with the development of tomographic piv introduced by elsinga et al. (2006), it is now possible to measure simultaneously the distributions of three velocity components in a threedimensional flow field, thus enabling us to measure all the velocity derivatives of a turbulent flow. however, for a thorough characterization of a turbulent flow, in addition to the velocity gradients, the instantaneous pressure distribution in the 3d flow field also needs to be measured. the instantaneous pressure distribution in a turbulent flow field can be measured non-intrusively by integrating the measured material acceleration using particle image velocimetry (piv), as demonstrated by liu and katz (2006, 2008, 2013), joshi et al. (2014), van oudheusden (2008) and ragni et al. (2009), to name a few. the pressure can also be obtained by solving the poisson equation, as shown in violato et al. (2011), and de kat and van oudheusden (2012). review and comparison of the two pressure reconstruction approaches can be found in charonko et al. (2010) and van oudheusden (2013). liu and moreto (2020) demonstrate the robustness and low noise sensitivity of the rotating parallel ray omnidirectional integration method, which is capable of measuring the instantaneous pressure distributions at high accuracy in a complex turbulent flow field. coupled with the time-resolved tomographic piv, the pressure reconstruction method enables the experimental characterization of all the terms including the pressure-related turbulence transport terms in the reynolds stress transport equation. liu and katz (2018) applied planar piv in conjunction with the virtual boundary omni-directional integration to the study of a shear layer flow impinging on a cavity trailing corner at a reynolds number of 4×104. they found that the distribution patterns of the pressure diffusion and the turbulence diffusion differ considerably, indicating that the conventional modeling for the transport terms is not adequate, at least for the turbulent shear layer flow over a cavity. their results also show that the turbulence fluctuation energy is redistributed from the streamwise component to the lateral ones, and this intercomponent energy transfer has an important impact on the flow dynamics around the cavity trailing corner area. however, due to the limitation in planar piv, they can only infer indirectly the spanwise intercomponent turbulence energy transfer based on the measured streamwise and wall normal components of the pressure-rate-of strain terms. in this paper, we will demonstrate the capability of measuring simultaneously all the reynolds stress tensor components and the instantaneous three dimensional distribution of pressure for a cavity flow at a reynolds number of 4×104 by time-resolved tomographic piv. the free stream velocity is set to 1.2 m/s, which is identical to the hopkins experiment (liu and katz, 2013, 2018). the 2d cavity geometry is 38.1 mm long, 101.6 mm wide and 30.0 mm deep, with the beginning part of the upstream ramp machined with tripping grooves. except the width, the geometry of cavity is also identical to that of the hopkins cavity setup, thus facilitating comparison and validation of the new tomo-piv measurement results. preliminary results on the reynolds normal stress measurement around the cavity trailing corner based on a limited sample of 149 instantaneous realizations (thus not converged yet) are shown in figure 1. time-averaged pressure distribution around the cavity trailing corner based on 4076 realizations (also not converged yet) is shown in figure 2. the selected image acquisition rate (4996hz) is sufficient to resolve the kolmogorov time scale based on a curve fit to the spatial energy spectra (liu and katz, 2013, 2018), according to which, the kolmogorov length scale is 26 µm and the taylor transverse microscale is 0.5 mm. the size of the tomo-piv measurement volume in the current study is approximately 42.6 × 11.7 × 6.9 mm3 to maintain sufficient resolution. in the current experiment, an interrogation volume of 40 pixel × 40 pixel × 40 pixel, which corresponds to 0.84 mm × 0.84 mm × 0.84 mm in physical dimension, is compatible with the taylor transverse microscale, but one order of magnitude larger than the kolmogorov length scale. a 75% overlap between the interrogation windows gives a vector spacing of 0.21 mm. in this paper, based on 140,000 instantaneous 3d realizations of the cavity flow, we will present converged turbulence statistics on all terms in the reynolds stress transport equation, with an emphasis on the characterization of the magnitude of the intercomponent turbulence energy fluctuations represented by the pressure-rate-of strain terms, so as to verify the conjecture raised in liu and katz (2018) about the magnitude of the third component of the intercomponent energy transfer. figure 1: normal reynolds stress profiles based on 149 realizations of tomo-piv measurement over a cavity trailing corner at a reynolds number of 4×104 (a) u′u′, (b) v′v′, (c) w′w′ distributions, which consist of, (i) 3d distributions, and (ii) planar contours at three selected spanwise planes that are located at the center of the measurement volume, and at the places close to the two edges of measurement volume in the spanwise direction, respectively. acknowledgements this work has been sponsored by the office of naval research grant no. n00014-20-1-2276 (dr. ki-han kim is the program officer). optics on loan from the naval surface warfare center carderock division is gratefully acknowledged. figure 2: time-averaged pressure distribution around the cavity trailing corner based on 4076 realizations. references adrian rj (1984) scattering particle characteristics and their effect on pulsed laser measurements of fluid flow: speckle velocimetry vs particle image velocimetry. applied optics 23:1690–1691 charonko jj, king cv, smith bl, and vlachos pp (2010) assessment of pressure field calculations from particle image velocimetry measurements. measurement science and technology 21:105401 de kat r and van oudheusden b (2012) instantaneous planar pressure determination from piv in turbulent flow. experiments in fluids 52:1089–1106 elsinga ge, scarano f, wieneke b, and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 joshi p, liu x, and katz j (2014) effect of mean and fluctuating pressure gradients on boundary layer turbulence. journal of fluid mechanics 748:36–84 liu x and katz j (2006) instantaneous pressure and material acceleration measurements using a fourexposure piv system. experiments in fluids 41:227–240 liu x and katz j (2008) cavitation phenomena occurring due to interaction of shear layer vortices with the trailing corner of a two-dimensional open cavity. physics of fluids 20:041702 liu x and katz j (2013) vortex-corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field. journal of fluid mechanics 728:417–457 liu x and katz j (2018) pressure–rate-of-strain, pressure diffusion, and velocity–pressure-gradient tensor measurements in a cavity flow. aiaa journal 56:3897–3914 liu x and moreto jr (2020) error propagation from the piv-based pressure gradient to the integrated pressure by the omnidirectional integration method. measurement science and technology 31:055301 pope sb (2001) turbulent flows ragni d, ashok a, van oudheusden b, and scarano f (2009) surface pressure and aerodynamic loads determination of a transonic airfoil based on particle image velocimetry. measurement science and technology 20:074005 van oudheusden b (2008) principles and application of velocimetry-based planar pressure imaging in compressible flows with shocks. experiments in fluids 45:657–674 van oudheusden b (2013) piv-based pressure measurement. measurement science and technology 24:032001 violato d, moore p, and scarano f (2011) lagrangian and eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic piv. experiments in fluids 50:1057–1070 westerweel j, elsinga ge, and adrian rj (2013) particle image velocimetry for complex and turbulent flows. annual review of fluid mechanics 45:409–436 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 phase separation and flow measurement of dilute bubbly jet with 2-d piv and lif hyunduk seo1, kyung chun kim1∗ 1 pusan national university, school of mechanical engineering, busan, south korea ∗ kckim@pusan.ac.kr abstract a measurement technique with a combination of piv and lif is suggested to measure gas-phase and liquidphase separately to resolve flow structures of a bubbly jet. in the bubbly jet, distribution of the bubble population shows a gaussian-like function but translated outward. spreading nature of each phase does not correspond to each other due to lack of the number of bubbles to be redistributed. 1 introduction investigations on the bubbly jet and plume have been conducted with several techniques. among those techniques, adv and ldv can provide 3-component velocity information, but there is a disadvantage of disturbing the flow or complex tuning for the gas phase. shadowgraphy, which is a kind of optical techniques, has been widely used to analyze bubbles, but it cannot resolve the specific structure inside the bubbly flow due to overlapped bubbles in an imaging plane. in this study, we investigate bubbly jet with 2-d piv and lif techniques, which can analyze the structure of bubbly jet inside the core region of the bubbly jet with a low void fraction (dulin et al., 2012). 2 method figure 1: schematic of experimental setup for (a) piv (b) lif the schematic of the experimental setup is shown in fig. 1. gas phase information was calculated from highlighted bubble edge. the air-water mixture was injected into a 1 m3 cubic tank from the outlet of 20 mm. diameter of bubbles was around 1.7 mm. 3 result radial profiles of the axial velocity mostly show good agreement with gaussian-like distribution (fig. 2 (a)). fig. 2 (b) shows the evolution of the centerline velocity of the bubbly jet along streamwise direction. the figure shows an acceleration of the bubbly jet and a potential core collapse in the early stage of the flow. higher void fraction results in much intense acceleration and earlier collapse of the potential core. it implies that buoyancy of bubbles results in the acceleration of the bubbly jet (morton and middleton, 1973). figure 2: axial mean velocity profiles (a) radial distributions of velocities (b) centerline velocity with height in fig.3, the population of bubbles is concentrated next to the centerline of the bubbly jet in a form of translated gaussian function. position of the center of each gaussian function spreads out as the bubbly jet flows. it does not significantly spread out in the far-field. it contrasts to the spreading of the liquid phase structures with linear self-similarity respect to the height. figure 3: radial population of bubbles with height 4 conclusions each phase in bubbly jet is successfully measured by the combination of piv and lif. the bubbly jet looks like an annular truncated cone shape due to different spreading nature of each phase. it is attributed to the low void fraction condition where the redistribution of bubbles does not sufficiently occur. acknowledgements this work was supported by the national research foundation of korea (nrf) grant, which is funded by the korean government (msit) (no. 2021r1a2c2012469, nrf-2018-global ph.d. fellowship program). references dulin vm, markovich dm, and pervunin ks (2012) the optical principles of pfbi approach. aip conference proceedings 1428:217–224 morton br and middleton j (1973) scale diagrams for forced plumes. journal of fluid mechanics 58:165– 176 introduction method result conclusions separation control of naca0015 airfoil using plasma actuators akira aiura*, kentaro kobayashi, jun sakakibara department of mechanical engineering, meiji university higashimita 1-1-1, tamaku, kawasaki, 214-8571, japan abstract separation control of naca0015 airfoil using plasma actuators was investigated. plasma actuators in spanwise array, which consists of 21 electrodes, were located at the leading edge of the airfoil to give temporal periodic disturbances with phase variations into its boundary layer. the cord length of the airfoil was c = 100mm and corresponding reynolds number was fixed at re = 63,000. non-dimensional frequency of the disturbance was chosen at f+ = 0.5 or 6. the gap between adjacent electrode was set as 1mm, and phase difference of the temporal periodic disturbances between adjacent electrode was set at φ = 0 or π. velocity field was measured by conventional two-component piv using a ccd camera (imperx, b1922, 1920 x 1460pixels) and nd-yag laser (quantel, evergreen, 140mj/pulse). both large field of view (fov) images capturing whole wing with surrounding flow and smaller fov images focused on the separation bubble near leading edge were evaluated. surface pressure was monitored by pressure transducers through pressure taps on the upper surface of airfoil. lift and drag against the airfoil were measured using a twocomponent force balance. figure 1 shows a lift coefficient profile of airfoil against angles of attack α. before a stall angle found at α = 11.25 degrees, improvements of lift coefficients are confirmed in a range from α = 9 to 11degrees under conditions of pa-on compared to that of pa-off. besides, lift coefficients under the conditions of f+ = 6 are greater than that of f+ = 0.5. among conditions of f+ = 6, the φ = π case provide the higher lift compared to the φ = 0 case by approximately 1.4% at α = 11 degrees. figure 2 shows a pressure profile on the surface of airfoil at α = 11 degrees. in addition to experimental values measured by the transducer shown by red markers, values estimated from large fov’s piv data are shown by blue lines. here, the pressure gradient directly computed from the measured velocity field based on mean momentum equation was spatially integrated from a point where the pressure was prescribed through a spatial marching procedure. pressures near leading edge are clearly different between cases, while not much difference is found downstream. maximum negative pressure values measured by the transducer is found under a pa-off case at x = -0.07c, which was the most upstream location of the pressure tap available to place. however, such a predominance of the pa-off case is not maintained towards leading edge, i.e. the negative pressure value under the φ = π case exceeds others in a range from x = -0.1c to -0.2c, as indicated by piv based pressure. figure 3 shows mean velocity distributions evaluated from the smaller fov images. separation bubbles are confirmed on conditions of pa-off and f+ = 6. comparing a condition of pa-off and conditions of f+ = 6, the separation bubbles at f+ = 6 cases are smaller than at a pa-off case. this might contribute to the increases of the lift coefficients, and it may be clarified through a pressure field estimated by piv data based on the smaller fov images. figure 4 shows surfaces of constant vorticity magnitude extracted from a stack of phaseaveraged planer velocity field at α = 11 degrees. while quasi-spanwise-oriented roller vortices are formed in a φ = 0 case, vortices arranged in a staggered manner are formed in a φ = π case. here, the layer of the vortices consists of series of lambda vortices, where the heads of each vortex are tilted away from the surface due to self-induction. fig. 1 a lift coefficient profile of airfoil against angles of attack. fig. 2 a pressure profile on the surface of airfoil at α = 11degrees. (a) pa off (b) f+ = 6, φ = 0 (c) f+ = 6, φ = π fig. 3 mean velocity distributions near leading edge at α = 11degrees. (a) f+ = 6, φ = 0 (b) f+ = 6, φ = π fig. 4 surface of constant vorticity magnitude / 12qc u = at α = 11degrees. references [1] sekimoto s., nonomura t., fujii k., 2017, burst-mode frequency effects of dielectric barrier discharge plasma actuator for separation control, j. aiaa, 55, pp.1385-1392. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 piv measurement of a jet from a gasper in an aircraft cabin mockup j. h. a. gouveia1∗, j. i. yanagihara1 1 university of são paulo, department of mechanical engineering, polytechnic school, são paulo, brazil ∗ jhagouveia@usp.br abstract the air conditioning system of most commercial aircrafts consists of a main system, which operates on the principle of mix ventilation, and a personalized system called gasper. field studies show that passengers prefer to keep gasper parcially open or redirect it away from the head due to the discomfort. therefore, there is a demand to characterize the flow of this device for future improvements. in this way, the present work aims to experimentally study the gasper jet inside a real cabin mockup using piv. the results indicate that passengers are subjected to a high speed jet and the air in their breathing zone is mostly supplied by the mixed ventilation system due to the large entrainment ratio. 1 introduction a way to improve air quality inside aircrafts cabins is through personalized ventilation and the typical system included in commercial aircrafts is the gasper, a small adjustable vent positioned above passengers’ head that provides an air jet directly to passengers’ breath region (li et al. (2018)). in previous studies focused on the gasper airflow, particle image velocimetry (piv) was used in mockups that did not faithfully represents the complex geometry of a real cabin. therefore, the present work is focused on the piv measurement of the gasper airflow under the influence of a mixing ventilation system to evaluate jet features as velocity decay and entrainment ratio. also, through measurement of multiple planes, a 3d airflow distribution of the gasper jet was obtained. these results allow a proper understanding of the gasper jet behavior and an assessment of its efficiency as a tool to increases passengers’ comfort and safety. 2 materials and methods a piv system was used to measure the gasper jet velocity field. this system consists of a 200 mj laser sheet with a thickness of 2 mm. and a wavelength of 532 nm. provided by a double-cavity nd:yag laser with a frequency of 7.4 hz. the images were recorded using a dantec flowsense 4m mk ii camera with 2048 x 2048 pixels. three traverse were used to move the piv system. the laser, the camera and all traverse devices were mounted inside a fully functional mockup of an embraer e-170 airplane, placed inside a low-pressure chamber. in each run the cabin environmental conditions were kept constant: the temperature was 21°c, the air flow in the main ventilation system was 1,050 m3/h and the mean flow rate in the gasper was 1.7 m3/h (ashrae (2018)).the diethylhexyl sebacate (dehs) particles with a mean diameter of 2 µm. were seeded in the environment through the cabin main ventilation inlets. for each measurement plane, a thousand of double-frame images from an area of 243.2 x 243.3 mm. was recorded. due to the cabin material and geometry, laser reflections caused a background noise in images; therefore, the first image preprocessing step was the subtraction of a mean image from each image. besides that, a 3 x 3 gaussian filter and in sequence a 3 x 3 laplacian filter was applied to reduce noise and increase the correlation peak (raffel et al. (2018)). all piv analysis presented in this work was made by a crosscorrelation algorithm with deforming interrogation window and grid refining that yielded a spatial resolution of 1.9 mm. after vector validation through primary peak ratio (ppr) and universal outlier detection algorithm (uod) (westerweel and scarano (2005); hain and kähler (2007)). 3 results from the jet middle plane (fig. 1(a)) was possible observe that the gasper produces an annular jet where velocity increase until the reattachment point is reached and after that the velocity begins to decay in the fully developed zone. in this way, in fig. 1(b) is presented the fitting formula for centerline non-dimensional velocity in the fully developed zone. the curve behaves in a similar way as presented in dai et al. (2015) despite gasper’s different physical characteristics. through piv measurement of 20 planes separated by 2.5 mm. it was built a 3d representation of the gasper jet (fig. 1(c) and fig. 1(d)). considering that the cross-section has a circular shape, the local air flow rate was calculated from the integral of the velocity profile for each axial position. it was notorious the fast increase in flow rate inside the jet (fig. 1(e)), meaning that the air in the passenger breath region is essentially air from the cabin environment that merges into the jet. figure 1: results summary 4 conclusions although the gasper jet measured in the present work differs from previous studies in terms of its geometry and the cabin environmental conditions, the non-dimensional centerline velocity decay obtained in the present study was very similar to the previous results. also, it was demonstrated that due to its small outer diameter (d0 = 10.5 mm in the present work), the gasper can provide a jet with a high-velocity that can increase passengers’ draft sensation. for this reason, usually the passengers prefer to adjust the jet direction to their trunk or lower limbs instead of their heads. from piv data evaluation was also indicated that the gasper is not an ideal barrier for virus and bacteria due to its high entrainment ratio. references ashrae (2018) ansi/ashrae standard 161-2018: air quality within commercial aircraft. ashrae dai s, sun h, liu w, guo y, jiang n, and liu j (2015) experimental study on characteristics of the jet from an aircraft gasper. building and environment 93:278–284 hain r and kähler j c (2007) fundamentals of multiframe particle image velocimetry (piv). experiments in fluids 42:575–587 li j, liu j, dai s, guo y, jiang n, and yang w (2018) piv experimental research on gasper jets interacting with the main ventilation in an aircrat cabin. building and environment 138:149–159 raffel m, willert c, wereley st, and kompennhans j (2018) particle image velocimetry: a practical guide. springer westerweel j and scarano f (2005) universal outlier detection for piv data. experiments in fluids 39:1096– 1100 introduction materials and methods results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 application of spod analysis to piv data obtained in the wake of a circular cylinder undergoing vortex induced vibrations christopher m. o’neill1, yannick schubert2, moritz sieber2, robert martinuzzi1, chris morton1∗ 1department of mechanical engineering, university of calgary, calgary, canada 2institut für strömungsmechanik und technische akustik, hermann-föttinger-institut, technische universität berlin, berlin, germany ∗ chris.morton@ucalgary.ca abstract vortex induced vibrations (viv) of a circular cylinder have been investigated experimentally using a cyberphysical apparatus with m∗ = 8, ζ = 0.005, and re = 4000. this study considers the application of proper orthogonal decomposition (pod) and spectral pod (spod) analysis to the wake dynamics of the low-massratio viv of a circular cylinder in the lower branch at u∗ = 7.5. spod has been previously shown to better separate frequency-centered modal dynamics, compared to pod. coherent pod and spod modes were compared and the newly separated third spod mode pair was found to have a periodicity characteristic of vortex shedding and a peak in the temporal coefficient spectra at st = f d/u∞ = 0.2248. the literature has identified that the wake dynamics within the lower branch are synchronized to the cylinder motion; however the present study suggests that some hidden dynamics persist at the strouhal frequency. low order models based on the first eight pod and spod modes were compared, and it was found that the filtering operation in spod removes the uncorrelated stochastic energy component of the pod modes while producing a comparable representation of the coherent deterministic part of the wake dynamics. using spod to separate the distinct frequency-centered dynamics into unique, interpretable mode pairs will simplify future efforts to develop sparse dynamical models of the flow. 1 introduction vortex-induced vibration of a circular cylinder is a fluid-structure interaction problem presenting engineering challenges to the design of civil structures (e.g., cable-tensioned bridges) as well as mechanical engineering devices (e.g., heat exchangers). comprehensive reviews of viv can be found in the works of sarpkaya (2004) and williamson and govardhan (2004). an elastically mounted cylinder in cross-flow is susceptible to vortex induced vibrations when the vortex shedding frequency is near the natural frequency of the system. the resonance of the structure and the associated ’lock-in’ phenomenon occur when the vortex shedding frequency is synchronized to the vortex induced oscillations of the body. the structural dynamics of the cylinder motion are given by: mÿ+ cẏ+ ky = fy (1) where m,c,k are the structural mass, damping, and spring constant respectively. fy is the transverse component of the fluid force on the cylinder. the natural frequency of the system is defined as fn = √ k/m. the following section discusses the contributions of the cylinder wake dynamics to the amplitude and frequency response of the system, and approaches in modeling of this fluid-structure interaction. 1.1 cylinder viv wake modes, amplitude and frequency response the viv amplitude response (a∗ = a/d, where d is the cylinder diameter) for a low mass-damping system (m∗ζ < 0.1, m∗ = 4m/ρπd2l, ζ = c/2 √ km) across a range of reduced velocities (u∗ = u∞/ fnd) is characterized by an initial branch, upper branch, lower branch, and a desynchronization region (khalak and williamson, 1997). the topology of the wake for a given reduced velocity and response amplitude has been characterized in controlled motion experiments and was classified into vortex shedding modes using phaseaveraging as described by morse and williamson (2009). the transitions between branches are somewhat sensitive to m∗ζ; for consistency with the literature, the following description of the amplitude response follows khalak and williamson (1997). a description of the amplitude response associated with the m∗ζ of the apparatus used in this study can be found in riches and morton (2018). in the initial branch (2 . u∗ . 4.75), with increasing u∗ the frequency of vortex shedding approaches the natural frequency of the system causing an increase in the oscillation amplitude. the vortex shedding frequency and the natural frequency are both present within the cylinder position spectrum. following the nomenclature of morse and williamson (2009), this branch is characterized by 2s-type vortex shedding in which single counter-rotating vortices are shed alternately from the cylinder sides. when the reduced velocity is increased further above u∗ ≈ 4.75, the amplitude response of the cylinder transitions to the upper branch, where the vortex shedding frequency becomes synchronized with the natural frequency of the system and structural resonance occurs leading to large oscillations. the wake topology in the upper branch is characterized by 2po-type vortex shedding, which consists of pairs of counter-rotating vortices. these pairs are shed alternately from the cylinder sides with the trailing vortex being significantly weaker than the leading vortex (morse and williamson, 2009). the lower branch occurs for 6.u∗. 9.5, and is characterized by a slightly-lower steady state amplitude response compared to the upper branch. the wake topology in the lower branch is characterized by 2ptype vortex shedding, where pairs of equally strong counter-rotating vortices shed from alternating sides of the cylinder. while oscillation and shedding remain synchronized, the peak in the cylinder oscillation spectra shifts to be slightly higher than the natural frequency. this synchronization of the natural and oscillation frequencies is known as ‘lock-in’. according to sarpkaya (2004), lock-in occurs when the motion of the cylinder becomes a dominant factor in the interaction of the separated shear layers that causes vortex shedding in the wake. the focus of this paper will be further analysis of the wake topology at u∗ = 7.5 in the lower branch. for reduced velocities above u∗ ≈ 9.5, the vortex shedding frequency is no longer synchronized with the natural frequency, and the amplitude response of the system decays. in the cylinder position spectra, the vortex shedding frequency and the natural frequency re-emerge as separate frequencies. 1.2 further analysis of cylinder viv and low order modeling beyond the phase-average based characterization of the topology of the wake by morse and williamson (2009), viv has been studied using several techniques including proper orthogonal decomposition (pod) riches et al. (2018), dynamic mode decomposition (dmd) freire et al. (2015), and deep learning raissi et al. (2019), based on time-resolved particle image velocimetry (piv) data. in addition to characterizing the flow topology, there is an interest in using these methods to develop physics-based models of the flow state. pod has been used to develop low order models (lom) of the flow state, such as described in liberge and hamdouni (2010) where a 6-mode lom was found to accurately reconstruct the velocity field for a computational study of cylinder viv at re = 1690. riches et al. (2018) applied pod to cylinder viv in the initial (re = 3100) and upper (re = 4100) branches and found that 6and 7mode loms, respectively, represented the coherent part of the cylinder wake. riches et al. (2018) also investigated the analytical relationships between the pod modes in order to develop a model of the flow. as explored in riches et al. (2018), discerning which modes correspond to the coherent dynamics can be challenging. for example, a temporal gaussian filter was applied to data in a pre-processing step in order to separate low-frequency and high frequency dynamics which could not be identified using pod alone. spectral proper orthogonal decomposition (spod)(sieber et al., 2016) involves a more robust filtering process, and has shown promise in decoupling modal dynamics for bluff body wakes. spod recently was applied to the wake of a fx63137 airfoil with a gurney flap, at rec = 180× 103, and was found to produce a simpler wake model by decoupling the interaction of the upstream vortex from the primary vortex shedding (sieber et al., 2016). 1.3 objective the objective of this paper is to consider the application of spod to decomposition of the lower branch of viv, and illustrate the advantages spod compared to pod in extracting dynamically relevant modes. this paper will first examine the effect of the spod filter length on the high energy modes, followed by analyzing the cylinder wake. pod-based and spod-based lom will be constructed and compared to examine the benefits spod offers in terms of representing the flow state. 2 methods experiments were carried out in a water tunnel facility at the university of calgary. a cyber-physical apparatus was employed to study viv of a circular cylinder, as described in riches and morton (2018). following the works of hover et al. (1997), mackowski and williamson (2011), and derakhshandeh et al. (2015), the apparatus operates by real-time simulation of the differential equation of the cylinder’s motion, given in equation 1. the transverse component of the force on the cylinder (fy) is taken as the input, and the structural mass, damping, and spring constant are applied in software to compute the desired kinematics. the cylinder is then forced to follow the desired kinematics using a motorized traverse. the transverse force on the cylinder was measured using an ati mini40 force transducer with a resolution of 0.005 [n]. the traverse was driven using a clearpath digital brushless servo motor (mcvc-2341p) and the position was measured using an omron optical encoder with a position resolution of 0.0375 [mm]. the block diagram of equation 1 was used to compute the kinematics, and is shown below in figure 1b. figure 1: (a) experimental apparatus placed in a section of the university of calgary water channel, with piv imaging setup shown. (b) cyber-physical apparatus path generation algorithm and system controller. additional details on this system can be found in riches (2018). figure 1 is adapted from riches and morton (2018). the parameters investigated in this study correspond to m∗ = 8, ζ = 0.005, re = 4000, and u∗ = 7.5. the free-stream velocity was set to fix the re, while u∗ was set by altering the natural frequency of the system. the structural natural frequency of the system is defined in air. the natural frequency and damping ratio were confirmed based on the system accurately reproducing an oscillating free decay after release from an initial displacement, as shown in riches and morton (2018). good agreement was found between the amplitude and frequency response of the cyber-physical apparatus with data from govardhan and williamson (2006) and klamo et al. (2006), as discussed in riches and morton (2018). time-resolved two-component planar piv measurements were obtained for a plane located at the midspan of the cylinder, as shown in figure 1a. images were captured using a high speed phantom miro m340 digital camera focused on the mid-span plane illuminated by a laser sheet generated by a photonics 20mj nd:ylf high repetition rate pulsed laser with a wavelength of l = 527 [nm]. piv images were processed using lavision davis 8.3 software. a total of n = 4767 vector fields were obtained at a sample frequency of 24 hz, spanning approximately 290 oscillation periods of the cylinder. velocity vector uncertainties were calculated using the correlation statistics method of wieneke (2015), as employed within davis 8.3 and were an average of 2.2% in the free stream and 4.0% in the wake. 2.1 proper orthogonal decomposition the velocity field u(x, t) is split into mean ū(x) and fluctuating u′(x, t) components and then the fluctuating component is decomposed into a finite sum of spatial eigenfunctions φi(x) multiplied by a time-dependent temporal modal coefficients ai(t) following the snapshot pod method of sirovich (1987): u(x, t) = ū(x)+u′(x, t) = ū(x)+ n ∑ i=1 φi(x)ai(t) (2) to compute the correlation between snapshots, the l2 inner product is first defined using 〈,〉. applying the inner product to some arbitrary velocity fields p(x) and q(x) gives: 〈p(x),q(x)〉= ∫ ω p(x)q(x)dω (3) where ω defines the spatial volume where the correlation is integrated. if velocity fields p(x) and q(x) are orthonormal, then 〈p(x),q(x)〉= δi, j. using the inner product, the elements of the snapshot correlation matrix ri, j can be computed according to: ri, j = 1 n 〈u′(x, ti),u′(x, t j)〉 (4) the temporal coefficients ai(t) and mode energies λi are determined from the eigenvectors and eigenvalues of the correlation matrix: rai(t) = λiai(t) (5) the spatial modes φi(x) are computed from the projection of the snapshots onto the temporal coefficients: φi(x) = 1 nλi n ∑ j=1 ai(t j)u′(x, t j) (6) the spatial modes are orthonormal by construction and therefore they satisfy the condition: 〈φi(x),φ j(x)〉= δi, j (7) the process of decomposing the fluctuating field using pod produces orthogonal modes and coefficients such that a minimal number of modes contain the maximum amount of energy within the field; however, the modes may contain energy at multiple frequencies and therefore may not represent a specific dynamical structure in the wake. once a decomposition of the flow has been performed, a low-order model of the field u′lom(x, t) can be created using an expansion of the first nt pod modes associated with coherent dynamics in equation 2, thus yielding the coherent part of the fluctuating velocity field (rowley (2005); noack et al. (2011); bourgeois et al. (2013)). this low order model can be found according to: u′lom(x, t) = nt ∑ k=1 φi(x)ai(t), (8) 2.2 spectral proper orthogonal decomposition spectral pod, as described in sieber et al. (2016), is an alternative decomposition method to pod. beginning with the snapshot correlation matrix defined in equation 4, a low-pass filtering is performed along the diagonal to form a filtered correlation matrix, which has elements si, j given by: si, j = n f ∑ k=−n f gkri+k, j+k (9) where n f is the filter length, and gk is an entry of the 1-d filter kernel g of length 2n f +1. sieber et al. (2016) showed that in the case of a box-filter with equal coefficients given by gk = 1/(2n f +1), that with n f = 0, spod is equivalent to pod. further with n f = n, spod is equivalent to the discrete fourier transform (dft). after the filtering, remaining steps in the decomposition proceed as described above in pod, yielding a set of spatial modes and temporal coefficients. based on sieber et al. (2016), a gaussian filter kernel is used in the following results, due to preferable properties of smooth roll off, except for n f = 0 and n f = 4767, where a box filter was used to recover pod and the dft. mode pairing was performed as described in sieber et al. (2016), including identification of the primary frequency for the temporal coefficient of each mode pair. 3 results 3.1 spod filter length investigation of the dynamical features of the flow was first carried out using a pod-based approach similar to that of riches et al. (2018). this corresponds to a filter length of n f = 0 in equation 9. the choice of filter length 0 < n f < n represents the trade off between the spectrally agnostic pod and spectrally pure dft. in a practical sense, as the filter length is increased from zero (pod), the spectral bandwidth of the mode temporal coefficients is constrained. the resulting spatial modes are affected through the projection operation, and energy outside the mode spectral bandwidth is redistributed to other modes. the filter length parameter n f determines the number of 2d piv vector fields averaged by the filter and thus proper selection depends on both the sample rate and the frequency of the underlying dynamics. the filter length can be examined with reference to the number of 2d piv vector fields for one oscillation of the cylinder (nosc). the cylinder oscillation frequency fosc = 1.753 [hz] (st = foscd/u∞ = 0.15) was determined based on spectral analysis of the cylinder position signal, see figure 2. the number of vector fields capturing a given oscillation cycle is: nosc = fs fosc = 24 1.753 = 13.69≈ 14 (10) the effects of the filter length on the spatial modes and temporal coefficient spectra was examined over a wide range of n f . for brevity only n f = [0,4nosc,5nosc,n] are shown in figure 3. figure 3(i) shows the energy distribution of mode pairs (y-axis) and their associated frequencies (x-axis). the size and color of the markers represents the correlation between the modes in the mode pair; pairs with large yellow markers are well correlated. figure 3(ii,iv,vi,viii) shows the u-component of the first four most energetic pod spatial mode pairs, or the equivalent spod mode pair. figure 3(iii,v,vii,ix) shows the temporal coefficient psdf corresponding to the mode pairs in figure 3(ii,iv,vi,viii). the spatial mode in figure 3a(ii) shows a periodicity that is characteristic of vortex shedding, and the corresponding temporal coefficient spectrum for the pair shown in figure 3a(iii) has a peak at the st = f d/u∞ = 0.15, which corresponds to the oscillation frequency of the cylinder. additional energy content in this pair is spread across multiple frequencies, including a secondary peak at f d/u∞ ≈ 0.2. the structures in the spatial mode in figure 3a(iv) show half the spatial wavelength compared to figure 3a(ii) and the psdf of the temporal coefficient in figure 3a(v) shows a peak at st = f d/u∞ = 0.30; therefore, this mode pair corresponds to the second harmonic of the vortex shedding at the oscillation frequency. the second harmonic mode pair has energy content spread across multiple frequencies, including a secondary peak at f d/u∞ ≈ 0.2. the spatial modes in figure 3a(vi) and (viii) contain large scale features and the corresponding temporal coefficient spectrum contains a broad range of scales, including broad peaks at f d/u∞ ≈ 0.1 and f d/u∞ ≈ 0.2. as the filter length is increased in the range 0 ≤ n f ≤ 4767, the trend towards decreasing spectral bandwidth can be observed by comparing the temporal coefficient spectra in figures 3(iii,v,vii,ix). for example in figure 3b(v), most of the mode energy in the temporal coefficient spectra is contained in the range approximately 0.26≤ f d/u∞ ≤ 0.35. increasing the filter length from n f = 56 to n f = 70, in figure 3c(v) most of the energy is now contained within 0.28≤ f d/u∞ ≤ 0.33. thus as the filter length increases, the temporal coefficients for the first two mode pairs are constrained to progressively narrower frequency bands without significant energy loss as shown by comparison of figures 3(i). within the temporal coefficient spectra, the secondary peak observed in figure 3a(v) and 3a(vi) at f d/u∞ ≈ 0.2 is absent for n f > 56. the broad peak in figure 3a(ix) is significantly weakened for n f = 56 and almost absent for n f = 70, suggesting n f ≥ 70 is required to separate the third mode pair from the fourth mode pair. comparing figure 3a-c(vii), the peak at f d/u∞ ≈ 0.2 is well defined for n f ≥ 56. increasing the filter length above n f = 70 further constrained the frequency content of the third mode pair and progressively reduced the energy of the mode pair. the frequency bandwidth of the third mode pair is broader than the first two mode pairs, thus further constraining the bandwidth of this mode would only exclude relevant dynamics and their energy content. higher filter lengths such as n f = 112 offered no clear benefit in separating the dynamics associated with the fourth mode pair. thus n f = 70 was chosen based on the trade off between increasing energy losses of the third mode pair and frequency separation of the fourth mode pair. figure 2: power spectral density function (psdf) for the cylinder displacement signal. the dotted line is located at f = 1.753 hz, and corresponds to the cylinder oscillation frequency ( fosc). 3.2 analysis of wake dynamics for spod with n f = 70 following selection of an appropriate filter length (n f = 70) for separating the relevant dynamics, it is important to consider what new fundamental physical insights have been established. for this purpose, figure 4 shows a direct comparison of the spatial modes and temporal coefficient spectra between pod (a) and spod (b). from left to right, each row of figure 4 consists of the uand v-component of the spatial modes for the first and second modes in the pair, followed by the temporal coefficient spectra. as previously discussed, the mode pairs (1,2) and (3,4) in both pod and spod have spatial modes and temporal coefficient spectra characteristic of the oscillation frequency and its second harmonic, respectively. the pod mode pairs are contaminated with low and high frequency content, with multiple peaks visible in the spectra for all four mode pairs in figure 4a. moreover, the third and fourth mode pairs (5,6 and 7,8) are difficult to interpret and contains a mixture of low frequency content with broad local maxima located at f d/u∞ ≈ 0.1 and f d/u∞ ≈ 0.2. in contrast, the spod mode pair (5,6) has a spatial wavelength and mode shape typical of a vortex shedding phenomena, and a well defined peak in the frequency domain at st = f d/u∞ = 0.2248, which is close to the expected strouhal number of ∼ 0.21 for a stationary cylinder at re = 4000 (norberg, 2003). these results suggest that spod modes (5,6) represent a natural vortex shedding process which is not synchronized to the cylinder oscillation, and that this process may persist within the lower branch. the spod mode pair (7,8) has a longer spatial wavelength with a peak in the frequency domain at f d/u∞ = 0.0753, which corresponds closely to the beat frequency ( f d/u∞ = 0.2248−0.1508 = 0.074) between the cylinder oscillation represented in spod modes (1,2) and the natural vortex shedding represented in spod modes (5,6). 3.3 comparison of low order models for pod and spod a low order model of the flow field dynamics was constructed from the first four mode pairs for both pod and spod decompositions of the wake, as described by equation 8. figure 5 shows the reynolds stresses from the raw piv images, and compares the residuals of the two low order models. the reynolds stress residuals for the two loms are similar overall; however, the spod-based lom has slightly higher u′u′ and v′v′ residuals in the near wake (approximately −1.8 < y/d < 0.4 and x/d < 0.4), compared to the pod lom. based on the lower energy of the spod modes compared to the pod modes, it is expected that the residuals will be slightly higher in the frequency constrained spod lom, for the same number of modes reconstructed. figure 6 shows the vorticity contours of the two lom for two vector fields in a representative shedding cycle. the two lom show remarkably similar representations of the coherent dynamics in the flow. the spod lom thus offers an advantage compared to the pod lom because each of the four mode pairs in the spod lom is associated with a distinct frequency-centered dynamic. essentially, spod has properly separated these four dynamics and removed the uncorrelated stochastic contributions seen in the pod modes, leaving a deterministic coherent representation of the flow, which is desirable from the perspective of further modeling. 4 conclusions this study considers the application of spod analysis to the wake dynamics of the low-mass-ratio viv of a circular cylinder in the lower branch, at u∗= 7.5. the effect of the spod filter length on the coherent modes figure 3: comparison of spod filter lengths n f = [0,56,70,4767] in (a-d). subplots: (i) mode pair energy content as a function of the strouhal number. circle size and color represent the correlation of the temporal coefficients of the mode pair. (ii,iv,vi,viii) spatial modes (u-component) for the first 3 most energetic mode pairs from pod, and the same modes in spod. (iii,v,vii,ix) power spectrum density functions (psdf) of the temporal coefficients for the mode pairs in (ii,iv,vi,viii). the dotted lines at f d/u∞ = [0.15,0.3] correspond to the cylinder oscillation frequency and second harmonic. was examined, and a filter length of n f = 70 was chosen to properly separate the four distinct frequencycentered dynamics within the first eight modes, while retaining as much energy as possible. the coherent pod and spod modes were compared and the newly separated third spod mode pair was found to have a periodicity characteristic of vortex shedding and a peak in the temporal coefficient spectra at st = f d/u∞ = 0.2248. the fourth spod mode pair was found to correspond to the beat frequency between the first and third spod mode pairs. while the literature has identified that the wake dynamics within the lower branch are synchronized to the cylinder motion, the present study suggests that some hidden dynamics persist at the strouhal frequency that were revealed only through application of spod analysis. low order models based figure 4: spatial modes and temporal coefficient spectra for the first three coherent mode pairs identified using pod (a) and spod (b). the dashed lines in the spectra are located at f d/u∞ = 0.15,0.30 and correspond to the cylinder oscillation frequency and second harmonic, respectively. on the first eight pod and spod modes were compared, and it was found that the filtering operation in spod removes the uncorrelated stochastic energy contributions seen in the pod modes while producing a comparable representation of the coherent deterministic part of the wake dynamics. using spod to separate the distinct frequency-centered dynamics into unique, interpretable mode pairs will simplify future efforts to develop sparse dynamical models of the flow. figure 5: comparison of reynolds stresses for the two lom based on the pod and spod decompositions of the wake. raw data is shown in (a), and the residuals for the pod and spod lom are shown in (b). figure 6: vorticity contours for the raw piv velocity fields (left column) and 8-mode low order models (lom) for pod (n f = 0, center column) and spod (n f = 70, right column). the contours shown are taken from a representative shedding cycle, for brevity two vector fields are omitted between the shown contours. references bourgeois ja, noack br, and martinuzzi rj (2013) generalized phase average with applications to sensorbased flow estimation of the wall-mounted square cylinder wake. journal of fluid mechanics 736:316– 350 derakhshandeh j, arjomandi m, cazzolato b, and dally b (2015) harnessing hydro-kinetic energy from wake-induced vibration using virtual mass spring damper system. ocean engineering 108:115–128 freire cm, meneghini jr, gioria rs, and assi grs (2015) comparison between the koopman modes for the flow around circular cylinder and circular cylinder fitted with helical strakes. in instability and control of massively separated flows. pages 117–122 govardhan rn and williamson chk (2006) defining the ‘modified griffin plot’ in vortex-induced vibration: revealing the effect of reynolds number using controlled damping. journal of fluid mechanics 561:147 hover f, miller s, and triantafyllou m (1997) vortex-induced vibration of marine cables: experiments using force-feedback. journal of fluids and structures 11:307–326 khalak a and williamson c (1997) fluid forces and dynamics of a hydroelastic structure with very low mass and damping. journal of fluids and structures 11:973–982 klamo j, leonard a, and roshko a (2006) the effects of damping on the amplitude and frequency response of a freely vibrating cylinder in cross-flow. journal of fluids and structures 2:845 – 856. bluff body wakes and vortex-induced vibrations (bbviv-4) liberge e and hamdouni a (2010) reduced order modelling method via proper orthogonal decomposition (pod) for flow around an oscillating cylinder. journal of fluids and structures 26:292–311 mackowski aw and williamson ch (2011) developing a cyber-physical fluid dynamics facility for fluidstructure interaction studies. journal of fluids and structures 27:748–757 morse tl and williamson chk (2009) prediction of vortex-induced vibration response by employing controlled motion. journal of fluid mechanics 634:5 noack br, morzyński m, and tadmor g, editors (2011) reduced-order modelling for flow control. springer vienna norberg c (2003) fluctuating lift on a circular cylinder: review and new measurements. journal of fluids and structures 17:57–96 raissi m, wang z, triantafyllou ms, and karniadakis ge (2019) deep learning of vortex-induced vibrations. journal of fluid mechanics 861:119–137 riches g, martinuzzi r, and morton c (2018) proper orthogonal decomposition analysis of a circular cylinder undergoing vortex-induced vibrations. physics of fluids 30:105103 riches g and morton c (2018) one degree-of-freedom vortex-induced vibrations at constant reynolds number and mass-damping. experiments in fluids 59 riches gp (2018) experimental investigation of vortex-induced vibrations using a cyber-physical system. master’s thesis. university of calgary rowley cw (2005) model reduction for fluids, using balanced proper orthogonal decomposition. international journal of bifurcation and chaos 15:997–1013 sarpkaya t (2004) a critical review of the intrinsic nature of vortex-induced vibrations. journal of fluids and structures 19:389–447 sieber m, paschereit co, and oberleithner k (2016) spectral proper orthogonal decomposition. journal of fluid mechanics 792:798–828 sirovich l (1987) turbulence and the dynamics of coherent structures. i. coherent structures. quarterly of applied mathematics 45:561–571 wieneke b (2015) piv uncertainty quantification from correlation statistics. measurement science and technology 26:074002 williamson c and govardhan r (2004) vortex-induced vibrations. annual review of fluid mechanics 36:413–455 introduction cylinder viv wake modes, amplitude and frequency response further analysis of cylinder viv and low order modeling objective methods proper orthogonal decomposition spectral proper orthogonal decomposition results spod filter length analysis of wake dynamics for spod with nf=70 comparison of low order models for pod and spod conclusions 14th international symposium on particle image velocimetry – ispiv 2021 chicago, il usa, august 1-4, 2021 energy spectra of sub-surface velocity fields beneath faraday waves raffaele colombi1∗, niclas rohde, michael schlüter1, alexandra von kameke2 1hamburg university of technology, institute of multiphase flows, hamburg, germany 2 hamburg university of applied sciences, department of engineering and production management, hamburg, germany ∗ raffaele.colombi@tuhh.de abstract faraday waves form on the surface of a fluid which is subject to vertical forcing, and are researched in a large range of applications. some examples are the formation of ordered wave patterns and the controlled walking or orbiting of droplets (couder et al. (2005); saylor and kinard (2005)). moreover, recent studies discovered the existence of a horizontal velocity field at the fluid surface, called faraday flow, which was shown to exhibit an inverse energy cascade and thus properties of two-dimensional turbulence (von kameke et al., 2011, 2013; francois et al., 2013). additionally, three-dimensionality effects have been part of recent investigations in quasi-2d flows (both electromagnetically-driven (kelley and ouellette, 2011; martell et al., 2019) or produced by parametrically-excited waves (francois et al., 2014; xia and francois, 2017)). furthermore, the occurrence of an inverse cascade in thick layers is also subject of current studies on the coexistence of 2d and 3d turbulence (biferale et al., 2012; kokot et al., 2017; biferale et al., 2017). by performing 2d piv measurements at horizontal planes beneath the faraday waves, we recently showed that pronounced three dimensional flows occur in the bulk, with much larger spatial and temporal scales than those on the surface (colombi et al., 2021), when the system is not shallow in comparison to typical length scales of the surface flow (fluid thickness exceeding half the faraday wavelength λf ). this in turn reveals that an inverse energy cascade and aspects of a confined 2d turbulence can coexist with a three dimensional bulk flow. in this work, 2d piv measurements of the velocity fields are carried out at a vertical cross-section xz-plane and at four distinct horizontal xy-planes at different depths in faraday waves. the results reveal that small and fast vertical jets penetrate from the surface into the bulk with fast accelerating bursts and strong momentum transport in the z−direction. furthermore, the fraction of flow kinetic energy in the vertical direction is found to peak inside a layer of approximately 10 mm (one faraday wavelength) below the fluid surface. (a) figure 1: (a) sub-surface velocity field in the xz-plane beneath faraday waves (forcing frequency f f = 50 hz, faraday wavelength λf = 9.5 mm). neutrally buoyant, red fluorescent particles are used as fluid tracers. fast vertical motion can be seen originating at the fluid surface. background-image obtained by averaging 16 successive piv frames (inverted). (right) wavenumber energy spectra of the horizontal velocity fields at the water surface (z = 0 mm) and at depth z = 3 mm. inset (c) net energy and enstrophy fluxes (πe and πz respectively) of the horizontal velocity fields at the water surface (z = 0 mm) and at depth z = 3 mm. the total depth of the water layer is 30 mm. k f denotes the wavenumber at which the forcing occurs for λf/2. below this depth, the fast vertical motion dissipates in the bulk flow in a fashion similar to impinging jets on a flat surface, which might be the driving force of the bulk flow, see fig. 1 a). this interpretation is supported by the analysis of energy spectra, as well as energy and enstrophy fluxes, see fig. 1 b)-d), which show the existence of a direct energy cascade (as shown by the positive net energy flux πe(k) and the zero net enstrophy flux πz(k), coexisting with the inverse energy cascade localized on the fluid surface. finally, for the first time we perform time-resolved tomographic particle tracking velocimetry (4d ptv) in the bulk flow beneath the fluid surface, in order to further investigate the 3d transport of energy and its dissipation mechanisms from the horizontal surface flow to the bulk flow at lower depths. a schematic of the experimental setup is depicted and described in fig. 2 a), whereas fig. 2 b) depicts reconstructed 3d trajectories of particles in a slice at the container centre. figure 2: (left) 4d ptv experimental setup. four high-speed cameras are arranged in a tetrahedron configuration, and high-power leds are used to illuminate a volume of approx. 160×160×30 mm3 at the center of the vertically-agitated container (ød = 300 mm), filled with 30 mm of di water and a solution of neutrally-buoyant, red fluorescent particles (150-180 µm). 4d ptv data is evaluated with the flow master tool (lavision). (right) reconstructed 3d particle trajectories coloured with absolute velocity |v |= √ u2 + v2 +w2 in a volume slice of 40×160×30 mm3. the blue line represents the container filling height. acknowledgements the authors gratefully acknowledge the financial support provided by the deutsche forschungsgemeinschaft (dfg) within the project 395843083 (ka 4854/1-1). references biferale l, buzzicotti m, and linkmann m (2017) from two-dimensional to three-dimensional turbulence through two-dimensional three-component flows. physics of fluids 29:111101 biferale l, musacchio s, and toschi f (2012) inverse energy cascade in three-dimensional isotropic turbulence. physical review letters 108:164501 colombi r, schlüter m, and von kameke a (2021) three dimensional flows beneath a thin layer of 2d turbulence induced by faraday waves. experiments in fluids 62:1–13 couder y, protiere s, fort e, and boudaoud a (2005) dynamical phenomena: walking and orbiting droplets. nature 437:208 francois n, xia h, punzmann h, ramsden s, and shats m (2014) three-dimensional fluid motion in faraday waves: creation of vorticity and generation of two-dimensional turbulence. physical review x 4:021021 francois n, xia h, punzmann h, and shats m (2013) inverse energy cascade and emergence of large coherent vortices in turbulence driven by faraday waves. physical review letters 110:194501 kelley dh and ouellette nt (2011) onset of three-dimensionality in electromagnetically driven thin-layer flows. physics of fluids 23:045103 kokot g, das s, winkler rg, gompper g, aranson is, and snezhko a (2017) active turbulence in a gas of self-assembled spinners. proceedings of the national academy of sciences 114:12870–12875 martell bc, tithof j, and kelley dh (2019) comparing free surface and interface motion in electromagnetically driven thin-layer flows. physical review fluids 4:043904 saylor jr and kinard al (2005) simulation of particle deposition beneath faraday waves in thin liquid films. physics of fluids 17:047106 von kameke a, huhn f, fernández-garcı́a g, munuzuri a, and pérez-muñuzuri v (2011) double cascade turbulence and richardson dispersion in a horizontal fluid flow induced by faraday waves. physical review letters 107:074502 von kameke a, huhn f, munuzuri a, and pérez-muñuzuri v (2013) measurement of large spiral and target waves in chemical reactiondiffusion-advection systems: turbulent diffusion enhances pattern formation. physical review letters 110:088302 xia h and francois n (2017) two-dimensional turbulence in three-dimensional flows. physics of fluids 29:111107 ispiv2021_leclaire_et_al_id148_finalabstract 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 first challenge on lagrangian particle tracking and data assimilation: datasets description and planned evolution to an op en online benchmark benjamin leclaire 1,*, ivan mary 2, cédric liauzun 2, stéphanie péron 2, andrea sciacchitano 3, andreas schröder 4, philippe cornic 5 and frédéric champagnat 5 1: onera, department of aerodynamics, aeroelasticity and acoustics, meudon, france 2: onera, department of aerodynamics, aeroelasticity and acoustics, châtillon, france 3: delft university of technology, faculty of aerospace engineering, delft, the netherlands 4: dlr, institute of aerodynamics and flow technology, göttingen, germany 5: onera, department of information processing and modelling, palaiseau, france *corresponding author: benjamin.leclaire@onera.fr in the last decade, lagrangian particle tracking (lpt) has emerged as one of the leading measurement techniques for the quantitative determination of fluid flows in three-dimensional domains (see e.g. schanz et al., 2016), due to its accuracy in reconstructing particles velocities and material accelerations. due to the scattered nature of the obtained result, at the particles positions only, significant research efforts have also been placed in the development of dedicated data assimilation (da) techniques, aiming at finally reconstructing full 3d velocity and pressure fields on regular cartesian grids (see, e.g., schneiders et al. 2016). within the framework of the horizon 2020 project homer (holistic optical metrology for aero-elastic research), research groups at dlr, onera and tu delft have jointly organized the 3rd workshop and 1st challenge on da & cfd processing for piv and lpt. the challenge purpose was to assess the state-of-the-art on lpt and da algorithms in a situation reflecting a typical experimental campaign. the turbulent wall-bounded flow in the wake of a cylinder was chosen, being a situation with important turbulent fluctuations due to the wake, both in velocity and pressure. diameter � = 0.01 � and gap from the wall � = 0.01 � of the cylinder were chosen in comparison with the targeted boundary layer thickness ≈ 60 ��, and with reference to studies in literature on vortex shedding with ground effect (see e.g. wang & tan 2008), in order to obtain standard shedding behaviour while maintaining large enough wall pressure fluctuations. monotone integrated large eddy simulations (miles) were performed with the onera hpc multi-block structured aerodynamic solver fasts, using second-order finite volume spatial discretization and second-order implicit time integration. the computational domain size is of 1.8 � × 0.1 � × 1.0 � in the streamwise (�), spanwise (�) and wallnormal (�) directions, with mesh cell number of 1367 × 500 × 247 = 168,824,500 cells. the flow zone used for the datasets is of 0.1 � × 0.05 � × 0.03 �; it is centred in span, with its upstream end located 0.035 � downstream of the cylinder centre, and extending from the wall to 0.03 � above the wall. typical cell size in this region was δ� = 0.4 ��, δ� = 0.2 �� and 0.0165 �� ≤ δ� ≤ 0.47 ��. the method of lund et al. (1998) was used to obtain a developed turbulent boundary layer, and periodicity was imposed in the spanwise direction. free-stream reynolds number per unit length was set to ���,� = 665,000, leading to a boundary layer momentum thickness reynolds number of ��� = 4,150 ten diameters upstream of the cylinder. from these simulations, similarity was used to transpose the initial air flow situation towards a water flow with similar dimensions, thereby leading to equivalent free-stream velocity �� = 0.667 �. � !. figures 1 and 2 respectively present a sample flow snapshot, and the timeand span-averaged mean and fluctuating streamwise velocity component, illustrating the intensity of the turbulent fluctuations, largely due to the shed vortices and their secondary structures. as shown in particular by figure 2, the flow zone of the dataset corresponds to a progressive wake recovery. simulations were run with embedded propagation of synthetic pointwise tracer particles, whose positions were initially chosen randomly, using interpolation of the velocity field and a 3rd order adams-bashforth time scheme. overall, 22 sets of particle trajectories of different lengths, each corresponding to different starting flow instants, were generated in order to build all datasets, consisting of two-pulse (tp), four-pulse (fp) or time-resolved (tr) data for the lpt challenge, and of tr data for the da challenge. analysis of the trajectories (not shown here) indicated that significant curvatures and accelerations logically coincided mostly with shed vortices, and in a lesser extent with near-wall turbulent structures. synthetic particle images for the lpt cases were obtained by considering four virtual cameras with a sensor size of 1920×1200 pixels and 10 µm pitch, using pinhole projection with no scheimpflug and no distortions, camera locations and focal lengths leading to an equivalent voxel size of 60 μ�. calibration data (list of points and projections), with no error, were provided to the participants. particles were given a polydisperse intensity distribution, then spread to form the images using a gaussian (# = 0.6) point-spread function, modelling diffraction-limited imaging. thermal and shot noise were also added in the images. datasets were generated corresponding to 0.005, 0.025, 0.05, 0.08, 0.12, 0.16 particles per pixel (ppp), for the tp and fp cases, and also to 0.2 ppp for the tr case. the three da cases (corresponding to 0.005, 0.025 and 0.16 ppp) were generated by adding a random gaussian position noise (with # = 0.1 voxel) to the raw trajectories. these datasets were publicly released for download on march 9th, 2020, see https://w3.onera.fr/first_lpt_and_da_challenge/. participants were then requested to upload their processed results by july 17th, 2020, consisting of particles positions and velocities (and possibly accelerations depending on the cases) for the lpt challenge, and of velocity, velocity gradient and pressure fields on a prescribed 3d grid for the da challenge. analysis of the participants results will be presented in two separate communications also submitted to the ispiv2021 symposium (sciacchitano et al. and sciacchitano et al.). future steps of this work, of which some are underway, are to complete the challenge data portal with an automatic assessment capability, with error and performance metrics computed and communicated to the participant upon data upload, in a similar idea as widely done in the computer vision community (see, e.g. geiger et al. 2012). additionally to a full presentation of the flow simulation and final datasets of the lpt and da challenges, this communication will present the first development steps and principles of this future open online benchmark, which is foreseen to be available to any team interested in development of lpt and da methods, and conceived to be, in the long run, progressively completed with further datasets relevant to the field. figure 1sample flow snapshot, including q-criterion iso-surfaces color-coded by streamwise velocity u, isocontours of pressure p at the lower and side walls. figure 2streamwise mean and fluctuating velocity components, with averaging performed in time and span. profiles on the right correspond to streamwise locations depicted by the vertical dashed lines in the left figures. references geiger, a., lenz, p., & urtasun, r. are we ready for autonomous driving? the kitti vision benchmark suite, 2012, june. in 2012 ieee conference on computer vision and pattern recognition (pp. 3354-3361). ieee. lund, t. s., wu, x., & squires, k. d. generation of turbulent inflow data for spatially-developing boundary layer simulations. journal of computational physics, 1998, 140(2):233-258. schanz d, gesemann s, schröder a. shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids, 2016 may 1;57(5):70 schneiders jf, scarano f. dense velocity reconstruction from tomographic ptv with material derivatives. experiments in fluids, 2016 sep 1;57(9):139 wang, x. k., & tan, s. k. near-wake flow characteristics of a circular cylinder close to a wall, 2008, journal of fluids and structures, 24(5):605-627. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 measurement of lagrangian tracks in a 3 l stirred tank reactor using 4d particle tracking velocimetry with shake-the-box j. fitschen1∗, a.v. kameke2, s. hofmann1, m. hoffmann1, m. schlüter1 1 hamburg university of technology, institute of multiphase flows, hamburg, germany 2 hamburg university of applied science, department of mechanical engineering and production, hamburg, germany ∗ corresponding: juergen.fitschen@tuhh.de abstract stirred tank reactors are widely used in the chemical industry and bioprocess engineering and, consequently, a large number of scientific publications deal with the characterization of those apparatuses. however, there is very little information about the flow conditions. this is mostly due to the fact that these apparatuses are generally made of stainless steel, which restricts optical access. furthermore, three-dimensional flow field measurements are still not trivial and involve costly equipment, therefore, investigations often reduce to two-dimensional piv measurements. nevertheless, recent works (rosseburg et al., 2018; taghavi and moghaddas, 2020; kuschel et al., 2021) impressively show the formation of compartments which hinder and delay mixing. however, these measurements are based either on instantaneous concentration profiles by means of plif measurements or on a two-dimensional projection of the system and thus do not allow conclusions about the development of the three dimensional compartments and the exchange rates between the compartments. in this work, for the first time, instantaneous flow field measurements with high spatial and temporal resolution are performed in the entire volume of a 3l stirred tank reactor based on 4d particle tracking velocimetry. the highly resolved particle trajectories further allow detailed lagrangian analysis of the mixing dynamics inside the reactor, data that was previously inaccessible. 1 experimental method and first results the fluid dynamics of a 3l stirred tank reactor are investigated (see figure 1) using 4d particle tracking. this measurement method allows not only the analysis of the three dimensional flow fields but also the analysis of the lagrangian trajectories, and thus, the material transport in the reactor. fluorescent and i ii iii figure 1: exemplary representation ( i) front view (1:5), ii) calibration target, iii) top view (1:10) ) of the stirred tank setup : a) reactor lid, b) bearing box, c) baffle and baffle holder, d) octahedral glycerol basin, e) stirrer shaft, f) rushton turbine buoyancy-neutral particles with a diameter of 150-180 µm are dispersed in the reactor and illuminated with four customized light sources build in-house using high power leds (osram). to track the particles, a camera setup consisting of four high-speed cameras as well as a recording and synchronization system from lavision (göttingen, germany) is used. two identical camera models are installed one above the other at angles of 30◦, while the two camera pairs are mounted at an angle of 45◦ to each other (see figure 1 (c)). the ”shake-the-box” method is used to determine the lagrangian tracks, which is currently the most efficient particle tracking algorithm available (schanz et al. (2016)). the acquisition of the images as well as the application of the 4d-ptv algorithms are performed with the commercial davis software and the flowmaster module from lavision (göttingen, germany). the images are recorded with a spatial resolution of 148 µm/px and a temporal resolution of up to 800 hz. in figure 2 first results are depicted. the instantaneous and time-averaged flow fields for a baffled and an unbaffled 3l stirred tank reactor (see i) are presented. in the oral presentation a first analysis of the measured lagrangian tracks (see figure 2 ii), but also the mixing dynamics will be discussed. i ii figure 2: i) time-averaged flow field on a sectional plane through the stirrer shaft. (left: without baffles, right: with baffles). ii) selection of 1% of total trajectories in the system (modified velocity magnitude indicates upor downwards motion, red: movement upwards; blue: movement downwards). references kuschel m, fitschen j, hoffmann m, von kameke a, schlüter m, and wucherpfennig t (2021) validation of novel lattice boltzmann large eddy simulations (lb les) for equipment characterization in biopharma. processes 9 rosseburg a, fitschen j, wutz j, wucherpfennig t, and schlüter m (2018) hydrodynamic inhomogeneities in large scale stirred tanks influence on mixing time. chemical engineering science 188:208 – 220 schanz d, gesemann s, and schroeder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids volume 70 taghavi m and moghaddas j (2020) flow characteristics of the rushton and pitched blade turbines in turbulent and laminar mixing. international journal of chemical reactor engineering 18 experimental method and first results 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 uncertainty estimation for ensemble particle image velocimetry a. ahmadzadegan1∗, s. bhattacharya1, a. m. ardekani1, p. p. vlachos1 1 school of mechanical engineering, purdue university, west lafayette indiana, 47907, usa ∗ aahmadza@purdue.edu abstract we present a novel approach to estimate the uncertainty in ensemble particle image velocimetry (piv) measurements. ensemble piv is widely used when the cross-correlation signal-to-noise ratio (snr) is insufficient to perform a reliable instantaneous velocity measurement. despite the utility of ensemble piv, uncertainty quantification for this type of measurement has not been studied. the existing uncertainty quantification algorithms for piv are developed and used only for instantaneous piv measurement and do not account for the improved snr in ensemble piv. existing instantaneous uncertainty quantification methods can be divided into direct and indirect categories. indirect methods require calibration based on the effect of various image parameters (such as noise, particle size, density, velocity gradient, etc.) on the correlation snr. indirect methods have not been calibrated for error sources relevant in an ensemble piv measurement. also, they have lower sensitivity to the error sources compared to direct approaches. direct methods, such as the moment of correlation (mc) and image matching (im), find the uncertainty based on the images and correlation planes without any calibration and are more reliable (bhattacharya et al., 2018; sciacchitano et al., 2013). ensemble piv is based on ensemble correlations; therefore, mc, which uses the generalized cross-correlation (gcc) plane as a measure of uncertainty, is the most suitable method to be modified to be applicable for the ensemble piv. the gcc plane is the inverse fourier transform of the phase correlation and represents the probability density function (pdf) of particles’ displacements (bhattacharya et al., 2018; eckstein and vlachos, 2009). we replaced instantaneous gcc with ensemble gcc and modified mc’s normalization factor to account for the number of ensembles. the mc’s primary limitation is that it assumes a gaussian shape for the pdf of displacements and estimate the standard deviation of the underlying pdf using a fitted gaussian. however, the pdf deviates from gaussian distribution due to velocity gradient or non-gaussian random displacements. therefore, mc’s reliability and applicability are reduced for flow fields with non-gaussian pdfs. also, our analysis shows that ensemble mc consistently underestimates the uncertainty. so, a generalized and reliable method for uncertainty quantification for ensemble piv is needed. to address this gap, we developed a method termed as moment of probability of displacement (mpd). we base our approach on directly estimating the pdf of particles’ displacement using the image-based probability estimation of displacement (iped) (ahmadzadegan et al., 2020). this method finds the pdf by deconvolving the ensemble autocorrelation from the ensemble cross-correlation as shown in eq.1. pdf = f −1(f (cce)/f (ace)) (1) we then calculate the second moment (standard deviation) of the estimated pdf (σpdf ). for calculating σpdf , unlike ensemble mc, we do not use any model to represent the pdf. instead, we calculate the σpdf in a discrete manner. to report the uncertainty of velocity measurement, σpdf needs to be scaled down by the square root of the number of samples contributing to the distribution to be consistent with the definition of standard error. therefore, the uncertainty in velocity measurements (σmpd) can be found using the normalization factor shown in eq. 2 that accounts for the number of image ensembles (n) and the average mutual information (mi) between the image pairs (xue et al., 2015). σmpd = σpdf/ √ (mi ×n) (2) we assess mpd’s performance by running a monte carlo analysis using synthetic images designed to study the response of mpd to different elemental piv error sources, namely, particle size, seeding density, amount of displacement randomness (diffusion coefficient), mean displacement, background noise, shear, and the number of image ensembles. it has been established that a reliable uncertainty quantification algorithm predicts uncertainties that match the expected root mean square (rms) of the error in the velocity measurements (sciacchitano et al., 2015). fig. 1 shows the rms of predicted uncertainty using mpd and ensemble mc compared to rms of the error for each primary error source. we show that in all cases, mpd predicted uncertainties that follow the rms error trend. so, mpd shows good sensitivity to the elemental piv error sources with around %86 accuracy in matching with the rms of error in the baseline data sets. mpd also outperforms the ensemble mc which consistently underestimates the uncertainty. 2 3 4 5 particle diameter [px] 0 0.05 0.1 0.15 0.2 2 4 6 8 10 particle seeding 10-3 0 0.05 0.1 0.15 0.2 10-1 100 x displacement [px/frame] 0 0.05 0.1 0.15 rms of error rms of uncertainty mc rms of uncertainty mpd 0 1 2 3 4 5 0 0.05 0.1 0.15 0.2 diffusion coefficient [px 2 /frame] 10-2 10-1 noise 10-1 100 0 0.05 0.1 shear [px/px/frame] 0 0.05 0.1 0.15 0.2 200 400 600 800 1000 0 0.1 0.2 0.3 0.4 0.5 number of ensemble r m s e rr o r a n d u n c e rt a in ty [ p x ] (c) (d) (f) (g)(e) (a) (b) figure 1: the sensitivity of mpd and ensemble mc compared to elemental error sources. the rms of error (black lines) compared to rms of uncertainty using mpd (red lines) and ensemble mc (blue lines) with respect to a) number of ensembles, b) diffusion coefficient, c) particle displacement, d) background noise, e) particle seeding density, f) particle diameter, g) shear rate. subsequently, we demonstrate the performance of mpd on experimental microscopy images of flow in a rectangular micro-channel. in fig. 2 we show that uncertainty and absolute error distributions. the horizontal lines show the rms for each distribution. we show that the rms of uncertainty from mpd agrees well with the rms of the error while outperforming the ensemble mc.thus, the proposed methodology shows good sensitivity to the rms error over a range of signal to noise ratio and flow conditions and establish itself as a reliable uncertainty quantification algorithm for ensemble piv. figure 2: error and uncertainty distribution for the µpiv experiment. references ahmadzadegan a, ardekani am, and vlachos pp (2020) estimation of the probability density function of random displacements from images. physical review e 102:033305 bhattacharya s, charonko jj, and vlachos pp (2018) particle image velocimetry (piv) uncertainty quantification using moment of correlation (mc) plane. measurement science and technology 29:115301 eckstein a and vlachos pp (2009) digital particle image velocimetry (dpiv) robust phase correlation. measurement science and technology 20:055401 sciacchitano a, neal dr, smith bl, warner so, vlachos pp, wieneke b, and scarano f (2015) collaborative framework for piv uncertainty quantification: comparative assessment of methods. measurement science and technology 26:074004 sciacchitano a, wieneke b, and scarano f (2013) piv uncertainty quantification by image matching. measurement science and technology 24:045302 xue z, charonko jj, and vlachos pp (2015) particle image pattern mutual information and uncertainty estimation for particle image velocimetry. measurement science and technology 26:074001 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 multi-resolution, time-resolved piv measurements of a decelerating turbulent boundary layer near separation c. willert1∗, d. schanz2, m. novara2, r. geisler2,m. schroll1, s. ribergård3, a. schröder2 1 institute of propulsion technology, german aerospace center (dlr), köln, germany 2 institute of aerodynamics and flow technology, german aerospace center (dlr), göttingen, germany 3 department of mechanical engineering, technical university of denmark (dtu), lyngby, denmark ∗ corresponding author: chris.willert@dlr.de abstract we report on measurements of the time-evolving velocity profile of a turbulent boundary layer subjected to a strong adverse pressure gradient (apg) at reynolds numbers up to reθ ≈ 55000 with an upstream friction reynolds number exceeding reτ≈ 10000. near the point of flow separation high-resolution imaging at high camera frame rates captured the time evolving velocity profile using the so-called “profile-piv” technique in a nested imaging configuration of two cameras operating at different image magnifications. one camera used an image magnification better than unity to resolve the viscous scales directly at the wall while the remainder of the roughly 200 mm thick boundary layer is simultaneous captured by the second camera. in the apg the variance of the stream-wise velocity exhibits no “inner peak” commonly found in turbulent boundary layers without pressure gradient influence. spectral analysis further shows that the peak energy within the boundary layer shifts away from the wall toward lower frequencies. the overlap between the simultaneously imaged areas allows to assess and, to first order, correct for the effect of spatial smoothing on statistical quantities, spectra and related quantities. a multi-frame cross-correlation algorithm was used to process the extensive data base. in addition, a newly developed 2d-2c “shake-the-box” algorithm (stb) provided highly resolved particle tracking data beyond the reach of conventional piv processing. 1 introduction the evolution and characteristics of turbulent boundary layers (tbl) subjected to a positive pressure gradient are common in many flows of industrial relevance and appear, for instance, on the suction side of high-lift aircraft wing sections or on turbomachinery blading. the positive pressure gradient is associated with a deceleration of the external flow which results in a thickening of the boundary layer and reduction of the wall friction. under strong adverse pressure gradient conditions the wall friction reduces to zero, ultimately leading to separated flow. from a numerical perspective these flows are difficult to model with methods of engineering relevance, such as reynolds averaged navier-stokes simulations (rans) and motivate experiments such as the one presented here to provide relevant validation data (see e.g. knopp et al. (2014, 2020). the present contribution provides an overview of the experimental facility, the design of the ramp model and focusses on the utilized measurement techniques that provide long records of time-resolved 2d 2c data of the tbl near the point of flow separation. the acquired data is compared with similar data obtained at the same flow conditions in the zpg domain further upstream. the aim is to document the differences between zpg and apg conditions at the point of flow separation, in particular, with respect to changes in the spectral properties. the presented power spectra are believed to be the first of their kind for experiments with both high reynolds numbers and strong apg conditions at the point of separation. 2 experimental setup and methods 2.1 wind tunnel facility and apg model the measurements were performed in a eiffel type wind tunnel with a cross section of 1.8 m width and 1.8 m height and length of 22 m into which a ramp model of about 7 m length was mounted vertically on one side of the tunnel (see figure1). the model was designed within the dlr project victoria and is based on a modification of a previous model design used in the dlr project rettina (knopp et al., 2014) in the same facility. the design is based on 2d rans using the dlr tau code using the saand sstturbulence models with the aim of inducing flow separation along the flat section of the apg region. about 4 m downstream of the test section entry the flow is first accelerated by a smooth ramp of 1.7 m length and 0.44 m height and is then allowed to relax along a nearly pressure gradient free flat plate of 4 m length. the flow then enters a curvilinear region of 1.2 m length inducing a small area of favorable pressure gradient (fpg) before entering the apg domain, which consists of a flat plate of 0.76 m length with an inclination of about 18.6◦ with respect to the tunnel centerline. in order to facilitate multi-camera based particle velocimetry measurements, the flat plate in the apg is fitted with a large, anti-reflection coated glass window. a similar window is present in the zpg region to assess the incoming boundary layer. with the model mounted in an upright fashion windows on the top of the tunnel provide access for cameras viewing the plane along the centerline of the model. in the scope of two measurement campaigns extensive measurements were performed on the configuration to globally characterize the flow using conventional piv as well as multi-pulse stb (novara et al., 2019). near the point of separation 3d-stb along a 90 mm long cylindrical volume provided fully resolved 3d-3c data at sample rates of 20-40 khz (schröder et al., 2018). the present material focuses on timeresolved profile-piv measurements recorded in the zpg domain at x = −3730mm (xt = 7.65 m) and in the apg at x =−620mm (xt = 10.76 m) which is in the immediate vicinity of the mean point of flow separation. here, xt is referenced to the entry of the test section, while x = 0 coincides with the downstream end of the ramp model. 8000 6000 4000 2000 0 x [mm] 0 500 1000 1500 y [m m ] flow uinf = uctrl apg region inclined flat plate at 18.6 0.76 m length ramp 0.45 m height 1.73 m length zpg region flat plate 4.0 m length curvilinear deflection: small fpg profile-piv, zpg profile-piv, apg 4 6 8 10 12 xt [m] figure 1: schematic of the ramp model within the wind tunnel test section with indication of the measurement locations for the profile-piv technique. 2.2 particle imaging methods for time-resolved profile measurements during the measurement campaigns a variety of piv and lagrangian particle tracking (lpt) techniques provided an extensive data base of the flow field extending from the zpg domain well into the apg area. an overview is provided in schröder et al. (2018). the present contribution focusses on time-resolved 2d 2c measurement configurations that provided time-resolved velocity profiles at selected positions. all particle image methods relied on aerosol seeding based on ≈ 1µm dehs droplets which was supplied upstream of the entry to the test section through several laskin-type atomizing seeding generators. both near-wall and global seeding was used. the large travelling distance of nearly 10 m to the measurement location ensured a homogenous distribution of particles throughout the tbl. 2.2.1 high-speed 2d2c piv imaging for the profile-piv measurements in the zpg region (x =−3730mm) the piv system was operated with a photron sa-x2 high speed camera with 20 µm pixel pitch equipped with a 200 mm f/4 lens (nikon micro nikkor 200/4) coupled to a 2x-teleconverter (nikon tc2.0e). depending on the flow velocity the camera was operated at frame rates between 30−50 khz in a reduced resolution mode of 152×1024 pixels which corresponds to a physical fov of 6.6×45mm2 in xand y-direction and image magnification of ≈ 23px/mm (≈ 43µm/px). illumination was provided in a focused beam of 6 mm extension in streamwise direction and 0.8 mm (spanwise) thickness by a high repetition rate q-switched laser (innolas photonics, blizz 30) with 38 w total power at 30 to 50 khz. in order to reduce pixel locking on the rather large sensor pixels, an optical diffuser filter (lavision) was placed in front of the sensor. for each of the ue velocities, two long time-resolved sequences of 294,000 images each were acquired. 2.2.2 nested high-speed 2d2c piv imaging in the apg region the boundary layer was simultaneously imaged at two magnifications using two cameras (vision research v2640) each with 144 gb of on-board memory and a detector array size of 2048× 1952 pixels with a square pitch of 13.5µm per pixel. to operate the cameras at a frame rate of 50 khz the active pixel area was reduced to 224(x)×2048(y ) pixel. while one camera (camera 1) operated at a magnification of better than unity to capture only the near wall flow, the second camera (camera 2) captured the entire extent of the boundary layer of approximately 200 mm thickness. the high image magnification at a working distance of about 950 mm for camera 1 could be achieved with a 300 mm f/4 lens (nikon 300 f4 if-ed af) combined with a 2x teleconverter (nikon tc2.0e) and an extension tube of about 100 mm length (see fig. 2, middle). camera 2 used a 100 mm f/2 lens (zeiss macro planar t 100/2.0 zf) to image a field of view of 250 mm height. a mirror placed in front of camera 2 was necessary to align the viewing axes parallel to each other as the camera cases were significantly larger than the required ≈ 100 mm separation between the two cameras (see fig. 2, right). the narrow field of view was illuminated by a double cavity high-speed laser (photonics industries) with a maximum integral power of 2×150 w capable of independently operating at up to 50 khz. its combined beam was spread to about 15 mm width and 1− 2 mm thickness across the field of view owing to laser beam’s divergence. measurement data was acquired for three free stream velocities either as contiguous long sequences of about 4.4 s length (220,000 frames) or as individual bursts of 10,000 frames each (0.2 s). in burst-mode, 300 uncorrelated samples were acquired for each free-stream condition to ensure statistical convergence. a minimum of 10 long records of 220,000 frames for each condition completes the raw image data base for the apg area, totaling about 24 tb in size (≈ 2.2×107 images). figure 2: left: diagram of nested piv imaging setup in the apg with camera 1 operating at m = 1.1 and camera 2 operating at m = 0.11; middle: photograph of installed camera 1 with 600 mm focal length imaging configuration; right: installation of both cameras above the wind tunnel as seen from the inside of the test section. 3 data processing 3.1 piv processing the acquired 2d 2c piv image data was processed using a combination of in-house and commercial software (pivview v3.8, pivtec gmbh) augmented with python-based batch processing and post-processing tools. to achieve optimal, noise-minimized velocity estimates, a pyramid correlation scheme, similar to an algorithm proposed by lynch and scarano (2013), was employed and used up to 7 consecutive frames. shown in fig. 3, left, the algorithm makes use of the fact that the images are uniformly spaced in time with increments of ∆t. this allows the calculation of cross-correlation on image pairs spaced at uniform intervals n∆t with 1 < n < nmax. results from the pair-wise correlation are combined in a weighted manner, either through summation of correlation planes or by averaging of the individual displacement estimates. underlying the correlation process is a coarse-to-fine scheme including sub-pixel image-shifting. iteratively, the images are thereby shifted toward the central image of the image sub-set, such that the correlation peaks move toward the origin and the residual offset between samples is minimized. due to the averaging of correlation planes noise peaks are attenuated. the processing time of the multi-frame processing scheme with respect to the number of sampled frames n is presented in fig. 3b. in comparison to dual-frame analysis, the 3-frame scheme requires roughly 30% more time which can be explained by the fact that the computationally heavy sub-pixel image shifting only needs to be applied on two of the three images. the additional correlations can be efficiently implemented by computing forward fourier transforms only once for each sample for re-use at different image strides. in spite of the algorithm’s overall efficiency, the large amount of raw image data (ca. 25 tb for apg and zpg combined) was processed with triple-frame sub-samples rather than the more accurate five-frame approach. using the above multi-framing processing strategy required about two months on a state-of-theart workstation with 16-core cpu (amd ryzen threadripper 2950x, 16 cores, 3.5 ghz, 64gb ram). the difference in magnification leads to a attenuation of fine-scale structures of camera 2 vs. camera 1. this leads to an underestimation of the velocity variances for camera 2. to first order, this can be compensated through the availability of data seen by both cameras and has been applied to correct the variance data shown in fig. 6d). figure 3: left: schematic of the utilized pyramid correlation scheme, here for 7 consecutive images. right: processing speed with respect to standard two-frame cross-correlation analysis. 3.2 2d-stb processing the image data was also processed using a 2d-2c-ptv algorithm, derived from the 3d-3c “shake-thebox” (stb) lagrangian particle tracking (lpt) method by schanz et al. (2016). for this purpose, the stb predictor/corrector-scheme was adapted to allow for the tracking of particles on time-resolved recordings based on single camera views, yielding time-resolved 2d-2c velocity data along tracks. the new 2d-stb evaluation scheme is based on the core functionality of stb involving particle position prediction followed by correcting for the introduced error by ‘shaking’ the predicted particle position (similar to ipr, wieneke 2012). however, the volume reconstruction is replaced by a simple peak search on the 2d image. the method works reliably in finding tracks in images with moderate particle image densities. the method is table 1: profile-piv imaging and processing parameters condition zpg apg apg camera 1 camera 2 magnification m 0.464 1.10 0.111 m 43.1 12.3 122 [µm/pixel] pixel size 20 13.5 13.5 [µm] field of view x×y 152×1024 224×2048 224×2048 [pixel] x×y 6.55×44.1 2.75×25.2 27.3×249.8 [mm2] piv sampling window x×y 64×3 32×12 24×12 [pixel] x×y 2.76×0.129 0.393×0.147 2.93×1.46 [mm2] piv grid spacing x×y 24×1 16×4 8×4 [pixel] x×y 1.03×0.043 0.197×0.049 0.976×0.488 [mm2] computationally efficient and scales with the number of tracked particles. for the present data the newly developed stb evaluation is able to identify and follow more than 2,200 particle tracks per time-step. an evaluation based on a fraction of the complete data set already shows the performance gain resulting in a much higher spatial resolution compared to the non-isotropic cross-correlation approach. to calculate the velocity statistics a bin-averaging scheme with bin-heights of 0.25 pixels (< 1+) in wall normal direction was used and results in about 100,000 entries per bin for one of three available runs. the limiting factor for fully converged statistics of such a time-resolved particle tracking measurement are the temporal scales or turn-over eddy times of superstructures embedded in the outer logarithmic region of the tbl flow (≈ 0.4δ), requiring a multitude of short (uncorrelated) records or very long image sequences covering many eddy turn-over times. camera 2 camera 1 figure 4: time-records covering 0.2 s (10,000 samples) of the stream-wise velocity profile u for camera 2 (top) spanning a wall-normal distance of y = 245 mm and camera 1 (bottom) spanning y = 24.5 mm at u∞ = 28.7 m/s. 4 results 4.1 velocity profile statistics most of the data post-processing is based on time-records of a single column of data extracted from the center of the piv processing domain, resulting in space-time records. an example of such space-time records visualizing the streamwise velocity component u simultaneously acquired by both cameras is shown in fig. 4. a detail of this figure is provided in fig. 5 for the high resolution camera 1. the colorbar is chosen such that strong upstream flow near the wall is highlighted as red-purple patches representing values on the order 20% of ue. on the whole, the highly dynamic near-wall flow fluctuates around a mean near zero (cyan color) which is due to the apg induced deceleration of the external flow, that is, the flow is on the verge of separation. the strong flow reversal in fig. 5 extend far beyond the viscous region. topologically these flow reversal features differ significantly from those previously observed under zpg and mild apg conditions in which figure 5: detail of the time-evolving streamwise velocity profile obtained from high-magnification camera 1 covering 1250 samples (0.025 s) at u∞ = 28.7 m/s. the vertical axis spans y≈ 24 mm. table 2: boundary layer parameters for different wind tunnel operating conditions condition zpg apg upstream velocity u∞ 29.0 35.0 28.7 35.2 41.8 [m/s] edge velocity ue 29.0 35.0 22.3 27.3 32.1 [m/s] boundary layer thickness δ99 80.0 79.0 207.8 205.0 201.3 [mm] displacement thickness δ∗ 9.16 9.05 61.3 57.0 51.8 [mm] momentum thickness θ 7.05 7.01 27.1 26.5 25.5 [mm] shape factor h = δ∗/θ 1.30 1.29 2.35 2.15 2.03 reynolds number reθ =ueθ/ν 12,200 14,700 40,000 48,000 55,000 friction velocity uτ 1.030 1.225 n.a. n.a. n.a. [m/s] viscous unit ν/uτ 16.4 13.7 n.a. n.a. n.a. [µm] estimated wall shear du/dyy=0 63 800 89 700 150 1050 4000 [s−1] they are both confined to the viscous layer at y+≤ 5 and much more short-lived (lenaers et al., 2012; willert et al., 2018a,b). the underlying mechanisms of the flow reversal phenomena observed here are believed to be completely different and unrelated to those previously observed. mean velocity profiles for several free stream conditions are provided in fig. 6a and 6b, normalized by the respective edge velocities ue and boundary layer thickness δ99. while the profiles for zpg are representative for this type of flow, the apg flow condition exhibits no clear logarithmic region such that an estimation of viscous scales based on a clauser fit (clauser, 1954) or based on the wall-shear stress is not straight forward and possibly not even adequate as the mean wall-shear stress approaches zero. for this reason and in order to compare the apg flow with that of zpg, all data have been normalized by the boundary layer thickness δ99 and local free stream velocity ue. fig. 6c and 6d show profiles of the variances 〈u′u′〉, 〈v′v′〉 and the associated reynolds shear stress 〈u′v′〉 for the two pressure gradient conditions. noteworthy is that the near-wall high-intensity turbulence or “inner peak” commonly found for zpg or mild apg conditions (c.f. fig. 6d) is completely attenuated in the present apg condition. remnants of the inner peak can be observed in the range (0.001 < y/δ99 < 0.01). instead, the streamwise turbulence peaks at about 0.15δ99, placing it several hundred viscous units away from the wall, assuming viscous units on the order of 20−50µm (the actual value has yet to be determined). the apg velocity profiles shown in fig. 6b show a very weak gradient near the wall which is highlighted more clearly by plots of the mean velocity gradient du/dy provided in fig. 7. in comparison to the zpg tbl (fig. 7a), where the highest velocity gradient is present in the immediate vicinity of the wall and rapidly decays with increased wall distance, the apg tbl exhibits a plateau of nearly constant shear rate in the range (0.01 < y/δ99 < 0.02), also peaking at about 0.15δ99 coinciding with the location of the peak streamwise turbulence. beyond 0.4δ99 the velocity gradient decays linearly toward zero at the outer edge of the tbl. to more clearly highlight the difference between zpg and apg plots of the velocity gradient with linear axis scaling are also shown in fig. 7. a) 100 101 102 103 104 y + 0 5 10 15 20 25 30 u + = 0.41 b = 5.45 dns, tbl re = 4060 u = 29.0 [stb] u = 35.0 [stb] b) 0.001 0.01 0.1 1 y / 99 0.0 0.2 0.4 0.6 0.8 1.0 u /u e u = 28.7 m/s u = 34.3 m/s u = 41.2 m/s 0.1 mm 1 mm 10 mm 100 mm c) 100 101 102 103 104 y + 2 0 2 4 6 8 10 u i u j + u u + v v + u v + dns, tbl re = 4060 u = 29.0 [stb] u = 35.0 [stb] d) 0.001 0.01 0.1 1 y / 99 0.005 0.000 0.005 0.010 0.015 0.020 u i u j /u 2 e u u v v u v 0.1 mm 1 mm 10 mm 100 mm figure 6: mean streamwise velocity profiles (a,b) and variances and covariance of the streamwise and wall-normal velocity components (c,d), for zpg condition (a,c) und apg (b,d). all profiles are scaled with respective edge velocities ue and boundary layer thicknesses δ99. solid lines in (b) are obtained from high-magnification camera 1 whereas dashed lines are associated with full-view camera 2. 4.2 velocity spectra the good temporal resolution and long record lengths permit the estimation of power spectral density distribution across the entire vertical extent of the field of view. to illustrate the construction of the 2d spectral maps from the velocity time records, a sample spectra for a fixed wall distance is provided in fig. 8 (left) for the stream-wise velocity u and wall-normal velocity v . the 2d contour map shown in fig. 8 (right) is assembled by plotting the individual spectra for all wall distances y. the discontinuity in the spectra at y = 20 mm is due to spatial filtering of camera 2 with respect to camera 1. the spatial filtering results in the attenuation of the smaller scales which typically are also associated with reduced time scales. in the following, spatially resolved spectra obtained in the zpg and apg are presented side-by-side for matching flow conditions at u∞ = 29.0m/s. it should be noted that the spectra are pre-multiplied by the frequency in order to better highlight the prominent features. due to spatial resolution limits in the zpg measurements, attenuation is present close to the wall for y+ < 20 (less than ≈0.2 mm). this leads to an attenuation of the spectral peak normally found at the position of the inner turbulence peak at y+ ≈ 15. nonetheless, the inner peak can be clearly identified in fig. 9a at reduced frequency near one with its wallnormal position indicated by the dashed black line. under the present apg conditions, at the point of flow separation, the peak energy shifts away from the wall to about 10% of the boundary layer thickness (fig. 9b). a near-wall energy peak can no longer be identified. also the peak energy shifts towards an order of magnitude lower frequency. for the energy spectra of the wall-normal fluctuations, shown in fig. 9c and 9d, the shift of peak energy content is not as pronounced in its spatial movement with its highest energy also shifting to 0.15y/δ. however, under apg conditions the reduced frequency of the wall-normal velocity shifts to a peak value centers close to unity. the dominant frequency indicates a periodic vertical motion at a timescale corresponding to the eddy turnover time δ/ue and may be interpreted as vortex shedding process in the free shear layer that begins to form as the flow undergoes separation. the spectral energy distribution of the reynolds stress 〈u′v′〉 is provided in fig. 9e and 9f. for the zpg condition, the distribution is in agreement with dns data reported in the literature (see e.g. ahn et al. 2015) a) 0.001 0.01 0.1 1 y = y/ 0.1 1 10 100 du dy 99 u 1 e u = 29.0 [stb] u = 35.0 [stb] 0 1 0 5 10 b) 0.001 0.01 0.1 1 y = y / 99 0.1 1 10 du dy 99 u 1 e u = 28.7 m/s u = 34.3 m/s u = 41.2 m/s 0.0 0.5 1.0 0 1 2 3 1 mm 10 mm 100 mm figure 7: mean velocity gradient du/dy for zpg condition (a) and apg (b) normalized by boundary layer thickness δ99 and edge velocity ue. inserts show the same data with linear axis scaling. table 3: spectral peak positions as indicated by white stars in fig. 9. zpg apg ratio y y/δ99 f f̂ y y/δ99 f f̂ f̂zpg/ f̂apg 〈u′u′〉 0.22 mm 0.0027 490 hz 1.35 34.3 mm 0.152 30.5 hz 0.29 4.7 〈v′v′〉 3.62 mm 0.045 1410 hz 3.88 33.3 mm 0.145 122 hz 1.15 3.4 〈u′v′〉 0.56 mm 0.007 1074 hz 2.97 34.4 mm 0.150 48.8 hz 0.46 6.5 with a broad distribution throughout the extent of the boundary layer. under apg conditions the reynolds stress is concentrated near 0.15y/δ, similar to the streamwise and wall-normal fluctuations. aside from the movement of peak energy away from the wall, there is also a shift toward lower frequencies by about one order of magnitude as the flow reaches the apg. when normalized against the increased boundary layer thickness δ99 and decreased edge velocity ue the reduction is less significant with the ratio changing from ue/δ99 |zpg= 363 hz to ue/δ99 |apg= 108 hz by a factor of ≈ 3.4, which is of similar magnitude as the change in normalized frequency (c.f. table 3). the frequency change can thus be explained by the strong thickening of the boundary layer along with its deceleration. the low frequency content is indicative of the formation of large scale (outer) structures as observed in large fov measurements. 5 conclusions highly resolved velocity data in both space and time were acquired in a high reynolds number turbulent boundary layer subjected to strong adverse pressure gradient conditions. a nested camera imaging configuration was chosen in order to capture both the near-wall dynamics and at the same time have access to velocity data throughout the entire boundary layer height. the acquired data was compared to similar profile data acquired in the near-zero pressure gradient zone upstream of the apg domain. at the point of separation the mean velocity gradient exhibits a region of uniform shear peaking at about 15% of the tbl thickness, the position at which both the velocity variances and reynolds stress have their maximum intensity and highest spectral intensity. the extensive data base still offers access to further quantities and associated analysis, such as the interaction of the unsteady wall-shear with the outer flow. on a general note, the data provided by the profile-piv technique is well suited for analysis methods commonly used by single-point measurements such as hwa and lda, but additionally offers a spacetime coherence across the field of view, providing possibilities for more advanced analysis yet to be fully explored. in a next post-processing step it is foreseen to compare a b-spline based 2d interpolation scheme (similar to flowfit (gesemann et al., 2016) applied to the scattered 2d-stb velocity and acceleration data of the particle tracks with the correlation based velocity fields from profile-piv. figure 8: power spectra obtained for the streamwise velocity component. highlighted curves in 1-d spectra (left) are lowpass filtered at 10 khz of the original signal shown in faded colors. solid blue line in left subfigure represents a rms fluctuation of 1 pixel. dashed light-blue line in right subfigure indicates a chosen boundary at y = 15 mm between camera view 1 and view 2. acknowledgements the authors would like to thank prof. christian kähler and his team for their support during the measurement campaigns and the use of the wind tunnel facility along with the high-power pulsed laser system. references ahn j, lee jh, lee j, kang jh, and sung hj (2015) direct numerical simulation of a 30r long turbulent pipe flow at reτ = 3008. physics of fluids 27:065110 clauser fh (1954) turbulent boundary layers in adverse pressure gradients. journal of the aeronautical sciences 21:91–108 gesemann s, huhn f, schanz d, and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser techniques to fluid mechanics. number 186 in conference proceedings online, book of abstracts. pages 1–17. paper 04.5 4 186 knopp t, novara m, schanz d, geisler r, philipp f, schroll m, willert c, and schröder a (2020) modification of the ssg/lrr-ω rsm for turbulent boundary layers at adverse pressure gradient with separation using the new dlr victoria experiment. in a dillmann, g heller, e krämer, c wagner, c tropea, and s jakirlić, editors, new results in numerical and experimental fluid mechanics xii. pages 80–89. springer international publishing, cham knopp t, schanz d, schröder a, dumitra m, hain r, and kähler cj (2014) experimental investigation of the log-law for an adverse pressure gradient turbulent boundary layer flow at reθ up to 10000. flow turbulence and combustion 92:451–471 lenaers p, li q, brethouwer g, schlatter p, and örlü r (2012) rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence. physics of fluids 24:035110 lynch k and scarano f (2013) a high-order time-accurate interrogation method for time-resolved piv. measurement science and technology 24:035305 novara m, schanz d, geisler r, gesemann s, voss c, and schröder a (2019) multi-exposed recordings for 3d lagrangian particle tracking with multi-pulse shake-the-box. experiments in fluids 60:44–63 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 schröder a, schanz d, novara m, philipp f, geisler r, agocs j, knopp t, schroll m, and willert ce (2018) investigation of a high reynolds number turbulent boundary layer flow with adverse pressure gradients using piv and 2dand 3dshake-the-box. in 19th international symposium on applications of lasers and imaging techniques to fluid mechanics. lisbon, portugal wieneke b (2012) iterative reconstruction of volumetric particle distribution. measurement science and technology 24:024008 willert c, cuvier c, foucaut j, klinner j, stanislas m, laval j, srinath s, soria j, amili o, atkinson c, kähler c, scharnowski s, hain r, schröder a, geisler r, agocs j, and röse a (2018a) experimental evidence of near-wall reverse flow events in a zero pressure gradient turbulent boundary layer. experimental thermal and fluid science 91:320 – 328 willert c, soria j, cuvier c, foucaut j, and laval j (2018b) flow reversal in turbulent boundary layers with varying pressure gradients. in 19th intern. symp. on applic. of laser and imaging techniques to fluid mecahnics. lisbon, portugal a) b) 10 8 10 7 10 6 10 5 10 4 f uu u 2 e c) d) 10 9 10 8 10 7 10 6 10 5 f vv u 2 e e) f) 10 9 10 8 10 7 10 6 10 5 f uv u 2 e figure 9: pre-multiplied power spectra obtained for the respective velocity components for u∞ = 29.0 m/s for zpg (left column) and apg conditions (right column); spectrum of streamwise velocity 〈u′u′〉 (a,b), wall-normal velocity 〈v′v′〉 (c,d) and reynolds stress 〈u′v′〉 (e,f). data is normalized by the respective edge velocity ue and boundary layer thickness δ99. dashed black line in left plots indicates the location of the inner turbulence peak at (y+ = 15). dashed light-blue line in right plots indicates a chosen boundary at y = 20 mm between camera view 1 and view 2. introduction experimental setup and methods wind tunnel facility and apg model particle imaging methods for time-resolved profile measurements high-speed 2d2c piv imaging nested high-speed 2d2c piv imaging data processing piv processing 2d-stb processing results velocity profile statistics velocity spectra conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 investigating optimal training and uncertainty quantification for cnn-based optical flow d. kurihara1, g. blois1, h. sakaue1, d.e. schiavazzi1,2 1 university of notre dame, department of aerospace and mechanical engineering, notre dame, usa 2 university of notre dame, department of applied and computational mathematics and statistics, notre dame, usa 1 introduction optical flow (of) techniques provide “dense estimation” flow maps (i.e. pixel-level resolution) of timecorrelated images and thus are appealing to applications requiring high spatial resolutions. of methods revolve around mathematical descriptions of the image as a collection of features, in which the pixel-level light intensity is the primary variable (horn and schunck, 1981). feature tracking often involves the notion of scale invariance. traditional of approaches, merely based on mathematical formulations, have suffered from many challenges, especially when directly applied to images of fluid flows textured with tracer particles (hereafter piv-like images). due to the limited number of computationally manageable features and suboptimal regularization methods, successful implementation of past approaches has been limited to highly textured images and small displacement dynamic ranges. recent deep learning-based methods have effectively removed several limitations, offering an opportunity to revitalize of techniques. being these based on structural features, the natural ability of artificial neural networks (ann) with deep architectures to extract a large collection of such features at multiple resolutions through convolutions with learnable kernels can be brought to bear. in this context, a number of newly proposed convolutional neural networks (cnns), originally developed for computer vision applications, have been successfully applied to the estimation of flows from dynamic scenes with moving objects. a recent example is liteflownet (fig. 1(a)), which provides state-of-the-art performance on a number of datasets including rigid body motion of objects in space, vehicles moving in traffic and, most notably, computer animated sequences (hui et al., 2018). however, there is still limited understanding of which network setup (e.g. architecture, hyperparameter selection, etc.) provides optimal flow accuracy for piv-like images. in this context, the goal of this study is to 1) provide a quantitative understanding of how liteflownet performs for piv-like images under different training paradigms and hyperparameter setups, and also to 2) extended the capabilities of liteflownet to quantify flow uncertainty. 2 methods liteflownet is a family of recently proposed deep neural networks for optical flow estimation (hui et al., 2018, 2020). its architecture consists of pyramidal feature extraction (netc) followed by a cascade of flow inference modules (nete), i.e., a matching module, a subpixel module, and a regularization module. the matching module identifies the corresponding features in the image pair, the subpixel module corrects the flow estimation and provides subpixel accuracy, whereas the regularization module is used to refine the flow estimate near the boundary of moving objects. the network progressively identifies flow features in a coarse-to-fine resolution pipeline, starting from level 6 (coarser resolution) to level 2 (finer resolution). the original liteflownet was trained using a staged process (see fig. 1(a)), and did not support quantification of flow uncertainty. the first portion of this work assesses the predictive performance of liteflownet using available pre-trained weights. tests targeted synthetic piv-like image sets with varying particle density, size and displacement. we then explored the potential of liteflownet when trained from piv-specific examples, following two different training paradigms proposed in the literature. in addition, we augmented the liteflownet architecture with dropout layers providing both a regularization mechanism and the possibility to estimate uncertainty from prediction ensembles. figure 1: (left) liteflownet architecture and schematics of a staged training sequence. (right) prediction of instantaneous flow fields: the first row (gt) refers to the ground truth. predictions are obtained from end-to-end training with dropouts (p1) and with optimal loss penalties from all levels (row p2). standard deviations from ensemble predictions for p1 and p2 are shown in u1 and u2, respectively. 3 results first, three sets of weights were tested (referred to as default, kitti and sintel), and their predictions compared against piv image processing using three interrogation window sizes (64, 32, and 16), with 50% overlap. the comparisons were made by statistical analysis of large samples, using average absolute pixel differences under different upand down-scaling interpolation strategies. sintel weights offered the best performance due to the presence of image deformation and shear in the training dataset, unlike default and kitti which are mainly trained from rigidly moving examples. sintel results were comparable to those obtained using piv correlations. the first newly tested training approach consisted of multiple sessions where finer image resolution levels are progressively activated at each successive stage (staged training, see fig. 1(a)). the second is referred to as end-to-end training, where the complete network is trained all at once, and the loss is calculated as a penalized aggregation of prediction errors from all levels. end-to-end training generally produces both minimal losses and best accuracy. however, it is less clear how to weight the losses from each level, particularly for a general system which may operate on a wide range of particle densities, for which the importance of the features at various levels may vary within the same training dataset. finally, we studied layouts with a dropout layer positioned after each flow inference module and after all modules, achieving the best performance when placing a dropout layer after each matching module for all levels. to compare all the approaches described, we trained our modified network on three piv-specific datasets generated through numerical simulation (cai et al., 2019). results in fig. 1(b) show consistent performance improvements of the proposed network leveraging dropouts (p1) which contained small uncertainty (u1) for all the datasets considered. we also determined optimal weighted losses from various levels, obtaining reduced accuracy (p2) and larger uncertainties (u2), confirming the key importance of high resolution losses and providing grounds for designing more efficient network layouts. references cai s, liang j, gao q, xu c, and wei r (2019) particle image velocimetry based on a deep learning motion estimator. ieee transactions on instrumentation and measurement 69:3538–3554 horn bk and schunck bg (1981) determining optical flow. in techniques and applications of image understanding. volume 281. pages 319–331. international society for optics and photonics hui tw, tang x, and loy c (2018) liteflownet: a lightweight convolutional neural network for optical flow estimation. in proceedings of ieee conference on computer vision and pattern recognition (cvpr). pages 8981–8989 hui tw, tang x, and loy c (2020) a lightweight optical flow cnn revisiting data fidelity and regularization introduction methods results 14th internationalsymposiumonparticleimagevelocimetry–ispiv2021 august1–5,2021 plunging jets from orifices of different geometry giorgio moscato*, giovanni paolo romano* university la sapienza, dept. mechanical & aerospace engineering, rome, italy *giorgio.moscato@uniroma1.it *giampaolo.romano@uniroma1.it background plunging jets are used in many industrial and civil applications, as for example in sewage and water treatment plants, in order to enhance aeration and mass transfer of volatile gases. they are also observed in natural processes as rivers self-purification, waterfalls and weirs. many investigations dealt with the plunging jets in different configurations, but the dependence on reynolds number and jet geometry were still not sufficiently addressed. for example, mishra et al. (2020) studied an oblique submerged water impinging jet at different nozzle-to-plate distances and impingement angles, but only at a rather small reynolds numbers (2600). on the other hand, different jet geometries have been extensively considered, but not for the plunging jet configuration (mi, 2000; hashiehbaf & romano, 2013). in this work, plunging water jets issuing in air from orifices of different shape are considered. the aim of the work is to detail and compare jet behaviors in terms of velocity fields generated after impacting the air-water interface, as a function of reynolds number and orifice geometry. however, air bubbles entrainment is mainly avoided in order to study the jet characteristics in a simpler case and use it as a reference starting point for future works. facility and set-up the experimental facility is composed of a settling chamber, a wide chamber which represents the plunging pool, two discharge tanks, a centrifugal pump and an upper reservoir, as reported in figure 1 on the left. water plunging jets develops in air, downstream sharp-edged orifice plates of two different shapes i.e. circular and rectangular. an example of plunging jet from the rectangular orifice is reported in figure 1 at the top right, where the axis switching phenomenon can be noted. measurements have been performed at different reynolds numbers in the range 1000026000, based on the orifice diameter (equal to 2 cm) and on the average exit velocity, as derived from flow rates. the velocity field behaviors are investigated by means of particle image velocimetry (piv), using a continuous laser diode (maximum power 15 w) and a high speed video-camera, fastcam mini ax100 (up to 4000 frames/s at the maximum spatial resolution of 1024x1024 pixels). glass microspheres of diameter in the interval 525 μm are used as tracers (stokes time scale around 310-5 s). results as examples of obtained results, the average velocity magnitudes are presented at the top of figure 2 for the cases of jets issuing from circular and rectangular orifices and plunging in water, for a reynolds number around 25000. for the circular case, the jet appears to develop in a symmetric way (close to the behavior of a free turbulent jet), having a first part characterized by the presence of the potential core till around 2 jet diameters downstream, while the jet axial velocity shows a linear decay from around 3 jet diameters. on the other hand, looking at the jet half velocity width trends, their behaviors appear to be different in the upper and lower part of the jet, suggesting a slightly different evolution of the two shear layers (but close to a symmetric condition). for the rectangular case, the jet velocity magnitude map and its vorticity field show a clear non-symmetric condition, characterized by the presence of a double-peak velocity along cross sections till a distance of about 4 diameters streamwise, from which the jet starts to have a gaussian-like distribution, as for the circular case. moreover, the vorticity field suggests the presence of 4 shear layers 14th internationalsymposiumonparticleimagevelocimetry–ispiv2021 august1–5,2021 which develop in a non-symmetric way and with a different axial velocity decay. this condition can be explained by the jet shape, which exhibits more than two collar-like meniscus forms at the plunging point. figure 1. the facility for generation and investigation of plunging jets (on the left) and an example of plunging jet issuing from the rectangular orifice (on the right at the top). figure 2. mean velocity magnitude fields (at the top) and mean vorticity fields (at the bottom) for the circular and rectangular plunging jets in water as derived at re25000. references hashiehbaf, a., & romano, g. (2013). particle image velocimetry investigation on mixing enhancement of non-circular sharp edge nozzles. international journal of heat and fluid flow elsevier. j. mi, g. j. (2000). centreline mixing characteristics of jets from nine differently shaped nozzles. experiments in fluids. mishra, a., yadav, h., djenidi, l., & agrawal, a. (2020). experimental study of fow characteristics of an oblique impinging jet. experiments in fluids springer. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 influence of span-wise coherence on the acoustic radiation in a cylinder wake lars siegel1, guosheng he2,3, karen mulleners2, arne henning1∗ 1 german aerospace center (dlr), inst. for aerodyn. & flow tech., göttingen, germany 2 institute of mechanical engineering, école polytechnique fédérale de lausanne (epfl), switzerland 3 school of astronautics, beijing institute of technology, china ∗ arne.henning@dlr.de abstract the aim of this study is to detect and visualise the influence of span-wise coherence on propagating sound waves emanating from a flow around circular cylinders with span-wise variations of the local radius. synchronous particle image velocimetry (piv) and microphone measurements are performed in a circular wind tunnel with a nozzle size of 0.4 m×0.4 m at a maximum flow speed of u∞ = 43ms−1. the test section is surrounded by a full anechoic chamber of approximately 9 m×9 m×5 m. the two components (2c) of the velocity field data are acquired in selected vertical two-dimensional planes (2d) using 2c2d-piv around the cylinder mid-span. all three velocity components (3c) are acquired using stereoscopic or 3c2d-piv in a horizontal spanand flow-wise oriented plane in the near wake of the cylinder. the pressure measurements are conducted with 4 microphones (type:1/4 40bf; g.r.a.s.) in the far field outside the flow to avoid unwanted influences on the flow field and vice versa. the microphones are installed above the cylinder and are distributed in a horizontal line at the mid-span of the cylinders in flow direction to take into account the directivity of the sound emission. the vertical positions were approximately 1.8 m (120 d) above the cylinder and the distance between the microphones was about 0.3 m (20 d). a multi-analyzer (type: dewe3; dewetron) simultaneously records the microphone-signals, the camera trigger, the q-switch of the laser and three components of the forces acting on the cylinders with a sampling frequency of fs = 100khz and a dynamic range of 24 bit. cylinders with different span-wise variations are investigated as illustrated in fig. 1. the geometric parameters of the cylinders are selected such figure 1: experimental setup with indicated light sheets for the 2c2d-piv (orange) and 3c2d-piv (green) (left); and the different cylinders tested (right). figure 2: instantaneous vector distributions of the velocity field (left) and the cross-correlation function (right) of the sinusoidal cylinder configuration in the horizontal plane. color-coded is the out-of-plane component. that the core or the average diameter d is 15 mm and the span-wise wavelength for the repeated variations are constant. figure 2(left) shows an example of the instantaneous distribution of the velocity field of the sinusoidal cylinder configuration in the horizontal plane. the axis are scaled with the cylinder diameter d and u∞ is the free-stream velocity. the out-of-plane component v pointing into the direction of the microphones is color-coded. the span-wise coherent detachment of the vortex patterns are superimposed by turbulent motions produced by the interaction between smaller scale locally detaching vortices along the sinusoidal protrusions of the cylinder. by correlating the velocity φ′ and pressure fluctuations p′ in the far field, we can identify the influence of the span-wise cylinder surface variations on the acoustic emission (siegel et al., 2018; henning et al., 2008). figure 2(right) depicts the instantaneous distribution of the cross-correlation function which is defined as follows: sp,φ(x,τ) = 1 n n ∑ i=1 p′(ti + τ) ·φ′(x, ti), with τ the time shift between the velocity and pressure measurement. again, the out-of-plane component is color-coded. the span-wise coherence becomes more apparent, while the wavelike characteristic of the coherent structures is a consequence of the sinusoidal variation along the span of the cylinder. the aim is to characterize the wake topologies behind the different cylinder geometries in detail and to determine the influence of the surface variations on the vortex shedding frequencies. the final analysis considers the acoustic signatures of the different topologies and the corresponding span-wise coherence. the analysis of the temporal and spatial evolution of these structures provides an insight into the sound generation mechanism. acknowledgements this work was supported by the swiss national science foundation lead agency programme under grant number 200021e-169841 and the deutsche forschungsgemeinschaft (dfg – german research foundation) under grant number he 7369/2-1. references henning a, kaepernick k, ehrenfried k, koop l, and dillmann a (2008) investigation of aeroacoustic noise generation by simultaneous particle image velocimetry and microphone measurements. experiments in fluids 45:1073–1085 siegel l, ehrenfried k, wagner c, mulleners k, and henning a (2018) cross-correlation analysis of synchronized piv and microphone measurements of an oscillating airfoil. journal of visualization 21 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 an experimental study to quantify the rotor-torotor interaction characteristics of a small unmanned-aerial-vehicle wenwu zhou, zhe ning, hui hu () 1 department of aerospace engineering, iowa state university, ames, iowa, 50011, usa () corresponding author. email: huhui@iastate.edu abstract: the flow interactions between laterally aligned rotors were investigated experimentally to study the rotor-to-rotor interactions on the aerodynamic and aeroacoustic performance of small unmanned aerial vehicles (uavs). two identical rotors, similar to the dimensions of phantom 3 (dji), were mounted separately on different stages in a wide-open space. high-accuracy force and sound measurements were conducted to document the thrust and noise at various separation distances. the detailed flow structures and corresponding vortex evolutions behind the rotors were resolved clearly by using high-resolution piv measurements. as the rotor separation distance decreased, intensified flow interactions were noted within the rotors. more specifically, the twinrotor with separation distance of l= 0.05d exhibited a significantly enhanced thrust fluctuation (i.e., ~ 240% higher) and augmented noise level (i.e., ~ 3db) in comparison with that of baseline case. measured piv results indicated that a strong recirculation region existed near the top-right of the twin-rotor case, which is believed to be the reason for the increased thrust fluctuations and aeroacoustic noise level. i. introduction recent advances in established control systems and inexpensive electronic devices have greatly encouraged the development of small unmanned aerial vehicles (uavs) (bouabdallah et al. 2007; lucieer et al. 2014; goebel et al. 2015). especially for uavs with rotary-wing system, they are becoming increasingly attractive to engineers due to their unique hovering ability (e.g. vertical take-off and landing) and user-friendly flight controllability. varieties of applications in civilian fields, such as package delivery, field site surveillance, disease control, video taking, and personal entertainment, are all driving incentives to adopt this new technique. for the sake of providing sufficient thrust, multi-rotor configurations are frequently used in small uavs during various tasks. for example, the quadrotor, which is one of the most widely-used configurations, can achieve 6 degrees of freedom movement by simply controlling the rotational speeds of individual rotors (otsuka and nagatani 2016). though uavs with multi-rotary-wing systems are promising technology for the civilian applications, technical improvements are highly desired for the sake of extending the operating mailto:huhui@iastate.edu time and reducing the aeroacoustic noise. typically, a representative operating time for small uavs is less than half an hour, which is far from sufficient for complex tasks. therefore, boosting the operation time of uavs is highly desired. one effective method is to improve the aerodynamic performance of multi-rotor uavs. since the knowledge pertinent to helicopter rotor dynamics can’t be applied to small uavs directly, it requires comprehensive studies to understand the aerodynamic performance of small uavs. bristeau et al. (bristeau et al. 2009), who studied the aerodynamic effects of the rotors and their interactions with the uav body motion, found that the rotor flexibility played an important role in the uavs’ aerodynamics. to obtain first-hand aerodynamic data on commercial uavs, russell et al. (russell et al. 2016) experimentally quantified the thrust coefficients of five multi-rotor uavs at various wind speeds, rotor speeds, and vehicle attitudes. similar studies were performed by brandt and selig (brandt and selig 2011) and merchant and miller (merchant and miller 2006), who quantified the performance of small propeller at low reynolds numbers. aside from the aerodynamic performance, the broadband noise associated with rotor rotating is another issue that needs to be addressed for small uavs (gur and rosen 2009). aeroacoustic noise not only can be an annoyance to human life, but to the well-being of animals as well(ditmer et al. 2015). leslie et al. (leslie et al. 2008) applied a straight transition strip at the leading edge of blade, and found that the broadband noise of the uav was greatly reduced. sinibaldi and marino (sinibaldi and marino 2013) experimentally measured the aeroacoustic signatures of two uav propellers, and reported that while the optimized propeller was much lower than that of the conventional one at lower thrust, the noise of the two would reach a similar magnitude as the thrust increased to a higher value. multi-rotor uavs commonly feature an even number of rotors that are designed into two sets with either clockwise or counter-clockwise rotations. very few studies can be found in literature that examined the rotor-to-rotor interactions on the aerodynamic and aeroacoustic performances of uavs. this is with the exception of yoon et al.(yoon et al. 2016), who computationally analyzed the aerodynamics performance of multi-rotor flows in a quadcopter, and found that the rotor interaction had significant effects on the vertical forces in hover motion. intaratep et al.(intaratep et al. 2016) measured the acoustic levels of a phantom ii at static thrust conditions and reported a dramatic increase in broadband noise as the rotor number increased from 2 to 4. though those studies documented the significant impacts of rotor interactions on the performances of small uavs, extensive work is still needed to understand the underlying fluid mechanics pertinent to multi-rotor interactions, and to uncover how rotor-to-rotor interactions affect the aerodynamic and aeroacoustic performances in small uavs. in the present study, an experimental investigation was performed to evaluate the rotor interactions on the aerodynamic and aeroacoustic performances of small uavs. two identical rotors with counter-rotating configuration were mounted separately on two stages and arranged laterally in a wide-open space. the separation distance between rotors was adjusted from l = 0.05d to l = 1.0d, which is 0.04d for the dji phantom 3. while high-accuracy measurements were conducted to quantify the thrust and noise at various separation distances, a high-resolution piv system was used to capture the detailed flow structures and the corresponding vortex evolutions behind the rotor. the effects of rotors separation distance (i.e., l = 0.05d, 0.1d, 0.2d, and 1.0d) on the aerodynamic and aeroacoustic performances of the uavs were examined comprehensively based on the measured results. finally, the resolved flow fields were correlated with the measured results to elucidate the underlying physics to explore/optimize design for next generation multi-rotor drones. ii. test model and experimental setups in the present study, the rotor models were made of hard plastic material and manufactured by a rapid prototyping machine (i.e., 3-d printing) that built the rotor models layer-by-layer with a resolution of about 25 microns. as shown schematically in fig. 1, the rotor has a diameter of 240 mm (d =240 mm), which is close to the size of phantom 3 rotor. an e63 airfoil profile was selected to generate the rotor blade due to its high lift to drag ratio at low reynolds numbers. the printed rotor was able to provide 3.0 newton thrust at a rotation speed of 4860 rpm. while the chord length of the rotor blade was set to 11 mm at the tip, as for other locations (i.e., from tip to 30% of the blade), they were determined by the optimal chord length equation 𝐶𝑟 = 𝐶𝑡𝑖𝑝 𝑟 , where ctip is the chord length at the tip, and r is a non-dimensional radius (i.e., 0.3 at 30% of the blade and one at the tip). the root section (i.e., from 30% to 5% of the blade) is considered as support part, which transits smoothly from the 30% chord section to the 5% chord section. it should also be noted that the twist angle of the blade from the tip to 30% of the blade was adjusted from 11.6° to 26.3°, and the solidity of the rotor blade was 0.12 in the present study. the rotor models, oriented horizontally, were installed ~300 mm above the test stage. the experiment stage was ~400 mm above the ground, therefore it is reasonable to neglect any rotor induced secondary flow effect on the test measurements. figure 1. schematic of rotor model used in the present study. the experimental study was performed in the advanced flow diagnostic and experimental aerodynamic laboratory located at iowa state university. figure 2 (a) shows the experimental setup used for the dynamic thrust and particle image velocimetry (piv) measurements in the present study, where the main test rig is a custom-built 8020 alumina stage. equipped with two identical rotors, the propellers in twin-rotor case were rotated in opposite directions (i.e., counterrotating). their rotational speeds were controlled separately by electronic speed control. the baseline case was simply achieved by removing an identical rotor from the twin-rotor configuration. comparisons were made between the twin-rotor and baseline cases to quantify the effect of flow interactions on the thrust performance of the uav rotor. as shown schematically in fig. 2 (a), a 16 mm aluminum rod was connected to a high-sensitivity force-moment sensor (jr3 load cell, model 30e12a-i40) to measure the dynamic thrusts of a single rotor. the jr3 load cell, which is composed of foil strain gage bridges, can measure the forces and moments on all three orthogonal axes. the precision for force measurements is within ±0.25% for the full range (40 n). note that the twin rotors were mounted on two separate stages in order to eliminate the induced mechanical vibration from the nearby rotor. during the experiment, the separation distance (l) between rotor tips was varied from 0.05d to 1.0d to study the rotor interactions on the aerodynamic and aeroacoustic performances of uav rotors. the jr3 was used to quantify the dynamic load acting on the rotors, which was acquired at a sampling rate of 3000 hz for 120s. the rotor rotational speed was monitored by a monarch instrument tachometer. as shown schematically in fig. 2 (b), an aeroacoustic noise measurement was performed in an anechoic chamber. this chamber has a physical dimension of 12×12×9 feet and its background noise level is lower than 20db with respect to the reference pressure of 20 µpa. during the experiment, the microphone was installed 6d away from the center point o of the twin-rotor system. the noise measurement was performed at 5 different angular positions with every 30◦ interval, starting from the front position of twin-rotor to 30◦ behind the rotors. all noise measurements were performed at the height of rotor hubs in the same plane with laser sheet. each sound measurement was recorded for 120s. in addition, planar piv measurements were made to quantify the flow interactions between the adjacent rotors, shown in fig. 2 (a). the air flow was seeded with ~ 2µm water based droplets generated by fog machine (i.e., rosco 1900). illumination was provided by a double-pulsed nd:yag laser (newwave gemini 200), adjusted on the second harmonic and emitting two pulses of 200 mj with the wavelength of 532 nm at a repetition rate of 2 hz. using a set of high-energy mirrors and optical lenses, the laser beam was shaped into a thin light sheet with a thickness of about 1.0 mm in the measurement interest. the illuminating laser sheet was firstly aligned horizontally along the induced flow direction, bisecting the hub in the middle of the rotor, to perform planar piv measurements in the x-z plane. in the present study, the planer piv includes both free-run and phase-locked cases. while the free-run piv were conducted to determine the ensemble-averaged flow statistics behind the rotor, the phase-locked piv were used to elucidate the dependence of unsteady wake vortices with respect to the position of rotor blades. for the phase-locked piv measurements, a digital tachometer was used to detect the position of a premarked blade. a pulse signal would be generated by the tachometer as the pre-marked blade passed through the vertical piv plane. the generated signal was then used as the input signal to digital delay generator (ddg) to trigger the piv system. through adjusting the time delays between the input signal from tachometer and the transistor-transistor logic signal from the ddg to trigger the piv system, different phase angles can be achieved. for each pre-selected phase angle, 300 frames of instantaneous piv were used to calculate the phase-averaged flow velocity behind the models. finally, a stereoscopic piv (spiv) experiment was performed to reveal the evolution of vortex structures at different downstream locations behind the rotors (i.e., in x-y planes). during the experiment, the laser sheet was rotated 90◦ from its original position to the vertical direction. image acquisitions were performed by two 14-bit high-resolution ccd cameras (pco2000, cooke corp.), which were arranged with an angular displacement configuration of about 45 degrees to get a largely overlapped view. with the installation of tilt-axis mounts and the laser illumination plane, the lenses and camera bodies were adjusted to satisfy the scheimpflug condition. the ccd cameras and double-pulsed nd:yag laser were both connected to a digital delay generator (berkeley nucleonics, model 565) to control the timing of the lasers and image acquisitions. a general in-situ calibration procedure was conducted to obtain the mapping functions between the images and object planes for the spiv measurements. a target plate (~350 × 350 mm2) with 2 mm diameter dots spaced at intervals of 8 mm was used for the in-situ calibration. the mapping https://app.quartzy.com/groups/86483/inventory/4511753?query=fog&sort=-type.name function used in the present study was a multi-dimensional polynomial function, which is third order for the directions parallel to the laser illumination plane (i.e., x and y directions), and second order for the direction normal to the laser sheet plane (i.e., z direction). (a) setup for dynamic loads and piv measurement (b) setup for aeroacoustic measurement figure 2. experimental setups used in the present study. in the present study, the instantaneous flow velocity vectors were obtained by using a frameto-frame cross-correlation technique to process the acquired piv images with an interrogation window size of 32 pixels × 32 pixels. an effective overlap of 50% of the interrogation windows was employed in planar piv image processing, which resulted in a spatial resolution of 2.4 mm (i.e., 0.01d) for the measurement results. similar processing methodology was also used for the spiv image processing. the instantaneous 2d velocity vectors were then used to reconstruct all three components of the flow velocity vectors in the laser illuminating plane by using the mapping functions obtained through the calibration procedure. after the instantaneous flow velocity vectors ( iu , iv , iw ) were determined, the distributions of the ensemble-averaged flow quantities such as mean velocity (u, v, w), normalized turbulence kinetic energy ( ( )'2 '2 '2 20.5 u v w u+ + ), spanwise vorticity ( i i y u w z x    = −   ) for the planar piv measurements, and streamwise vorticity ( i i z v u x y    = −   ) for the spiv measurements were obtained from a sequence of 1,000 instantaneous piv results (i.e., 300 for phase-locked piv). the uncertainty level for the piv measurements is estimated to be within 3% for the instantaneous velocity vectors, and within 5% for the measured ensembleaveraged quantities such as vorticity distributions. iii. measurements results and discussion a. dynamic load measurement results figure 3 presents the normalized thrust coefficient and standard deviation profiles for the twinrotor and baseline cases at various separation distances, where the thrust coefficient (i.e., 2 4 3 4 t t c n d  = ) and standard deviation are normalized by the corresponding quantities of the single rotor, which are 0.013 and 0.21 newtons, respectively. during the experiment, the rotational speed of each rotor (i.e., n) was kept constant at 81hz, but the separation distance between rotor tips was adjusted from l/d = 0.05 to 1.0. as shown clearly in fig. 3, though the separation distance was shortened by a factor of 20, the measured thrust coefficient for the rotor in twin-rotor case was found to drop less than 2%. this suggests that the generated mean thrust is independent of the separation distance. similar results were also reported by yoon et al.(yoon et al. 2016), who computationally studied the aerodynamic interactions of multi-rotor flows. it is worth mentioning that the separation distance also has a negligible effect on the power consumption of rotors. for a fixed rotating frequency, consumed power for the twin-rotor case was approximately same (i.e., difference within 1%) for all test cases. while the separation distance had a limited effect on the thrust coefficient of the rotor, the force fluctuations (i.e., thrust standard deviation) for the monitored rotor in twin-rotor system were found to increase dramatically as the separation distance reduces. more specifically, the measured thrust fluctuations for the l = 0.05d case was found to be ~2.4 times larger than that of the l= 1.0d case. as mentioned above, since the rotors were mounted on two separated stages, the significant augmentation in force fluctuation for the l= 0.05d case was believed to be only caused by the intensified flow interactions rather than mechanical vibrations induced by the second rotor. it should also be noted that for l > 0.5d, the thrust fluctuation for the twin-rotor case mitigated greatly and eventually reached a similar level with that of the single case. in general, the rotor interaction effect becomes negligible as l larger than 1.0d. (a). mean thrust coefficient (b). standard deviation of the measured thrust figure 3. effects of separation distance on the mean thrust coefficient (a) and standard deviation (b) of monitored rotor in twin-rotor case, where the thrust coefficient and standard deviation of single rotor (i.e., baseline case) are 0.013 n and 0.21 n, respectively. b. sound measurement results the twin-rotor configuration was then investigated to identify the rotor interaction effect on the aeroacoustic performance of small uavs. the experiment was performed in an anechoic chamber located at iowa state university. figure 4 represents the measured sound pressure level (i.e., spl) distributions at various separation distances (i.e., l = 0.05d, 0.2d, 1.0d). the microphone was installed at five different azimuthal positions (i.e., β = 60°, 90°, 120°, 150°, 180°), which were 6d away from the center and can be approximately treated as far-field locations. note that, the spl results displayed in fig. 4 were the result of the integration of the energy spectrum starting from 20 hz to 20,000 hz. as shown clearly in fig. 4, the measured spls were found to increase monotonously as the azimuthal angles increased from 90° to 180°, reached highest levels at position right ahead of the rotors, while exhibited smallest values by the side of rotor. it is well known that the noise map around a single rotor features a dipole distribution (i.e., symmetric along the rotor plane) (blackstock 2000). it would reach a maximum noise level at the positions right ahead or behind the rotor (i.e., β = 0°, 180°) but minimum noise at the side positions (i.e., β = 90°, 270°). as for the twin-rotor configuration, it can be treated as quasi-dipole distribution due to the relatively small gaps within the rotors compared to the microphone locations. it should also be noted that as the separation distance becomes smaller, the measured spls would gradually increase. a maximum enhancement of about 3 db can be observed for the l = 0.05d case in comparison to the l = 1.0d case at β = 180°, which is believed to be caused by the enhanced rotorto-rotor interactions. figure 4. spl distributions measured at 6d away from the center of the twin-rotor configuration. a spectrum analysis was performed to uncover the noise enhancement in terms of tonal noise and broadband noise. figure 5 shows the measured sound spectrums as a function of blade passing frequency harmonics at azimuthal angles of β =120° and 180°. clearly, the measured spls for the l = 0.05d case were found to be much higher than that of the l = 1.0d case at the integral multiple of the bpf (i.e., bpf, bpf2…), indicating an enhanced tonal noise component around the uav rotors. for incompressible flow condition, tonal noise is dominated by the loading noise (blackstock 2000), which is directly associated with the dynamic loading of the rotor blade. therefore, the augmented tonal noise for the l = 0.05d case is believed to be caused by the intensified thrust fluctuations as mentioned in fig. 3. it is worth mentioned that the high sparks at bpf ≈ 20 were confirmed to be the signal from the electronic motors that used to drive the rotors during the experiment. compared to the l = 1.0d case, the broadband noises for the l = 0.05d were found to increase mildly at the azimuthal angles of β =120°, 180°. recalling the lighthill’s stress tensor (blackstock 2000), the broadband noise is largely determined by the complex turbulent flow structures and shear layers, such as secondary flow distortions, blade trailing edge vortices, and tip vortices. as reported by carolus et al. (carolus et al. 2007), turbulent kinetic energy (tke) is important parameters that can be used to evaluate the broadband noise level. enhanced tke level will lead to augmented broadband noise. therefore, the broadband noise measurements in the present study suggest an augmented tke level for the twin-rotor configuration as the separation distance decrease, which was confirmed by the measured piv results shown below. (a) β = 120◦ (b) β = 180◦ figure 5. comparison of the measured sound spectrums between the l = 0.05d and the l = 1.0d cases at azimuthal angles of 120◦ and 180◦. c. free-run piv measurement results as mentioned above, free-run piv measurements were conducted in the present study to understand how the rotor-to-rotor interactions affect the aerodynamic and aeroacoustic performances of small uavs. figure 6 shows the measured free-run piv results in terms of ensemble-averaged flow velocity and normalized in-plane turbulence kinetic energy (tke, ( )'2 '2 20.5 tipu w u+ ) for the single and twin-rotor cases, where the rotor tip speed (i.e., / 2tipu d= ) is 61 m/s. as shown quantitatively in fig. 6 (a), the twin-rotor case presents a similar velocity distribution with that of the single rotor case. this explains the negligible effect of separation distance on measured mean thrusts as indicated in fig. 3(a). interestingly, as the induced flow convected downstream, the high-velocity region was found to converge from around the blade tip location (i.e., ~0.4d) to near the root position (i.e., ~0.2d), leading to the significant radial contraction behind the rotors. though the global features of the velocity distribution behind the rotors were similar for both cases, some differences can still be identified from the velocity contours. compared to the single rotor case, the measured velocity field in the twin-rotor case was slightly ‘dragged’ toward the adjacent rotor, which is believed to be caused by the coanda effect (i.e., a phenomenon in which a flow tends to attract to a nearby object). as a result, the w velocity component behind the twin-rotor was slightly lower than that of the single rotor in the corresponding down-part region (-0.5 < x/d < -0.2). fig. 6 (b) shows the comparisons of the normalized in-plane tke distributions between the single and twin-rotor cases. clearly, for the single rotor case, regions near the rotor tips were characterized with elevated in-plain tke, which was caused by the periodic vortex shedding from the blade tip. a similar phenomenon can be observed for the twin-rotor case, except the region with enhanced in-plain tke was found to be approximately doubled in the lateral direction, but reduced by half in the streamwise direction compared to the single rotor. since the two rotors were only 0.05d apart, the tip vortexes from rotors would interact severely with the nearby vortices, rendering enhanced in-plane tke distributions in contrast to the single rotor case in the near rotor region. however, because of the intensive interaction within rotors, the associated coherent structures behind the twin-rotor would also dissipate much faster than that of the single rotor, therefore the region with the augmented in-plain tke level would reduce rapidly as flow convected downstream. the elevated tke level is believed to be not only related to the significant enhancement of thrust fluctuations discussed in the twin-rotor case (i.e., shown in fig. 3), but also leaded to the augmentation of broadband noise (i.e., shown in fig. 5), which will discuss further in the following stereoscopic piv results. (a) ensemble-averaged velocity field (b) normalized in-plane tke distribution figure 6. measured piv results for the single rotor (left) and twin-rotor (right, l=0.05d) cases: (a) ensemble-averaged velocity field, (b) normalized in-plane tke distribution. d. phase-locked piv measurement results in the present study, phase-locked piv measurements were also employed to produce “frozen” images of the unsteady vortex structures behind the rotor at different phase angles. note that only the phase of left-hand rotor (i.e., shown in fig. 2(a)) in the twin-rotor system was monitored during the phase-locked piv test, whereas the other rotor can be treated as a free-run condition. figure 7 shows the comparison of phase-averaged velocity distributions between the single and twin-rotor cases at two different phase angles (i.e., θ = 0º, 120º). during the experiment, the phase angle is defined as the angle between the vertical y-z plane and the position of a pre-marked rotor blade. the pre-marked blade was in the most upward position (i.e., within the vertical y-z plane) for the phase angle of θ = 0º. as shown clearly in fig. 7, the existence of wave-shaped flow structures can be observed clearly at the tip height for the single rotor case, which is closely related to the periodical shedding of tip vortices behind the rotor. the wave-shaped structures would propagate downstream as the phase angle increased. however, due to the rotor interactions for the twin-rotor case, the wave-shaped structures were found to dissipate much faster and become less pronounced in comparison with that of the single rotor case. in addition, these flow structures behind rotors were found to shift radially downward to the adjacent rotor, which is consistent with the measured results shown in fig. 6. (a). phase angle θ = 0º (a). phase angle θ = 0º figure 7. phase-locked flow velocity distributions for the single rotor (left) and twin-rotor (right, l=0.05d) configurations figure 8 shows the comparison of the phase-locked vorticity distributions between the single rotor and twin-rotor cases, which can be used to reveal the effect of rotor interactions on the unsteady vortices more clearly. here, the separation distance is 0.05d. as expected, the general features of the vorticity distributions were found to be quite similar for both cases, especially for the upper-part region (i.e., as indicated using red dash line). flows behind the rotors were distinguished by pairs of tip vortices (i.e., # 1 5) and shear layers (i.e., # a d) that trailed after the blades. note that, the tip vortices were formed because of the pressure differences within the two sides of blade, while the shear layers were generated due to the merging of boundary layers from the upper and lower surfaces of the blade. (a) phase angle θ = 0º. (b) phase angle θ =120º figure 8. phase-locked vorticity distributions for the single rotor (left) and twin rotors (right, l=0.05d) configurations: for the single rotor case, when the pre-marked blade rotated over the piv measurement plane, a tip vortex would shed from the tip and propagate axially downstream, shown in fig. 8 (a). during this process, pairs of vortex structures (i.e., such as vortex # 4 with # 3, and vortex # 2 with # 1) would slowly merge into an integral one at ~ 0.7d. as the flow convected further downstream, they would completely vanish beyond 1.0d due to the aperiodic and highly turbulent flow in the rotor wake. as for the twin-rotor case (i.e., l = 0.05d), though similar distributions can be observed for the shear layer (i.e., # a – d), tip vortices were found to merge and dissipate much faster in comparison with that of the single rotor case. representative examples are the isolated vortices (i.e., # 1, # 2, # 3, # 4), shown in the case of single rotor, that become much harder to discern as z/d >0.2 in twin-rotor case. as the phase angle increased to θ = 120°, the associated turbulent structures, such as the shear layers and tip vortices, were found to propagate downstream in contrast to that of θ = 0°. focusing on the evolution of the vortex sheet # d (i.e., shear layer # d), it was initially adjacent to tip vortex # 4. as vortices convected axially downstream, however the outboard edge of the shear layer # d in fig. 8 (b) was found to interact with the tip vortex # 3 rather than vortex # 4. this is because the convecting speed (i.e., w velocity shown in fig. 7) of the shear layer was much higher than that of the tip vortex, thus the outboard edge of the shear layer would surpass the corresponding vortex, leading to complex vortex interactions. very similar phenomena were also reported by leishman (leishman 2006), who described the wake characteristics behind a helicopter rotor. e. stereoscopic piv measurement results to further explore the underlying physics pertinent to rotor-to-rotor interactions of small uavs, a stereoscopic piv (spiv) system was also utilized to quantify the complex flow field behind the rotors at multiple locations along the induced flow direction. note that the vectors shown in figure 9 and 10 are the resultant vectors of in-plane radial and tangential velocities behind the rotor. fig. 9 and fig. 10 show the comparisons of the ensemble-averaged turbulent quantities between the single rotor and twin-rotor cases at the downstream locations of x/d = 0.1 and 1.0 respectively. as revealed clearly in fig. 9 (a), the mean velocity contour (i.e., w component) behind the single rotor was found to be circular and symmetric as expected. interestingly, the rotating direction of the wake flow was found to be in the same direction with that of the rotor blade (i.e., both in counter-clockwise), which is contrary to the wind turbine scenario (hu et al. 2016; wang et al. 2016), where the swirling direction of the wake is opposite to the wind turbine rotation. this phenomenon is caused by an inherent working mechanism difference where the rotor drives the flow in the uav case, but the it is the flow that drives the rotor in the wind turbine case. it should also be noted that while the velocity distribution behind the single rotor was in a circular shape, a droplet-shaped velocity field was observed for the twin-rotor case due to the flow disturbance from the nearby rotor. carefully inspecting the flow features behind the twin rotors, a region with flow separation was identified at the top-right corner, which is believed to be the resultant effect of upwash flow and radial flow. within the interaction region, the two rotors would generate a steady upwash flow that interacts severely with the radial flow, resulting in the flow separation shown in fig. 9 (a). as the airflow traveled further downstream to the x/d = 1.0 plane, illustrated in fig. 10 (a), the previous circular-shaped velocity field behind the single rotor was transformed into a ‘horseshoe’ shape. not only that but also the orientation of the velocity contour was found to rotate by ~35° from its original position (i.e., in x/d = 0.1 plane). due to the flow inertia, the air stream would continue rotating after being accelerated by the blade as it traveled further downstream. though a similar deviation angle was observed for the twin-rotor case, the velocity contour was found to bend slightly toward the adjacent rotor in comparison with that of the baseline, especially for the region close to the flow separation region (i.e., region in black dash line). this phenomenon is believed to be closely related to the aforementioned coanda effect (i.e., fig. 6) where the induced airflow behind the twin rotors would be attracted and bent toward the nearby rotor. fig. 9 (b) shows the measured normalized tke distributions ( ( )2 2 2' ' ' 20.5 / tipu v w u+ + ) for the single rotor case in comparison with that of the twin-rotor case in the x/d = 0.1 plane. clearly, an o-ring shaped tke distribution was found to be the dominant feature for the single rotor case, which is because of the periodic vortex shedding from the rotor tip. the measured results are in accordance with the measured planar piv results shown in fig. 6. though the general pattern was found to be similar for both cases, except a region with significantly high tke levels was observed at the top-right corner for the twin-rotor case. as expected, flow separation would lead to greatly enhanced turbulence fluctuations (i.e., tke), which consequently resulted in dramatically intensified thrust fluctuations for the twin-rotor case as mentioned in fig. 3 (b). this also confirmed the conjecture that the enhanced broadband noise shown in fig. 5 was caused by the augmented tke level. imagine that as the blade struck through the separation region, it would certainly suffer strong fluctuations, leading to augmented tke and broadband noise. due to the viscous dissipation within the shear layer, the measured tke levels for both cases were found to decrease rapidly and reach a similar level at the location of x/d = 1.0 (i.e., shown in fig. 10 (b)). therefore, high tke zone could only exist in the near-blade region since it dissipates rapidly as induced flow propagated downstream. figure 11 shows the evolution of the ensemble-averaged streamwise velocity and the normalized tke distributions for the single and twin-rotor cases at three typical streamwise locations (i.e., x/d = 0.1, 0.5, and 1.0). as shown clearly in the figure, the mean velocity fields for both cases were found to become more uniform as induced flow convected downstream. in addition, the orientation of the induced flows was found to rotate by approximately 35° (i.e., in the plane of x/d = 0.1) in comparison with its original vertical position (i.e., in the plane of x/d = 1.0). as for the normalized tke distributions given in fig. 11 (b), a significantly higher tke level was initially observed at the top-right region of twin-rotor case in x/d = 0.1 plane, but it then decreased rapidly and reached a similar level with that of the single rotor due to the viscous dissipation within the shear layer. based on above measured results, the twin-rotor case with l/d = 0.05 experienced the strongest flow interactions within the rotors. adding a wingtip, rather than enlarging the separation distance, might be a practical method to alleviate the flow interaction effects if uav designers aren’t willing to sacrifice the compactness of the drones. (a) ensemble-averaged velocity field (b) normalized tke distribution figure 9. measured spiv results for the single rotor (left) and twin-rotor (right, l=0.05d) configurations in the x/d = 0.1 cross plane. (a) (a) ensemble-averaged velocity field (b) normalized tke distribution figure 10. stereoscopic piv results for the single rotor (left) and twin-rotor (right, l=0.05d) configurations in the x/d = 1.0 cross plane (a) ensemble-averaged velocity field, b) normalized tke distribution. figure 11. stereoscopic piv results for the single rotor (left) and twin rotors (right, l=0.05d) configurations at x/d = 0.1, 0.5, and 1.0 locations. iv. conclusions an experimental investigation was performed to study rotor-to-rotor interactions on the aerodynamic and aeroacoustic performances of small uavs. while the jr3 force transducer and microphone were used to quantify the thrust and noise levels of the rotors, a high-resolution particle image velocimetry (piv) system was used to conduct detailed flow field measurements to reveal the dynamic interactions between the rotors. the effects of separation distance (l = 0.05d, 0.1d, 0.2d, and 1.0d) on the aerodynamic and aeroacoustic performance of uavs were evaluated in detail based on the quantitative force, noise, and piv measurements. it was found that, while the separation distance had a negligible effect on the thrust coefficient of the rotor (i.e., variation within 2% for all test cases), the thrust fluctuations (i.e., thrust standard deviation) were found to increase dramatically as the separation distance became smaller. more specifically, the measured thrust fluctuations for the twin-rotor case (i.e., l= 0.05d) were found to be ~2.4 times larger than that of the baseline case. this is believed to be caused by the complex flow interactions within rotors as revealed by the detailed piv measurements. it was also found that the noise distribution for the twin-rotor case is a function of both azimuthal angle and separation distance, where the measured noise was found to increase as the azimuthal angle increased from 90° (i.e., side position) to 180° (i.e., right ahead the rotors), and to increase as the separation distance reduced from l = 1.0d to l = 0.05d. a maximum noise enhancement of ~3 db was recorded for the l = 0.05d case in comparison to that of the l = 1.0d case, which is the result of both tonal and broadband noise augmentations as indicated in the sound spectrum analysis. as shown quantitatively from the planar piv and stereoscopic piv measurement results, the induced flow behind the rotors was found to contract radially toward the axis of the rotor as the flow convected downstream. for the single rotor case, while most of the regions in the wake were devoid of flow structures, only the region near the blade tips was characterized by elevated inplain tke (i.e., in x-z plane) due to periodic tip vortex shedding. a similar phenomenon was observed for the twin-rotor case, except that the tke region was significantly higher at the topright area than that of single rotor case. due to the resultant effect of upwash and radial flows in the near wake of the twin-rotor case, a region with a flow separation was identified in the x-y cross plane, which led to significantly higher tke distributions and thrust fluctuations behind the twin rotors. it should also be noted that the velocity field for the twin-rotor case was found to be attracted and bent toward the nearby rotor due to the coanda effect. in general, the measured quantitative results given in the present study are believed to be very beneficial in understanding how rotor-rotor interactions affect the aerodynamic and aeroacoustic performances of small uavs. it depicted a vivid picture regarding the complex flow features behind the rotors, which further explained their correlations with the enhanced force fluctuations and noise levels. such quantitative information is highly desirable to elucidate the underlying physics pertinent to rotor interactions, and to explore/optimize design paradigms for better commercial uav designs. acknowledgments the supported of national science foundation (usf) usa with grant numbers of cbet 1438099 is gratefully acknowledged. references blackstock dt (2000) fundamentals of physical acoustics. a wiley-interscience bouabdallah s, becker m, siegwart r (2007) autonomous miniature flying robots: coming soon! research, development, and results. ieee robot autom mag 14:88–98. https://doi.org/10.1109/mra.2007.901323 brandt j, selig m (2011) propeller performance data at low reynolds numbers. in: 49th aiaa aerospace sciences meeting including the new horizons forum and aerospace exposition. american institute of aeronautics and astronautics bristeau p, martin p, salaün e (2009) the role of propeller aerodynamics in the model of a quadrotor uav. in: control conference (ecc carolus t, schneider m, reese h (2007) axial flow fan broad-band noise and prediction. j sound vib 300:50–70. https://doi.org/10.1016/j.jsv.2006.07.025 ditmer ma, vincent jb, werden lk, et al (2015) bears show a physiological but limited behavioral response to unmanned aerial vehicles. curr biol 25:2278–2283. https://doi.org/10.1016/j.cub.2015.07.024 goebel me, perryman wl, hinke jt, et al (2015) a small unmanned aerial system for estimating abundance and size of antarctic predators. polar biol 38:619–630. https://doi.org/10.1007/s00300-014-1625-4 gur o, rosen a (2009) design of quiet propeller for an electric mini unmanned air vehicle. j propuls power 25:717–728. https://doi.org/10.2514/1.38814 hu h, wei t, wang z (2016) an experimental study on the wake characteristics of dual-rotor wind turbines by using a stereoscopic piv technique. 34th aiaa appl aerodyn conf intaratep n, alexander wn, devenport wj, et al (2016) experimental study of quadcopter acoustics and performance at static thrust conditions. in: 22nd aiaa/ceas aeroacoustics conference. american institute of aeronautics and astronautics, reston, virginia leishman g (2006) principles of helicopter aerodynamics. cambridge university press leslie a, wong kc, auld d (2008) broadband noise reduction on a mini-uav propeller. in: 14th aiaa/ceas aeroacoustics conference (29th aiaa aeroacoustics conference). american institute of aeronautics and astronautics, reston, virigina lucieer a, turner d, king dh, robinson sa (2014) using an unmanned aerial vehicle (uav) to capture micro-topography of antarctic moss beds. int j appl earth obs geoinf 27:53–62. https://doi.org/10.1016/j.jag.2013.05.011 merchant m, miller ls (2006) propeller performance measurement for low reynolds number uav applications. in: 44th aiaa aerospace sciences meeting and exhibit. american institute of aeronautics and astronautics, reston, virigina otsuka h, nagatani k (2016) thrust loss saving design of overlapping rotor arrangement on small multirotor unmanned aerial vehicles. in: 2016 ieee international conference on robotics and automation (icra). ieee, pp 3242–3248 russell c, jung j, willink g, glasner b (2016) wind tunnel and hover performance test results for multicopter uas vehicles. in: ahs 72nd annual forum. fl sinibaldi g, marino l (2013) experimental analysis on the noise of propellers for small uav. appl acoust 74:79–88. https://doi.org/10.1016/j.apacoust.2012.06.011 wang z, tian w, ozbay a, et al (2016) an experimental study on the aeromechanics and wake characteristics of a novel twin-rotor wind turbine in a turbulent boundary layer flow. exp fluids 57:150. https://doi.org/10.1007/s00348-016-2233-6 yoon s, lee hch, pulliam th (2016) computational analysis of multi-rotor flows. in: 54th aiaa aerospace sciences meeting. american institute of aeronautics and astronautics, reston, virginia 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 fluorescent piv using atomized liquid particles adit s. acharya1*, k. todd lowe1, wing f. ng1 1 virginia tech, advanced propulsion and power laboratory, blacksburg, va, usa * aacharya@vt.edu abstract it is shown that aerosolized fluorescent particles generated using a venturi-type atomizer, from a solution of fluorescent kiton red 620 dye in a water/glycol fluid, provide effective flow seeding for fluorescent piv. the atomized liquid particles were found to be of acceptable size for piv purposes, with 92% of detected particles by number concentration measuring < 1 μm in diameter. a piv application was conducted in a wind tunnel (freestream velocity u∞ = 27 m/s), using the particles for measurement of the boundary layer flow approaching a forward-facing step (approach boundary layer momentum thickness reynolds number of 𝑅𝑒𝜃 = 5930), to identify potential benefits in near-wall regions normally affected by unwanted laser reflections from tunnel surfaces. particles were generated from solutions with dye molar concentrations of 2.5 × 10−3 and 1.0 × 10−2 mol/l, and piv images were obtained for both elastic mie scattering and filtered, stokes-shifted fluorescent light. raw images indicate that the fluorescence yield of the 1.0 × 10−2 mol/l solution provides piv images with high contrast, even in the near-surface regions where mie scattering images are highly affected by surface reflections. boundary layer profiles are processed in the adverse pressure gradient region leading up to the forward-facing step, where the fluorescent piv performed comparably to the most optimized mie scattering piv; both obtained data as near to the wall as 30 μm, or 2 viscous wall units in our flow of interest. these results indicate that the new seeding method holds excellent promise for near-surface measurement applications with more complicated three-dimensional geometries, where it is impossible to arrange piv cameras to reject surface-scattered light. 1 introduction particle image velocimetry (piv), which involves the optical measurement of light-scattering tracer particles, has become a ubiquitous flow diagnostic technique over the past few decades. in piv, a fluid flow of interest is seeded with small particles which have negligible inertia compared to drag forces (i.e., a low stokes number) and thus effectively follow streamlines [raffel et al. (2018)]. the particles are illuminated with laser light, which they scatter elastically at the wavelength of the incident laser (i.e., mie scattering, in the case of spherical particles). their motion is recorded with a quick succession of photographs, after which their velocities are obtained by image cross-correlation. a frequent challenge for piv experimentalists is the occurrence of surface laser reflection, or “flare”, in flows around models [paterna et al. (2013)], flows involving free surfaces [pedocchi et al. (2008)], and studies of near-wall regions in general [cadel et al. (2016)]. flare is detrimental to piv correlations because it decreases the image contrast and signal-to-noise ratio (snr) in the vicinity of surfaces. light that is scattered by surfaces can be far more intense than particle light scattering, potentially leading to saturation of sensor pixels and the loss of flow vectors [chennaoui et al. (2008)]. paterna et al. (2013) also note the possibility of camera sensor damage from intense flare, although with modern cmos cameras this is less of a concern. attempts to reduce laser flare often involve modifications to surfaces themselves, such as a coat of black paint [wernet (2000)] or clear surfaces that match the fluid’s index of refraction [uzol et al. (2002)]. the comparative study of materials and surface treatments by paterna et al. (2013) concluded that a coating of fluorescent paint was the most effective method of reducing flare in air-based experiments, given that no material can match the refractive index of air. the fluorescent paint technique relies on laser-induced fluorescence (lif), the emission of light that is red-shifted relative to any absorbed laser light. this alteration of wavelength is also known as the stokes shift (as opposed to much weaker, blue-shifted fluorescence, termed anti-stokes shift). surfaces covered with fluorescent paint emit stokesshifted light that can be blocked with a band-pass filter to limit their impact on piv measurements; miescattered light at the laser wavelength from tracer particles is still allowed through. alternatively, laser flare reduction may be accomplished with the use of fluorescent tracer particles; their stokes-shifted light may be collected through a long-pass filter that blocks surface reflections at the laser’s wavelength. fluorescent piv has been used in water-based experiments [poussou and plesniak (2006)], but is more challenging for gas flows, which require smaller particles and careful consideration of particle inhalation hazards [maisto et al. (2013)]. for example, the study by chennaoui et al. (2008) successfully demonstrated flare reduction with fluorescent piv in air, but made partial use of hazardous materials that warranted protective measures. a more recent study by petrosky et al. (2015) demonstrated piv with fluorescent dye-doped particles, with the goal of avoiding hazardous substances; kiton red 620 (kr620) dye was selected for its low toxicity. the kr620 dye was used to dope polystyrene latex (psl) microspheres, which are commonly used as piv tracer particles [raffel et al. (2018)]. the ensuing experiments successfully allowed for accurate piv measurements very near the surface of a flat plate, where conventional piv techniques were shown to be severely hampered by flare. this result was notable for its combined use of safe materials and tracer particles small enough to be suitable for gas flows; as noted by petrosky et al., the intensity of fluorescent light from particles is typically two to three orders of magnitude lower than mie scattering intensity, and this difference is exacerbated for small particles. notably, all examples of fluorescent piv to this point have involved the use of solid tracer particles. while effective, solid particles bring about a variety of undesirable challenges. the generation of dye-doped particles can be cumbersome, involving an emulsion polymerization process [wohl et al. (2015)] or the grounding and dispersal of solidified resin [pedocchi et al. (2008)]. these processes can be lengthy and expensive, requiring special facilities and materials. while researchers may order dye-doped particles for delivery, doing so constrains an experiment to a limited set of dye concentrations, which can have an impact on fluorescent piv results. in the current study, the authors expand on the work of petrosky et al. (2015), exploring a novel method of liquid fluorescent tracer particle generation and injection that is relatively simple and inexpensive when compared to the aforementioned solid particle techniques. the particles are first shown to be of acceptable size for piv purposes. then, they are used in a piv experiment in the boundary layer of a wind tunnel approaching a forward-facing step. both fluorescent and mie piv are conducted and comparisons are made between their wall boundary layer profiles and skin friction coefficient results, showing the ability of the fluorescent piv to perform comparably to the most optimized mie-piv case. 2 experimental methods liquid fluorescent tracer particles were generated with a method the authors recently developed for the seeding of high-pressure nozzles [acharya et al. (2021)]. this method, depicted conceptually in figure 1, involved two main components: the nozzle/preceding tubing, and a separate liquid reservoir. the reservoir was connected to the throat of a venturi contraction upstream of the nozzle. when both the nozzle and reservoir were supplied with the same total pressure, the static pressure drop at the venturi throat created suction, drawing the reservoir’s liquid into the nozzle tubing. once in the tubing, strong shear forces atomized the liquid into fine particles. note in figure 1 the inclusion of a needle valve between the liquid reservoir and venturi throat; this was added after the initial study to aid with mass flow rate control. figure 1: schematic of venturi seeding method for a high-pressure nozzle [acharya et al. (2021)] while the original intent of the device was for laser-based velocimetry and visualization of the nozzle plume itself, the authors saw potential in using the dense spray for piv on external areas of interest, or even for seeding in wind tunnels. additionally, it was thought that a solution of fluorescent dye in a suitable liquid would be atomized in the same way as depicted in figure 1, creating fluorescent tracer particles for piv. kiton red 620 dye was chosen for its safety and previous success in the study by petrosky et al. (2015). the dye was dissolved in a non-toxic, proprietary water/glycol solution (i-fog fluid, martin lighting), used for long-lasting fog generation. two separate dye concentrations were used: 1.0 × 10−2 mol/l and 2.5 × 10−3 mol/l. experiments aimed to assess the suitability of the generated particles for fluorescent piv and to demonstrate the potential advantages of such a method for near-wall measurements. first, a tsi 3321 aerodynamic particle sizer (aps) was used to extract and analyze particles from the nozzle’s plume. this device determines aerodynamic size distributions of ingested particles over a range of 0.5 to 20 μm in diameter. the venturi device was supplied with 4.34 mpa (630 psia) from a compressed nitrogen tank, with its reservoir filled with i-fog fluid and its needle valve 92% closed. this generated a spray that was directed at the inlet of the tsi 3321 aps for 30 seconds. the sizing test was followed by a piv experiment in the small boundary layer (sbl) wind tunnel at virginia tech. the sbl tunnel is an open-circuit wind tunnel that features a blower capable of delivering 62.30 m3/min of air, a series of honeycombs and screens to eliminate large-scale turbulence, and a 24.13 cm x 11.03 cm x 199.39 cm acrylic/float glass optical test section with roughness introduced at the test section inlet for boundary layer tripping and thickening. the tunnel was operated such that the freestream flow velocity was nominally 27 m/s in the test section. relevant flow parameters were obtained with the piv experiment (details below) and a pitot-static probe; to fill in the outer region missed by the highly magnified piv setup, piv data were fit to a profile of 𝑈 𝑈∞ = ( 𝑦 𝛿 ) 1 7 , where 𝑈 is velocity, 𝑈∞ is the velocity of the freestream, 𝑦 is the height above the wall, and 𝛿 is the boundary layer thickness. this allowed for determination of the thickness and approximate velocities for the full boundary layer. flow parameters are shown in table 1, where uτ is friction velocity, wu is the wall unit height, δ* is displacement thickness, θ is momentum thickness, reθ is momentum reynolds number, and h is shape factor. table 1: sbl wind tunnel flow parameters parameter u∞ uτ wu δ δ* θ reθ h value 27 0.9880 15 39 4.29 3.25 5930 1.32 units m/s m/s μm mm mm mm the piv experimental setup is depicted in figure 2. the venturi seeding mechanism was placed such that its spray was directed into the suction inlet of the tunnel. from there, seeded flow passed through the blower, plenum, and contractions into the optical test section. there, a flat aluminum plate of height 4.78 mm was secured to the floor to create a forward-facing step flow configuration to challenge the measurement system. a two-dimensional/two-component piv arrangement was used, in the common wall-grazing view imaging configuration optimized for boundary layer measurement [willert (2015)]. an evergreen dual-pulsed 532 nm laser was fitted with sheet-forming optics to produce a laser sheet aligned with the streamwise/normal-to-wall plane. a lavision imager scmos camera (2560 x 2160 pixels), fitted with a 100 mm focal length lens, was used to acquire images from a 32 mm x 32 mm region in the wall boundary layer, capturing the leading edge of the forward-facing step and a 27-mm-long section of the tunnel upstream of it. for fluorescent piv measurements, an omega optical 560 nm long pass filter (model 560hlp) was attached to the camera lens to reject 532 nm laser light. it was expected, as per petrosky et al. (2015), that kr620 dye would emit stokes-shifted light mostly above 560 nm. first, a set of 1000 mie images was taken with the lens aperture set at f/2.8, the widest possible aperture setting. another set of 1000 mie images was taken with the aperture set to f/22, reducing flare and particle intensities alike. finally, the aperture was set to f/2.8 and the high-pass filter was attached to the lens. two sets of 1000 fluorescent images were taken; one for a dye concentration of 1.0 × 10−2 moles per liter of i-fog, and one for 2.5 × 10−3 mol/l. figure 2: sbl wind tunnel piv experiment setup (not to scale); red dashed square indicates camera fov piv processing was done in lavision’s davis 8.4 software. the time domain filter method developed by sciacchitano and scarano (2014) was used on all data sets to improve performance in flareaffected regions. acquired images were processed with a multi-pass technique; the first pass used 64 x 64 pixel interrogation windows with 50% overlap, and the second pass used 32 x 32 pixel interrogation windows with 87% overlap. spurious vectors were detected with the peak ratio q, or the ratio of the highest to next-highest displacement correlation peak for a given interrogation window. vectors were considered “spurious” if they had a q of 1.3 or greater. additional spurious vector detection was performed with the median test introduced by westerweel (1994). vectors were removed if their residual value, r, was greater than 2. removed vectors were replaced with interpolated data. 3 results as previously stated, the goals of the experiments were to prove the suitability of the generated particles for piv, and to demonstrate promising fluorescent piv performance in regions close to the acrylic lower wall of the wind tunnel which are normally affected by surface flare. in this section, the former is addressed with statistical measurements from the tsi 3321 aps, and the latter is shown through raw piv images along with comparisons of piv-based boundary layer profiles and skin friction coefficients for fluorescent and mie piv cases. 3.1 particle sizes the tsi 3321 aps collected 721,602 particles; statistical size parameters of the particles are displayed in table 2, and a histogram of aerodynamic diameters is presented in figure 3. note that the aps was unable to determine diameters below 0.523 μm, which included nearly 8% of particles by number concentration; this created a possible bias in statistical results. despite this, the aerodynamic median diameter was found to be 0.725 μm, and 92% of particles by number concentration were at, or below, 1 μm in diameter. while ideal particle diameter limitations in any flowfield depend on the expected accelerations, melling (1997) states that 1 μm or less is typically suitable for gas flows. further information on the performance of these particles can be obtained from relevant stokes numbers. using the aerodynamic median diameter of 0.725 μm, the particle lag timescale was found to be 1.7 μs. in the boundary layer flow used for this study’s piv experiment, this corresponds to a stokes number of 0.0012 for the integral timescale and 0.3121 for the kolmogorov timescale. raffel et al. (2018) report that tracer particles with stokes numbers below 0.1 typically yield acceptable accuracy, implying that the analyzed particles are suitable for measuring all but the smallest fluctuations in such a boundary layer. the aps data therefore suggests that the venturi device’s generated liquid particles are generally acceptable for piv purposes for subsonic aerodynamics experiments at the stated pressure and needle valve settings. table 2: statistical data for diameters of particles collected by tsi aerodynamic particle sizer statistical parameter value [μm] aerodynamic median 0.725 aerodynamic mean 0.933 geometric mean 0.829 geometric standard deviation 1.540 figure 3: histogram of aerodynamic diameters of particles collected by tsi 3321 aps 3.2 piv imaging the piv experiment was conducted to confirm the effectiveness of the fluorescent particles for piv and to highlight differences between fluorescent and mie piv. example instantaneous raw images for the four data sets are shown in figure 4. in these images, both axes are nondimensionalized using the height h of the aluminum step. the lower tunnel wall, at y/h = 0, is highlighted with an artificial blue line. notably, the liquid seeding particles for the 1.0 × 10−2 mol/l case were clearly visible even through the fluorescent filter which blocked the incident laser wavelength, as shown in figure 4d. particles for the 2.5 × 10−3 mol/l case were also visible (figure 4c), though dimmer. the fluorescent piv images, as expected, had lower general particle intensities than their mie piv counterparts – most 1.0 × 10−2 mol/l fluorescent particles were roughly 50 times less intense than mie piv particles at the same aperture setting (f/2.8). they also appeared to show fewer particles, but this was an artifact of the images’ unchanged intensity axes. some small near-wall regions of brightness were visible in the fluorescent piv images; these were likely accumulations of out-of-focus fluorescent particles on the wall itself, as they were seen to grow and shift over time. as expected, background intensity counts were considerably higher for the mie f/2.8 case than the other three. figure 4a shows significant flare in the near-wall region, despite the transparent acrylic. this was exacerbated at lower x/h values, closer to the reflective forward-facing step, which itself was located at x/h = 0. figure 4b shows that reducing the aperture by 6 full stops to f/22 (thus reducing passing light by a factor of 64) significantly mitigated the flare, but horizontal flare streaks and a discernable thin layer of extreme brightness just above y/h = 0 were still visible. in figures 4c and 4d, the fluorescent cases, many of the near-wall flare issues were reduced or eliminated. the region of extreme brightness just above y/h = 0 appeared thinner, and the horizontal streaks of flare visible in figure 4b were no longer present. figure 4: example raw piv images for select region upstream of forward-facing step (x/h = 0); tunnel wall (y/h = 0) highlighted with blue line 3.3 boundary layer comparisons boundary layer data were extracted for the streamwise mean velocities of each data set. figure 5 is a plot of the boundary layer profiles at an x-position that was 5.5 step heights upstream of the step (x/h = -5.5), where step-induced pressure gradient effects would be the least amongst the analyzed stations. the plot is presented in common wall coordinates, which normalize the velocity and height using friction velocity, which itself relates to the wall shear stress and velocity gradient as 𝜏𝑤 = 𝜈 𝜕𝑈 𝜕𝑌 | 𝑦=0 = 𝜌𝑢𝜏 2. the friction velocities were determined using the well-known clauser chart method [clauser (1956)], which assumes that the velocity profiles follow a universal logarithmic form in the “log-law” region, chosen here to be 35 < y+ < 100. for comparison throughout the near wall region, the spalding profile [spalding (1961)] was also plotted; this profile blends the viscous sublayer (where u+ = y+) and the log-law region with a fit through the buffer region between them. figure 5 shows good agreement between the spalding profile, mie f/22 piv, and fluorescent f/2.8 piv at 1.0 × 10−2 mol/l. below the log-law region, these profiles nearly match the spalding profile as it transitions towards the viscous sublayer. this is not the case for mie f/2.8 piv and fluorescent f/2.8 piv at 2.5 × 10−3 mol/l, which both diverge from the spalding profile in the buffer region. the clear improvement between mie f/2.8 piv and mie f/22 piv suggests that the effects of increased laser flare significantly hampered f/2.8 piv measurements near the wall. there exists a similar clear improvement between the fluorescent piv at 2.5 × 10−3 mol/l and 1.0 × 10−2 mol/l; the increased dye concentration is necessary for accurate piv results. the fluorescent yield of tracer particles is generally proportional to dye concentration [lemoine et al. (1999)]; so, there must exist a threshold below which piv performance is negatively affected. however, dye concentrations in the present study were far higher than those used by lemoine et al., a regime where significant self-quenching and loss of fluorescence yield would normally be expected. it is possible that the tracer particles experienced low levels of excitation flux, only absorbing a small amount of the laser energy and thus keeping the particles in the regime where fluorescent yield remains proportional to dye concentration. the forward-facing step created an adverse pressure gradient in the upstream near-wall region; the log-law region of the boundary layer profile could not necessarily be expected to match the spalding profile closer to the step than x/h = -5.5. as shown by aubertine and eaton (2005) and wang et al. (2016), boundary layer profiles are significantly affected by adverse pressure gradients at their higher y+ values. the general trend is for u+ values in these regions to increase across the gradient. however, at lower y+ values, the boundary layer profiles remain relatively unchanged across the gradient and continue to match the spalding profile well. thus, in the present study, the lowest values of the boundary layer profiles (y+ < 11) were matched with the spalding profile by way of adjusting the friction velocity at each axial station. the resulting profiles in wall scaling are shown in figure 6 for all four piv cases, in the same style as wang et al. (2016). as expected, u+ values in the upper regions tended to increase across the adverse pressure gradient (approaching x/h = 0) due to the wall friction reduction. a friction velocity was found at each axial station of each piv case through the aforementioned adjustments. these were converted to skin friction coefficients, as cf = 2uτ 2 / uref 2, where uτ is the friction velocity and uref is a reference velocity, chosen here to be the freestream velocity of 27 m/s. the resulting friction coefficients are plotted in figure 7. all piv cases demonstrated a general decreasing trend as the step was approached, consistent with previous computational and oil-film interferometry findings regarding skin friction coefficient in an adverse pressure gradient [na and moin (1998), pailhas et al. (2009)]. the data for mie f/2.8 piv and fluorescent piv at 2.5 × 10−3 mol/l descend erratically, however; this conflicts with the smoothness and consistency of the curves found by na and moin and pailhas et al. the data for mie f/22 piv has less variance as the flow approaches the step, but the friction coefficient of the fluorescent piv at 1.0 × 10−2 mol/l exhibits the most physically consistent variation across the pressure gradient. figure 5: boundary layer profiles for all four cases far upstream of step (symbols not shown above y+ = 13); spalding profile shown for comparison figure 6: boundary layer development across the adverse pressure gradient approaching the step; spalding profile shown for comparison figure 7: skin friction coefficients for all piv cases upstream of the step 4 conclusions aerosolized fluorescent particles generated using a venturi-type atomizer were found to be suitable for piv purposes; this was demonstrated in multiple ways. first, the particles were found to be of acceptable size for piv in many aerodynamic flows, with a median aerodynamic diameter of 0.725 μm. second, the fluorescent particles with a dye concentration of 1.0 × 10−2 mol/l produced raw piv images with good contrast when a filter was used to eliminate the incident 532 nm laser light and long-pass stokes-shifted fluorescence from the particles. using the fluorescence-passing filter resulted in significantly reduced laser flare in near-wall regions. third, the measured boundary layer streamwise mean velocity profile of the fluorescent piv case with a dye concentration of 1.0 × 10−2 mol/l was in close agreement with the theoretical spalding profile. this method of liquid fluorescent piv shows promise for potentially generating more accurate results in near-wall regions of a flow. the streamwise evolution of skin friction obtained from fits to the spalding profile for 𝑦+ < 11 showed noticeable reduced variance in the 1.0 × 10−2 mol/l case throughout the adverse pressure gradient compared with the three other cases considered. the smooth and monotonic decrease of the skin friction coefficients from the 1.0 × 10−2 mol/l fluorescent piv case was in qualitative agreement with trends observed in previous studies of adverse pressure gradients using computational means and oil-film interferometry. taken together, the results indicate that using a dye concentration of 1.0 × 10−2 mol/l and the venturi-based atomizer is a viable, scalable, and cost-effective approach for implementing fluorescencebased piv for measurements near surfaces in aerodynamic flows. potential future studies may investigate the method’s use for piv in complex geometries where flare is otherwise difficult to mitigate. references acharya as, lowe kt, ng wf, and danehy pm (2021) seeding mechanism for high-pressure nozzles. in aiaa scitech 2021 forum – virtual event, january 11-21 aubertine cd and eaton jk (2005) turbulence development in a non-equilibrium turbulent boundary layer with mild adverse pressure gradient. journal of fluid mechanics 532:345-364 cadel dr, shin d, and lowe kt (2016) a hybrid technique for laser flare reduction. in 54th aiaa aerospace sciences meeting – san diego, ca, usa, january 4-8 chennaoui m, angarita-james d, ormsby mp, angarita-james n, mcghee e, towers ce, jones ac, and towers dp (2008) optimization and evaluation of fluorescent tracers for flare removal in gas-phase particle image velocimetry. measurement science and technology 19:115403 clauser f (1956) the turbulent boundary layer. advances in applied mechanics 4:1-51 lemoine f, antoine y, wolff m, and lebouche m (1999) simultaneous temperature and 2d velocity measurements in a turbulent heated jet using combined laser-induced fluorescence and lda. experiments in fluids 26:315-323 maisto pmf, lowe kt, byun g, simpson r, verkamp m, danley je, koh b, tiemsin pi, danehy pm, and wohl cj (2013) characterization of fluorescent polystyrene microspheres for advanced flow diagnostics. in 43rd fluid dynamics conference – san diego, ca, usa, june 24-27 melling a (1997) tracer particles and seeding for particle image velocimetry. measurement science and technology 8:1406-1416 na y and moin p (1998) the structure of wall-pressure fluctuations in turbulent boundary layers with adverse pressure gradient and separation. journal of fluid mechanics 377:347-373 pailhas g, barricau p, touvet y, and perret l (2009) friction measurement in zero and adverse pressure gradient boundary layer using oil droplet interferometric method. experiments in fluids 47:195-207 paterna e, moonen p, dorer v, and carmeliet j (2013) mitigation of surface reflection in piv measurements. measurement science and technology 24:057003 pedocchi f, martin je, and garcia mh (2008) inexpensive fluorescent particles for large-scale experiments using particle image velocimetry. experiments in fluids 45:183-186 petrosky bj, lowe kt, bardet pm, tiemsin pi, wohl cj, danehy pm, and andre m (2015) particle image velocimetry applications using fluorescent dye-doped particles. in 53rd aiaa aerospace sciences meeting – kissimmee, fl, usa, january 5-9 poussou s and plesniak mw (2006) near-field flow measurements of a cavitating jet emanating from a crown-shaped nozzle. journal of fluids engineering 129:605-612 raffel m, willert ce, scarano f, kahler cj, wereley st, and kompenhans j (2018) particle image velocimetry: a practical guide. springer sciacchitano a and scarano f (2014) elimination of piv light reflections via a temporal high-pass filter. measurement science and technology 25:084009 spalding d (1961) a single formula for the law of the wall. journal of applied mechanics 28:455-458 uzol o, chow yc, katz j, and meneveau c (2002) unobstructed particle image velocimetry measurements within an axial turbo-pump using liquid and blades with matched refractive indices. experiments in fluids 33:909-919 wang qc, wang zg, and zhao yx (2016) on the impact of adverse pressure gradient on the supersonic turbulent boundary layer. physics of fluids 28:116101 wernet mp (2000) development of digital particle imaging velocimetry for use in turbomachinery. experiments in fluids 28:97-115 westerweel j (1994) efficient detection of spurious vectors in particle image velocimetry data. experiments in fluids 16:236-247 willert ce (2015) high-speed particle image velocimetry for the efficient measurement of turbulence statistics. experiments in fluids 56:17 wohl cj, kiefer jm, petrosky bj, tiemsin pi, lowe kt, maisto pmf, and danehy pm (2015) synthesis of fluorophore-doped polystyrene microspheres: seed material for airflow sensing. acs applied materials & interfaces 7:20714-20725 mytitle 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 stereo piv measurements of oscillatory plasma forcing in the cross-plane of a channel flow m. t. hehner1∗, l. h. von deyn1, j. serpieri1, s. pasch1, t. reinheimer2, d. gatti1, b. frohnapfel1, j. kriegseis1 1 institute of fluids mechanics (istm), karlsruhe institute of technology (kit), germany 2 institute for applied materials (iam), karlsruhe institute of technology (kit), germany ∗ marc.hehner@kit.edu abstract the present work describes an experimental investigation that applies stereo particle image velocimetry in a cross-plane of a turbulent channel flow that is additionally perturbed by spanwise oscillatory body forces, induced by a plasma actuator and designed to mimic the effect of spanwise wall oscillations. the experiment is aimed at retrieving the forcing-correlated scales and the turbulent flow stochastic fluctuations for the measured cross-plane. the first are macroscopic scales and require a larger investigation domain while the latter benefit of a higher resolution. furthermore, the extended flow-field dynamic range posed a challenge on the experiment design, finally leading to an optimal tradeoff. the results of the unactuated flow compare well to the direct numerical simulations of hoyas and jiménez (2008), while the actuated case demonstrates strong near-wall momentum addition and spanwise modulation of the streamwise flow component. 1 introduction control of wall-bounded flows is a broad topic at which many numerical investigations were focused on friction-drag reduction in turbulent channel flows (see review quadrio (2011)) that can be achieved by streamwise traveling waves (sttws) of spanwise wall velocity (quadrio and ricco (2011), gatti and quadrio (2016)). experimental realization of sttws typically require complex devices with actively moving components (choi et al. (1998), auteri et al. (2010)). whereas implementations of sttws without any moving parts are currently being investigated by means of plasma actuators (jukes et al. (2006), hehner et al. (2019, 2020)), a particular class of actuator which can be flush-mounted to the surface and produces a mainly wall-parallel body force (see reviews benard and moreau (2014), kotsonis (2015), kriegseis et al. (2016)). therefore, the objective of this work is to provide an advanced measurement system for which underlying mechanisms of a manipulated/controlled flow and the inherent effects on friction drag can be studied in a channel and compared to an uncontrolled flow. the means of choice, as shown in figure 1, is a stereo particle image velocimetry (spiv) setup which captures a cross-plane of the channel flow (y, z) (see also kriegseis et al. (2015) for this type of setup). this setup allows reconstruction of spanwise (w), wall-normal (v) and streamwise (u) velocity components. hence, the present work particularly revolves around both qualification of the spiv setup in an uncontrolled fully-developed turbulent channel flow and topological interplay effects between oscillatory plasma discharges and external flow. 2 experimental procedure the windtunnel test section is a channel with a length, width and height of 4000 mm × 300 mm × 25.2 mm (channel semi height h = 12.6 mm), respectively, and the measurement plane of the spiv setup was arranged 100 mm upstream of the channel exit. note that the coordinate system (x, y, z) and corresponding flow components (u, v, w) are indicated in the inset of figure 1 (upper left) which also shows the operating plasma-actuator array at the channel wall. the spiv setup was run in double-frame mode and image acquisition was carried out by two photron fastcam sa4 high-speed cameras that were placed at the left and mailto:marc.hehner@kit.edu right side (angles of about 27 degrees) of the channel exit. the seeding particles (di-ethyl-hexyl-sebacate) were illuminated by a quantronix darwin-duo nd:ylf laser (pulse width: 0.12 µs) that accesses the channel test section through a convex lens window, used to parallelize the light sheet to the walls, thus minimizing reflection issues from the walls. a central synchronizer control unit (ila 5150 gmbh) was used to drive the laser pulses, camera exposures and the high-voltage transformers for the plasma discharges. accordingly, for the plasma-actuated flow the spiv measurements were phase-locked, in order to resolve 24 bins of the plasma oscillation cycle. figure 1: experimental spiv setup in the cross-plane of a fully-developed turbulent channel flow; top left inset shows the corresponding coordinate system and the investigated plasma-actuator array. as a peculiarity of this spiv framework, due to the cross-plane measurement of the main flow, there is a difference of at least an order of magnitude between the acquired inand out-of-plane flow components. for a light-sheet thickness of about 30 px, the maximum particle out-of-plane displacements were locked at ∆x = 10 px. the cameras were operated (sampling frequencies 500 to 1400 hz) at full sensor size (1024×1024 px2, 12 bits), spanning a field of view (fov) of 16× 14 mm2 in width and height, respectively. in order to gain a spatial resolution of res≈ 60 px/mm and to prevent the cameras from blocking the channel exit at the same time, both cameras were each equipped with a teleconverter (magnification factor 2) and a nikon nikkor 200 mm lens ( f# = 11). hence, the pulse delay dt was dt = ∆x res ucl 10−3 s (1) where ucl is the (out-of-plane) center-line velocity that was continuously measured with a prandtl tube near the channel exit, in order to determine the flow conditions (see sec. 3.1 for ucl range). the fov was located in the horizontal center of the channel (and of the actuator array, see also fig. 3) on the lower wall and imaged the area up to the semi height h of the channel. given the extended dynamic range and the underlying stochastic field, about 14,000 vector fields were acquired to guarantee minimal measurement random error and converged flow. data processing was performed with pivtecs pivview software (version 3.8.5) applying a multigrid approach, where the raw images were cross-correlated on a final interrogation window size of 24 × 48 px2 (y, z) with an overlap factor of 50 %. as such, the resulting velocity information was derived with a vector spacing of 0.2 and 0.4 mm in y and z directions, respectively. 3 results and discussion 3.1 unforced flow initially, no forcing was applied such to retrieve a measurement of the naturally-evolving channel flow (referred to as the reference measurements) and in order to verify the quality and performance of the spiv system. various flow conditions (3.7 < ucl < 10.6 m/s) were tested and the evaluated friction velocity uτ (see eq. 3) was used to compute the friction reynolds number reτ (= uτh/ν) and both streamwise velocity profiles u+(y+) and reynolds-stress profiles of the timeand spanwise-averaged velocity fields. since the spatial resolution was not sufficient, for directly computing uτ from the velocity gradient du/dy in the viscous sublayer (y+ ≤ 5), the estimation of uτ was performed both by a least-sqaure fitting of the analytical form for the mean-velocity profile, provided by luchini (2018), with the actual velocity profile and by the computation of the total stress (pope (2000)) τxy = µ du dy −ρuv. (2) the differences between both methods were less than 2.5 %. since from the total stress in equation 2 the wall-shear stress τw can also be computed, it is directly retrieved from the acquired velocity data. therefore, the total-stress approach, as shown in figure 2 (a), was used to estimate uτ by applying uτ = √ τw ρ (3) to all flow conditions. in case of known wall position from the experiment, τw results from a linear extrapolation of τxy (at y= 0, i.e. at the wall). hence, the required wall position, in this work, was extracted from the raw piv images. as the inherent decrease of the total stress in the vicinity of the wall is unphysical and can be attributed to errors from both particle reflections and resolution limits of the spiv, the linear extrapolation of τxy is based on a least-square fit (see fig. 2 (a), dashed line). for cases of unknown wall position, another robust approach that exploits the expression (pope (2000)) τxy(y) = τw ( 1− y h ) (4) can be used to compute τw, by averaging the slope of the total stress τxy(y) along y. this procedure was also applied as a means of verification and culminated in less than 1 % deviation from the results of the linear extrapolation. figure 2: comparison of spiv results and dns (reτ = 180, 550, hoyas and jiménez (2008)). (a) evaluation procedure of τw from the total stress. (b) streamwise velocity profiles u+(y+). (c) root-mean-squared profiles √ uu+ and mean shear-stress profiles uv+. the resultant streamwise velocity profiles u+(y+) (black lines) of the turbulent channel flow are shown in figure 2 (b), scaled in viscous units, for the tested range of reynolds numbers (174≤ reτ ≤ 431). the comparison of the spiv results and the direct numerical simulations (dns) of hoyas and jiménez (2008) (red lines) depict a slight offset in the logarithmic region (50 < y+ < 120, pope (2000)), whereas in the viscous sublayer (y+ ≤ 5) the data points almost match the dns. however, it is evident that the sublayer region was resolved by a single data point, for reτ ≤ 252, only. therefore, the differences of the experimental data with respect to the dns originate either from an overestimation of uτ or a slightly increased friction drag caused by the surface structure of the actuator dielectric. for clarity, figure 2 (c) shows only the root-mean-squared profiles √ uu+ and the mean shear-stress profiles uv+ that clearly indicate an excellent fit between the experimental results at the tested reτ range and the dns. typically, the uncertainty of piv increases very close to the wall due to large velocity gradients in the turbulent boundary layer. this effect can be observed for√ uu+ for the near-wall data points. the peak at y+ ≈ 15 is underestimated and even closer to the wall √ uu+ reaches large values, diverging from the dns data. the uv+ component, instead, shows strong agreement with the dns even in the near-wall region. as an intermediate summary, the spiv results have demonstrated that the compliance of the velocity data in viscous units, from estimation of uτ by the total stress, and the dns of hoyas and jiménez (2008) provide a solid basis for the second part in which topological interplay effects of oscillatory plasma discharges and channel flow will be investigated. it is further to be noted that the scope in this part was to create a reliable experimental framework that allows for comparisons of uncontrolled and controlled flows which was accomplished by assessing the deviations of the experimental data set and the dns reference. 3.2 forced flow in previous studies, it has been demonstrated that plasma actuators can be driven such to generate oscillating plasma discharges (wilkinson (2003), jukes et al. (2006)), in order to mimic spanwise wall oscillations. one of the electrode arrays featured the configuration of the exposed (light gray) and encapsulated (dark gray) electrodes in the bottom part of figure 3 (jukes et al. (2006)), neglecting the red electrodes. the discharge is generated above the encapsulated electrodes (dark gray) and induces a flow that periodically changes direction. as a drawback in terms of spanwise flow homogeneity, no discharge is generated in the gaps (positions of red electrodes). therefore, further encapsulated electrodes (red) were added, achieving an array of side-by-side arranged exposed (light gray) and encapsulated (red and dark gray) electrodes. hence, formerly existing gaps of no discharge jukes et al. (2006) were closed and, at the same time, minimized to the width of the exposed electrodes. this particular electrode configuration, as developed by hehner et al. (2019, 2020), was applied in the present work. figure 3: flush-mounted plasma actuator for spanwise oscillating discharges. positions x+ = 0 and 1500 for reτ = 252, fov and flow direction are indicated. the sketch below shows a cross-section of the electrode configuration of the actuator (exposed electrodes: light gray; encapsulated electrodes: dark gray and red). the full plasma-actuator array consists of 9 exposed and 8 encapsulated electrodes of 1 and 3 mm width, respectively (spanwise wavelength λz = 4 mm). the dielectric material was a polyester foil (mylar®a, 500 µm thickness) and the electrodes consisted of silver ink (silverjet dgp-40lt-15c, sigma-aldrich®) applied to the dielectric by a fully-automated inkjet-printing method (printer model: autodrop professional by microdrop technologies gmbh), resulting in an electrode thickness of < 1 µm. the actuator was flushmounted on the surrounding substrate, by means of a cutout of a polyethylenterephthalate foil of equal thickness as the dielectric (see fig. 3). in two recent works, this type of plasma actuator was operated either in burst-modulation (hehner et al. (2019)) or beat-frequency mode (hehner et al. (2020)) and the underlying results from quiescent air have confirmed its capability to impose an oscillatory spanwise fluid motion on the surrounding air. due to the non-linear nature of the forcing with plasma, modifying the flow and the flow influencing the forcing, a superposition of plasma-induced flow in quiescent air and channel flow is prohibitive. yet, this arises the question for the inherent interplay effects of external flow on the plasma-induced flow topology and vice versa. therefore, and as a next logical step, the measurements were now performed both in quiescent air and in the channel flow when the plasma actuator was switched on in beat-frequency mode. figure 4: velocity contours of u/ucl (ucl = 5.86 m/s, reτ = 252) and velocity vectors (v, w). (a) timeaveraged non-actuated flow at reτ = 252. (b), (c) phase-averaged (∆ϕ = 5/6π after discharge onset) flow topology for actuation in quiescent air and at reτ = 252, respectively. the white vectors in (b) were copied from (c) for comparison with the induced flow in quiescent-air conditions. (d) time-averaged flow topology for actuation at reτ = 252. the exposed and encapsulated electrodes are indicated by the light and dark gray rectangles, respectively. the case of reτ ≈ 250, anticipated in hehner et al. (2019, 2020), was selected. accordingly, the operating parameters were such to generate a spanwise oscillation at frequency f = 50 hz and a plasma frequency fac = 16 khz. the streamwise length of the plasma actuator was x+ = 1620, where x+ = 0 refers to the upstream edge of the plasma. the measurements were conducted at x+1500 (see also fig. 3), near the downstream edge of the actuator. the style of figure 4 is such that the out-of-plane component u/ucl (ucl = 5.86 m/s) is shown as velocity contours, the velocity vectors of the in-plane components (v, w) are superimposed and the electrodes are indicated by the gray rectangles below the fields. the time-averaged velocity field of the uncontrolled reference flow at x+ = 1500 is shown in figure 4 (a). no modulation effect from the surface irregularities, due the electrodes, on the streamwise flow component is detected. it is further to be noted that the results of figure 2 also refer to x+ = 1500. for the plasma cases phase-resolved data was recorded and divided into 24 bins of the oscillation cycle (phase difference of consecutive snapshots ∆ϕ = π/12). hence, the velocity field in quiescent air as an average of a single phase is shown in figure 4 (b). the typical inhomogeneity of the the spanwise flow due to discharge gaps of the exposed electrodes can be observed (hehner et al. (2019, 2020)). as an important aspect, the reconstructed out-of-plane component u/ucl is identical to zero. the velocity field of the same phase position as in figure 4 (b) is displayed in figure 4 (c), when the windtunnel was turned on at set to cause a center-line velocity of about 5.86 m/s. the plotted velocity vectors were copied and added to figure 4 (b) in white, in order to allow for a better comparison of the non-linear effect of the channel flow on the plasma-induced flow topology. at first glance, the differences appear minor, however, there is a decrease of the velocity magnitude of the in-plane components at 0.2 < y/h < 0.4 and in the near-wall region on the side of the large velocity components some vectors occur at a more shallow angle as compared to quiescent air. the plasma actuation, on the other hand, has significant effect on the channel flow which is expressed by a spanwise modulation of the streamwise flow component which occurs at λz of the plasma actuator. the time-averaged topological effect of the plasma actuation on the channel flow is shown in figure 4 (d). as a difference to figure 4 (c), the length of the wave-like spanwise modulation of u/ucl is increased. while in the near-wall region (blue contours) the footprint of the modulation at λz can be retrieved, the time-averaged velocity vectors show weak vortical structures in the center and on the sides of the velocity field. this is supposed to be a consequence of slight differences in the induced velocity magnitudes along the oscillation cycle of the plasma discharge. 4 concluding remarks the present work has verified the suitability of the chosen spiv setup used to investigate a fully-developed turbulent channel flow and to study the interplay effects of external flow and plasma discharges. the total stress has been computed to evaluate τw and estimate uτ, showing very good agreement with the dns of hoyas and jiménez (2008). the drawback of the spiv setup is the resolution limit that hinders a direct evaluation of uτ from the velocity gradient du/dy in the viscous sublayer (y+ ≤ 5). the comparison of plasma actuation in quiescent air and in a channel flow yields weak differences of the in-plane velocity fields (v, w), whereas a significant effect on the turbulent boundary layer, exhibiting a spanwise modulation, was achieved. acknowledgements the authors acknowledge the provision of lab equipment from the research group of marios kotsonis at tu delft. references auteri f, baron a, belan m, campanardi g, and quadrio m (2010) experimental assessment of drag reduction by traveling waves in a turbulent pipe flow. physics of fluids 22:115103 benard n and moreau e (2014) electrical and mechanical characteristics of surface ac dielectric barrier discharge plasma actuators applied to airflow control. experiments in fluids 55:1–43 choi ks, debisschop jr, and clayton br (1998) turbulent boundary-layer control by means of spanwisewall oscillation. aiaa journal 36:1157–1163 gatti d and quadrio m (2016) reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing. journal of fluid mechanics 802:553–582 hehner m, gatti d, mattern p, kotsonis m, and kriegseis j (2020) beat-frequency-operated dielectricbarrier discharge plasma actuators for virtual wall oscillations. aiaa journal 59:1–5 hehner mt, gatti d, and kriegseis j (2019) stokes-layer formation under absence of moving parts—a novel oscillatory plasma actuator design for turbulent drag reduction. physics of fluids 31:051701 hoyas s and jiménez j (2008) reynolds number effects on the reynolds-stress budgets in turbulent channels. physics of fluids 20:101511 jukes t, choi ks, johnson g, and scott s (2006) turbulent drag reduction by surface plasma through spanwise flow oscillation. in 3rd aiaa flow control conference. page 3693 kotsonis m (2015) diagnostics for characterisation of plasma actuators. measurement science and technology 26:092001 kriegseis j, mattern p, nawroth g, vaas m, and frohnapfel b (2015) coherent secondary flow patterns in turbulent open duct flow. 11th international symposium on particle image velocimetry piv15, santa barbara, ca, usa kriegseis j, simon b, and grundmann s (2016) towards in-flight applications? a review on dielectric barrier discharge-based boundary-layer control. applied mechanics reviews 68:020802 luchini p (2018) structure and interpolation of the turbulent velocity profile in parallel flow. european journal of mechanics-b/fluids 71:15–34 pope sb (2000) turbulent flows. cambridge university press quadrio m (2011) drag reduction in turbulent boundary layers by in-plane wall motion. philosophical transactions of the royal society a: mathematical, physical and engineering sciences 369:1428–1442 quadrio m and ricco p (2011) the laminar generalized stokes layer and turbulent drag reduction. journal of fluid mechanics 667:135–157 wilkinson sp (2003) investigation of an oscillating surface plasma for turbulent drag reduction. 41st aerospace sciences meeting & exhibit 1 introduction 2 experimental procedure 3 results and discussion 3.1 unforced flow 3.2 forced flow 4 concluding remarks 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 examining the effects of fluid velocity gradients on 4d digital holographic piv/ptv measurements y. j. xia∗, b. sun, g. a. ahmed, j. soria 1 laboratory for turbulence research in aerospace & combustion (ltrac), department of mechanical and aerospace engineering, monash university (clayton campus), melbourne, victoria 3800, australia ∗ yuan.xia@monash.edu abstract 4d digital holographic piv/ptv (4d-dhpiv/ptv) methods have demonstrated theoretical viability due to their relative ease of setup and high spatial resolution (soria (2018)). this study investigates how velocity gradients related to different flow regimes and their magnitudes affect 3-component–3-dimensional (3c-3d) digital holographic piv measurement uncertainty. figure 1: diagram of simulated digital holographic piv/ptv setup the error introduced by velocity gradients within the interrogation volume is studied by simulating particles in a velocity field, with a given constant velocity gradient superimposed on a uniform flow from which a time-series of hologram pairs are generated and the 3c-3d velocity fields and their errors are determined using 4d-dhpiv/ptv sun et al. (2020). hologram pairs are simulated by modelling the propagation and particlediffraction of coherent laser light using the angular spectrum method (goodman (1996)). the hologram reconstruction then involves direct reconstruction, followed by deconvolution, a particle position refinement and a hologram subtraction step (sun et al. (2020)). the particle positions obtained from 4d-dhpiv/ptv are then used to resolve particle displacement measurements using 3d cross-correlation digital analysis with a 3d gaussian fit to sub-pixel resolution (soria (2006)). the effects of velocity gradients on the displacement uncertainty and bias error have been investigated by undertaking monte carlo simulations under a range of velocity gradient environments. specifically, 5 common velocity gradients have been studied, which included pure strain, pure vorticity and x, y and z-directional shear. (a) uniform mean velocity (b) pure strain velocity (c) pure vorticity velocity (d) pure x shear velocity (e) pure y shear velocity (f) pure z shear velocity figure 2: the 6 different flow regime displacement vector plots used in this study. all test cases are subjected to a mean velocity field (a) superimposed with a velocity gradient flow regime (b-f). vector plots (b-f) have been scaled by a factor of 2 for visualisation purposes. all axes are in pixels. the results indicate that the novel 4d-dhpiv/ptv has poorer accuracy and precision in the z-propagation axis, resulting in larger minimum uncertainties and bias errors. the errors in the z axis are also significantly less affected by velocity gradients in the z direction when compared to the effects of x and y directional velocity gradients on x and y errors respectively. furthermore, the rate of cross-correlation maximum and snr decrease are approximately 1.36 times slower due to velocity gradients in the z axis than other axes. acknowledgements the authors gratefully acknowledge the support of this project through arc and ncmas (nci, massive). yuan jing xia gratefully acknowledges the support through james mcneill foundation and monash university scholarships. references goodman j (1996) foundations of scalar diffraction theory. in introduction to fourier optics. pages 55–57. mcgraw hill, new york city, usa soria j (2006) particle image velocimetry application to turbulence studies. in lecture notes on turbulence and coherent structures in fluids, plasmas and nonlinear media. pages 307–347. world scientific, singapore soria j (2018) three-component three-dimensional (3c-3d) fluid flow velocimetry for flow turbulence investigations. in proceedings of the 21st australasian fluid mechanics conference, adelaide, australia, december 10-13 sun b, ahmed a, atkinson c, and soria j (2020) a novel 4d digital holographic piv/ptv (4ddhpiv/ptv) methodology using iterative predictive inverse reconstruction. measurement science and technology 31 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 experimental study of darrieus turbines in confined free-surface flows l. kara mostefa1*, l. chatellier1, l. thomas1 1institut pprime, upr3346, cnrs – université de poitiers – isae-ensma, france *mohamed.larbi.kara.mostefa@univ-poitiers.fr abstract both scientific and industrial communities have a growing interest for marine renewable energies. there is a wide variety of technologies in this domain, with different degrees of maturity. our work focuses on two models of an h-type vertical axis darrieus (1931) tidal turbine with the objective of studying the effect of fluid-structure interactions on their performances. the experimental studies were carried out on the 15m long and 1m² square section free surface channel of the environmental hydrodynamics platform at pprime institute (figure 1). the maximum flow discharge through the channel is q = 500 l/s. figure 1: free surface hydrodynamic channel two prototypes are used on the experimental studies. the first prototype is a down-scaled model of the one used in the study of gorle et. al (2016). the prototype is composed of four straight rigid blades maintained by circular flanges on both ends of the rotor (figure 2a). for this work, we propose a second prototype. it is equipped with free-ended interchangeable blades attached to a single flange (figure 2b). a configuration of the second prototype mounted with rigid stainlesssteel blades are first used for comparison with the dual-flange turbine. a configuration using peek blades of significantly lower young modulus is investigated in order to address the fluid-structure interaction problem. mailto:mohamed.larbi.kara.mostefa@univ-poitiers.fr 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 both turbine models have a rotor diameter of 400mm and 80mm-chord naca0015 blades of 400m length, their section is a=0.16 m2. the rotor is driven by a servo motor and equipped with torque and angular position sensors. torque measurements are first carried out to characterize the performances of the turbines in a range of operating conditions with different combinations of water level h, flow discharge q and reduced speed λ. on the first studies, the water level has been varied from 0.55 m to 0.75 m and the flow velocity is fixed to v=0.66 m/s. the results are shown in figure 2. it can be seen that the water level has little influence on the operation of the turbine and the cop values are relatively close to the tested water level values. the coefficient of performance cop is calculated by the following expression: cop=p/(0.5∙∙a∙ 𝑉3)).  is the water density defined as 1000kg/m3 and p is the turbine’s power. prototype 1: rigid blades and assembly. prototype 2: free-ended stainless steel blades (rigid) prototype 3: free-ended peek blades (deformable) figure3 : influence of rigidity, immersion and tsr on the turbine performances figure 2: dual(a) and single-flange (b) straight blade h-type darrieus turbines (a) (b) 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 figure 4 shows the results obtained for a constant water level of h=0.555 m and two flow velocities (v=0.66m/s and 0.909 m/s). as expected, the three types of typical operating regimes in darrieus turbines are recovered. a first regime for lowest values of tested reduced speed (λ=𝜔𝑅 𝑉⁄ ), the blades are subject to intense stalls due to a high blade angle of attack. this regime is characteristic of the dynamic stall that will be described in the piv results section. for highest values of tested parameters, the performance of the turbine is limited by the drag generated by its components. the last regime is a transition zone presenting a balance between dynamic and viscous effects. on this transition zone, the best performance is obtained for the darrieus turbines. for the higher incident speed v=0.909 m/s (froude number 𝐹𝑟𝐼𝐼= 0.36), the best performance of prototype 1 (model blades and rigid assembly) has been identified for a reduced speed λ=2.25, for a cop=38%. for the prototype 2 and 3, the optimal speed is obtained for a reduced speed λ=2.10 for getting a cop=28%. however, for all tested values of reduced speed, the best performance is obtained by the prototype 1. the cop values of prototype 2 have almost the same behavior than prototype 3. figure 4: torque measurement; influence of the operating regime the piv measurements are conducted within the mid-plane of the rotor. two 200 mj doublecavity quantel evergren, 532nm nd: yag laser have been used in order to limit the masking of the measurement zone during the passage of the blades (figure 2a). a lavision imager pro lx 16mp ccd camera is positioned below the glass bed of the channel, imaging a 1200 mm x 800 mm measurement region through a 45° mirror. the piv timing is adjusted so that successive phase-locked velocity fields correspond to angular displacements of 7.5°, thus guaranteeing a complete coverage of the turbine rotation cycle (figure 6). 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 figure 5: particle image velocimetry apparatus and setup figure 6 : illustration the angular positioning of the blades and corresponding global position of turbine θ figure 7 shows the vorticity field for each prototype on their optimal configuration. the same behavior is observed for the three-vorticity fields in which a dynamic stall vortex of positive vorticity is identifiable. a second vortex appears also on the three configurations next to the first vortex. the value of the vorticity on this second vortex depends on the rigidity of the blades. for a rigid blade, as used on the prototype 1, the peak vorticity increases reaches a maximum. the magnitude of the vorticity decreases with decreasing rigidity. vortex shedding of negative vorticity is also observable in the upper part of the wake. prototype 1 :  =2.25 prototype 2 : =2.10 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 conclusion an experimental study has been conducted on 3 versions of a darrieus turbine with either rigid or flexible assembly and blades. torque measurements indicate the influence of rigidity, which is materialized in the performance curves of each prototype. phsae-locked piv results show a very satisfactory agreement with and the literature concerning dynamic stall (bossard et al, 2006). the different experiments carried out on the turbine model allowed us to identify the blade-vortex structure interactions. which exhibit similar dynamics for the 3 turbine configurations at their optimal operating conditions. this work will be extended by the study of the dynamics of vortex releases and their interactions with the blades. tests deformation measurements on free-ended rigid an flexible will be conducted blades in order to characterize their response fluctuating hydrodynamic forces and the influence of their flexibility on the efficiency of the turbine. references darrieus g, turbine having its rotating shaft transverse to the flow of the current, us pate nt n°1835018a, 1931 gorle jmr, chatellier l, pons f, ba m, flow and performance analysis of h-darrieus hydroturbine in a confined flow: a computational and experimental study. journal of fluids and structures 2016; 66 :382– 402, 2016 maître t, bossard j, vignal l, franc jp, darrieus turbine modellings comparisons with performance measurements and piv fields. international symposium on transport phenomena and dynamics of rotating machinery, apr 2016, honolulu, united states. prototype 3 : =2.10 figure 7: phase-averaged vorticity fields 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 combining high-speed planar piv and motion tracking of a flexible cylinder in cross-flow d. g. gundersen1, k. t. christensen1,2, g. blois1 1 university of notre dame, department of aerospace and mechanical engineering, notre dame, usa 2 illinois institute of technology, depts. of mechanical, materials & aerospace engineering and civil, architectural & environmental engineering, chicago, usa 1 introduction most modeling studies investigating the flow dynamics in vegetation canopies are limited to rigid models as proxies for vegetation elements. however, most canopies embody some degree of structural flexibility, resulting in aeroelastic mechanisms coupling the motion of the vegetation with the surrounding flow. studies addressing flexible canopies typically quantify either the flow or the plant motion independently, thus missing the instantaneous coupling between turbulent stresses and structural deformations. few experiments have been devoted to measuring both quantities simultaneously. okamoto and nezu (2009) utilized a combined piv-ptv technique to capture both flow and canopy motion. however, only the motion of the stem tips was captured, as opposed to the deformation of the entire stem. py et al. (2006) employed digital image correlation (dic) to quantify the motion of crop canopies using in-field images. however, the wind itself was not measured across the domain. the present work presents an experimental technique that can be utilized to study the flow–structure interaction in flexible canopies, and that could be extended to other flexible and/or moving objects. high-speed piv data of the flow surrounding an idealized canopy element, consisting of a flexible cylinder, together with the corresponding displacement field throughout the cylinder were simultaneously obtained combining fluorescent imaging and refractive index matching (rim). 2 methods laboratory experiments were performed in the refractive index-matched (rim) flow facility at notre dame (blois et al., 2020). the rim approach involved using an aqueous solution of sodium iodide (nai) as the working fluid and solid models whose ri matches that of the fluid, thus obtaining an optical continuum between the solid model and the surrounding fluid. the operating principle of the technique presented herein involved seeding the two phases with different tracers, facilitating image segmentation and interrogation of each effect independently. the working fluid was seeded with silver-coated particles with a 14-micron diameter and a specific gravity of 1.7. the cylinder models were fabricated from a polyurethane rubber with an index of refraction of n = 1.4865 and a young’s modulus of e = 2.9 mpa. a small volume of orange fluorescent dye was embedded within the polyurethane during the casting process at a concentration of 1µl/g. the casting protocol was refined over multiple iterations to maximize particle dispersion uniformity and to optimize dye-to-solid ratio. the cylinder was mounted on the bottom wall of the test section with its axis oriented in the normal direction. the cylinder had a length of l = 43 mm and a diameter of d = 4.5 mm. the model was fully immersed in the boundary layer, with a thickness of δ99 = 58.4 mm. the laser sheet was oriented in the streamwise–wall-normal plane intersecting the center of the cylinder. all particles were illuminated by the same laser sheet formed from a 50 mj, dual-head nd:ylf high-speed laser. a single high-speed digital camera was available for these tests. the camera captured both the light scattered by the silver-coated particles seeding the fluid flow and the light emitted by the particles seeded within the cylinder. the signal was separated using robust segmentation algorithms. the displacement field at any point in the flow and within the cylinder was obtained by standard cross-correlation schemes. the segmentation scheme was automated, allowing for the very large datasets produced by the high-speed imaging arrangement to be processed. (a) 𝑈 (m/s) (b) figure 1: (a) instantaneous snapshot of the streamwise velocity, u , with vectors displaying the fluctuating velocities. the cylinder location is shown in gray. (b) instantaneous displacement vectors relative to the previous image. for better visualization, the vector magnitudes are exaggerated by a factor of 10, and a reference vector of 0.5 mm is shown in the top left. 3 results time-resolved planar piv data was acquired with a sample frequency of 640 image pairs per second and a sample size of 2734 image pairs. the flow data were processed with an iterative multi-pass interrogation method, resulting in a vector grid spacing of 0.33 mm. a representative example of the instantaneous distribution of streamwise velocity, u , around the cylinder model subjected to an oncoming turbulent boundary layer is shown in fig. 1(a). the results shows that, despite a slight decrease in illumination energy in the shadow region underneath the cylinder, the data quality is relatively uniform throughout the field of view. fig. 1(b) shows the cylinder displacement map at a given snapshot. the vectors are oriented perpendicular to the model centerline and the vector magnitudes increase with distance from the base. these observations are qualitatively consistent with the expected displacement distribution of a cantilever beam that is fixed to the wall and subjected to an oncoming turbulent boundary layer. this experimental technique allowed for the accurate calculation of quantities such as power spectra of the cylinder vibrations and the vortex shedding frequency. in addition, it also facilitated temporal correlations between the cylinder and flow dynamics. 4 conclusions the preliminary results presented herein demonstrate a technique to successfully embed fluorescent particles in a transparent flexible vegetation model. the utilization of this model in a rim environment allows one to quantify the motion and deformation of the illuminated object subjected to a turbulent flow. high-speed piv data allowed for the observation of the dynamic link between a deformable object and the surrounding flow, thus giving the ability to probe the fluid–structure coupling. the experimental method could be utilized to aid in the study of other aeroelastic flow–structure interactions. references blois g, bristow nr, kim t, best jl, and christensen kt (2020) novel environment enables piv measurements of turbulent flow around and within complex topographies. journal of hydraulic engineering 146:04020033 okamoto ta and nezu i (2009) turbulence structure and “monami” phenomena in flexible vegetated openchannel flows. j hydraul res 47:798–810 py c, de langre e, and moulia b (2006) a frequency lock-in mechanism in the interaction between wind and crop canopies. j fluid mech 568:425–449 introduction methods results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 detecting vortical structures in time-resolved volumetric flow fields karuna agarwal1, omri ram1, jin wang1, yuhui lu1, joseph katz1* 1johns hopkins university, department of mechanical engineering, baltimore, usa *katz@jhu.edu abstract the detection of three-dimensional coherent vortical structures that get advected as well as deformed with time is a challenge. however, it is critical for the statistical analysis of these vortices, for example, the quasi-streamwise vortices (qsvs) in the near field of a turbulent shear layer, where cavitation inception typically occurs. these structures exhibit underlying correlations among different properties that can be derived from the velocity gradients. exploiting these correlations, a pseudolagrangian vortex detection method is proposed that uses k-means clustering based on vorticity magnitude and direction, values of λ2, strain rate structure, axial stretching, and location. the method facilitates the finding that qsvs have pressure minima that are lower than those in the surrounding flow, including the primary spanwise vortices. these minima typically appear after a period of axial stretching and before contraction events. 1 introduction the evolution of vortical structures is of interest in a plethora of turbulent flows since they play major roles in momentum and energy transport, interactions with boundaries, and are primary sites for cavitation inception. hence, many previous studies have attempted to identify them based on several criteria e.g., the second velocity gradient invariant or the q-criterion (hunt et al., 1998), the intermediate eigenvalue (λ2) of the sum of squares of symmetric and asymmetric parts of the velocity gradient tensor (jeong and hussain, 1995), and swirling strength (adrian et al., 2000). these eulerian methods are localized in space and require selection of appropriate thresholds. hence, they might not be continuous in time owing to e.g. experimental errors. lagrangian techniques that are based on the trajectories of fluid particles, such as finite time lyapunov exponents (haller and sapsis, 2011) or coherent structure coloring (schlueter-kuck and dabiri, 2017), have also been implemented for structures that are relatively low-ranked in space and time. the detection of complex evolving threedimensional structures has remained a challenge. with the advent of time-resolved tomographic particle tracking involving shake-the-box (stb, schanz et al., 2016) method and subsequent pressure calculations (wang et al., 2019), it is possible to measure the 3d evolution of vortices in turbulent flows. in this study, these methods are employed to characterize the evolution of intermittent quasi-streamwise vortices (qsvs) that develop between the kelvin-helmholtz vortices in a turbulent shear layer (bernal and roshko, 1986). this study is motivated by prior cavitation studies showing that the qsvs are the primary site for cavitation inception in high reynolds number shear layers (katz and o’hern, 1986). the present shear layer is generated by a backward-facing step with height of h=10 mm, and the measurements have been performed at free-a stream velocity (u) of 1.45 and 5.3 m/s, corresponding to a step-height based reynolds number of 1.45×104 and 5.3×104 (agarwal et al., 2018). the measurements have been 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 performed in a 12.5×7.5×4.5 mm3 sample volume where the cavitation inception events are most likely to occur along the core of 1-2 mm diameter qsvs. the sample volume is illustrated in figure 1(a). to perform statistical analysis of the qsv properties and pressure, the data is processed using the presently proposed pseudo-lagrangian method that segregates the qsvs from the surrounding flow domain. figure 1: (a) the backward-facing step with a map of cavitation probability in the shear layer. the tomographic field of view is marked in red. (b) pdf of correlations of λ2 with different variables used in detecting the qsv. 2 method the experiments have been performed in a small water tunnel fitted with a backward-facing step. the optical setup for the time-resolved tomographic ptv (fig. 9b) involves four pco.dimax cameras, arranged in the same horizontal (x, z) plane as the test section. the data are recorded at 14925 hz with an image size of 624×380 pixels for 5.3 m/s, and at 7407 hz with an image size of 1008 × 596 pixels for 1.45 m/s. in both cases, the spatial resolution is compromised to facilitate the high frame rates. the flow field is illuminated by a photonics dm60-527 nd:ylf laser, and the flow is seeded with 13 µm diameter silver-coated hollow glass spheres. a total of 3500-5000 tracks are resolved in each instantaneous realization, with a typical distance between particles of 275 µm. the unstructured velocity and acceleration data from the particle tracks are interpolated using a constrained cost minimization technique (agarwal et al., 2021) to obtain structured data on velocity, material acceleration and their spatial gradients, at a grid resolution of 200µm. the corresponding pressure distribution is obtained by spatially integrating the material acceleration using the 3d omnidirectional method described in wang et al. (2019). a pseudo-lagrangian detection method involving 95,000 synthetic particles is used to insure the spatial and temporal continuity of the detected structures. the particle motions are tracked using a fourth-order runge kutta method and cubic interpolation in space. the 3d velocity gradients are used for calculating the vorticity components i, λ2, and vortex stretching terms (⍵i∂iuj). the qsv axis n is identified as being perpendicular to the direction of spatial gradients of the vector sum of ⍵x and ⍵y. to identify the qsvs and its evolution, the following parameters are utilized: (i) spanwise vorticity ⍵z, (ii) vorticity perpendicular to spanwise-direction, ⍵xy, (iii) λ2, (iv) projection of vortex stretching term along the qsv axis (⍵∙∂u∙n), (v) projection of the strain rate tensor on the axis of the vortex (n∙∂u∙n), and (vi) the strain state parameter (lund and rogers, 1995). the position and the abovementioned six variables are recorded for each particle in five consecutive time steps, moving both forward and backward in time. for particles that are advected out of the volume (~10% of the 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 total), only unidirectional time steps are considered. the resulting 45-dimensional dataset (9 variables at 5 times) is divided into 10 clusters using the correlations-based k-means method (lloyd, 1982). before clustering, the mean of each variable is removed and the quantities are normalized by their variance. the clusters with centers that have λ2 lower than the mean, as well as ⍵xy and vortex stretching magnitude higher than the mean, at all 5 times are chosen as qsv candidates. the detected qsv field is projected back to the grid using cubic interpolation. the grid-points that are have fewer than half of its neighbors classified as qsvs are re-labelled as not being qsv. figure 1(b) shows the probability density function of the correlation between λ2 with the variables used for detecting the qsv, both within and outside of the qsvs. as is evident, within the qsv, λ2 is more correlated with ⍵xy, axial vortex stretching, and axial strain rate, but is less correlated with ⍵z compared to other regions (i.e. those not classified as qsvs). to visualize the high-dimensional data, t-distributed stochastic neighbor embedding (t-sne, van der maaten et al., 2008) is employed in figure 2. this procedure reduces the data to two dimensions, while preserving the probability of being similar in higher dimensions. the maps are color coded by qsv detection, ⍵xy, λ2 and pressure for one instance. as can be noted, the regions selected as qsvs are organized in clusters that typically have high ⍵xy, low λ2 and low pressure. these clusters coincide with the points detected by the kmeans algorithm. figure 2: the t-sne plots of the 45-dimensional matrix colored by: (a) detection of qsv based on the selected criteria, with 1.0 corresponding to qsvs, along with the corresponding mean-centered and variance-normalized values of: (b) vorticity in x-y direction, (c)λ2, and (d) pressure. 3 results figure 3: samples of advected qsvs detected using the pseudo-lagrangian method. the structures are color-coded with the pressure fluctuations in pa. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 figure 3 shows sample qsvs detected using the present method at the specified three times. the structures are evolving in time, while being convected at speeds of about 50% of the free-stream velocity. the structures are about 1-2 mm in diameter and over 5 mm in length, consistent with the size of the cavities. statistical analysis of 28000 realizations for 5.3 m/s and 15000 for 1.45 m/s shows (figure 4) that the pressure inside these structures is lower and the duration of pressure minima is longer than those in the surrounding fluid. the structures experience both high stretching (⍵∙∂u∙n >0, in figure 4c) and contraction (⍵∙∂u∙n <0). the lagrangian correlations among variables are computed following the synthetic tracks, while recording the associated pressure, vorticity, stretching and the status of being either inside or outside of a qsv. figure 5 shows the correlations of pressure at time t+δt with the vorticity (fig. 5a), stretching (fig. 5b) and contraction (fig. 5c) for the same particle at time t, averaged over different instances and particles. inside the qsvs, the pressure minima are more likely to occur in regions with high ⍵xy at the same time (δt =0), follow (appear after) a stretching event (δt >0), and precede a contraction (δt<0). these trends are much weaker outside of the qsvs. these trends appear to be stronger for the lower velocity, presumably because of increase in turbulence level with increasing reynolds number. meanwhile, the lagrangian pressure-pressure correlations (not shown) are higher for the higher velocity, with values of ~0.3 at tu/h=1 for 1.45 m/s and ~0.4 for 5.3 m/s. figure 4: probability density functions of: (a) pressure (b) durations of pressure lower than given thresholds and (c) vortex stretching term, inside and outside of the qsvs. figure 5: lagrangian correlations of low-pressure events (<-0.025⍴u2) at t+δt with vorticity, stretching (>2u2/h2) and contraction (<-2u2/h2) at time t. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 4 conclusions a pseudo-lagrangian vortex detection method is proposed that uses k-means clustering of particle positions and variables associated with the velocity gradients to detect secondary quasi streamwise vortices in the near field of a turbulent shear layer. results show that regions with pressure minima are more likely to be located within the qsvs than outside of them. these low-pressure events are more likely to occur after periods of stretching with duration of tu/h~1 and before contraction events. ongoing analysis focuses on characterizing the structure of these vortices, for example, how the pressure is distributed along their axes and for how long. these data could then be used for predicting the rate of cavitation inception events. acknowledgement this project has been supported in part by onr muri grant: predicting turbulent multi-phase flows with high fidelity a physics-based approach, and in part by onr grant no. n00014–18-1–2635. references adrian r.j., christensen k.t., and liu z.c.(2000) analysis and interpretation of instantaneous turbulent velocity fields, exp. fluids 29, pp. 275–290. agarwal, k., ram, o. and katz, j. (2018) cavitating structures at inception in turbulent shear flow. in proceedings for 10th international symposium on cavitation, baltimore, usa. agarwal, k., ram, o., wang, j., lu, y., & katz, j. (2021). reconstructing velocity and pressure from noisy sparse particle tracks using constrained cost minimization. experiments in fluids, 62(4), 1-20. bernal, l. p., & roshko, a. (1986). streamwise vortex structure in plane mixing layers. journal of fluid mechanics, 170, 499-525. haller, g., & sapsis, t. (2011). lagrangian coherent structures and the smallest finite-time lyapunov exponent. chaos: an interdisciplinary journal of nonlinear science, 21(2), 023115. hunt j. c. r., way a., moin p.(1998) eddies, stream, and convergence zones in turbulent flows. center for turbulence research report ctr-s88, standford university, 1, 5. jeong j., hussain f. (1995) on the identification of a vortex. journal of fluid mechanics 285, 1, 69–94. 1, 5. katz, j., & o’hern, t. j. (1986). cavitation in large scale shear flows. journal of fluids engineering. lund, t. s., & rogers, m. m. (1994). an improved measure of strain state probability in turbulent flows. physics of fluids, 6(5), 1838-1847. lloyd, s. (1982). least squares quantization in pcm. ieee transactions on information theory, 28(2), 129-137. schanz, d., gesemann, s., & schröder, a. (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids, 57(5), 70. schlueter-kuck, k. l., & dabiri, j. o. (2017). identification of individual coherent sets associated with flow trajectories using coherent structure coloring. chaos: an interdisciplinary journal of nonlinear science, 27(9), 091101. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 van der maaten, l.j.p.; hinton, g.e. (2008). visualizing data using t-sne. journal of machine learning research. 9: 2579–2605. wang, j., zhang, c., katz, j. (2019) gpu-based, parallel-line, omni-directional integration of measured pressure gradient field to obtain the 3d pressure distribution. experiments in fluids, 60(4), p.58. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 micro-piv measurements of multiphase flow in deforming porous media subject to mineral dissolution r. molla1, n. raventhiran1, y. li1∗ 1 montana state university, mechanical&industrial engineering, bozeman, usa ∗ yaofa.li@montana.edu abstract mineral dissolution is studied in novel calcite-based porous micromodels under singleand multiphase conditions, with a focus on the interactions of mineral dissolution with pore flow. microscopic particle image velocimetry (piv) was utilized to simultaneously characterize the local velocity field and the instantaneous shapes of the dissolving grains. the preliminary results provide a unique view of the coupled dynamics between pore flow and mineral dissolution. 1 introduction mineral dissolution in porous media coupled with singleor multi-phase flows is pervasive in natural and engineering systems. in subsurface environments, the solid porous matrix is composed of various types of minerals, through which subsurface water flows. dissolution of minerals occurs as chemicals in the solid phase is transformed into ions in the aqueous phase, effectively modifying the physical, hydrological and geochemical properties of the solid matrix as well as the chemistry in the aqueous phase daccord (1987). these processes play a defining role in a broad range of applications including carbon capture and sequestration (ccs) ott and oedai (2015) and acid stimulation in reservoir engineering daccord (1987). for instance, ccs is considered as a viable technology to reduce carbon emissions to the atmosphere, thus effectively mitigating global climate change. however, injection of co2 into geologic formations leads to dissolution of minerals comprising reservoirs rocks, potentially creating leakage pathways that threaten the safety and security of co2 storage ott and oedai (2015). therefore, to successfully model, predict, control and optimize these many processes, a comprehensive understanding of mineral dissolution is crucial. mineral dissolution in porous media is subject to chemical reaction and transport via advection and diffusion. on the one hand, pore flow plays a defining role in mixing and transporting the reactants to the reaction sites as well as transporting reaction products away, significantly affecting the mineral dissolution rate. on the other hand, mineral dissolution continuously modifies the porous media both structurally and chemically, which in turn reshapes the pore flow. therefore, local dissolution rate and pore-scale flow are strongly coupled. however, our fundamental understanding of this coupling effect at the pore level is still limited, leading to strong challenges in the effort of predicting mineral dissolution at much larger scales. 2 experimental methods the micromodels used in the experiments were fabricated in calcite as shown in figure 1li et al. (2017). to fabricate a calcite-based micromodel, the porous patterns, which is inspired by real geological structures, was precisely formed in calcite substrate using photolithography and wet etching. the etched substrate was then bonded with adhesive to a glass slide to form a micromodel, to which nanoports were attached, to serve as fluid delivery ports. these surrogate porous media offer precise control over the structures and chemical properties, and facilitate unobstructed and unaberrated optical access to the pore flow with micropiv methods. white field microscopy and the fluorescent micro-piv method were simultaneously employed by seeding the water phase with fluorescent particles, in order to achieve simultaneous measurement of the velocity fields of the aqueous and structure evolution of the solid phase 1 micro-piv measurements of multiphase flow in deforming porous media subject to mineral dissolution razin molla, nishagar raventhiran and yaofa li montana state university key words: micro-piv, porous media, multiphase flow, mineral dissolution introduction mineral dissolution in porous media coupled with singleor multi-phase flows is pervasive in natural and engineering systems. in subsurface environments, the solid porous matrix is composed of various types of minerals, through which subsurface water flows. dissolution of minerals occurs as chemicals in the solid phase is transformed into ions in the aqueous phase, effectively modifying the physical, hydrological and geochemical properties of the solid matrix as well as the chemistry in the aqueous phase [1]. these processes play a defining role in a broad range of applications including carbon capture and sequestration (ccs) [2], acid stimulation in reservoir engineering [1] and contaminant transport in soil [3]. for instance, ccs is considered as a viable technology to reduce carbon emissions to the atmosphere, thus effectively mitigating global climate change. however, injection of co2 into geologic formations leads to dissolution of minerals comprising reservoirs rocks, potentially creating leakage pathways that threaten the safety and security of co2 storage [2]. therefore, to successfully model, predict, control and optimize these many processes, a comprehensive understanding of mineral dissolution is crucial. mineral dissolution in porous media is subject to chemical reaction and transport via advection and diffusion. on the one hand, pore flow plays a defining role in mixing and transporting the reactants to the reaction sites as well as transporting reaction products away, significantly affecting the mineral dissolution rate. on the other hand, mineral dissolution continuously modifies the porous media both structurally and chemically, which in turn significantly reshape the pore flow. therefore, local dissolution rate and porescale flow are strongly coupled. however, our fundamental understanding of this coupling effect at the pore level is still limited, leading to strong challenges in the effort of predicting mineral dissolution at much larger scales. to this end, mineral dissolution is studied in novel calcite-based porous micromodels under singleand multiphase conditions, with a focus on the interactions of mineral dissolution with pore flow. experimental methods the micromodels used in the experiments were fabricated in calcite as shown in figure 1 [4]. to fabricate a calcite-based micromodel, the porous patterns, which is inspired by real geological structures, was precisely formed in calcite substrate using photolithography and wet etching. the etched substrate was then be bonded with adhesive to a glass slide to form a micromodel, to which nanoports were attached, to serve as fluid delivery ports. these surrogate porous media offer precise control over the structures and chemical properties, and facilitate unobstructed and unaberrated optical access to the pore flow with µpiv methods. white field microscopy and the fluorescent micro-piv method were simultaneously employed by flow hcl figure 1: schematic diagram of the calcite-based micromodel comparing an inlet, a porous section, and an outlet. figure 1: the calcite-based micromodel consiting of an inlet, a porous section, and an outlet. 3 results the preliminary results provide a unique view of the flow dynamics during mineral dissolution. figures 2a and 2b show the sample velocity fields of the pore-scale flow under single and multiphase flow conditions, respectively. when hcl concentration is low but the pore flow rate is relatively high, the reaction product (i.e., co2) is instantaneously dissolved in the aqueous phase leading to a single phase flow. however, when hcl concentration is high such that the produced co2 cannot be instantaneously dissolved, it will emerge as a separate phase, leading to a multiphase flow. while the flow field with single-phase flow is relatively simple, that flow is significantly modified in the multiphase flow case due to the presence co2 bubbles that are generated in-situ as a result of chemical reaction between the liquid and solid phases. the separate co2 phase is expected to not only divert the hcl flow, but also shied the solid surfaces from further reaction, thus significantly modifying the local dissolution pattern and rate. 2 seeding the water phase with fluorescent particles, in order to achieve simultaneous measurement of the velocity fields of the aqueous and structure evolution of the solid phase. initial results the preliminary results provide a unique view of the flow dynamics during mineral dissolution. figures 2a and 2b show the sample velocity fields of the pore-scale flow under single and multiphase flow conditions, respectively. when hcl concentration is low but the pore flow rate is relatively high, the reaction product (i.e., co2) is instantaneously dissolved in the aqueous phase leading to a single phase flow. however, when hcl concentration is high such that the produced co2 cannot be instantaneously dissolved, it will emerge as a separate phase, leading to a multiphase flow. while the flow field with single-phase flow is relatively simple, that flow is significantly modified in the multiphase flow case due to the presence co2 bubbles that are generated in-situ as a result of chemical reaction between the liquid and solid phases. the separate co2 phase is expected to not only divert the hcl flow, but also sheild the solid surfaces from further reaction, thus significantly modifying the local dissolution pattern and rate. figure 2. sample flow fields under single-phase (a) and multiphase (b) flow conditions, showing water velocities as color contours; gas and calcite grains as yellow and grey regions, respectively. experiments are ongoing for a broad range of conditions to study the sensitivity of these flow patterns on pore flow rate and acid concentration. in addition, based on the pore-scale measurements, correlations between pore-scale flow and dissolution rates will be developed for several representative conditions. references [1] g. daccord, physical review letters 58.5: 479, (1987). [2] h. ott and s. oedai, geophysical research letters 42.7: 2270-2276 (2015). [3] n. f. spycher, e. l. sonnenthal, and j. a. apps, journal of contaminant hydrology 62: 653-673 (2003). [4] y. li, g. blois, f. kazemifar and k. t. christensen, water resources research 55.5: 3758-3779 (2015). acknowledgements this work was performed in part at the montana nanotechnology facility, an nnci facility supported by nsf grant eccs-1542210, and with support by the murdock charitable trust. yl thanks the norm asbjornson college of engineering and the center for faculty excellence at montana state university for their support through the faculty excellence grants. velocity magnitude [mm/s] 0 0.8 0.4 (a) (b) figure 2: sample flow fields under single-phase (a) and multiphase (b) flow conditions, showing water velocities as color contours; gas and calcite grains as yellow and grey regions, respectively. acknowledgements this work was performed in part at the montana nanotechnology facility, an nnci facility supported by nsf grant eccs-1542210, and with support by the murdock charitable trust. yl thanks the norm asbjornson college of engineering and the center for faculty excellence at montana state university. references daccord g (1987) chemical dissolution of a porous medium by a reactive fluid. physical review letters 58:479 li y, kazemifar f, blois g, and christensen kt (2017) micro-piv measurements of multiphase flow of water and liquid co2 in 2-d heterogeneous porous micromodels. water resources research 53:6178–6196 ott h and oedai s (2015) wormhole formation and compact dissolution in single-and two-phase co2 -brine injections. geophysical research letters 42:2270–2276 introduction experimental methods results 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a network-based perspective on coherent structure detection from very-sparse lagrangian data giovanni iacobello1, david e. rival1,∗ 1 queen’s university, department of mechanical and materials engineering, kingston, canada ∗ d.e.rival@queensu.ca abstract coherent structure detection (csd) is a long-lasting issue in fluid mechanics research as the presence of spatio-temporal coherent motion enables simpler ways to characterize the flow dynamics. such reducedorder representation, in fact, has significant implications for the understanding of the dynamics of flows, as well as their modeling and control (hussain, 1986). while the eulerian framework has been extensively adopted for csd, lagrangian coherent structures have recently received increasing attention, mainly driven by advancements in lagrangian flow measurement techniques (haller, 2015; hadjighasem et al., 2017). lagrangian particle tracking (lpt), in particular, is widely used nowadays due to its ability to quantity fluid-parcel trajectories in three-dimensional volumes (schanz et al., 2016). differently from eulerian coherent structures – that are mainly based on velocity gradient tensor (chen et al., 2015), thus requiring higher data resolutions –, the lagrangian framework provides a more suitable representation to characterize sparse data. accordingly, coherent motion detection in the lagrangian viewpoint naturally fits real-world dataset availability such as, among others, biological flows (tallapragada et al., 2011), atmospheric flows (shnapp et al., 2019), as well as oceanic currents (gould, 2001). characteristic flow length-scale, d streamline track lenght network temporal evolution & lcs detection t 0 t i spatio-temporal coherencesparse data: λ/d ≈ 10à1 very-sparse data: λ/d ≈ 1 λ figure 1: schematic of the conceptual framework for csd from sparse and very-sparse lagrangian data. (left) sketch of a vortical flow (blue dashed arrows) seeded with sparse and very-sparse tracers (green filled dots) and their tracks (orange dotted arrows); λ is the mean inter-particle distance. (right) network evolution for csd, where tracers correspond to nodes (green dots) while links are shown as black lines. several techniques have been proposed so far to identify coherent motion from lagrangian data (hadjighasem et al., 2017), including finite-time and finite-space lyapunov exponents (haller, 2015), trajectory complexity (rypina et al., 2011), transfer operator-based methods (ser-giacomi et al., 2015), lagrangianaveraged vorticity deviation, as well as fuzzy-clustering (froyland and padberg-gehle, 2015), and spectral clustering (schlueter-kuck and dabiri, 2017; schneide et al., 2018; martins et al., 2021). although all these techniques have been tested to work reasonably well for 2d flows through densely-seeded particle distributions, they usually tend to fail in identifying the flow behavior for sparse or very-sparse data. in this regard, sparse and very-sparse lagrangian data are characterized by extremely low particle densities per characteristic flow scale, namely o(10−1) and o(100) tracers per integral length scale in the flow, respectively (see figure 1, left). moreover, short track lengths contribute to the strong sparsity of the data. our work proposes a new network-based framework (figure 1, right) that can be specifically suitable for very-sparse lagrangian data from 3d experimental (realistic) flows. in particular, our methodology aims to exploit the instantaneous features of the trajectories (e.g., local geometry or local flow fields) to provide a spatio-temporal characterization the flow. this procedure is in contrast with the classical integral approaches of previously-proposed techniques (as mentioned above), where the features of the whole trajectory are evaluated over an extended temporal interval. this operation, in fact, reduces the features of the whole trajectory to a scalar value at the starting or final particle position, thus leading to a very-sparse representation of the flow dynamics when very-sparse data are used. moreover, our new perspective can be suitable for the analysis of unsteady flows, since the behavior of the particle trajectories are assessed over time. although very-sparse lagrangian trajectories represent a challenge for csd, they frequently appear in experiments. accordingly, we have been carrying out experimental measurements on three-dimensional vortical flows to test our ideas based on the aforementioned network-based approach. in particular, particle tracking of seeded bubbles is currently in development to extract very-sparse trajectories that allows us to assess the effectiveness of the proposed method. results related to the test case can hence pave the way for the analysis of a variety of other experimental data sets, so as to gain insight into realistic flows characterized by very-sparse lagrangian trajectories. in conclusion, the combination of advances in lpt and the wide spectrum of possible applications, in conjunction with the growing development of networkbased techniques in fluid mechanics (iacobello et al., 2020), potentially makes our approach an effective alternative for csd. references chen q, zhong q, qi m, and wang x (2015) comparison of vortex identification criteria for planar velocity fields in wall turbulence. physics of fluids 27:085101 froyland g and padberg-gehle k (2015) a rough-and-ready cluster-based approach for extracting finitetime coherent sets from sparse and incomplete trajectory data. chaos 25:087406 gould wj (2001) direct measurement of subsurface ocean currents: a success story. ucl press hadjighasem a, farazmand m, blazevski d, froyland g, and haller g (2017) a critical comparison of lagrangian methods for coherent structure detection. chaos 27:053104 haller g (2015) lagrangian coherent structures. annual review of fluid mechanics 47:137–162 hussain af (1986) coherent structures and turbulence. journal of fluid mechanics 173:303–356 iacobello g, ridolfi l, and scarsoglio s (2020) a review on turbulent and vortical flow analyses via complex networks. physica a: statistical mechanics and its applications page 125476 martins f, sciacchitano a, and rival d (2021) detection of vortical structures in sparse lagrangian data using coherent-structure colouring. experiments in fluids 62:1–15 rypina ii, scott s, pratt lj, and brown mg (2011) investigating the connection between complexity of isolated trajectories and lagrangian coherent structures. nonlinear processes in geophysics 18:977–987 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:70 schlueter-kuck kl and dabiri jo (2017) coherent structure colouring: identification of coherent structures from sparse data using graph theory. journal of fluid mechanics 811:468–486 schneide c, pandey a, padberg-gehle k, and schumacher j (2018) probing turbulent superstructures in rayleigh-bénard convection by lagrangian trajectory clusters. physical review fluids 3:113501 ser-giacomi e, rossi v, lópez c, and hernández-garcı́a e (2015) flow networks: a characterization of geophysical fluid transport. chaos 25:036404 shnapp r, shapira e, peri d, bohbot-raviv y, fattal e, and liberzon a (2019) extended 3d-ptv for direct measurements of lagrangian statistics of canopy turbulence in a wind tunnel. scientific reports 9:1–13 tallapragada p, ross sd, and schmale iii dg (2011) lagrangian coherent structures are associated with fluctuations in airborne microbial populations. chaos 21:033122 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 experimental investigation on flow structures of steadily translating low-aspect-ratio wings in low reynolds number flow yichen zhu1, jinjun wang1∗ 1 beijing university of aeronautics and astronautics, key laboratory of fluid mechanics (ministry of education), beijing, china ∗ jjwang@buaa.edu.cn abstract in recent decades, micro air vehicles (mavs) have been a hot topic for their promising future. but the promotions of mavs are hindered by their short endurances. to solve this problem, inspirations are brought from migratory butterflies who utilize the ‘flapping-gliding’ skill during long-distance migration to improve the flight efficiency. the butterfly’s gliding flights, which can be simplified by considering the steadily translating fixed wings, have drawn high attentions. previous studies mainly focus on the aerodynamics of the low-aspect-ratio fixed wings at re ≈ 105 via force measurements. however, few experimental studies have measured the 3d flow fields. consequently, the underlying high lift-to-drag ratio mechanisms in the steadily translating butterfly-shaped wings are still not clear. to shed new light on this problem, the 3d flow structures around butterfly-shaped wings were captured and investigated in detail. in the present work, experiments were conducted in a low-speed recirculation water channel at beijing university of aeronautics and astronautics. the channel has a test section of 60cm(height)× 60cm(width) ×300cm(length). three kinds of flat-plate models were tested in our experiments. fig. 1 shows the schematics of the wing planforms. the outline of the danaus plexippus model (dp, fig. 1(a)) was derived from the typical museum specimen of the corresponding butterfly species. this planform has been used in our previous study(zhu et al. (2020)). to better understand the effects of wing planform, two simplified models were also investigated. the models with forward-sweep and straight leading edges were called the forward-sweep trapezoid model (fst, fig. 1(b)) and the nonesweep trapezoid model (nst, fig. 1(c)), respectively. the chord, span and thickness of the models were l = 80mm, c = 60mm and t = 1mm, respectively. all edges were left square. the models were suspended upside down into the test section from a strut system which can control the angle of attacks (aoas, α) precisely. the aoas varied from 4◦ to 10◦ with a step of 2◦ in our study. the strut system was installed on a robotic translator, which can translate the models along the freestream direction. the free-stream velocity was u∞ = 100mms−1 resulting in a chord-based reynolds number rec = 5.4× 103. the free-stream turbulent intensity was less than 1%. the stereo-piv measurements were employed to obtain the three-component velocity fields with a fixed laser sheet placed perpendicularly to the free-stream direction. the models were translated via robotic translator in increments of ∆x = 0.05c. thus, the approximations of the time-averaged volumetric flow fields were reconstructed by the multiple-plane data. the coordinate system used here originates at the trailing edge of the models at the midspan location, where x, y and z axes refer to the streamwise, spanwise and normal directions, respectively. the measurement volume was in the coordinate range of [−c,0.5c]× [−0.75c,0.75c]× [−0.25c,0.5c]. in order to investigate the evolutions of flow structures, the time-resolved 2d2c piv measurements were also performed with a laser sheet placed perpendicularly to the spanwise direction. for each case, two independent sets of 13431 instantaneous velocity fields were acquired at a sampling rate of 288hz. the analysis begins by examining the 3d time-averaged flow structures of the three models. the representative flow fields of these models at α = 8◦ are shown in fig. 1. the vorticity magnitudes ‖ωc/u∞‖2 are used to visualize the vortex sheets where vortex cores are identified by an isosurface of q-critierion (q = 43). in the leeward side of the dp and fst models, two elongate vortical structures are identified by q, which represent the leading-edge vortices (levs) and might be casused by the presence of curved leading edges. the levs remain attached to these two models, which are probably the sources of additional non-linear lift. however, the levs cannot be identified from the time-averaged flow fields for the cases of nst model. in fact, the individual lev convects downstream once detaching from the leading-edge shear layer. the temporal-spatial evolutions of the levs are reconstructed based on the long short term memory (lstm) method. in addition to the levs, the wingtip vortices (wtvs) are identified for each case in fig. 1, as a pair of counter-rotating vortices trailing from the wing tips. the instantaneous locations of wtv centers are determined by γ1 criterion, which is recently used by dghim et al. (2020). the detected γ1 peaks are fitted by gaussian model to locate wtv centers more precisely. the mean locations of wtv centers are then carculated and fitted by straight lines in the streamwise range of x/c= [−0.65,0.5]. fig. 2 shows the detected results at α = 10◦. furthermore, the wtv parameters such as trajectory,core radius and core circulation are obtained. it is found that the wtv trajectories move inward and downward with increasing aoas regardless of the wing planforms. to compare the effects of the wing planforms quantitatively, the induced drag coefficients cdi are calculated based on the maskell induced-drag model. the variations of cdi with α are shown in fig. 3. interestingly, the dp model has the smallest cdi of the three models in the range of α= [4◦,10◦]. thus, it is likely that the butterfly-shaped wings have relatively small induced drags, which contribute to improve the high lift-to-drag ratio. (a) dp model 3 6 9 12 15 18 21 24 27 300 ǁωc/u ǁ ∞ (b) fst model y x z (c) nst model figure 1: perspective view of the time-averaged flow fields at α = 8◦. shown in red is the isosurface of q= 43.the planforms are also sketched at the bottom left. dp model fst model nst model 0 0.7 0.08 0.50.65 0.25 0.6 0.16 00.55 -0.25 0.5 -0.5 -0.75 -1 x/cy/c z/c wing tip -β z β y freestream figure 2: mean locations of wtv centers with x/c in the rang of [−0.65,0.5] at α = 10◦ 4 6 8 10 0.01 0.02 0.03 0.04 dp model nst model fst model c di α figure 3: variations of cdi with α. references dghim m, ferchichi m, and fellouah h (2020) on the effect of active flow control on the meandering of a wing-tip vortex. journal of fluid mechanics 896:a30 zhu y, qu y, wang j, and ma b (2020) near-wall topological patterns and flow structures over a simplified danaus plexippus model. chinese journal of aeronautics 33:2527–2534 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 extended-pod based acoustic analysis of separated aerofoils via simultaneous time-resolved piv and force measurements d. w. carter1∗, m. ferreira1, b. ganapathisubramani1 1 university of southampton, dept of aeronautical & astronautical engineering, southampton, united kingdom ∗ d.w.carter@soton.ac.uk abstract we present a cross-correlation based analysis of the acoustic field generated in the wake of naca 0012 and naca 65410 aerofoils at a chord-based reynolds number rec = 75000 as obtained from pressure fields reconstructed from a series of planar time-resolved particle image velocimetry (piv) experiments. the experiments are performed in a water channel facility located at the university of southampton with an overhead carriage system to allow precise control of the angle of attack α of the aerofoils as well as to mount them to a six-axis force/torque transducer to allow for simultaneous load measurements. angles of attack in the range 4◦ < α < 17◦ are explored corresponding to a range of conditions from zero flow separation to fully stalled. a high-speed nd:ylf laser is directed in from either side of the facility to simultaneously illuminate the pressure, suction, and trailing regions of the aerofoil and three 4 megapixel high-speed phantom veo 640-s cameras are synchronized to capture the entire flow surrounding the aerofoil. piv post-processing is performed on the individual fields of view separately and then stitched using a calibration reference (fig 1(a)). the instantaneous planar pressure fields are reconstructed from the stitched time-resolved velocity fields through the application of taylor’s hypothesis (de kat and ganapathisubramani, 2012) and dirichlet boundary conditions approximated from the free stream using bernoulli’s equation. the pressure reconstruction is assessed using the naca 0012 case at low-angle of attack α = 4◦ and is shown to provide reasonable mean surface pressure distribution as compared to a dynamically matched rans simulation employing a k-ω sst model (fig 1b,c). by altering the domain size of the rans simulation, it was determined that the limited domain size of the stitched piv adversely impacts the accuracy of the pressure reconstruction particularly near the leading edge where the gradients are largest. the far-field acoustics emanating from the aerofoil surface are approximated from the pressure fields through the application of curle’s analogy (koschatzky et al., 2011). the present study focuses on the dipole noise sources emanating from the surface of the aerofoil. motivated by the relationship between vorticity and sound production (powell, 1995), the extended proper orthogonal decomposition (epod, borée, 2003) was used to reconstruct the pressure and unsteady pressure fields that are most correlated with three quantities: the out-of-plane vorticity, the partial unsteady lamb vector, and the forces and moments experienced by the foil. these correlated reconstructed fields are then applied to curle’s analogy in order to investigate far-field acoustic features that result. we find the resulting far-field acoustics obtained from the correlation-based pressure reconstructions are found to be more closely related to the temporal behavior of the vorticity fields compared to the unsteady partial lamb vector and the forces and moments based on their overall sound pressure level. the directivity however is not significantly impacted by the correlating quantity, suggesting that the propagation direction is primarily driven by the geometry of the aerofoil. acknowledgements we gratefully acknowledge financial support from eu h2020 project homer (grant ref no: 769237) and epsrc (grant ref no : ep/r010900/1). 0.1 0.2 0.3 0.4 0.5 0.6 -2 0 2 figure 1: pseudo-color of mean velocity magnitude from the stitched piv for the naca 0012 at α = 4◦ (a). the suction, pressure, and trailing regions corresponding to the individual piv fields of view are shown with dashed, dashed-dot, and solid rectangles respectively. pseudo color of the mean pressure coefficient field is shown in (b) with corresponding surface pressure distribution in (c) from the piv (solid) and from dynamically matched rans model (dashed). references borée j (2003) extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. experiments in fluids 35:188–192 de kat r and ganapathisubramani b (2012) pressure from particle image velocimetry for convective flows: a taylor’s hypothesis approach. measurement science and technology 24:024002 koschatzky v, moore p, westerweel j, scarano f, and boersma b (2011) high speed piv applied to aerodynamic noise investigation. experiments in fluids 50:863–876 powell a (1995) vortex sound theory: direct proof of equivalence of “vortex force”and “vorticityalone”formulations. the journal of the acoustical society of america 97:1534–1537 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 volumetric lagrangian particle tracking of the water surface flow produced during the movement of a mechanical insect leg thomas steinmann1∗, laurent david2, patrick braud2, jérôme casas1 1 institut de recherche en biologie de l’insecte, irbi umr cnrs 7261, tours, france 2 institut pprime, upr 3346, cnrs-université de poitiers-ensma, france ∗ thomas.steinmann@univ-tours.fr abstract over a thousand animal species are capable of walking on the interface between air and water. these species include water striders, a family of insects from the order hemiptera that has an almost unique ability to walk on the surface of the water without penetrating it. they achieve this outstanding feat by making use of the surface tension and their long hydrophobic legs. experiments have revealed that water striders transfer some momentum to the underlying fluid through capillary waves and hemi-spherical vortices and that both waves and vortices contribute to the mechanism of propulsion. however, the exact momentum and energy carried by waves and vortices have never been quantified together, and only the energy of the surface waves has been quantified to date. an analysis of the complete energy balance between the interface and the body of the water requires measurement of the free surface topography, together with the three-dimensional (3d) flow field in the water under the surface. the ultimate aim of this work was to develop a method capable of doing this. 1 introduction water striders (1.a) are semi-aquatic bugs that slide on the surface of ponds, using their hydrophobic legs to move. we seek to understand the physical mechanisms of momentum exchanged, involved during the propulsion of these insects. these mechanisms are twofold, (i) on one hand the insect legs exchange momentum with the air/water interface through the emission of capillary-gravitational waves ((steinmann et al. (2018))) and (ii) on the other hand the insect transfers momentum under the water surface (1.b). this exchange, under the water surface, is realized through pressure and viscosity forces and results in the emission of a semi-annular vortex (1.b, (steinmann et al. (2021b)). a leg pushes a much larger volume of water than itself and thus acts as a virtual oar made of leg-plus-dimple (1.a). the uniqueness of the water strider locomotion is due to the presence of this added mass of water, absent in most other organisms moving at the air-water interface. our ultimate goal is to achieve a complete energy balance evaluation of this interfacial flow. it requires simultaneous coupled estimations of the free surface topography and of the flow velocity beneath the surface. the combined estimation of the interface topography and the 3-d velocity field below the interface is especially challenging. the choices we made, concerning laser illumination direction, camera position and water tank geometry, have consequences. for instance, the side illumination of a wavy air–water interface often results in the appearance of shadow patches at the surface, due to wave crests. these shadow patches sometimes prevented the identification of the particles at the interface. we proposed and developed an advanced method which circumvents some of these limitations. this technique will be tested on an artificial mechanical insect leg, mimmicking the movement of a water strider leg during propulsion. a b figure 1: water strider, virtual oar and vortices produced bellow the air-water interface during the propulsion. (a) photograph of gerris palludum and illustration of the virtual oar geometry during propulsion in perspective view. the virtual oar is the leg-plus-dimple that pushes a much larger volume of water than the leg itself. (b) dynamics of surface topography and bulk flow during the propulsion of a water strider. three-dimensional snapshot representation of body position, surface topography and vorticity isosurface in the underlying fluid. we also illustrate the flow velocity field in the fluid at the interface. the estimated position of the leg is indicated as a dotted red line. the two counter-rotating cylinders typical of a dipolar vortex are visible (figures from steinmann et al. (2021b)). 2 volumetric lagrangian particle tracking we applied an extension of the volumetric lpt technique to this coupled measurement (2.a, steinmann et al. (2021a)). our original setup made it possible to monitor, in real time, the 3d position of fluorescent tracer particles, both on the surface and in the bulk flow. we overcame the shadow effect due to the presence of waves at the interface by illuminating the flow through the underside of a truncated squared pyramidal water tank. we chose to use a water tank of this shape to ensure that optical access could be established orthogonally through the walls of the tank. four high-speed cameras were focused on the illuminated volume of the flow through the four lateral sides of the pyramidal water tank. the images of the four cameras were analyzed by 3d lagrangian particle tracking velocimetry. with this technique, we were able to track particles accurately at seeding densities compatible with the thresholds for tomographic piv and to reduce considerably the number of ghost particles. we then obtained local 3d velocities by interpolating vector volumes from the discrete particles. 3 artificial mechanical insect leg measurements however, it is difficult to accurately characterize the forces exchange involved in the water striders propulsion because of the lack of reproducibility in their legs movement (steinmann et al. (2021b)). therefore, cameras shake the box analysis mechanical leg measurement volume laser a b c figure 2: (a) volumetric lpt experimental setup for the visualization of moving artificial leg at air-water interface. the mechanical leg is guided by a translation plate. the previously seeded flow and the air / water interface are illuminated by a laser volume. (b) photography of the mechanical leg pushing down the air-water interface statically. a micromanipulator, placed on the translation plate, allows us to precisely position the leg on the interface. the static leg initially exerts pressure on the interface creating a meniscus. the blue line figures out the vertical cross section of the initial deflection of the air-water interface. (c) result of the shake the box analysis of the flow produced during the movement of the artificial leg. we designed a mechanical system that mimics the kinematics of the insect legs (2.b). we simulated the water strider leg using a cylinder (d = 0.1 mm, l = 40 mm) made of steel, of identical diameter and similar length to real animals. it has been shown that the leg may undergo a large deformation while pushing on the air–water interface. the curved shape of the mechanical leg was chosen to mimic the deformed shape of the tarsi. this shape, which is similar to the curvature of interface, greatly reduces the forces exerted on the air–water interface and prevents its breaking while sculling at high velocity. the surface was furthermore covered with a super-hydrophobic coating (ultra ever dry, tap france, plaisir), which reproduced the hydrophobic characteristic of natural legs and allowed us to reach a contact angle of 175 degrees, very close to the 168 degrees of gerris legs. the mechanical leg was held by a micromanipulator (newport m-mtab2) placed on a horizontal translation stage (throlabs ddsm50) and positioned in contact with the water surface. the translation stage allowed a precise movement along the x axis at a velocity of 25 cm/s. using this mechanical device, we were able to reproduce accurately the water strider legs kinematic. the use of the artificial leg allows us to generate both capillary-gravitational waves and half-ring vortex, as involved in the insect locomotion (2.c). the energy balance was determined by evaluating interface position and bulk flow velocity. surface curvature and potential energy were determined from surface topography. the kinetic energy of the flow was derived from the bulk flow velocities. 4 results and conclusions our 3d ptv measurements allow us to determine the dynamics of the air–water interface topography and bulk flow velocity, as presented in 3. the artificial leg pushes down and creates a depression of the free surface. the interface is rapidly displaced by the leg. this displacement of the water surface establishes the boundary conditions between air and the underneath fluid. there is an immediate generation of vorticity, as seen by the two vortices in the (x, y) plane (3). the vortex also develops under the interface in the (x, z) plane. according to helmholtz’s theorem, a vortex line cannot start or end in the fluid, but must end either at a solid boundary or form a closed loop. in our particular case, it ends at the boundary of the fluid. thus these apparent three vortices form in fact a single semi annular vortex. the vortex geometry is related to the dimple geometry and closely follows the displacement of the dimple. the vorticities, circulations and velocities are large in both horizontal and vertical plane, the vortex being flattened in the horizontal plane. to validate the accuracy of the 3d reconstruction of the flow, we compared these 3d measurements (4.a) to 2-d piv measurements on the same mechanical leg moving at the same depth and same velocity (4.b), as already presented in steinmann et al. (2021b). this comparison of mechanical experiments shows that the 3d ptv results are quite robust, even for key details, such as the temporal changes in dimple morphology, or the magnitudes of the bow wave. when starting a stroke, the meniscus is symmetrical. as velocity increases, the process of momentum transfer appears. in 4, we notice the growing asymmetry of the meniscus, reflecting an increase of the water surface resistance. the posterior and anterior angles of the dimple deformation are similar in both experiments. the progressive increase of the bow wave and its shape are also similar. t = 100 ms x= 0 mm x= 3 mm x= 3 m m x= 0 m m x= 3 m m x= -3 mm t = 100 ms y= 0 mm y= 5 mm y= -5 mm 5 mm y x z x z x z x y x y= -5 mm y= 0 mm y= 5 mm figure 3: snapshot of the superimposed tracked particles at the surface and in bulk flow at t = 100 ms (∆t=10 ms) during the during the movement of a mechanical insect leg curving the interface. the green lines represents the x-axis ( x= -3, 0 and +3 mm) and y-axis ( y= -5, 0 and +5 mm) vertical cross-section, depicted in the right panels. in these 6 panels, the green lines represent the cross sections of the interface. we have numerically computed the interfacial flow during the sculling of a leg using finite-element simulations (5.c). we modelled the air–water interface as a diffuse interface using the phase field method implemented in comsol multiphysics 5.3 (comsol, inc®) (steinmann et al. (2021b)). these simulations a vertical cross section of the 3d ptv measurements b 2d vertical piv t = 0 ms t = 20 ms t = 60 ms t = 0 ms t = 20 ms t = 60 ms figure 4: comparison between a cross section of the 3d ptv experiments and 2d vertical piv experiments of the dynamics of the interface and underlying flow during the transverse motion of a model leg. the depth of propulsion was hl = 3 mm and the velocity was vl = 25 cm/s. (a) snapshots at 3 differents times (t=0ms, t=20ms, t=60 ms) of the cross section of the reconstructed position of particles from 3d ptv measurements. (b) snapshot of the vertical cross-section of the seeded water flow and of the surface, as obtained by the high-speed camera. the complete 2d vertical piv setup is described in details in steinmann et al. (2021b) have been validated with the results of the 2-d piv experiments with a mechanical leg, to quantify the pressure forces in the fluid. we show that the pressure drag force acts on the dimple, as illustrated on 5.c. in this example, the presence of a zone of large pressure (∆p = 30 pa) in the 3 mm high bow wave indicates that the pressure force acts essentially on this bow wave. we prove that water strider locomotion at the air-water interface is, thus, very effective and different from flying and swimming. in flying animals, drag and lift, the forces resisting wing movement during flight, are integrated over the entire surface of the wing. the wing serves as both the physical interface on which the forces are integrated and the interface pushing the fluid. in striders, the forces act on the large meniscus that pushes the fluid, like an oar blade, rather than the tiny leg. the size of this virtual oar is function of both hydrophobicity-enhancing structural and material properties and leg kinematics. 3d ptv measurement ∆𝑡 = 6 ms 2d vertical piv ∆𝑡 = 6 ms 2d numerical simulation 5 mm 5 mm 5 mm z x z x z x a b c figure 5: comparison between 3d ptv experiments (a) and 2d vertical piv experiments (b) and numerical simulations (c) of the dynamics of the interface and underlying flow during the transverse motion of a model leg. numerical simulation of the pressure force acting on the moving dimple resulting from the displacement of a leg at a depth of hl = 3 mm and a velocity of vl = 25 cm/s. this figure illustrates the equivalence between the magnitude of the capillary force fs acting on the leg and the magnitude of the drag pressure force fdimple acting on the dimple. the presence of a zone of high pressure (∆p = 30 pa) in the 3 mm high bow wave indicates that the pressure force acts essentially on this part of the virtual oar, where the bow wave appears. the resulting pressure drag force (per unit length) can be obtained by multiplying this pressure by the height of the wave to obtain fdimple = 0.90 n/m. references steinmann t, arutkin m, cochard p, raphaël e, casas j, and benzaquen m (2018) unsteady wave pattern generation by water striders. journal of fluid mechanics 848:370–387 steinmann t, casas j, braud p, and david l (2021a) coupled measurements of interface topography and three-dimensional velocity field of a free surface flow. experiments in fluids 62:1–16 steinmann t, cribellier a, and casas j (2021b) singularity of the water strider propulsion mechanisms. journal of fluid mechanics 915:1–31 introduction volumetric lagrangian particle tracking artificial mechanical insect leg measurements results and conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 experimentally obtained velocity and pressure fields of an open channel flow around a cylinder using rim-spiv w. j. reeder1∗, j. r. moreto2, x. liu2, d. tonina1 1 center for ecohydraulics research, university of idaho, boise, u.s.a 2 department of aerospace engineering, san diego state university, san diego, california, u.s.a. ∗ wjreeder@uidaho.edu abstract the quantification of velocity and pressure fields over streambeds is important for predicting sediment mobility and water exchange between stream and sediment interstitial spaces (schmeeckle and nelson, 2003; tonina and buffington, 2009). the latter is typically referred as hyporheic flow, which consists of surface water that flows through the streambed sediment pores (tonina and buffington, 2009). these fluxes are mainly driven by pressure gradients at the water sediment interface. in this paper, we report an experimental investigation of the time-averaged velocity and pressure field, quantified in a set of laboratory experiments using stereo piv (particle image velocimetry) with a non-toxic index-matched fluid, for an open channel flow around a barely submerged vertical cylinder as a model for plant stalk over a plane bed of coarse granular sediment, mimicking a stream gravel bed. this is the first time that such a velocity and pressure field is characterized experimentally for a free surface flow with irregular floor contour. (a) (b) figure 1: experimental set up (left) with vertical cylinder and the distortion corrected spiv image (right). the near-bed pressure distribution can be complex and difficult to measure with direct techniques such as piezometers, pressure transducers or pitot tubes because of small magnitude variations riding on top of a large hydrostatic pressure field. this is true in both field and laboratory setting. in the latter case, recent advances in stereoscopic particle imaging velocimetry, spiv, allow detailed and high-resolution measurements of the flow field including turbulent fluctuations (de kat and van oudheusden, 2012; van oudheusden, 2013) from which the pressure field can be quantified by knowing the pressure at one location. spiv has the advantage of being non-intrusive and providing the three velocity components along with accurate quantification of their uncertainties. however, being an optical method, it relies on “seeing” the flow within the entire area of interest. this is not possible in case of solid objects immersed in the fluid because they can cause shadows or partially/fully block the view of the flow. to avoid this problem, laboratory experiments use refractive index matching (rim) techniques (budwig, 1994), in which both solid and fluid exhibit similar optical properties, such that they are virtually indistinguishable (figure 1), i.e., the solid is functionally transparent, and spiv can see through the solid and map the flow field all around it. application of this technique is typically expensive and/or hazardous, because of the use of specialized and toxic liquids coupled with commonly used transparent solid materials, typically glass (budwig, 1994). the pressure field is then reconstructed from spiv velocity data by first locally applying the momentum (navier-stokes) equations in differential form and successively integrating the pressure gradient to obtain the pressure field (de kat and van oudheusden, 2012; liu and katz, 2006; van oudheusden, 2013). (a) (b) figure 2: sample mean velocity (left) and mean pressure (right, without accounting the body force) along the symmetry plane through the center of the cylinder. please note the flow direction is from right to left. this pressure reconstruction has been shown to be effective in several previous works (joshi et al., 2014; de kat and van oudheusden, 2012; liu and katz, 2006, 2008, 2013; liu and moreto, 2020; liu et al., 2016). however, these applications were based on geometries with smooth boundaries, well-defined location of the water surface elevation and without large solid bodies protruding within the flow. however, such protrusions are typical in experimental studies of flows over coarse sediments with large macro-roughness elements, such as boulders, bedforms and aquatic vegetation, which depending on their submergence may cause complex water surface elevation patterns. here, we investigate the velocity and pressure fields around a submerged vertical cylinder, which mimics a single rigid stem of aquatic vegetation over a rough bed. the experiment was in a 7 m long and 0.5 m wide flume with glass wall (figure 1(a)). the flume bottom was covered with granular material made of crashed glass with mean diameter of 2.5 mm arranged to mimic a plane bed. the cylinder was placed in the center of the flume and made of a transparent polymer with specific gravity of nearly 2 and refractive index of 1.36 similar to that of water (1.33). to match the solid refractive index, we added 15 % in weight of epsom salt to the water. this fluid mixture is non-toxic, with density 1,158 kg/m3 and dynamic viscosity 2.97 10−3 kg/(m · s). it is relatively inexpensive and allows using refractive index matching (rim) technique (figure 1(b)). we adopted coupled rim and spiv to measure the flow field simultaneously upstream and downstream the cylinder along its center (figure 2(a)). the cylinder with a 1.0 cm diameter was 10 cm tall and the flow field had a mean hydraulic depth of approximately 10.1 cm and mean velocity of approximately 0.12 m/s. we reconstructed the pressure field around the cylinder over the rough bed by using the parallel-ray omni-directional algorithm from the measured flow field (liu and moreto, 2020; liu et al., 2016). to accommodate the constant pressure along the free surface and the irregular shape of the channel bed, appropriate adaptation of boundary treatment for the pressure reconstruction code were implemented. the use of rim-piv allowed us to map the flow hydraulics continuously around the cylinder. the method shows that mapping of the hydrodynamic fields around solids can be achieved experimentally with the use of low-cost and non-toxic fluids or solids coupled with suitable pressure field reconstructing algorithms. the analysis presented here can be extended to study flow and pressure fields around and within solids for various hydraulic applications. acknowledgements this project is partially funded by the national science foundation under award number ear1559348, usda national institute of food and agriculture, hatch project 1012806 and the san diego state university. references budwig r (1994) refractive index matching methods for liquid flow investigations. experiments in fluids 17:350–355 de kat r and van oudheusden bw (2012) instantaneous planar pressure determination from piv in turbulent flow. experiments in fluids 52:1089–1106 joshi p, liu x, and katz j (2014) effect of mean and fluctuating pressure gradients on boundary layer turbulence. journal of fluid mechanics 748:36–84 liu x and katz j (2006) instantaneous pressure and material acceleration measurements using a four exposure piv system. experiments in fluids 41:227–240 liu x and katz j (2008) cavitation phenomena occurring due to interaction of shear layer vortices with the trailing corner of a two-dimensional open cavity. physics of fluids 20:041702 liu x and katz j (2013) vortex-corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field. journal of fluid mechanics 728:417–457 liu x and moreto jr (2020) error propagation from the piv-based pressure gradient to the integrated pressure by the omnidirectional integration method. measurement science and technology 31:055301 liu x, moreto jr, and siddle-mitchell s (2016) instantaneous pressure reconstruction from measured pressure gradient using rotating parallel ray method. in 54th aiaa aerospace sciences meeting. volume 0. pages 1–8. american institute of aeronautics and astronautics, reston, virginia schmeeckle mw and nelson jm (2003) direct numerical simulation of bedload transport using a local, dynamic boundary condition. sedimentology 50:279–301 tonina d and buffington jm (2009) hyporheic exchange in mountain rivers i: mechanics and environmental effects. geography compass 3:1063–1086 van oudheusden bw (2013) piv-based pressure measurement. measurement science and technology 24:032001 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 on the determination of 3d position and orientation of spheroidal particles using defocusing and deep learning m. rossi1∗ 1 technical university of denmark, department of physics, dtu physics building 309, dk-2800 kongens lyngby, denmark ∗ rossi@fysik.dtu.dk tracking the 3d position of tracer particles or small objects like cells or unicellular organisms in miniaturized lab-on-a-chip or biomedical devices is complicated since it is often not possible in these setups to use multi-camera approaches. most successful single-camera approaches for these applications are based on holography or defocusing. holographic methods have been used to track complex objects such has bacteria (bianchi et al. (2019)) and even to estimate their orientation (wang et al. (2016)). however, these methods require a complex and expensive experimental setup which is not always available in research laboratories. on the other hand, defocusing methods work with conventional microscopic optics, are easy to implement, and have shown excellent results in 3d ptv experiments (qiu et al. (2019)). one main drawback is that they normally work only with spherical and mono-dispersed tracer particles. a defocusing method that has potential to measure non-spherical particles is the general defocusing particle tracking (barnkob and rossi (2020)) which is based on pattern recognition and can be conceptually extended to more complex tasks by extending the reference library of particle images, including not only spherical particles at different depth positions, but also non-spherical particles at different orientations. however, whether this approach could work in practice is still unknown. first, is the information contained in simple defocused images sufficient to reconstruct depth and orientation of non-spherical particles, and eventually under which circumstances? second, how to practically collect the labelled reference images? in this work we address the first question using synthetic images of defocused, non-spherical particles generated by the synthetic image generator microsig (rossi (2020)), based on ray-tracing (figure 1). specifically, we consider spheroidal fluorescent particles (prolates or oblates), randomly placed at different depth positions (z) and orientations. due to rotational symmetry, the orientation is here fully determined only by two euler angles, α and β. the in-plane position (x,y) can be obtained with conventional segmentation procedures and is not analyzed here. therefore, the problem reduces to the determination of z, α, and β for a set of single particle images. for pattern recognition, we use a resnet-50 convolutional neural network (he et al. (2016)), a well-known architecture used for complex image recognition tasks, adapted to address a regression problem (i.e. we have here three continuous outputs z, α, and β). the neural network is programmed in the python language using the keras/tensorflow platform. figure 1: working principle used in microsig to generate synthetic images of spheroidal particles. black dots on the surface of the spheroid represent uniformly-distributed point-sources of light. a ray-tracing approach is used to reconstruct the image on the sensor. due to the rotation symmetry of the spheroid, the orientation is fully determined by two euler angles α and β. figure adapted from rossi (2020). zx y zx y zx y zx y zx y zx y 0.0 0.5 1.0 z/h 0.0 0.5 1.0 z′ /h 0 2 0 1 2 3 ′ 0 1 0.0 0.5 1.0 1.5 ′ (a) (b) figure 2: (a) synthetic images of a prolate spheroid with different positions and orientations. (b) measured versus true values of particles’ depth position, z, and euler angles α and β. the average normalized uncertainty for the three output variables is 1.5% for z, 3.5% for α, and 1.5% for β. results for the case of prolate spheroids with an equatorial radius a = 2 µm and a polar radius c = 8 µm, simulated assuming a 20× magnification lens are shown in figure 2. the particles are randomly oriented with 0 ≤ α ≤ 2π and 0 ≤ β ≤ π and randomly placed along a total depth h = 40 µm. the resnet-50 is trained on 5000 labelled images for 110 epochs with a batch size of 64 and adam as optimizer. after training, the neural network is tested on 1000 new images giving an average normalized uncertainty for the output variables of σz/h = 0.015, σα/2π = 0.035, and σβ/π = 0.015. further results obtained on different shapes (prolates and oblates spheroids) and different simulated optics will be presented and discussed in the presentation. in conclusion, this work provides a first proof-of-principle of this method on synthetic images and opens up possible applications in fields such as swimming of micro-organisms, or non-spherical colloids. on-going research is planning to apply this method to study the motion of the micro-organism euplotes vannus and preliminary results will be presented in the conference. the author acknowledges financial support by the villum foundation under the grant no. 00022951. references barnkob r and rossi m (2020) general defocusing particle tracking: fundamentals and uncertainty assessment. experiments in fluids 61:1–14 bianchi s, saglimbeni f, frangipane g, dell’arciprete d, and di leonardo r (2019) 3d dynamics of bacteria wall entrapment at a water–air interface. soft matter 15:3397–3406 he k, zhang x, ren s, and sun j (2016) deep residual learning for image recognition. in proceedings of the ieee conference on computer vision and pattern recognition. pages 770–778 qiu w, karlsen jt, bruus h, and augustsson p (2019) experimental characterization of acoustic streaming in gradients of density and compressibility. physical review applied 11:024018 rossi m (2020) synthetic image generator for defocusing and astigmatic piv/ptv. measurement science and technology 31:017003 wang a, garmann rf, and manoharan vn (2016) tracking e. coli runs and tumbles with scattering solutions and digital holographic microscopy. optics express 24:23719–23725 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 smartpiv an app for flow visualization by cross-correlation and optical flow using smartphones patrick mäder1∗, constanze poll1, jonas hüther1, sebastian jeschke1, henning otto2, christian cierpka2∗∗ 1 technische universität ilmenau, data-intensive systems and visualization group, ilmenau, germany 2 technische universität ilmenau, institute of thermodynamics and fluid mechanics, ilmenau, germany ∗ patrick.maeder@tu-ilmenau.de, ∗∗ christian.cierpka@tu-ilmenau.de in recent years smartphones considerably changed our communication and are used on a daily (or even every minute) basis especially by students without any difficulties. fluid flows also belong to our daily experiences. however, the education of the basic principles of fluid mechanics is sometimes cumbersome due to its non-linear nature. this problem may be tackled in practical sessions applying flow visualization techniques in wind or water tunnels and directly learn from own observations. nowadays, often optical methods like particle imaging velocimetry (piv) or particle tracking velocimetry (ptv) are used for these purposes. a typical piv/ptv setup consists of a (double)pulse laser, a scientific camera and a synchronization device. the costs for this equipment can easily add up to more than 100,000 euros and the installations and set up of the systems requires experiences and is complex. for these reasons universities often only offer practical courses for a small amount of students and the students may not be allowed to use and set up the systems by their own as the equipment is also needed for scientific research. due to the covid-19 pandemic it is also often not allowed to share equipment or even to work in larger groups during practical sessions. however, modern smartphones offer a great selection of different sensors and are easy to set up, at least for students. the high frame rates of several hundred hz provided by modern smartphones also enable their use for piv. cierpka et al. (2016) have shown that it is possible to use a smartphone with a cw-laser for reliable velocity estimates in a plane. käufer et al. (2021) extended the system to stereoscopic piv using two action cameras and a modulated cw-laser and aguirre-pablo et al. (2017) even used smartphones with colored leds for a tomographic reconstruction of the velocity field in a water jet. all these attempts were based on recorded videos that were later processed on a computer with conventional piv software. however, only recently a survey among engineering students showed, that there is a strong interest in a mobile application (app) to perform piv measurements (minichiello et al., 2021). therefore, the aim of the current study was to provide an app that allows for a direct (on-line) evaluation of the data in order to enable the students to directly see how the flow behavior changes when certain boundary conditions are varied and to already estimate if the data processing with the current video/evaluation setting will be successful. the app can also be used to determine the different effects of parameter changes for the piv evaluation later at home. the app was developed within a student software project in close collaboration between students of engineering and computer science. it is available for android and ios in the app stores and can be downloaded and used free of charge (tu ilmenau, 2021). since the ability for on-line flow visualization was most crucial concerning computer performance also optical flow algorithms were implemented as these request much less resources. after choosing the processing parameters (cp. fig. 1, right) the user can directly process the images from the live preview (cp. fig. 1, left insert), record videos or process already stored videos. images as well as videos can be stored for later export for lab reports. in addition to the images a text file and a csv file containing the data and parameter settings will be created that can be used for later analysis for example to test different mean estimators and outlier detection methods that will typically be taught in lab courses. since for the conversion of the particle image displacement to physical coordinates the knowledge of the optical magnification is necessary a module that allows for a quick calibration using a square on a white paper with known side length was also included. since typical fields of view are in the range of 1– 20 cm the side length of the calibration target can be adopted to these values. the app can be intuitively controlled by users that are familiar with the video or photo function of their smartphones as the menus are designed very similar. a photograph of the application of smartpiv for a test flow of a cylinder wake using a low power cw-laser diode is shown in fig. 1(left). figure 1: experimental setup for a students exercise evaluation the flow past a cylinder. the setup includes a cw-laser diode for illumination and the smartphone with the preview screen of the smartpiv app (left). menu for the different evaluation methods optical flow or cross-correlation (right). in the presentation the implementation on the smartphones and the accuracy will be discussed and a typical lab setup will be demonstrated. acknowledgements financial support in the frame of the fellowships for ”innovations for digital teaching” from the thüringer ministerium für wirtschaft, wissenschaft und digitale gesellschaft are gratefully acknowledged. the authors would also like to thank all the students, namely julia bruischütz, teresa bravo roger, jonas stephan, jonas hiese, marcus orban, marcel john, christian engelhardt as well as jörg könig for the support in the lab. references aguirre-pablo aa, alarfaj mk, li eq, hernández-sánchez jf, and thoroddsen st (2017) tomographic particle image velocimetry using smartphones and colored shadows. scientific reports 7:3714 cierpka c, hain r, and buchmann na (2016) flow visualization by mobile phone cameras. experiments in fluids 57:108 käufer t, könig j, and cierpka c (2021) stereoscopic piv measurements using low-cost action cameras. experiments in fluids 62:57 minichiello a, armijo d, mukherjee s, caldwell l, kulyukin v, truscott t, elliott j, and bhouraskar a (2021) developing a mobile application-based particle image velocimetry tool for enhanced teaching and learning in fluid mechanics: a design-based research approach. computer applications in engineering education 29:517–537 tu ilmenau (2021) smartpiv. https://play.google.com/store/apps/details?id=de.tu_ilmenau. secsy.smartpiv https://apps.apple.com/us/app/smartpiv/id1471308387 https://play.google.com/store/apps/details?id=de.tu_ilmenau.secsy.smartpiv https://play.google.com/store/apps/details?id=de.tu_ilmenau.secsy.smartpiv https://apps.apple.com/us/app/smartpiv/id1471308387 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 time-resolved flow field investigation in an industrial centrifugal compressor application involving tr-piv synchronized with unsteady pressure measurements j. klinner1, m. voges1∗, m. schroll1, a. bassetti2, c. willert1 1 inst. of propulsion technology, engine measurement dept., german aerospace center (dlr), köln, germany 2 inst. of propulsion technology, acoustics dept., german aerospace center (dlr), berlin, germany ∗ melanie.voges@dlr.de keywords: time-resolved piv, correlation analysis, time-resolved pressure measurements, rotating instability abstract we report on combined velocity and unsteady pressure measurements obtained on an radial compressor with vaneless diffuser and asymmetric volute. time-resolved piv recordings were acquired at 26 khz both upstream of the impeller as well as within the vaneless diffusor at several rotation speeds at clean conditions and prior to the onset of instabilities within the rotor. the velocity data was acquired with a high-repetition rate, double-pulse laser system consisting of two combined dpss lasers and a high-speed cmos camera that was synchronized with multi-point unsteady pressure measurements. details on the facility, the utilized instrumentation and data processing are provided with particular focus on the spectral and coherence analysis. power spectra obtained from time records of the inlet velocity and unsteady pressure reveal an increase of low-frequency fluctuations below the blade passing frequency and the occurrence of a mode-locked behaviour indicating the presence of rotating instabilities. high levels of correlation between velocity and unsteady pressure signals not only confirm the temporal coherence of the acquired data but also reveal a direct coupling between flow field and pressure signature that is more prominent upstream of the rotor rather than in the diffusor. 1 introduction the present investigation is aimed at capturing the signatures of instabilities in a centrifugal compressor that are reported to develop in the impeller (rotor) or vaneless diffuser or both (cf. (sorokes et al., 2018)) when operated outside of nominal performance. the unsteady flow phenomena are believed to start from a localized flow separation (stall) that frequently will orbit within the stage at sub-harmonic rotational speeds (rotating stall or rotating instability, ri). if not damped sufficiently, the stall cells will eventually develop into more hazardous self-excited pressure oscillations within the entire compressor stage leading to surge phenomena that can induce high aero-elastic loads on the rotor itself leading to premature aging (fatigue) or ultimate failure of the stage. predicting the onset of the instabilities is a prerequisite to maintain compressor operating within safe operating margins. although the application of conventional piv techniques in rotating turbomachinery flows has reached state-of-the-art level (wernet, 2000; liu et al., 2006; voges et al., 2013; gancedo et al., 2016), very few studies are known in the current literature that investigate rotating stall using transient pressure measurements in combination with high speed or phase-locked piv at high pressure ratios and operation conditions near the surge margin. besides the challenging task to provide safer operation of the machine near surge in such experiments, advanced piv methods in combination with unsteady pressure measurements can provide important insights into the formation of stall cells and the interactions between pressure and velocity fluctuations as well as the propagation of aeroacoustic modes in the machine (cf. (pardowitz et al., 2015)). the tr-piv implementation presented herein follows the procedures described by (willert, 2015), in which a narrow image domain is captured at high frame rates with large sample counts, typically at high (a) (b) figure 1: (a) numerical model of the rossini compressor stage with a vaneless diffuser and a volute (rosemeier, 2017). (b) photograph of the tr-piv set up for investigation of the impeller exit flow, the arrow indicates the measurement location upstream of the impeller. table 1: rossini compressor stage dimensions number of blades 15 shroud (inlet) radius rs 79.37 mm impeller le tip radius r1 78.97 mm impeller te tip radius r2 127.84 mm diffuser exit radius r3 214.13 mm diffuser passage height h 14.37 mm design speed 23,900 rpm pressure ratio, π 1.9 mass flow, ṁ 2.8 kg/s image magnification, to provide time-records of a single column of velocity vectors evolving in time. the present work demonstrates the applicability of a recently developed high-repetition rate double-pulse laser system (klinner et al., 2021) in a rotating machine. the tr-piv measurements in the inlet section upstream of the rotor were aimed at characterizing the properties of the inflow at the domain inlet for accompanying les and urans computations (not covered in the present contribution). a second tr-piv measurement domain was located in the diffuser channel for investigation of the flow exiting the rotor. data analysis was focused on time history of the signals, spectra and combined correlation analysis of the transient pressure and velocity information analogous to previously conducted measurements on axial compressor rigs (see (pardowitz et al., 2014, 2015)). 2 description of test rig and centrifugal compressor the single-stage centrifugal compressor geometry provided by liebherr aerospace toulouse sas (lts) consists of an impeller with 15 unshrouded blades in backswept design, a vaneless diffuser and an asymmetric volute, as shown in fig. 1(a). in its original application the compressor stage is operated inside of the cabin air conditioning system of a civil aircraft. for the present investigation the original geometry was adapted at dlr to facilitate the integration of extensive instrumentation. at its design point the realized stage operates a rotational speed of about 23,900 rpm and a total stage pressure ratio of π ≈ 1.9. the inlet and outlet sections consist of straight pipes. the characteristics of the compressor stage are given in table 1. the performance map, shown in fig. 2(a), provides six measured speed lines from 40% to 120% of the design rotational speed in comparison with selected cfd results of the numerical twin of the compressor stage as described in (voges et al., 2021). the agreement between numerical and experimental results is very good, especially regarding the unsteady rans calculations (black squared symbols in fig. 2. prior to the experimental study presented herein, a detailed investigation of the stability limit and surge behavior of the rig was performed. online ffts of the unsteady pressure probe signals were used to identify the beginning of unstable flow conditions and possible entry into rotating stall when throttling the flow, which is visible as a low-frequency ‘hump’ and ‘ripples’ in the spectra below the blade passing frequency (bpf) and above the rotor frequency frotor (see fig. 2(b)). in comparison to clean conditions the ‘hump’ indicates an increase of broadband fluctuations below the bpf, whereby the ‘ripples’ indicate a further increase of fluctuations and some mode-locked behaviour and are seen as a precursor of a rotating instability (ri) (voges et al., 2021; pardowitz et al., 2015). the operating conditions for combined tr-piv and unsteady pressure array measurements at four different rotational speeds were chosen to correspond to either conditions where instabilities occur (i.e. ‘hump’ or ‘ri’), or clean reference conditions as indicated by the white circles in the performance map (fig. 2(a)). reduced mass flow [kg/s]  to t [] 0 0.5 1 1.5 2 2.5 3 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 nred_exp_40% nred_exp_60% nred_exp_80% nred_exp_100% nred_exp_110% nred_exp_120% nred_num_rig config_100% nred_num_40% (nlr, unsteady) nred_num_100% (nlr, unsteady) surge line 120% 110% 100% 80% 60% 40% tr-piv hump clean ri (a) 102 103 104 105 frequency [hz] 10 9 10 7 10 5 10 3 10 1 ps d [ v 2 hz 1 ] bpffrotor 246 hz run 42,44,46 kulite 544-6.2 clean hump ri (b) figure 2: (a) performance map of the rossini rig. solid circles represent data from experiment, solid diamonds from rans and solid squares from urans simulation. white circles indicate conditions for tr-piv measurements. (b) typical spectra for clean and unstable conditions at 60% speed calculated from a unsteady pressure signal of the rig used for setting up ‘clean’, ‘hump’ and ‘ri’ conditions. 3 unsteady pressure measurements and transient recording of signals to enable spatio-temporal analyses of the unsteady pressure fluctuations in the centrifugal compressor rig (pardowitz et al., 2014, 2015), time-resolved pressure array measurements were recorded using 19 miniature unsteady pressure transducers (kulite, xce-062) that were flush-mounted in the impeller casing. these sensors were arranged in an asymmetric distribution at irregular circumferential positions, that is, their positioning does not follow the same periodicity when considering characteristic modal structures of unsteady phenomena related to stall and its precursors. the sensors are grouped to form arrays at 3 different meridional positions (see fig. 3 and table 2). depending on pressure amplitude the pressure transducers have a total accuracy to capture unsteady fluctuations least of 0.07 mbar increasing to 0,12 mbar at 3.5 bar (full scale).using a dewetron 808 data acquisition system with a dewe-orion-0824 multichannel 24 bit ad-converter the unsteady pressure signals were acquired at a sample rate of 200 khz, with a -3 db bandwidth of 150 khz for the relevant measurement range. the data acquisition system also recorded the rig’s spindle speed, piv image acquisition triggers, several microphone signals and gap sensors. to synchronize record start times across multiple measurement sequences, a satellite time reference (irig-b) was also acquired with each transient recording. figure 3: positioning of the unsteady pressure probes (kulites) on the impeller casing. table 2: kulite array positions on the impeller casing kulite sensor position start angle angle increments x/sm [%] [◦ ] [◦ ] impeller inlet k1 -10 190 array 1 k21-k25 5 190 27;36;43;115 impeller k3 25 195 array 2 k41-k45 50 190 27;36;43;115 impeller k5 75 200 array 3 k61-k65 95 205 27;36;43;115 impeller k7 110 170 4 tr-piv instrumentation and image evaluation with the aim of measuring both the upstream and downstream propagation of ri-induced disturbances, planar two-component high-speed piv (2d 2c tr-piv) was performed at two locations (fig. 4). one measurement area (location #1) is located in center of the intake tube 3.0r1 upstream of the impeller leading edge (le), while the location #2 is positioned in the diffuser immediately downstream of the impeller exit at 1.1r2. velocity magnitudes up to 70 m/s at the impeller inlet and up to 350 m/s at the outlet required the use of a double-pulse high speed laser system, which enables pulse separations in the required regime between 1− 20 µs at repetition rates of double pulses of fs=26 khz. the laser system consists of a pair of diodepumped solid state lasers (innolas photonics, nanio air 532-10-v-sp), each providing an average power of up to 10 w. further details on the above tr-piv instrumentation can be found in klinner et al. (2021). an in-house beam-combining optics superimposes the beams from the resonators into a common beam which is then collimated into a narrow, 2.5 mm wide light-sheet with a thickness between 250 µm (location #1) and 450 µm (location #2). the thickening of the light-sheet at the latter location was necessary to minimize the loss-of-pairs in the turbulent impeller exit flow. dense smoke oil-based seeding was provided by a smoke generator (vicount) into the intake section of the test rig through a centrifugal pump and settling chamber to facilitate aerosol sizes < 1 µm. the light scattered by the tracers was imaged with a cmos high speed camera (vision research, phantom v1840) camera using frame-straddling at a frame rate of 54 khz. to improve statistical convergence, two runs were recorded per rig test point each containing 8 bursts at 0.5 hz repetition, which each burst is containing 10,642 double images recorded at 26,000 image pairs per second (∼ 0.4 s). the camera was equipped with a macro lens (nikon, nikkor micro f200/4) with a magnification set near unity which enabled imaging ratios of 11.6 µm/pixel at location #1 (inlet) and of 13.3 µm/pixel at location #2 (impeller exit, inside the diffuser). while location #1 had optical access through a glass window in the inlet tube with an overall working distance of 220 mm, location #2 required a complex imaging setup via a 125◦ mirror and a window, thus requiring a larger working distance of 250 mm. the longer stand-off distance resulted in a slightly lower spatial resolution (see fig. 1(b). at frame rates of 54 khz the highspeed camera provided reduced image sizes of 1792× 160 pixel, which corresponded to an image area of (a) inlet configuration (b) impeller exit configuration figure 4: measurement stations for tr-piv. 20.78×1.85 mm2 at location #1 and of 23.9×2.1 mm2 at location #2. inlet flow particle images recorded at location #1 (cf. fig. 4(a)) exhibit a very high particle image density and allow for high spatial sampling of piv analysis. thus, using state-of-the-art piv processing techniques, a final interrogation window sizes of 16× 16 pixel (190× 190 µm2) with validation rates of 100% were feasible for all operation conditions. the corresponding validation scheme involves a normalized median filter with a threshold of 3.0. at the downstream location #2, the increased turbulence levels required the use of a larger sampling window size of 32× 32 pixels (430× 430 µm2) for the 40% ri condition. with increasing rotational speeds the window size was further increased to 64×32 pixels (860×430 µm2), which is due to the increased tangential velocity along with higher fluctuations. using a normalized median filter with a threshold of 3.0, validation rates of at least 95% and typically of 98-99% could be achieved for measurements at the impeller exit. to enhance particle image contrast and thereby improve the cross-correlation analysis, a mean intensity image, calculated from each burst’s image sequence, was subtracted. all particle images were evaluated using commercial software (pivview 3.9) and an in-house python-based piv package. 5 results 5.1 time-resovled velocity records fig. 5 shows time traces of the axial (u) and transverse (v) velocity components on the inlet center-axis. the shown single burst of 0.4 s length were recorded at 100% rotational speed at both clean and disturbed (throttled) conditions. as the flow is throttled to ‘hump’ conditions, the mean axial inlet velocity u decreases and is accompanied with an increasing occurrence of low-frequency modulations of the axial velocity u. when ‘ri’ conditions are reached, the axial velocity exhibits a nearly sinusoidal modulation near 40 hz with amplitudes of about ±10% of the mean, which believed to be directly associated with presence of a single rotating stall cell inside of the stage. it should be noted, that the transverse velocity component (v) exhibits no such signature. at measurement location #2 (fig. 4(b)), the laser light sheet was periodically scattered by the impeller blades leading to over-exposed image background intensities with low particle image visibility (poor signalto-noise ratio) and drop-out in the velocity records. at 40% speed this affected about 10% of the piv samples, increasing to 26% at 110% speed. fig. 6 presents exemplary velocity time records of the impeller exit flow at 60% speed. each column in the plot represents the circumferential velocity measured in the central column of successive piv samples. as indicated in fig. 4(b), the y-axis is aligned with the radial direction originating at the machine axis. piv data affected by strong laser flare due to the light scattered from the impeller blading could be reliably 5 0 5 x x [p ix el ] 10 0 10 u u [m /s ] 2 0 2 y y [p ix el ] 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 time [s] 5 0 5 v v [m /s ] clean u = 76.8m/s hump u = 59.5m/s ri u = 56.4m/s figure 5: time traces of axial (top) and transverse (bottom) velocity at location #1 and y = 0 at 100% speed showing increasing low-frequency modulations of the axial velocity at ‘hump’ and ‘ri’ conditions. with the present scaling a displacement of 0.1 pixel corresponds to approx. ±0.2 m/s. identified by imposing a threshold in the circumferential (i.e. tangential) velocity ui < 0.3u. furthermore, frames strongly affected by laser reflections were rejected when the total validation rate per frame dropped below a threshold of 70%. this results in blanked (white) columns in fig. 6. due to aliasing between the bpf and image sample rate, this blanking is not equidistant such that certain blade passages remain unaffected. when comparing circumferential velocity variations of the exit flow over time, fig. 6 (top) shows more or less a homogeneous spatial distribution for ‘clean’ conditions and seems uncorrelated with the phase angle of blade passing. in contrast, ‘hump’ (middle) and ‘ri’ (bottom) conditions exhibit a clear deficit of tangential velocity after blade tip arrival (probably the blade’s wake flow) which is followed by a region of increased circumferential velocity shortly before the following blade arrives (indicated by the following white bar). for ‘hump’ and ‘ri’ conditions, these regions of increased circumferential velocity appear at the impeller exit (y =−10 mm) and propagate radially outward with time, as indicated in the dashed line in fig. 6 (middle). 5.2 spectral analysis of the inlet flow the power spectral density (psd) of the inlet velocity data was obtained using welsh’s method (welch, 1967) by summing of hann-weighted ffts accumulated in equi-spaced slots of interval 4096/ fs (157 ms) with 2730/ fs (105 ms) spacing (66% overlap), corresponding to a spectral binwidth of 6.35 hz. lowpass filtering with a cut-off of 0.4 fs was applied to attenuate random noise. the spectra were additionally averaged over the eight bursts to improve statistical convergence. for the inlet flow, the interrogation window size was varied between 16, 32 and 64 pixel which was found to have very little effect on the shape of the spectrum. also, shape variations of the spectra in the transverse y direction over the 21 mm image height (see fig. 4(a)) are marginal, thus allow averaging along the extent of the field of view to further decrease random noise. fig. 7 (left) shows the resulting velocity spectra recorded at 100% rotor speed for the three throttle positions. the −5/3 slope is added to indicate kolmogorov’s scaling law which seems to partially apply to the transverse component. with increased throttling of the stage at constant rotor speed there is strong increase in harmonic components below the rotor frequency for the axial component (u) which results in a maximum near 44 hz for ‘ri’ conditions that already was clearly visible in the corresponding time trace in fig. 5. this is accompanied by additional spikes present between bpf and fr for the spectra of the transverse velocity. integration of the spectra confirms an increase of turbulence intensity u′/u from 0.8% at ‘clean’ conditions to 2% at ‘hump’ conditions up to 10% at ‘ri’. the latter increase of the standard deviation u′ stems from the strong low-frequency modulation, also visible in the time trace show in fig. 5 (top). a comparison to psds of the unsteady pressure signals obtained at the rotor inlet (k1) in fig. 7 (right) reveals similar spikes near 40 hz as in the u-psd which were also used to verify the temporal coherence between the pressure and velocity signals and thereby confirm synchronized data acquisition. this is described in the following section. figure 6: piv timetraces of circumferential velocity u of the impeller exit flow and along the radial direction y recorded with 26 khz at location #2 near the casing wall at ’clean’ (top), ’hump’ (middle) and ’ri’ (bottom) conditions. white bars represent measurements affected by laser reflections on the impeller blades. 5.3 velocity-pressure correlations and verification of phase coherence for the present time-resolved database, velocity-pressure correlations and evaluations of co-spectra are feasible on the basis the measurements were acquired synchronously. to verify the consistency, the start-triggers of each of the piv burst was recorded by the data acquisition system described in sec. 3. these signals are automatically detected in the transient recordings by first binarizing the signal at a threshold of half of the ttl voltage level. in a second step the position was detected were the gradient of the binarized signal is half of the ttl level. this allowed the absolute positioning each piv sequence with a jitter in the range of [−5,+15 µs] with respect to the time-base associated with the pressure signals. while piv validation rates of 100% were achieved for the inlet measurements, the outlet measurement data is incoherent due the laser flare caused by the passing blades and first needs to be interpolated to obtain equidistant samples and to enable correlations. for this purpose, a third order cubic spline interpolation was applied using the velocity data from previous and subsequent piv samples. the signal coherence between pressure and piv data could be clearly verified at the 100% speed ‘ri’ test point. here the presence of the previously mentioned modulation near 44 hz is present in both the pressure and the velocity signal (see fig. 7 bottom). fig. 8 shows the resulting associated time traces for pressure and velocity data for inlet measurements (left) and outlet measurements (right) for a single burst. the unsteady pressure data are equivalent to those shown in the spectra in fig. 7 and were downsampled from 200 khz to 26 khz through linear interpolation to obtain a common time base. velocities represent the value averaged over the y-axis excluding outliers, where outliers due to blade reflections were interpolated after spatial averaging. the 40 hz modulation is clearly visible in the inlet measurements but is attenuated in the outlet measurements. for better visualization, fig. 8 also includes a low-pass filtered version of velocity signal (red line) at the outlet with cut-off at the rotor speed (1/15th of bpf). by comparing these combined plots of pressure and velocity for all of the eight burst per run, the temporal coherence between the pressure and velocity could be verified. cross-correlation between the spatially averaged velocities and the unsteady pressures at the rotor inlet and outlet are shown in fig. 9 for 100% speed at ‘ri’ conditions. each correlation is averaged over eight bursts and reveals clearly a dominant sinusoidal modulation near 44 hz as visible in unsteady pressure and velocity spectra. interestingly, the correlation coefficient is much weaker for the exit velocity which probably means that, under given operation conditions near surge, wall pressure fluctuations have a greater influence on the velocity field upstream of the rotor than on the velocity in the diffuser. 101 102 103 104 frequency f [hz] 10 10 10 8 10 6 10 4 ps d u 2 bpffrotor 412 hz run 49 (u = 76.7 m/s u /u=0.8% v /u=2.1%) u/u v/u (x10) 101 102 103 104 105 frequency [hz] 10 9 10 7 10 5 10 3 10 1 ps d [ v 2 hz 1 ] bpffrotor 412 hz run 49: kulite data: 544-6.2, 553-6.19 k2.1 k7 101 102 103 104 frequency f [hz] 10 10 10 8 10 6 10 4 ps d u 2 bpffrotor 412 hz run 51 (u = 59.4 m/s u /u=2.0% v /u=2.1%) u/u v/u (x10) 101 102 103 104 105 frequency [hz] 10 9 10 7 10 5 10 3 10 1 ps d [ v 2 hz 1 ] bpffrotor 412 hz run 51: kulite data: 544-6.2, 553-6.19 k2.1 k7 101 102 103 104 frequency f [hz] 10 10 10 8 10 6 10 4 ps d u 2 bpffrotor 412 hz run 53 (u = 56.6 m/s u /u=10.1% v /u=2.2%) u/u v/u (x10) 101 102 103 104 105 frequency [hz] 10 9 10 7 10 5 10 3 10 1 ps d [ v 2 hz 1 ] bpffrotor 412 hz run 53: kulite data: 544-6.2, 553-6.19 k2.1 k7 figure 7: psds of velocities (left) measured at location #1 (y = 0) and psds of unsteady pressure (right) on impeller casing entry at x/sm = 5% (k21) and immediately downstream of the rotor at x/sm = 110% (k7) at 100% speed and at ’clean’ (top), ’hump’ (middle) and ’ri’ (bottom) conditions. faded colors represent the raw un-filtered data. 6 conclusions the present contribution describes the implementation of tr-piv synchronized with unsteady pressure measurements in an industrial single-stage centrifugal compressor. the rig was operated at four speed lines near design point and near surge in order to provide experimental data with regard to the precursors of instabilities or even stall. in total approximately 3 terabytes of particle image data were acquired at two measurement locations, one upstream of the impeller leading edge and the other immediately downstream of impeller exit within the vaneless diffuser. the analysis of power spectra for inlet velocities and unsteady pressure data located at 5% and 110% of meridional span revealed the increase of low-frequency fluctuations below the bpf as well as below the rotor frequency and the occurrence of a mode-locked behaviour (‘ripples’) indicating the presence of rotating instabilities near surge. exemplarily correlations between measured velocity and unsteady pressures revealed consistency of the data in terms of a large correlation signal at the dominant low-frequency peak at 100% speed in both pressure and velocity spectra. future work could make use of measured phase differences of such correlations to compute propagation velocities and direction of perturbations in the velocity field related to unsteady surface pressure. the available data is suitable for fourier decomposition of the signals obtained by unsteady pressure array which can provide time-resolved information on the occurrence of rotating instabilities in the impeller casing and which, ideally, can be used for further conditional analysis of the flow field data provided by tr-piv. 0.0 0.1 0.2 0.3 0.4 0 20 40 60 80 pr es su re p [k pa ] 0.18 0.20 0.22 time t [s] 0 20 40 60 80 pr es su re p [k pa ] 45 50 55 60 65 70 v el oc ity u [m /s ] 45 50 55 60 65 70 v el oc ity u [m /s ] kulite1 kulite7 upiv (a) 0.0 0.1 0.2 0.3 0.4 0 20 40 60 80 pr es su re p [k pa ] 0.18 0.20 0.22 time t [s] 0 20 40 60 80 pr es su re p [k pa ] 150 200 250 300 350 v el oc ity u [m /s ] 150 200 250 300 350 v el oc ity u [m /s ] kulite1 kulite7 upiv upiv filt (b) figure 8: time traces at 100% speed ‘ri’ of unsteady pressures of two kulites at inlet and impeller exit and axial velocity measured at inlet location #1 (a) and radial velocity measured at impeller outlet location #2 (b). top: entire burst; bottom: enlarged section between the dashed lines. 20 15 10 5 0 5 10 15 20 lag [ms] 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 c or r. co ef f. r run 53 u k2.1 u k7 (a) 20 15 10 5 0 5 10 15 20 lag [ms] 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 c or r. co ef f. r run 100 u k2.1 uflt k2.1 u k7 uflt k7 (b) figure 9: cross-correlations of velocities of the inlet flow at location #1 (a) and the impeller exit flow at location #2 (b) at 100% speed ‘ri’ correlated with unsteady pressure signals on impeller casing entry at x/sm = 5% (k21) and immediately downstream of the rotor at x/sm = 110% (k7). acknowledgements the material presented herein was funded through the clean sky 2 joint undertaking project rossini (radial compressor surge inception investigation) under the european union’s horizon 2020 research and innovation program. (grant agreement no 717081). the authors gratefully acknowledge the contributions of all project team members, namely mr. schindel and the workshop team from dlr, for their effort and valuable contribution during rig design and instrumentation phase. references gancedo m, gutmark e, and guillou e (2016) piv measurements of the flow at the inlet of a turbocharger centrifugal compressor with recirculation casing treatment near the inducer. experiments in fluids 57:16 klinner j, hergt a, grund s, and willert ce (2021) high-speed piv of shock boundary layer interactions in the transonic buffet flow of a compressor cascade. experiments in fluids 62:58 liu b, yu x, liu h, jiang h, yuan h, and xu y (2006) application of spiv in turbomachinery. experiments in fluids 40:621–642 pardowitz b, peter j, tapken u, thamsen pu, and enghardt l (2015) visualization of secondary flow structures caused by rotating instability: synchronized stereo high-speed piv and unsteady pressure measurements. in 45th aiaa fluid dynamics conference. american institute of aeronautics and astronautics, dallas, tx pardowitz b, tapken u, sorge r, thamsen pu, and enghardt l (2014) rotating instability in an annular cascade: detailed analysis of the instationary flow phenomena. journal of turbomachinery 136:061017 rosemeier j (2017) numerische analyse eines radialverdichters mit spiralgehäuse und unbeschaufeltem diffusor. master’s thesis. ruhr universität bochum sorokes jm, marshall df, and kuzdzal mj (2018) a review of aerodynamically induced forces acting on centrifugal compressors and resulting vibration characteristics of rotors. in 47th turbomachinery and 34th pump symposia. houston, texas voges m, klinner j, willert c, bassetti a, reutter o, and van rooij m (2021) the challenge of time-resolved flow investigation of a one-stage centrifugal compressor with a non-symmetric volute. in 14th european turbomachinery conference. gdansk, poland voges m, willert c, mönig r, and schiffer hp (2013) the effect of a bend-slot casing treatment on the blade tip flow field of a transonic compressor rotor. in proceedings of the asme turbo expo, san antonio, texas, usa welch p (1967) the use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. ieee transactions on audio and electroacoustics 15:70–73 wernet mp (2000) a flow field investigation in the diffuser of a high-speed centrifugal compressor using digital particle imaging velocimetry. measurement science and technology 11:1007–1022 willert ce (2015) high-speed particle image velocimetry for the efficient measurement of turbulence statistics. experiments in fluids 56:17 introduction description of test rig and centrifugal compressor unsteady pressure measurements and transient recording of signals tr-piv instrumentation and image evaluation results time-resovled velocity records spectral analysis of the inlet flow velocity-pressure correlations and verification of phase coherence conclusions an intensity-based and a lifetime-based psp imaging method with enhanced sensitivity s.someya1, s.yamashita1,2, t.munakata1, h.ito1, 1 national institute of advanced industrial science and technology, 1-2-1 namiki, tsukuba, ibaraki 305-8564, japan 2 the university of tokyo, 5-1-5 kashiwanoha, kashiwa, chiba 277-8563, japan a pressure-/temperature-sensitive paint (psp/tsp) has been developed and used as a measurement tool for the two-dimensional distribution of pressure and temperature on aerodynamic surfaces. in recent years, although the concern with measuring a pressure difference of several pa, such as countermeasures against the noise of small fans, has been growing, the resolution of current psp measurements is limited to several 10 pa, even with carefully conducted measurements. for highly accurate measurements, researches on the advanced coating films in psp/tsp have eagerly been conducted to date. however, measurement resolution and accuracy deteriorate when quantum efficiency or lifetime decrease under high pressure or high temperature conditions. in this study, we propose an advanced evaluation method by improving an imaging procedure, by combining intensity-based and lifetime-based methods. it is expected to improve accuracy as compared to the case where a single method is used. we evaluated the pressure sensitivity and temporal fluctuation of measured values, with comparing to a standard intensity-based method and a standard lifetime-based method under steady and unsteady pressure conditions. due to the limitation of the length of extended abstract, two standard and two proposed concepts of imaging procedure were illustrated in figure 1 and 2. here, we defined the method which required a reference image as the intensity-based method, and the method without any reference image as the lifetime-based method. fig.1 a concept of revised intensity-based method with a reference image. fig.2 a concept of revised lifetime-based method without a reference image. fig.3 pressure sensitivities of standard and proposed imaging methods near the atmospheric pressure condition. figures 3 show pressure sensitivity of each method near the atmospheric pressure. as shown in figs.3, proposed methods had higher pressure sensitivity than those of standard methods. the high sensitivity leads to a large value of the signal-to-noise-ratio and clear visualization of pressure distribution. in the full length paper and the presentation, detail of these methods and results are shown. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 approximate bayesian framework for 3d reconstruction in a volumetric piv/ptv measurement sayantan bhattacharya*, ilias bilionis and pavlos p. vlachos school of mechanical engineering, purdue university, west lafayette, in 47907, usa *bhattac3@purdue.edu abstract non-invasive flow velocity measurement techniques like volumetric particle image velocimetry (piv) (elsinga et al., 2006; adrian and westerweel, 2011) and particle tracking velocimetry (ptv) (maas, gruen and papantoniou, 1993) use multi-camera projections of tracer particle motion to resolve threedimensional flow structures. a key step in the measurement chain involves reconstructing the 3d intensity field (piv) or particle positions (ptv) given the projected images and known camera correspondence. due to limited number of camera-views the projected particle images are non-unique making the inverse problem of volumetric reconstruction underdetermined. moreover, higher particle concentration (>0.05 ppp) increases erroneous reconstructions or “ghost” particles and decreases reconstruction accuracy. current reconstruction methods either use voxel-based representation for intensity reconstruction (e.g. mart (elsinga et al., 2006)) or a particle-based approach (e.g. ipr (wieneke, 2013)) for 3d position estimation. the former method is computationally intensive and has a lesser positional accuracy due to stretched shape of the reconstructed particle along the line of sight. the latter compromises triangulation accuracy (maas, gruen and papantoniou, 1993) due to overlapping particle images for higher particle concentrations. thus, each method has its own challenges and the error in 3d reconstruction significantly affects the accuracy of the velocity measurement. though, other methods like maximum-a-posteriori (map) estimation have been previously developed (levitan and herman, 1987; bouman and sauer, 1996) for computed tomography data, it has not been explored for piv/ ptv 3d reconstruction. here, we use a map estimation framework to model and solve the inverse problem. the cost function is optimized using a stochastic gradient ascent (sga) algorithm. such an optimization can converge to a better local maximum and also use smaller image patches for efficient iterations. our method uses a uniform prior model for the unknown 3d particle positions (𝑥) and a forward model (𝑓) of the measurement chain to estimate the posterior distribution. here, we assume a uniform probability distribution, 𝑥𝑖 ∼ 𝑈([𝑥𝑚𝑖𝑛, 𝑥𝑚𝑎𝑥]) , for each of the 𝑁 particle positions within the measurement domain bounds, 𝑥𝑚𝑖𝑛 and 𝑥𝑚𝑎𝑥. the observations 𝑦1:𝑀 = (𝑦1, … , 𝑦𝑀) are recorded images from m cameras with image size 𝑃𝑟 × 𝑃𝑐 pixels. we define the row and column position of a pixel using 𝑟 and 𝑐 respectively. the camera calibration function (ℂ𝑟 𝑚(𝑥), ℂ𝑐 𝑚(𝑥)) provides the forward mapping from 3d particle space (𝑥1:𝑁) to the image pixel coordinates (𝑟, 𝑐) for 𝑚th camera. thus, the projected pixel intensity using the forward model is written as, 𝑓𝑚𝑟𝑐(𝑥1:𝑁) = 𝐼0 2𝜋𝜎𝑑 2∑ exp⁡ (− (𝑟−ℂ𝑟 𝑚(𝑥𝑝)) 2 +(𝑐−ℂ𝑐 𝑚(𝑥𝑝)) 2 2𝜎𝑑 2 )𝑁 𝑝=1 (1). in equation (1), 𝐼0, 𝜎𝑑 are image parameters estimated from the optical transfer function (otf) of particle images. the likelihood of all observed data conditioned on particle positions is: 𝑝(𝑦1:𝑀| 𝑥1:𝑁) = ∏ ∏ ∏ 𝑝(𝑦𝑚𝑟𝑐|𝑓𝑚𝑟𝑐(𝑥1:𝑁)) 𝑃𝑐 𝑐=1 𝑃𝑟 𝑟=1 𝑀 𝑚=1 (2), where, each pixel is considered as an independent observation. assuming a log-normal noise the individual pixel likelihood is defined as a normal distribution 𝒩(log 𝑦𝑚𝑟𝑐| log 𝑓𝑚𝑟𝑐(𝑥1:𝑁) , 𝜎 2), with noise variance 𝜎2.the posterior 𝑝(𝑥1:𝑁 | 𝑦1:𝑀) is expressed as a function of the likelihood and the prior and finally, the map estimate is given by 𝑥𝑀𝐴𝑃 = argmax[log(𝑝(𝑥1:𝑁 | 𝑦1:𝑀)), which we solve using stochastic gradient descent. this framework was implemented using pytorch with tensor formulations. the adam optimizer was used with varying learning rates (0.001 to 0.1) and a polynomial calibration function was used to build the forward model. synthetic piv images of size 64x64 pixels were generated with varying particle concentrations (0.01 to 0.1 ppp) to validate the algorithm. figure 1a) shows better convergence with increasing learning rate. however, the initial results with random initializations show lower particle yield across the range of seeding density (figure 1b)). the rms error for the valid measurements were close to 0.2 pixels. the sga algorithm was also tested with different batch size, and suitable learning rates. lower batch size showed higher oscillations (figure 1c)) in mean square loss as smaller random patches from different camera images did not contain the projections of the same particles. subsequently, random image patches corresponding to the same sub-volume resulted in better convergence. the reconstructed positions for a random initialization tended to get trapped in local minima and to avoid such cases perturbed stochastic gradient ascent (psga) (jin et al., 2021) was also implemented. every 100 iterations if the change in loss function was less than 1%, the gradients were perturbed by a zero mean normal distribution with varying standard deviations. the methodology is also tested for triangulation-based initializations and for random corresponding patches for each camera image. furthermore, the sensitivity of the optimization framework to different image noise models (e.g., bernoulli or poisson distributions) is explored. finally, we compare the current estimation of the reconstruction error with existing methods for a synthetic vortex ring case. figure 1: subplot (a) shows algorithm convergence for different learning rate for a whole image optimization. subplot (b) shows rms error in reconstructed positions for valid measurements and % of valid measurements or particle yield for different particle concentrations in particles per pixel (ppp). subplot (c) shows variation in mean square loss for the cost function for different batch size. references adrian, r. j. and westerweel, j. (2011) particle image velocimetry, cambridge aerospace series. bouman, c. a. and sauer, k. (1996) ‘a unified approach to statistical tomography using coordinate descent optimization’, ieee transactions on image processing, 5(3), pp. 480–492. doi: 10.1109/83.491321. elsinga, g. e. et al. (2006) ‘tomographic particle image velocimetry’, experiments in fluids, 41(6), pp. 933–947. doi: 10.1007/s00348-006-0212-z. jin, c. et al. (2021) ‘on nonconvex optimization for machine learning: gradients, stochasticity, and saddle points’, j. acm. new york, ny, usa: association for computing machinery, 68(2). doi: 10.1145/3418526. levitan, e. and herman, g. t. (1987) ‘a maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography’, ieee transactions on medical imaging, 6(3), pp. 185–192. doi: 10.1109/tmi.1987.4307826. maas, h. g., gruen, a. and papantoniou, d. (1993) ‘particle tracking velocimetry in three-dimensional flows’, experiments in fluids, 15(2), pp. 133–146. doi: 10.1007/bf00190953. wieneke, b. (2013) ‘iterative reconstruction of volumetric particle distribution’, meas. sci. technol. meas. sci. technol, 24(24), pp. 24008–14. doi: 10.1088/0957-0233/24/2/024008. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 uncertainty quantification for ptv/lpt data and adaptive track filtering t. janke1∗, d. michaelis1 1 lavision gmbh, anna-vandenhoeck-ring 19, 37081 gttingen, germany ∗ tjanke@lavision.de abstract particle tracking velocimetry (ptv) or lagrangian particle tracking (lpt) picked up a lot of interest over the last years due to their ability to acquire global flow fields at high spatial and temporal resolution. the most recent research focused mainly on algorithmic advancements in order to increase the obtainable data density and on its application to new flow cases. only a small amount of studies tried to quantify the measurement uncertainties linked to these volumetric measurement approaches. within this contribution we want to present how to acquire measurement uncertainties for the position, velocity and acceleration for each data point along a trajectory by means of linear regression analysis tools. based on these uncertainties, an adaptive filtering approach is introduced, which eliminates the user’s choice of the filter kernel length and which automatically determines its optimal value. 1 introduction although being in research and in application since several decades, the correct quantification of all measurement uncertainties for the particle image velocimetry (piv) technique is still an open research topic. only very recently, a further uncertainty quantification approach has been proposed by rajendran et al. (2021), building upon previous works of sciacchitano et al. (2015), wieneke (2015) and bhattacharya et al. (2018). this may seem surprising as the first piv measurement applications have already been done in the late 1970s and early 1980s (adrian (2005)). but in fact, it only shows how complex the whole measurement chain from the image acquisition to the final velocity field reconstruction is. in addition, many measurement and evaluation parameters exhibit non-trivial and non-linear influences on the measurement uncertainties, which makes it even harder to develop a universal uncertainty quantification framework. nevertheless, by being able to state a reasoned estimate of the involved measurement uncertainties, not only a more complete measurement result can be given, but the knowledge of these uncertainties can also be leveraged to enhance the velocity reconstruction, e.g. by hdr-piv (persoons (2015)) or anisotropic denoising (wieneke (2017)), or the pressure field reconstruction (zhang et al. (2020)). with that in mind, it is not surprising, that there is only a limited amount of dedicated research concerning the measurement quantification of 3d-particle tracking velocimetry (ptv)/ lagrangian particle tracking (lpt) techniques, which even further enhances the measurement complexity in comparison to planar piv methods. two studies shall be mentioned here. these are the works of schneiders and sciacchitano (2017) and bhattacharya and vlachos (2020). with the track benchmarking method schneiders and sciacchitano (2017) proposed a technique, where the flow field is not reconstructed from the total amount of all tracked particles but from a reduced sub set. all particles not considered in the flow field reconstruction are then utilized to estimate the measurement uncertainty. an approach to cover the whole data analysis chain from the calibration to the final velocity calculation is proposed by (bhattacharya and vlachos, 2020) and may present the most complete uncertainty quantification framework up until now. here, among other things, the uncertainty in the velocity calculation is modeled as the combined positional uncertainty of two paired particles. this may be a suitable approach for 2-pulse or double-frame ptv/ lpt measurements but dismisses the trajectory filtering step applied in most time-resolved or 4-pulse ptv/ lpt applications. within this work, we want to highlight this aspect of a 3d-ptv analysis by introducing a simple procedure to quantify the local, random measurement uncertainty associated with the filtering process. our approach is utilizing linear regression analysis methods to calculate the confidence bands of polynomial trajectory filters and yields uncertainty estimates for the position, velocity and acceleration for every reconstructed particle trajectory. based on these uncertainties, an adaptive filtering approach is introduced, which eliminates the user’s choice of the filter kernel length and which automatically determines its optimal value. 2 uncertainty quantification 2.1 linear regression analysis in many cases the flow velocity is, as already mentioned, retrieved from the discretely sampled trajectory data by a polynomial regression. when utilizing such a least-square regression approach, not only the actual values of the modeled polynomial coefficients, and therefore the filtered position, velocity and acceleration data, are obtainable but also their corresponding uncertainty estimations. these are often not considered or simply neglected although their calculation is quite simple. the starting point of this analysis are the discrete one-dimensional positional time-dependent measurement points y (see fig. 1). now, our main goal is to obtain the velocity at every measurement position along the trajectory. in order to achieve this, a polynomial regression is performed. the linear equation system to solve this regression can be written as ab = y . (1) here, the matrix a contains the information of all time steps t for all coordinate points within the considered filter window a =  1 t0 t2 0 ... t p 0 1 t1 t2 1 ... t p 1 ... ... ... ... ... 1 tn t2 n ... t p n  . (2) the vector b contains the polynomial coefficients to be fitted b =  b0 b1 ... bp  (3) and vector y holds all measured positions belonging to t0 .. tn y =  y0 y1 ... yn  . (4) the index n denotes the number of sample points within the defined regression window length, and p corresponds to the order/ degree of the polynomial. at this point, the number of coefficients k as k = p+1 and the degree of freedom dof of the regression dof = n− k = n− p−1 (5) shall be further defined. in order to determine the polynomial coefficients b, eq. (1) is rearranged to b = (at a)−1at y (6) and can be solved by any least square matching method. finally, the fitted/ filtered positions ŷ of the original measurement data y can be retrieved. for every regression coefficient b an additional confidence interval 0.2 0.1 0.0 0.1 0.2 time [s] 3 4 5 6 7 8 co or di na te [m m ] ground truth ygt fitted data y measurement data y confidence interval ci figure 1: exemplary synthetic lpt data including the known ground truth ygt, the noisy measurement data y, the filtered data after the polynomial regression ŷ and the estimated confidence/ uncertainty interval ci. ci can be assigned further, which gives an uncertainty estimate of exactly this coefficient. the confidence interval is commonly chosen to have a confidence level of 95%. this can be interpreted as the following: if we would infinitely repeat the regression with different measurement values y, which scatter around the ground truth ygt , we can be confident, that in 95 % of all cases our true value ygt lies within the calculated confidence band ŷ±ci. if we define the confidence level at 68 %, 90 % or any arbitrarily chosen value, the interpretation is accordingly. the equation to obtain the confidence interval for each polynomial coefficient is commonly defined as ci = t∗(dof,1−α/2) · √ mse ·diag ( ata )−1 (7) here t∗(dof,1−α/2) is the student t multiplier and is dependent on the degree of freedom dof of the regression problem and 1 α/2 defines the confidence level. for example, if α is chosen to be α = 0.05, this would correspond to a confidence level of 95%. if the underlying uncertainty in the data would be known, its standard deviation σ could be directly applied here. but since we do not have any prior information on the measurement noise in our case, σ is estimated by the root mean square error √ mse multiplied with the t∗ multiplier, for which no further information about the underlying noise distribution is necessary and which is generally recommended, when the sample size is quite low. the variable mse denotes the mean square error with mse = ssr dof . (8) within this equation the sum of the squared residuals ssr is needed and can be calculated by ssr = n ∑ i=1 (ŷi− yi) 2 (9) the expression mse · ( at a )−1 is also defined as the covariance matrix cov of the regression system. now, as a final result we can state for each polynomial coefficient b0...p its estimated value and its confidence interval/ uncertainty b0...p±ci0...p (10) based on these coefficients, the whole filtered trajectory ŷ can be determined with its corresponding uncertainty ûy band in the following way ŷi±ûy = (b0±ci0)+(b1±ci1) · ti +(b2±ci2) · t2 i + ...+(bp±cip) · t p i . (11) for sliding window approaches, where not the whole trajectory is considered during the filtering but only segments of it, it is convenient to shift the time axis in a way, that the middle entry of the regression window is at t = 0. by doing this, the above equation simplifies to 0.0 0.1 0.2 0.3 uy 0 1000 2000 3000 4000 5000 # o f e n tr ie s (a) 0.00 0.05 0.10 0.15 uy 0 1000 2000 3000 4000 5000 # o f e n tr ie s (b) 0.05 0.10 uy 0 1000 2000 3000 4000 5000 # o f e n tr ie s (c) 0.025 0.050 0.075 0.100 uy 0 1000 2000 3000 4000 5000 # o f e n tr ie s (d) figure 2: distribution of the estimated position uncertainties uy for the different filter lengths n = 5 (a), 7 (b), 9 (c) and 11 (d) calculated from 100.000 polynomial regressions (2nd order) with an added noise level of σnoise = 0.1. ŷ0±uy = (b0±ci0) (12) and the position uncertainty uy corresponds directly to the uncertainty of the first polynomial coefficient ci0. if the uncertainty of the velocity uv is of interest, the fitted polynomial has to be derived (ŷ′ = dŷ/dt) and evaluated at t = 0 as well. it the following, one can find, that the velocity uncertainty uv corresponds to the uncertainty of the second polynomial coefficient ci1 (also at t=0). ŷ0 ′±uv = (b1±ci1) (13) accordingly, the uncertainty of the acceleration ua is equal to the confidence interval of ci2 ŷ0 ′′±ua = (b2±ci2) . (14) all in all, the proposed methodology should yield results for any arbitrarily chosen window size and polynomial degree as long as dof > 0. therefore, it is applicable for fully time-resolved recordings and even 4-pulse lpt measurements. since no over determined regression system can be correspondingly built for 2-pulse/double-frame data, no uncertainty information can be extracted with this approach. as with every fitting/ regression model, a few underlying assumptions and limitations should be mentioned. standard regression methods are very prone to outlier values and cannot cope with them without any special treatment. but since modern 3d-ptv/lpt methods are very successful in suppressing large outliers within a continuous track, the occurrence of outliers should be minimal. the presented uncertainty quantification method does not include any quantification of systematic uncertainties but only focuses on the random parts. in order to ensure that no systematic errors are introduced during the filtering, the polynomial model should be suitable for the raw measurement data and no truncation should occur. in other words, the polynomial filter should only filter the random noise components without altering the real flow motion. this may be a problem in many application, since no prior knowledge about optimal filter parameters is available and it is most probable, that a single set of filter parameters is not suitable for the whole flow field. in order to tackle this problem, we want to propose an adaptive filter approach, which will be described in sec. 3. 20 40 60 0 2 4 6 8 10 noise = 0. 075 noise = 0. 1 noise = 0.2 noise = 1. 0 |u y � �i t| � � it [% ] �ilter length n figure 3: relative deviation of the estimated position uncertainty uy from the ground truth uncertainty σfit as a function of the filter length n and the noise level. 2.2 numerical analysis but first, some numerical experiments shall be conducted with the aim of testing the aforementioned uncertainty quantification approach. as a result of these calculations, the dependency of the estimated uncertainties on the filter length and on the applied noise level shall be identified. furthermore, it shall be tested, whether the specified confidence interval is a good estimator for the true underlying noise. for this, we create 100.000 discretely sampled polynomial functions ygt (ground truth) for the different polynomial lengths of n = 5, 7, 9, 11, 21, 31, 51, 61 and 71. for each polynomial realization the polynomial coefficients bi are randomly chosen. uniformly distributed noise ynoise with zero mean and varying standard deviation σnoise is added to the ground truth to simulate real noisy measurement data y. for the following regression analysis, the polynomial degree is kept constant at p = 2 and the confidence interval ci is defined at a confidence level of 68.3% (corresponding to 1 ·σ for uniformly distributed noise). by doing so, the calculated confidence intervals of the polynomial fits should be an equal estimate for the true standard deviation of the added noise σnoise. before performing the actual comparison between the estimated measurement uncertainty and the known ground truth, it was checked if the total number of 100.000 independent regressions was large enough to reach statistical convergence. this was done by testing the core statement of the confidence band calculation: when calculating the confidence interval at the defined 68.3% confidence level for all 100.000 realizations, 68.3% of all ground truth values should lie within the estimated confidence interval. this could be confirmed during all considered cases and the further analysis of the results is continued. typical distributions of the estimated uncertainty for the velocity term shall now be presented in fig. 2 for four different filter lengths n at a noise level of σnoise = 0.1. for a wide filter, the uncertainty distribution is uniformly distributed and symmetric. as the filter length gets narrower, the distribution starts to show a higher positive skewness. therefore, the median of the uncertainty distribution will be used to estimate the underlying global measurement uncertainty instead of the mean. when looking closely on the x-axis of the plots, the peak values of the distributions are smaller than the added synthetic noise of σnoise = 0.1. this is due the filtering characteristics of the polynomial regression, where the fitted particle positions ŷ are already much closer to the ground truth coordinates y. as a result, if one is interested, if the estimated uncertainty uy correctly predicts the ground truth uncertainty, it has to be compared to the remaining noise σfit of the fitted positions. by looking at the uy distributions, it becomes clear, that the polynomial filtering process substantially reduces the remaining noise in the measurement data. dependent on the actual filter length n a reduction of 30% 50% was found between the raw measurement noise σnoise and the remaining noise after the regression σfit. now, an overview of the relative deviation of the estimated position uncertainty uy by the liner regression analysis and the modeled ground truth uncertainty after the regression σfit as a function of the filter length n and the original noise level σnoise is given in fig. 3. two main results can be stated by the curves given here. at first, the true uncertainty can be estimated very well with filter lengths larger than 21. for smaller 0.02 0.01 0.00 0.01 0.02 time [s] 0.0022 0.0021 0.0020 0.0019 0.0018 0.0017 co o rd in a te [ m ] measurement data ci ci extrapolated re si d u a ls [ m ] figure 4: adaptively determined polynomial filters for a sample trajectory (left: 2nd order polynomial, right: 3nd order polynomial). the confidence interval ci (red) for the evaluated measurement points is extrapolated at the filter ends (blue) to check, if the filter can be extended further. filter lengths, a strong increase in the relative error can be observed. for the smallest considered filter length n = 5 the relative error reaches 10%. as a second result it can be seen, that the uncertainty estimation is independent of the added noise level as long as the used polynomial filter matches the underlying raw data, which is always the case in this numerical investigation. 3 adaptive track filter based on the determined uncertainties, it becomes possible to implement an adaptive track filter similar to the anisotropic denoising filter introduced for piv techniques by wieneke (2017). the theoretical advantage of such an approach is, that the filter automatically adopts to an optimum between denoising strength and truncation error and objectively sets the most suitable filter length, without the need of a user’s input. the implementation of the adaptive track filter is achieved by iterative updating of the polynomial regression (starting from a small filter length), calculating the confidence band and checking if the next points along the trajectory are still within the estimated uncertainty band. if so, the filter length is extended, and if not, the final filter length is reached. as it is shown in fig. 4, the optimal filter length can be very different, when approximating the trajectory by polynomials of different order. in order to test the performance of the adaptive track filter to real experimental data, it is applied to the measurement data obtained from violato and scarano (2011). the particle trajectory reconstruction is performed on a time series consisting of 50 time steps with the shake-the-box (stb) method, as implemented in davis 10.1.2 (lavision gmbh). from the final stb processing, only trajectories, which are tracked for more than 10 time steps, are kept to minimize the probability of having any potential ghost tracks in the data set. after that, 10.000 trajectories are randomly selected from the totality of all tracked particles. furthermore, only the y-component of the position coordinates and the middle point of all trajectories will be evaluated with respect to their uncertainty value, so that any influences from the ends of the trajectory can be neglected for now. as a first result a comparison between the distribution of the reconstructed trajectory lengths and the automatically determined optimal polynomial filter length in presented in fig. 5. most of the reconstructed trajectories are between 10-20 time steps long and the distribution shows a successive decrease in the number of longer tracks. but a significant amount of particles could also be tracked during the whole time series. when looking at the distribution of the applied filter sizes during the adaptive track filter method, the peak of the distribution is between 10 and 12.5 time steps. but a few trajectories could also be fitted with filter sizes > 30 time steps. in the following fig. 6, the goodness of the polynomial fit r2, as defined as (a) (b) filter length ntrajectory length n nu m be r of e nt rie s nu m be r of e nt rie s figure 5: comparison between (a) the distribution of the reconstructed trajectory lenghts and (b) the automatically determined optimal polynomial filter length size for a 2nd order polynomial (a) (b) filter length nfilter length n figure 6: assesment of the goodness of the fit r2 for different constant filter sizes and the adaptive track filter by using (a) 2nd order polynomials or (a) 3nd order polynomials. r2 = 1− n ∑ i=1 (yi− ŷi) 2 n ∑ i=1 (yi− y)2 , (15) is compared for the considered set of trajectories between polynomial fits of constant filter lengths (n = 5, 7, 9, 11, 21 and 31) and the adaptive track filter and for the polynomial degrees of 2 (a) and 3 (b). at this point, it has to be noted , that when a constant filter size is chosen but the observed trajectory is smaller than this value, the total available length of the trajectory is set as the filter size. for all cases, the r2 value is well above 0.9, indicating a reasonable good performance of the polynomial model. for the fit with a 2nd order polynomial, the adaptive track filter exhibits the highest r2. when increasing the polynomial order to 3, the adaptive track filter is showing the second best goodness of the fit. as a further result, an assessment of the estimated uncertainty in the velocity magnitude is presented in fig. 7 (a) and (b) in the same manner as in the previous figure. here, a clear trend towards lower mean uncertainties with higher filter sizes are observable for both considered polynomial orders. but the overall uncertainty level is around two to three times higher for the 3nd order polynomial. in comparison with the polynomial fits of constant length, the adaptive track filter exhibits similar values as the largest constant (a) (b) (c) (d) filter length nfilter length n filter length n filter length n figure 7: assesment of the mean uncertainty of the velocity magnitude for different constant filter sizes and the adaptive track filter ((a) and (b)) and the underlying uncertainty distributions ((c) and (d)) by using 2nd order polynomials ((a) and (c)) or 3nd order polynomials ((b) and (d)). filter length n = 11, 21 and 31. a more detailed look on the estimated uncertainties is given in fig. 7 (c) and (d), where the velocity uncertainty distribution is plotted for the adaptive track filter against three polynomials of constant sizes (n = 5, 11 and 31). it stands out, that the width of the uncertainty distribution is strongly depended on the filter size with narrower peaks for wider filter windows. for both considered polynomial degrees ((a): 2nd order, (b): 3nd order) the adaptive track filter estimates the uncertainties nearly identical as the highest considered constant filter length n = 31. 4 conclusions within this work, we proposed an uncertainty quantification method to determine position, velocity and acceleration uncertainties during the trajectory filter procedure. the proposed approach is applicable for polynomial filters of arbitrary lengths and orders. by performing numerical experiments, it could be shown, that the determined uncertainties are within 1% errors of the modeled noise for filter lengths > 21. for a minimum filter length of 5, the uncertainties are overestimated by around 10%. as long as the measurement noise does only exhibit random components, the proposed method is not effected by the magnitude of the noise level as long as the polynomial is suitable for the trajectory data. with the aim of automatically finding the optimal filter length at a fixed filter order, the adaptive track filter was introduced. it could be shown, that the adaptive track filter is able to find the filter length, which minimizes the measurement uncertainty and maximizing the goodness of the fit and therefore ensuring, that no truncation errors are introduced during the filtering process. in future work, it shall be investigated how the adaptive track filter influences the quality of the global velocity reconstructed by binning operations or data assimilation methods, such as vic#. references adrian rj (2005) twenty years of particle image velocimetry. experiments in fluids 39:159–169 bhattacharya s, charonko jj, and vlachos pp (2018) particle image velocimetry (piv) uncertainty quantification using moment of correlation (mc) plane. measurement science and technology 29:115301 bhattacharya s and vlachos pp (2020) volumetric particle tracking velocimetry (ptv) uncertainty quantification. experiments in fluids 61:197 persoons t (2015) time-resolved high-dynamic-range particle image velocimetry using local uncertainty estimation. aiaa journal 53:2164–2173 rajendran lk, bhattacharya s, bane spm, and vlachos pp (2021) meta-uncertainty for particle image velocimetry. measurement science and technology 32:104002 schneiders jfg and sciacchitano a (2017) track benchmarking method for uncertainty quantification of particle tracking velocimetry interpolations. measurement science and technology 28:65302 sciacchitano a, neal dr, smith bl, warner so, vlachos pp, wieneke b, and scarano f (2015) collaborative framework for piv uncertainty quantification: comparative assessment of methods. measurement science and technology 26:74004 violato d and scarano f (2011) three-dimensional evolution of flow structures in transitional circular and chevron jets. physics of fluids 23:124104 wieneke b (2015) piv uncertainty quantification from correlation statistics. measurement science and technology 26:74002 wieneke b (2017) piv anisotropic denoising using uncertainty quantification. experiments in fluids 58 zhang j, bhattacharya s, and vlachos pp (2020) using uncertainty to improve pressure field reconstruction from piv/ptv flow measurements. experiments in fluids 61:131 introduction uncertainty quantification linear regression analysis numerical analysis adaptive track filter conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 calibration correction of arbitrary optical distortions by non-parametric 3d disparity field for planar and volumetric piv/lpt d. michaelis1*, j. wiswall2, a. mychkovsky2, r. prevost3, d. neal3, b. wieneke1 1 lavision gmbh, 37081 goettingen, germany 2 naval nuclear laboratory, west mifflin, pa 15122, usa 3 lavision inc., ypsilanti, mi 48197, usa *dmichaelis@lavision.de abstract in this study, a new image calibration approach is presented that corrects arbitrary optical distortions by utilizing non-parametric, 3d disparity fields. a calibration plate with a high spatial resolution (i.e., high density of calibration marks) was used to identify optical distortions that remain after the initial calibration, which were then used to create a correction field for the pinhole or polynomial mapping functions. results from a pipe flow experiment with four cameras using volume self-calibration (vsc) and shake-the-box lagrangian particle tracking (stb lpt) are presented and the impact of the improved calibration is discussed. using the calibration marks with the correction field, distortions of initially more than 20 pixels are reduced below 1 pixel. using vsc with the correction field allows further reduction of average calibration disparities below 0.02 pixels (maximum 0.5 pixels), whereas without a correction field the remaining average disparity is much higher at 1 pixel (maximum 5 pixels). stb analysis of the data shows a considerable higher spatial resolution at the pipe wall and a consistent spatial distribution of the number of detected particles in the measurement volume. 1 introduction optical flow-measurement techniques, such as particle image velocimetry (piv) and lpt, require precise imaging of tracer particles in the fluid to yield accurate velocity field measurements. many practical internal flows are through conduits with curved surfaces and experimental setups often consist of water or air as the working fluid with glass or acrylic viewing windows. small radius window curvatures, large camera viewing angles, and large refractive index differences create strong optical distortions; and optical flow-measurements in even simple tubes or pipes become challenging (see van doorne (2007)). optical distortions can be reduced or prevented by refractive index matching the working fluid and viewing window materials: bai and katz (2014), northrup et al. (1991) and wright et al. (2017). such experiments can yield excellent results if the setup in question allows for the application of this technique. index matching, however, cannot be applied in every relevant case. the index matched fluid may not have the desired fluid properties, like viscosity or density, can be corrosive or even toxic, and can be very expensive. also, the experiments may require delicate temperature control as the refractive index changes with temperature, which adds complexity to the setup. finally, for all experiments with typical gases, including 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 the most common case of air, index matching simply is not possible, as there are no solid materials which match an index of refraction close to unity. in the cases where refraction index matching is not applied, the optical distortions often lead to an inadequate image calibration. the mapping functions in common use (e.g., the pinhole: tsai (1987) or polynomial model: soloff et al. (1997)) are not able to correct for strong optical distortions, so that the corrected images, which should represent a regular cartesian coordinate space, still contain considerable distortions after the image correction process. this is because the commonly used mapping functions, mentioned above, are not able to correct for arbitrary optical distortions due to their limited number of degrees of freedom. these high distortions result in large velocity measurement errors or prevent a successful particle matching process for particle tracking methods. historically, these distortions have been mostly ignored or circumvented by restricting the measurement domain to regions with weaker, acceptable optical distortions. this, unfortunately, may in many cases exclude regions that are of special interest, like areas close to the surface where sometimes very complex, flow structure interactions occur. 2 description of new correction method concept the mapping functions m map 3d world coordinates xw to 2d camera sensor positions xc: 𝒙𝑐 = 𝑴(𝒙𝑤) (1) these mapping functions can be arbitrary functions and common choices are the aforementioned pinhole or polynomial models. to correct for strong optical distortions, the mapping function model needs to be extended to allow the description of arbitrary distortions. therefore, a correction field c is added to the result of the original mapping function to provide a 2c correction vector for each position in 3d space: 𝒙𝑐 = 𝑴(𝒙𝑤) + 𝑪(𝒙𝑤) (2) note that a different mapping function m and correction field c will exist for every camera in a multicamera setup. in the current implementation c is a 3d2c vector field, which allows a simple and effective initial correction based on calibration marks. the real-world grid positions of the 2c correction vectors in the 3d correction field correspond to the real-world position and spacing of the calibration marks in x and y and to the position and shift of the calibration plate in z. correction from calibration marks for each 2d mark position in the camera image xmc the corresponding 3d real word mark position xmw is known from the calibration process and is used to solve for the mapping function m. 𝒙𝑚𝑐 = 𝑴(𝒙𝑚𝑤) (3) for a perfect mapping function, the mapping of a world point xmw on the regular grid of calibration marks coincides with the position where the mark has been detected on the camera sensor xmc. in the presence of strong optical distortions, the remapped world positions of the marks in the corrected images can deviate considerably from the expected positions on the grid xw (fig. 3, left) due to the limited number of degrees of freedom of the common mapping functions. the correction field c, for each mark position in all calibration z-planes, is determined by subtracting the mapped position m(xw) from the actual mark position in the camera image xmc for each position on the grid xw (note that the 2d correction vectors are defined in the 2d camera space): 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 𝑪(𝒙𝑤) = 𝒙𝑚𝑐 −𝑴(𝒙𝑤) (4) form the discrete 2c-3d correction field on a regular grid, the correction for any world position is calculated by linear vector interpolation. remaining disparities from volume self-calibration vsc is a procedure for optimizing mapping functions based on the remapped triangulation error of individual tracer particles: wieneke (2008). with this procedure, calibration inaccuracies can be removed down to and below 0.1 pixels. in experiments with strong or high-order optical distortions, often the remaining disparity cannot be lowered below 0.3 to 1.0 pixel. in such cases, the insufficient number of degrees of freedom of the mapping functions prevents further optimization. the disparity maps from volume self-calibration (wieneke (2008)) have the same format as the correction fields c, which means that the remaining disparity fields after volume self-calibration can directly be used as additional correction fields cvsc. if vsc is performed using a calibration that already has a correction field, then the updated correction field cupdate can simply be calculated by adding the remaining disparities cvsc to the existing correction field c: 𝑪𝑢𝑝𝑑𝑎𝑡𝑒(𝒙𝑤) = 𝑰(𝑪(𝒙𝑤)) + 𝑪𝑉𝑆𝐶(𝒙𝑤) (5) where i is an interpolator that converts correction vectors from the grid of calibration mark positions to the grid of the disparity maps. 3 experimental setup figure 1. left: test setup used to obtain particle image data. right: test section design shown in a cad model rendering. fig. 1, left shows a photograph of the experimental setup used to obtain data for the present study and fig. 1, right shows an illustration of the test section used for flow visualization. the test section is a hexagonal block of acrylic with a 101.5 mm +/0.2 mm diameter hole bored along the centerline connecting two opposing faces. the tomographic piv system was setup such that cross-sectional volumes, shown in figure 1, of the pipe flow through the test section can be visualized. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 water at room temperature was used as the fluid for the test. steady, well-conditioned pipe flow was provided to the test section, and swirl in the flow was induced by an upstream swirl generator that injects a fraction of the total flow tangentially to the pipe. the design of the swirl generator followed haden and lorentz, (2018). the total flow through the test section, the sum of the axial and swirl injection flows, was 23 gallons per minute (gpm) with a standard deviation of 0.5 gpm. the fluid temperature was controlled to 74.5 ˚f ± 3 ˚f. the fraction of flow delivered through the swirl generator was 20 % of the total flow and the remaining flow was delivered as well-conditioned pipe flow. four high-speed, digital cameras were used to obtain images of the flow (phantom veo440l). the cameras were arranged at the four corners of a rectangular configuration, all viewing toward the upstream direction. the cameras were outfitted with 60 mm focal length lenses (nikon) with scheimpflug adapters (lavision) and fluorescence bandpass filters that have 620 nm center wavelength and 56 nm band width (edmund optics #33-911). fluorescent orange tracer particles, 50 µm diameter with a peak emission wavelength of 606 nm, were used to visualize the flow (cospheric uvpms-bo-1.00 45-53µm). the water was seeded to a target concentration of 0.02 particles per pixel as observed in the illuminated volume. the volume was illuminated using a dual cavity nd:ylf laser (quantronix darwin duo). the z-axis of the illuminated volume was aligned to be in-line with the pipe axis. volume optics (lavision inc.) were used in conjunction with an aperture to achieve an illuminated volume 7 mm thick in the z-direction and spanning the entire pipe cross section in the xand y-directions. a single-plane calibration plate, mounted to a traverse, was used to provide the initial calibration for the images. the calibration plate consists of 1,909 dots, each with a 1 mm diameter and a center-to-center spacing of 2 mm (fig. 2). the traverse has a resolution of 0.02 mm in its position and was aligned with the z-direction parallel to the pipe axis. the calibration plate was inserted into the test section through the slot (shown in fig. 1, right) and rotated 90 degrees, similar to a butterfly valve, to provide the x y plane of for the piv images. the plate was traversed along the slot length to obtain images at multiple z locations. images of the calibration plate were taken at 1 mm increments and spanned the entire illuminated volume. figure 2. 2d calibration plate with 2 mm dot spacing (sum of corrected images from all four cameras). 4 results calibration with correction field 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 for the initial calibration, a z-scan of 12 views from the calibration target was recorded with an increment of 1 mm in the z-direction (-2 to +9 mm, where z = 0 mm corresponds to the downstream end of the illuminated volume). the calibration dot finding algorithm in lavision davis 10.2 was used to identify the marks in each image. only 0-3 marks at the border were not detected in each image due to strong distortions, so that nearly all of the marks were used to calculate the initial polynomial mapping functions (fig. 3, left), as well as the correction vectors for each detected mark (fig. 4). the original polynomial mapping function is not able to compensate the strong optical distortion near the pipe wall (fig. 3, left), showing that this mapping is inadequate in these border regions. applying the correction field (eq. (4)) compensates for these optical distortions and results in a nearly perfectly corrected image (fig. 3, right). inspecting the correction fields in more details reveals that all cameras show a systematic distortion/correction field, which is related to the cameras position and viewing angle (fig. 4). the correction field is similar between cameras, due to the symmetry of the camera setup. the scatter plot in fig. 5 provides a quantitative visualization of the distortion range and magnitudes. up to 22 pixels of distortion can be observed. such large and uncorrected distortions prevent any further meaningful analysis in these regions, either by particle (particle tracking) or interrogation window based (planar piv, tomographic piv) techniques. volume self-calibration (vsc) with correction field vsc is a mandatory step for high-particle-density particle tracking or tomographic piv (wieneke (2008)). it removes any remaining disparities of the calibration and/or compensates for slight camera dislocations after the recording of calibration images. vsc was performed using the same particle images, from the 7 mm thick illuminated volume, that were later used for the final flow analysis. the disparity map and disparity vectors for each sub-volume were calculated using 20 x 20 x 2 sub-volumes. vsc was applied iteratively in up to 13 steps, to improve disparity vector precision, especially at the borders. without a correction field, the polynomial mapping function is not able to adapt to the resulting complex disparity field. the initial average disparity magnitude (fig. 6, left) is 1.8 pixel (6.4 pixel maximum) and figure 3: cutout of corrected calibration image from a pipe flow experiment. left: polynomial calibration model (systematic misalignment between markers and cartesian grid of up to 22 pixel), right: polynomial model with correction field (all calibration marks are centered on the cartesian grid). the red arrow exemplifies a single correction vector according to eq. (2). 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 the average disparity remains at 1.0 pixel (4.8 pixel maximum) after the 8th iteration (fig. 6, right). the large remaining disparity after vsc is problematic for high accuracy particle tracking and tomographic piv and indicates that an accurate calibration over the measurement region cannot be achieved. performing vsc in the present study using the calibration with a correction field, eq. (5), behaves similarly to experimental cases without strong distortions. in the initial iteration, disparities of up to 1.7 pixels were detected (fig. 7, left). the remaining disparity reduced to an average disparity of only 0.02 pixels after the 13th iteration, with very few outliers of up to 0.5 pixels (fig. 7, right). figure 4: correction fields for the different cameras (one from 12 planes at z = 3 mm). correction vectors outside the circle are extrapolated from the vectors based on calibration marks (inside the circle). note how the vectors in the “fig. 3” area point from the expected position on the grid to the actual mark position. particle tracking with correction field stb software in the upcoming davis 10.2.1 version (lavision gmbh) was used to calculate multi-pass stb, where the time series of particle images is utilized multiple times, both in the forward and backward direction, to improve the results from pass to pass. three passes over 1112 time-steps are applied to obtain an average of 7488 matched particles per time-step, without, and 8463 matched particles per time-step, with cam 1 cam 2 cam 3 cam 4 figure 3 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 the correction field. time-averaged velocities on a regular grid were calculated from particle tracks using gaussian average binning with a bin size of 1 x 1 x 1 mm³ at 75% overlap, resulting in 0.25 mm vector spacing and about 500 particles per bin (figs. 8 and 9). in these figures, the swirl induced in the pipe flow is clearly visible, both with and without a correction field. also, the overall flow structure and the peak velocity are similar in both cases. however, without a correction field, the strong gradient at the pipe wall cannot be resolved. the calculated w-component levels without using a correction field are unphysical resulting in 0.1 m/s (about 50% of peak velocity) within 2 mm distance from the pipe wall (fig. 8, left). with a correction field, the gradient is well resolved and the measured out of plane components drops to a realistic 0 m/s in a ring of 0.25 mm width at the wall (fig. 8, right). figure 5: scatterplot of vector components vx and vy in pixel from all correction vectors (figure 5). note the inverted y-scale: positive y components point downwards in image 4. cam 1 cam 2 cam 3 cam 4 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 figure 6: scatter plot of the two components, vx and vy, of disparity vectors from the 1st (left) and the 8th (right) iteration of volume self-calibration without correction field applied (camera , vx and vy in pixels) figure 7: scatter plot of the two components, vx and vy, of disparity vectors from the 1st (left) and the 13th (right) iteration of volume self-calibration with correction field applied (camera 1). the units of vx and vy are in pixels. note the different scales compared to fig. 6. the pattern of the number of particles contributing to a single bin (or vector) is considerably different with and without a correction field (fig. 9). for the case with a correction field, the number of particles contributing to a bin is nearly constant (about 500) and homogeneously distributed in the plane (fig. 9, left). this flat distribution is expected as the seeding distribution in the particle images is also very homogeneous. the number only drops in a small ring at the wall, because the overlapping bins at the border reach outside the circular pipe region and therefore collect fewer particles than bins that are completely inside the pipe region. without a correction field on the other hand (fig. 9, right), the pattern of the number of particles is very uneven and complex. the number of particles is low in the regions of any camera view where the distortion is high. this is especially evident in a ring of about 2 mm width at the pipe wall. this can be explained by the allowed triangulation error (3 pixel in this case) not being high enough to find matching particles in these regions with stronger distortions. more particles are detected for the case with no correction field as compared with the case with a correction field. such a result may seem surprising; 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 however, this may be explained by a strategy used for stb, which favors the detection of particles with small triangulation errors. . figure 8: out of plane component w (color coded) and in plane vectors of the average flow field from central z-plane (out of 31 z-plane). left: without correction field, right: with correction field applied, (every 8th vector displayed, original vector spacing is 0.25 mm). figure 9: number of matched particles per bin (color coded) and in plane vectors in central z-plane (out of 31 z-planes), every 8th vector displayed. left: without correction field, right: with correction field. if no particle with a small triangulation can be detected, then there will be many possible particle-matches with similar high triangulation errors, from which only one is a real particle and the others are ghost particles. as stb cannot differentiate between them, all of them will end up as matching particles and in this way increase the number of particles per bin. 5 conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a new method that addresses the longstanding problem of strong optical distortions for particle velocimetry has been proposed. using correction fields, large distortions of up to 22 pixels could be compensated for and subsequently refined by volume self-calibration down to 0.02 pixel disparity. the resulting successful volume self-calibration enables precise particle tracking throughout the measurement volume, including the region close to the border of the measurement domain (in this case the inner wall of the pipe). experimental results show that near-wall gradients could be resolved reliably once this correction field was implemented, whereas without the correction field, the velocity at the border was overestimated (being 50% of the peak velocity). the concept of the correction field has been demonstrated for a pipe flow. this approach is expected to apply in general to experiments that exhibit optical distortions from curved walls. acknowledgements notice: this report was prepared as an account of work sponsored by an agency of the united states government. neither the united states government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the united states government or any agency thereof or its contractors or subcontractors. the views and opinions of authors expressed herein do not necessarily state or reflect those of the united states government or any agency thereof. references bai k, katz j (2014) on the refractive index of sodium iodide solutions for index matching in piv. experiments in fluids 55, 1704 haden, r. e., and lorentz, d. g. (2018) apparatus and method for generating swirling flow, united states patent us 9,956,532 northrup ma, kulp tj, angel sm (1991) fluorescent particle image velocimetry: application to flow measurement in refractive index-matched porous media. applied optics (21):3034-40 schanz, d., gesemann, s., & schröder, a. (2016). shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids, 57(5), 1-27. soloff s, adrian r and liu z (1997) distortion compensation for generalized stereoscopic particle image velocimetry. meas sci technol 8:1441-1454. tsai ry (1987) a versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses. ieee journal of robotics and automation 4: ra-3 van doorne, c. w. h., & westerweel, j. (2007). measurement of laminar, transitional and turbulent pipe flow using stereoscopic-piv. experiments in fluids, 42(2), 259-279. wieneke b (2008) volume self-calibration for 3d particle image velocimetry. experiments in fluids 45:549-556 wright, s. f., zadrazil, i., & markides, c. n. (2017). a review of solid–fluid selection options for opticalbased measurements in single-phase liquid, two-phase liquid–liquid and multiphase solid–liquid flows. experiments in fluids, 58(9), 1-39. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 simultaneous two-phase flow measurements in a high-speed particle-laden under-expanded jet miguel x. diaz-lopez1, juan sebastian rubio1, and rui ni1 1johns hopkins university, baltimore, md 21218 abstract the objective of this study is to understand the dynamics of a high-speed particle-laden under-expanded jet, motivated by landings on extraterrestrial bodies. in this setup, inertial particles are entrained and accelerated by an under-expanded jet. but, due to their inertia, the particle velocity is significantly lower than that of the surrounding gas close to the nozzle, so the two phases are coupled through aerodynamic drag. sub-micron oil droplets are dispensed upstream to serve as tracers, whose velocity is determined through a piv system; inertial particles, after image segmenting is performed to separate them from piv data, will be tracked over time with a ptv system. this was accomplished with a single laser pulse and the camera straddle time to produce image pairs and shorten the pulse width. the results will help to understand particle-laden flow in a new regime where the background flow is compressible and the mach number based on the slip velocity is not negligible, which may help to pave a foundation for future studies in compressible multiphase flows. 1 introduction particle-laden compressible flows are ubiquitous in nature and in many engineering applications, including volcano eruptions cigala et al. (2017), particle ingestion in gas turbines dunn (2012), and powered descent and landing on extraterrestrial bodies morris et al. (2015). despite its importance, experimental work in this area is scarce, especially in the compressible regime, where two phases are strongly coupled through aerodynamic drag. one of the key challenges is to simultaneously track inertial particles and measure the surrounding gas flows with velocities at o(10−1000 m/s) buchmann et al. (2014). previous studies of particle dynamics in a compressible shear layer showed that when the particle stokes number becomes large, the slip mach number can be supersonic, resulting in local bow shocks around particles samimy and lele (1991). when the particle mass loading increases, the effect could be so strong that the mach disk location can be moved upstream close to the nozzle exit due to the momentum transfer between the two phases sommerfeld (1994). however, these observations were limited to qualitative measurements without access to the dynamics of both phases at the same time. the goal of this work is to simultaneously measure the gas and particle velocities using particle image velocimetry (piv) and particle tracking velocimetry (ptv), which has been conducted before in incompressible flows. previous simultaneous piv/ptv measurements have used dual-camera systems with optical discrimination elhimer et al. (2016) and single-camera systems with image segmentation of raw images kiger and pan (2000) to obtain both particle and velocity fields. using our ultra-high-speed diagnostics systems, we plan to extend the simultaneous piv/ptv technique to the compressible flow regime. 2 experimental methodology the johns hopkins university jet (jhu jet) facility is a cold-air system that accelerates gas to subsonic, sonic, and supersonic speeds. to study the dynamics of inertial particles, a particle injector and accelerator were employed to inject particles from a particle chamber into the gas stream along the centerline of the jet. additional technical details of the facility can be found in ref. kim et al. (2020). an aerosolizer is used to suspend tracer particles, consisting of dehs mineral oil droplets with a modal diameter of 0.25 µm. the sufficient large scale separation between inertial particles with size in the range of o(10)–o(100) µm and aerosol tracer particles makes it easy to segment their images from the piv data. in many piv applications, the pulse width of the laser is infinitesimally small because of its short span compared to the rest of the time scales. however, since one of the goals of this experiment is to obtain slip velocities close to the inertial particles, a small field of view (fov) is necessary to sufficiently resolve both phases within this regime. the fov is 13.5 by 8 mm with particles traveling at 340 m/s (sonic speed) or even greater. for this reason, the particle will move several pixels within the 200 ns pulse width of the laser causing traces in the image. the solution to this issue was to utilize a single pulse which is placed within the straddle time of the camera. with the straddle time being slightly shorter than the laser pulse width, the laser is cut such that the rising edge of the pulse is in the first frame while the falling edge of the laser is in the second frame. this technique creates image pairs for piv analysis while also cutting the pulse width for each frame. one issue that arose from this is that the decay time for the pulse is much slower than the rise time causing there to still be small traces in the second image but significantly reduced from previous experiments. more work will have to be done to remove traces from both phases. finally, the acquired images were segmented to separate the two phases then analyzed using piv and ptv methods, respectively. 3 results after analyzing the data, there were slight overestimates for both the inertial and tracer particles velocities when compared to simulation. this is likely due to traces in the second image making it difficult for the piv algorithm to distinguish where the particle is exactly. even with this overestimation, the overall trend matches literature and simulation closely. further work will have to be done to either fix the traces in post processing or modify the method to remove the traces. figure 1 shows sample images (left) with their respective segmentation and the normalized velocities of both the inertial and tracer particles (right). figure 1: a) sample piv/ptv correlated frames at the top with segmented images to separate inertial from tracer particles underneath. b) normalized results between inertial phase (orange) and tracer particles (blue). both are normalized with their respective exit velocities at the nozzle. 4 conclusion a system consisting of a compressible particle-laden jet facility and a piv/ptv diagnostic method was constructed to understand the interaction between inertial particles with the surrounding compressible gas. although this diagnostic method has been used before in other types of incompressible multiphase flow, it would be the first attempt in the compressible regime. valuable lessons and new results will be shared with the community to advance the diagnostic methods and our understanding of the compressible multiphase flow. acknowledgements this material is based upon work supported by the national aeronautics and space administration under grant no. 80nssc19k0488 issued through plume surface interaction (psi) by the space technology mission directorate game changing development. we would also like to thank kyle d. gilroy, ph.d. and andy kubit from vision research, ametek, materials analysis division for playing essential roles in helping to design the synchronization setup. references buchmann na, cierpka c, kähler cj, and soria j (2014) ultra-high-speed 3d astigmatic particle tracking velocimetry: application to particle-laden supersonic impinging jets. experiments in fluids 55:1842 cigala v, kueppers u, peña fernández jj, taddeucci j, sesterhenn j, and dingwell db (2017) the dynamics of volcanic jets: temporal evolution of particles exit velocity from shock-tube experiments. journal of geophysical research: solid earth 122:6031–6045 dunn mg (2012) operation of gas turbine engines in an environment contaminated with volcanic ash. journal of turbomachinery 134. 051001 elhimer m, praud o, marchal m, cazin s, and bazile r (2016) simultaneous piv/ptv velocimetry technique in a turbulent particle-laden flow. journal of visualization 20 kiger kt and pan c (2000) piv technique for the simultaneous measurement of dilute two-phase flows. technical report kim t, ni r, capecelatro j, yao y, shallcross gs, mehta m, and rabinovitch j (2020) the dynamics of inertial particles in underexpanded jets: an experimental study. in aiaa scitech 2020 forum. page 1326 morris a, goldstein d, varghese p, and trafton l (2015) approach for modeling rocket plume impingement and dust dispersal on the moon. journal of spacecraft and rockets 52:1–13 samimy m and lele sk (1991) motion of particles with inertia in a compressible free shear layer. physics of fluids a: fluid dynamics 3:1915–1923 sommerfeld m (1994) the structure of particle-laden, underexpanded free jets. shock waves 3:299–311 introduction experimental methodology results conclusion data reconstruction of homogeneous turbulence using lagrangian particle tracking with shake-the-box and machine learning dong kim, kyung chun kim school of mechanical engineering, pusan national university, 46241 busan, south korea this paper proposes a data reconstruction of homogeneous turbulent flow combined machine learning (ml) approach using experimental lagrangian particle tracking (lpt) data with shake-the-box (stb). the lpt with stb was adopted to measure a von kármán flow with a homogeneous turbulent region in the center [1]. the stb results have been stored and a temporal filter using 3rd order b-splines has been applied with optimal weighting coefficients to be used as input for flowfit data assimilation method [2]. flowfit data was used as ground truth to train ml algorithm. the low-resolved data of the velocity and acceleration field was reconstructed using an adaptive neuro-fuzzy inference system (anfis) with the downsampled lpt data as an input to predict homogeneous turbulent flow [3]. the training process can be mathematically regarded as an optimization problem to determine the weighting factor. fig. 1 data reconstruction methods and anfis learning structure. given the input data set 𝑥 (low resolved stb data) and the desired output data set 𝑦 (flowfit results), we aim to find the optimal weight 𝑤 in a machine-learned model 𝐹 that acts as a nonlinear regression function such that 𝐹(𝑥; 𝑤) ≈ 𝑦. in the present case, 𝑥 and 𝐹(𝑥; 𝑤) represent the lowresolution and reconstructed high-resolution data, respectively. the weight 𝑤 is optimized between the desired high-resolution output 𝑦 and the ml model output 𝐹(𝑥;𝑤) is minimized. the anfisbased data assimilation was first trained with flowfit data assimilation result as ground truth. four anfis training inputs on the x, y, z coordinates, and time t of flowfit results were assigned to 1st layer of anfis algorithm. the training targets on velocity, acceleration components were assigned to final layer of anfis algorithm to get weighting factor. the computations were performed on a computer with an intel® core™ i5-8250u cpu @ 1.60 ghz 1.80 ghz and 8.0 gb of ram. with 300 epochs and 4 input membership functions, the anfis training satisfied the convergence criterion of rmse < 0.01. the training time takes 2 hours. figure 2 shows the spatial data reconstruction of anfis model with different ratio of raw particle density, 𝜌𝑝. the particle density was downsampled by random reduction from raw stb data (~100,000 particles to 75, 50). compared to flowfit, anfis model can be well reconstructed above 50% particle density. it revealed much more small-scale vortical structures. machine learning based data assimilation provide a better understanding of the small turbulence structures and allow for more in-depth analysis by recovering data due to the resolution limit of the experiment. to provide a full turbulence spectrum, full time-series of stb results will later be trained and in-depth analyzed for anfis training. fig. 2 (top) (a) raw stb result (b, c) downsampled stb data as input. (bottom) contour colored by xcomponent of acceleration and iso-surface of q-criterion, q = 5,000 s-2 from (a) flowfit and (b, c) anfis. acknowledgements this research was supported by basic science research program through the national research foundation of korea (nrf) funded by the ministry of education (2020r1a6a3a03038341) and the korean government (msit) (2021r1c1c2011538). we acknowledge daniel schanz, florian huhn, sebastian gesemann and andreras schröder (german aerospace center) for providing the lpt and flowfit data, daniel garaboa-paz (university of santiago de compostella) and eberhard bodenschatz (max-planck institute for dynamics and self-organization) are acknowledged for their contributions to the experiment references [1] schröder, a., et al. (2019) measuring the full velocity gradient and dissipation rate tensor in homogeneous turbulence using shake-the-box and flowfit. 17th etc, torino, italy. [2] gesemann, s., huhn, f., schanz, d., & schröder, a. (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th lxlaser, lisbon, portugal, 4-7. [3] kim, d., safdari, a., & kim, k. c. (2021) sound pressure level spectrum analysis by combination of 4d ptv and anfis method around automotive side-view mirror models. scientific reports, 11(1), 1-15. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 enhanced functional binning for oneand two-point statistics using a posteriori uncertainty quantification of lpt data p. godbersen1∗, a. schröder1 1 german aerospace center (dlr), institute of aerodynamics and flow technology, göttingen, germany ∗ philipp.godbersen@dlr.de abstract in the evaluation of lagrangian particle tracking (lpt) measurement data the use of spatially binned flow statistics in the form of one, two or multi-point statistics is often an essential step towards better understanding of the measured flow fields. increasingly there is a focus towards uncertainty quantification of the measurement system however these evaluations are seldom used to directly improve the statistics by directly involving them into the calculation. we present our functional binning approach which makes use of such uncertainty information as a core component for the calculation of improved statistics. the improvements towards prior approaches are shown utilizing synthetic data as well as data from a real-world subsonic jet experiment. beyond the initial formulation for one-point statistics, we show that this approach is readily extended towards two-point statistics and explore more advanced utilizations of uncertainty information for the optimal selection of particle pairs. furthermore, the benefits of more individualized particle error estimations are investigated and some strategies for archiving such information are investigated. 1 introduction lagrangian particle tracking enables the accurate measurement of the position, velocity and acceleration of particles moving within fluid flows (ouellette et al., 2006; schanz et al., 2016). the scattered nature of the individually tracked particles provides a great advantage over other related measurement techniques such as piv. instead of a fixed regular grid of convolution windows, whose size imposes a low pass filtering effect on resolvable structures, particle positions are distributed in a stochastic manner and provide local point measurements. this can be exploited in eulerian ensemble averaging using spatial binning to realize very fine resolutions, since the bin size is not directly linked to measurement technique and is primarily limited by the amount of available data. this allows a direct trade-off between bin size and convergence of the underlying statistic. one particularity of lpt is that we do not just have the position and velocity of a particle at each timestep but inherent to the processing a continuous track over a certain time range. this provides additional information as the single time steps are not independent but instead temporally linked. within this paper we will focus on the shake-the-box (stb) approach for lpt where the two variants for time-resolved stb (schanz et al., 2016) and multi-pulse stb (novara et al., 2019) express this temporal connection in slightly different ways. for time-resolved stb tracks can span up to the entire measurement duration directly providing significant temporal information. the multi-pulse variant necessary for faster flows provides temporal information only for the short bursts typically consisting of four pulses. this variant relies on collecting many bursts that are temporally uncorrelated from each other to build flow statistics. a small amount of temporal information is nevertheless available for each burst and within this paper we will mostly focus on the processing of such multi-pulse data. the presented approaches are generally not limited to multi-pulse stb but adaptable to any lpt measurement that provides access to this temporal data. the core idea for our functional binning approach (godbersen and schröder, 2020) to lpt data processing relies on the fact that this additional temporal information is available which is not utilized in other current binning approaches. instead of just evaluating the position or velocity at a certain point along the short multi-pulse track ( at the pulse times or the midpoint) we now consider a continuous functional track over time. this provides an opportunity to increase the convergence speed of spatially binned statistics simply because now more information is considered. the functional approach extracts the maximum amount of available data neighbour bin neighbour binbin tmid neighbour bin neighbour bin wbin(x) bin t0 t1p(t) figure 1: sketch of convetional binning utilizing the midpoint (left) and the functional binning approach (right). graphics from (godbersen and schröder, 2020) from the tracks provided by the stb processing. due to the general formulation of the functional binning approach, most prior discrete binning strategies can also be expressed within this functional framework (evaluation at midpoint, evaluation at particle positions, spatial weighting strategies, etc.). the approach was initially presented for single point statistics but is readily extended to two-point statistics as well, with the resulting advantages and possibilities being a focus of this paper. one significant property of functional binning is the inherent use of uncertainty information for the calculation of the statistics. uncertainty quantification of lpt data is of great interest not just for the evaluation of experiment setups but also when processing the resulting data for further statistics. a comprehensive a priori uncertainty estimation trough the full evaluation chain of a lpt measurement is presented by bhattacharya and vlachos (2020) allowing for insight into the different error terms contributing to the total measurement error. a different approach is conducted in the strategies by novara et al. (2016); gesemann et al. (2016) focusing on an a posteriori uncertainty evaluation starting from a point further along the lpt processing chain (see as well contribution of gesemann et al. to this ispiv’21). the approach relies on estimation of the particle position uncertainty and builds the error for all further processing steps by propagating this error instead. for the multi-pulse stb algorithm this approach is utilized to motivate the use of the track midpoint for velocity evaluations as the location of lowest error. the trackfit approach from gesemann et al. (2016); gesemann et al. (2021) applied to time-resolved stb data presents an elegant method to estimate the position accuracy directly from the measurement data and utilizes this knowledge to select optimal smoothing parameters for the track building. within this paper we will make use of this second approach, utilizing particle position accuracy as a posteriori uncertainty source for further propagation within the functional binning approach for evaluation of the presented binning approaches we utilize synthetic data using same setup as in the original functional binning paper (godbersen and schröder, 2020). synthetic data is useful as it allows full control over the input data and error values that are passed into the processing approaches. the synthetic data used here directly provides tracked particles instead of images that need to be processed by the stb algorithm. we are not directly interested in the performance stb processing itself but want to analyze the postprocessing of such data and need to directly control the particle position error. for an evaluation of the performance of the stb processing in itself we refer the reader to the results of the lpt-challenge (sciacchitano et al., 2021) instead. synthetic data is attractive because it provides exact ground truth data to judge the resulting statistics against. however, ultimately these post-processing techniques will be applied to real world data so only investigating synthetic data is not satisfying. therefore we will also present some of these methods applied to a real multi-pulse stb jet experiment (manovski et al., 2021; godbersen et al., 2019). as no exact ground truth is available any more, only qualitative comparisons can be made however the improvement in convergence is readily apparent when considering only a subset of the available data. 2 functional binning a detailed introduction of the functional binning approach can be found in godbersen and schröder (2020) but we will provide a short introduction here to provide context for the further developments. functional binning relies on the fact that we have a functional expression of the particle position over time available from the stb processing (including trackfit). for the multi-pulse stb data considered here, tracks take the form of second-order polynomials. just as we have the tracks in a functional expression, the bins now need to be brought into a functional form as well. this takes the form of spatial weighting functions with compact support, defined only in the region we want the bin to be located. in addition to this spatial weight function we also assign a temporal weight function to the track, selecting regions from which we want to extract information from the track. using these two weighting functions together with the individual track functions we can calculate a continuous weighted average expressed using integrals over the track time: mv = ∑ n n=1 v̄nw̄n ∑ n n=1 w̄n = ∑ n n=1 ∫ t1 t0 vn(t)wn(t)dt ∑ n n=1 ∫ t1 t0 wn(t)dt with w(t) = wbin(p(t))wtrack(t), (1) with the velocity function v(t) and the weight function w(t) as product of the temporal track weight function and the spatial bin weight function using the track position function p(t). this general formulation allows to represent most existing spatial binning strategies by selecting certain functions for the track weight or the bin weight function respectively. the simple binning approach based on cartesian bins can be replicated by selecting a multidimensional top hat function for the bin weight, defined only within the extent of the cartesian bin. a spatial gaussian bin weighting strategy for such cartesian bins (agüı́ and jiménez, 1987) can directly be implemented by using a gaussian bin weight function. a similar consideration can be made for the track weight function, allowing to replicate existing discrete track evaluation schemes within this functional framework. the midpoint approach from novara et al. (2016) can be directly replicated by considering a dirac pulse at the midpoint time, selecting just this discrete value in the integration. similarly, the classic approach of using the four particle positions resulting from the four pulses in time can be replicated by a comb of four such dirac pulses positioned at the appropriate times (see fig. 2). the functional bin definition allows arbitrary bin definitions far beyond these examples, enabling easy implementation of variable bin sizing, bin orientation and positioning simply by defining an appropriate spatial weighting function for each bin. adaptive bin shaping could be facilitated based on statistics of an initial evaluation or a curvature based approach as presented by raiola et al. (2020). one interesting binning concept that is not readily interpreteable in the functional framework is the polynomial fit technique for spatial binning presented in agüera et al. (2016). the approach improves among other goals the accuracy of statistics in the presence of velocity gradients within the bins. for functional binning this is not as relevant as a main aim here is to allow for higher bin resolutions, thereby reducing the impact of velocity gradients within each individual bin in this manner. the special cases for the trackweight function mentioned above make apparent where the gain of additional information for the statistics comes from in the functional case. both of these discrete evaluation schemes waste a lot of available information simply because the weight function is zero for a majority of the track time. for functional binning we select a track weight that is non-zero for the entire track time taking into account an uncertainty quantification of the velocity function. the process is further described in the section on uncertainty quantification below. this approach was initially designed for one-point statistics like mean velocities or reynolds stresses however some initial extension towards two-point statistics was already presented within the original paper. the functional approach is readily extended to also cover relations between two or multiple particles/tracks. for a two-point correlation on lpt data the distance between particle pairs is relevant for spatial binning as the velocity correlation is performed by spatial binning with respect to the distances of particles to some reference particle at a designated position. instead of operating on the discrete particles such calculations can also be performed in the functional space. for the multi-pulse data considered here the function space is that of polynomials and many operations are well defined there. polynomials can be added and subtracted from one another resulting in a new polynomial of the same order. additionally, multiplication between polynomials is also defined, in this case generally changing the order of the resulting polynomial. p1(t)+ p2(t) = p1+2(t), p1(t)− p2(t) = p1−2(t), p1(t)∗ p2(t) = p1∗2(t), (2) with two polynomials p1 and p2 and resulting functions also within the polynomial function space. such operations can be readily expressed in terms of operations on the polynomial coefficients allowing for easy implementation. statistics are then expressed as integrals over functions in combination with the temporal and spatial weight functions. for the implementation the goal is to stay as long as possible within this functional space but for the actual final calculation of the statistics we need to return to discretized evaluations of these functions at some point. this is usually done at the stage where we numerically solve the integrals to provide a concrete value to add to the statistic in a bin. doing the discretization at this late point has the advantage that the whole theory for the numerical calculation of integrals can be relied upon, i.e. the gauss-legendre quadrature approach tells exactly where to sample the integrand for a limited number of points while providing certain 0 0.5 1 time tr ac k w ei gh t (a) evaluation at midpoint 0 0.5 1 time (b) evaluation at particle positions 0 0.5 1 time (c) functional binning + uncertainty figure 2: different track evaluation schemes expressed as track weight functions of track time within the functional binning framework. optimality guarantees (bogaert, 2014). alternatively, for complicated weight functions it might be desirable to utilize an adaptive sampling of the integrand to efficiently concentrate evaluation in regions where more resolution is needed. again, we can draw upon the well-established methods for numerical integration and could utilize an adaptive gauss-kronrod quadrature instead. doing these calculations in the functional space we can nearly directly attach these two-point statistics to the existing machinery implemented for one-point statistics. a two-point correlation is very similar to the calculation of a velocity mean, except the spatial binning is now done in the relative distance space to some reference track and instead of simply averaging the velocity of a single track, we now consider a mean over the relation of the velocities between tracks. there is one additional benefit in the calculation of two-point statistics that did not present itself in the original formulation of single-point statistics. as conceptionalized in the initial functional binning paper, two-point statistics also benefit from better resolution for close distances. they are generally calculated over a large distance range but the values for close distances are often the most important. one such example is the calculation of taylor micro-scales based on two-point correlations. for discrete binning approaches these close values are often not very well resolved, especially when utilizing the particle positions directly. this is due to the diffraction limited imaging typically used, where the particle image size is much larger on the cameras than the physical size of the particle itself. as particles get close to one another their images start to overlap on the cameras much earlier than might be expected from their physical size. such image overlaps then provide a challenge for the lpt processing leading to increased position error or in extreme cases might make them impossible to tell apart. such concerns do not apply to the midpoint approach as commonly used for multi-pulse stb, but even here benefits are expected as the functional approach simply provides more opportunities for the tracks to get very close to one another. these ideas as presented in godbersen and schröder (2020) are used in a recent contribution by hammond and meng (2021) to calculate more accurate radial distribution functions for inertial particles. 3 uncertainty propagation an important element of functional binning is the utilization of uncertainty information to design the track weight functions, thereby directly incorporating such knowledge into the calculation of statistics. a constant weight along the track would be feasible, (and sensible for time-resolved stb evaluations barring additional individual knowledge about time-steps), for multi-pulse stb evaluations we know this not to be optimal based on the initial introduction of the method in novara et al. (2016) the midpoint approach was suggested there directly because of an uncertainty propagation of particle position error trough the tracking scheme and velocity calculation, showing the midpoint to be the location of lowest velocity error. figure 7(b) shows the result of such an analysis for the velocity error, clearly showing the v-shaped nature of the velocity error with the error increasing towards the edges of the track. the inverse of this curve can directly be used as a track weight for the functional binning procedure taking into account that the additional information away from the midpoint is associated with a larger error and should therefore be weighted less when performing the evaluation. all uncertainty quantification we consider within this paper relies on the propagation of a posteriori particle position uncertainty trough further processing. it was chosen this way because the raw particle position accuracy can be evaluated from the experiment itself as a ”primal” uncertainty of the measurement scheme that then be propagated further along through the processing easily without having to dive too deep into exact uncertainty chain of the concrete measurement technique. this provides an uncertainty ”interface” of sorts, making the implementation agnostic to the concrete measurement technique utilized even though this is inspired by the choices made in the two mentioned stb variant developments. especially for the time-resolved stb approach this particle position error is readily available from the parametrization of the trackfit scheme. by calculating the position spectrum of the measured particles, it is possible to identify the noise floor of the measurement in respect to that spectrum which is then translated into a cutoff frequency for an optimal wiener filter for track building. they can then also translate this cutoff frequency into a particle position error value thus providing a direct path for an a posteriori error estimation directly on the concrete measurement data of the experiment which can then be used in further processing. for multi-pulse stb evaluations this approach is not available due to the missing time resolution across the snapshots. here we rely on the estimations about typical error values of the method as stated in the introducing paper (novara et al., 2016) which are supported by results from the critical evaluation of the method in the pressure challenge (van gent et al., 2017) as well as the recent lpt-challenge (sciacchitano et al., 2021). such results can be verified on the actual measurement data utilized within this paper due to a diagnostic run employed at the start of the experiment campaign. a special run was conducted that captured images from all cameras at the same time both separate imaging systems should therefore reconstruct the particles at the exact same position and any deviation can be attributed to random positioning error from the processing forming the basis for this approach described by manovski et al. (2021). as this should be the dominating error for a well calibrated imaging system utilizing volume self calibration (wieneke, 2008) this allows a pathway to verify these error assumptions for a concrete experiment for a posteriori particle position error estimation. for this experiment this error is within the expected positioning error of 0.1 px (see fig. 8(a)). this particle positioning error then forms the basis for further propagation as described above. linear gaussian error estimation is used to propagate the error through the polynomial fit of the track building stage and the necessary derivation of the polynomial with respect to time to acquire the velocity information or all further derived data. 4 application to measurement data to provide an overview on the performance the functional binning approach is applied to a synthetic dataset with known ground-truth data with velocity values: u = sinh(y) cosh(y)+ εcos(x− ct) + c and v = εsin(x− ct) cosh(y)+ εcos(x− ct) , (3) and coeficients c = 3 and ε = 0.7. synthetic tracks are generated for the spatial domain ω = [−2π,2π]× [−π,π] and over the time domain t = [0,2π]. in addition the the synthetic data we also consider the real-world jet measurement. used here is the jet with the round nozzle, at mach 0.85 for the measurement domain close to the nozzle. a thorough description of the jet measurement can be found in the referenced publications. even though a large amount of data is available for this data set, we will show statistics calculated only on a small subset of the available data to make differences in convergence between the methods visually apparent in the profiles. since no direct ground truth data is available we perform only a qualitative comparison. figure 3 shows such comparisons of profiles on small amounts of data for the mean velocity profile of the synthetic data-set. a comparison between axial reynolds stresses for the jet data set is shown in figure 4. for the synthetic case a strong improvement is immediately apparent. the improvement for the jet data-set is not as drastic but a smoother statistic is visible. this was to be expected as here we are mostly interested in fine profiles along the radial direction to resolve the shear layer. as this direction is orthogonal to the jet axis, and therefore mostly of the track direction, less tracks cross across into neighboring bins in this direction diminishing the effectiveness of the functional approach. this is in contrast to the synthetic experiment where the track movement is within the plane of interest making this well suited for the functional approach. nevertheless the functional binning approach enhances the statistic for the jet and demonstrates the applicability of the method to real-world data. in addition to the one-point statistics shown we now also evaluate two-point velocity correlation functions. figure 5 shows such an evaluation for the synthetic data-set and compares the usual midpoint method with a −3 −2 −1 0 1 2 3 2 3 4 y ū (a) mean velocity value from synthetic experiment utilizing only 2000 images. 101 102 103 104 0 1 2 3 4 ·10−2 snapshots m ea n er ro r (b) convergence behavior of the error of the mean velocity figure 3: comparison of the functional to midpoint binning approach for the synthetic experiment. ——midpoint; ——functional; -truth. figures adapted from godbersen and schröder (2020) function based approach. similar qualitative improvements as with the one-point statistics are apparent. the features are smoother and the inflow region is filled as information along the entirety of the track is utilized. both effect mirror those within the mean velocity field for both methods as shown in detailed one-point statistic evaluations in godbersen and schröder (2020). 5 further uses of uncertainty information so far examples of one-point statistics and two-point correlations were presented. but a functional view including uncertainty quantification is also beneficial for more complex two-point statistics as well. this approach can be very attractive for all statistics where relations between pairs of particles or triads have to be considered, for example the calculation of velocity gradients or velocity differences for structure functions. these calculations pose the problem of finding suitable pairs for these comparisons based on criterions such as a close enough distance. instead of just considering the midpoint, we now have the entire length of the track segment to find eligible comparison points. a systematic approach for selection of comparison points is now also facilitated through the use of uncertainty quantification by propagating the particle positioning error. this is even more important here as the use of velocity or position differences for small position or velocity differences relies less directly on the absolute error but rather the relative error. instead of just estimating a rough rule of thumb for the closest feasible minimum distance based of the position accuracy we can derive a direct functional expression for the respective relative errors along the length of the tracks by use of error propagation. this directly informs which regions in time along the track pair are unsuited for such comparisons. by prescribing some criterions for the admissible errors, such as some maximum value for the relative errors, we can directly determine permissible regions for calculating comparisons. additionally, we can utilize this knowledge to help calculate an optimal point for calculating the comparison value. typically, there is a desired criterion for calculating such a comparison value that based on the desired statistic. for a velocity gradient the particles should be as close together as possible in order to reduce truncation error in the velocity difference quotient used for the calculation. such a goal can now be combined with the constraints imposed by the error analysis to identify the optimal point along the track pair for such a calculation. to illustrate this approach, we present an example on a synthetic track pair in two dimensions. these two tracks were randomly generated in the box [0,1]× [0,1] and do not aim to represent an actual experiment but to provide an interesting illustration for the approach. in this example the velocity difference quotient is the targeted value for selecting an optimal point: vdq = v2 − v1 p2 − p1 , (4) as this allows to showcase multiple relative error values for distance and velocity difference. we now desire the optimal point along the track to evaluate this quotient, meaning the optimal value for the time t. optimal in −1 −0.5 0 0.5 1 0 1 2 3 ·103 y/d u′ u′ [m 2 / s2 ] (a) using only 1000 snapshots −1 −0.5 0 0.5 1 0 1 2 3 ·103 y/d u′ u′ [m 2 / s2 ] (b) using 30 000 snapshots figure 4: comparison of the functional to midpoint binning approach for the real-word data. axial reynolds stress profile located ca. 1.5 nozzle diameters donwstream. utilizing 3px bin size in axial and radial direction. ——midpoint; ——functional. figure 5: qualitative comparison of two-point correlation results for the midpoint approach (left) and the functional approach (right) this case means the closest point between the tracks that still conforms to some value of permitted maximum relative error. for illustration the two relative errors for distance and velocity difference are considered separately here but could also be joined into one single common error expression. propagating the particle position error through the track building process and the further calculations as defined in (4) provides the relative errors as continuously defined functions within the track segment as shown in figure 6. we use a software package to provide automatic propagation of uncertainty trough these functions (giordano, 2016) allowing for easy generation of these error functions independent of the complexity of the input functions. it would generally still be possible to manually derive the functions if a mathematical expression is desired for further study. as visible in the figure the relative errors vary quite strongly for the tracks considered here. it is easy to identify regions were either one of the errors is significantly increased. as expected the relative difference error is higher the closer the two tracks approach each other. but also, the relative velocity difference error changes quite dynamically along the track showing the value of having such a direct continuous varying error value available. as mentioned earlier, only the particle positioning error was the required input for these results whereas all further influence of the processing and derivation of variables is directly captured by error propagation with no further input needed. the resulting error functions can now be utilized to identify an optimal point for the calculation in (4). we minimize the distance between the tracks with a maximum constraint on the two relative errors resulting the in optimal point shown in figure 6. the cost function for the optimization could easily be extend to include additional concerns, such as penalizing close contact for the four pulse times where the particles are imaged. this provides the additional knowledge that close contact during those times could result in overlapping particle images. currently we utilize a simulated annealing algorithm implemented in mogensen and riseth (2018) and manually include the constraints into the cost function using logarithmic 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 x y 0 0.2 0.4 0.6 0.8 1 0 0.5 1 time d is ta nc e 0 0.2 0.4 0.6 0.8 1 0 0.05 0.1 0.15 0.2 time r el at iv e di st an ce er ro r 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 time r el at iv e ve lo ci ty di ff er en ce er ro r figure 6: error analysis for the calculation of the velocity difference quotient for two tracks with calculated optimal point in green. the red horizontal lines signify the selected upper constraints for the optimizer barrier functions. the choice of simulated annealing was motivated by the desire to avoid local minima, other algorithms might be better suited for this application. further work in this area will include a more systematic study of optimization algorithms, including ones natively supporting constraints. 6 individual uncertainty in the evaluation shown so far, only one global common particle position error value is used for all particles of the experiment. this already provides a diverse set of uncertainty in calculated values for tracks as these common errors are then individually propagated for each calculated variable leading to possibly quite complex interactions as seen in figure 6. still one expects that there is some variation in the errors associated with individual particles due to different effects in the stb processing. a particle that is far away from any other particles in all camera images is very easy of the stb algorithm to generate good position for resulting in a lower than average positioning error for that particle. on the other hand, a particle that is very close to several other particles on the images might see a slightly higher position error due to overlap in the particles making reconstruction more challenging. as the camera images and positions of particles are known, it should be feasible to model this effect at least to some degree. a series of other effects can also be imagined such as distortion of images in some regions due to measurement windows, optical effects close to the edges of the camera lenses, illumination differences closer to the edges of the volume, etc. some of these have probably have a minimal effect on the accuracy but most of the mentioned possible influences also have in common that it might be feasible to model them, even if just roughly. many rely on particle locations with respect to the measurement volume or the camera image, information which is available from the measurement data. while all examples shown so far only utilize one common particle position error value this is not due to a limitation of the method as nowhere in the derivation was this assumed. the method as currently implemented already allows for such individual values. an illustration of the effect of individual particle positioning errors for each of the particles within a track is provided in figure 7(a). the general v-shape stays the same since this is a result of the polynomial fit, however the location of minimal error shifts to different time points and the value of the errors changes. this information can then be propagated in the functional binning approach by utilizing individual track weights based on these error functions. the effect of this individual consideration on the resulting statistics will largely depend on the amount of variation in error between the tracks. for 0 0.2 0.4 0.6 0 2 4 6 ·10−2 time v el oc ity er ro r (a) calculated velocity error curves for randomized individual particle positioning errors. each line is based on a random draw of individual position error values for the four particles. shown in thick black is the curve using identical particle error values. −3 −2 −1 0 1 2 3 0 0.5 1 1.5 y r ea lti ve er ro ro f u′ u′ (b) relative error to ground truth for the three different evaluations showing very similar values for the class based variant and the individual variant. both show reduced error in some regions compared to the variant with a fixed global particle positioning error. ——global; ——individual; ——class based. figure 7: the individual particle positioning error values allow for more detailed uncertainty knowledge. experiments where there is little variation in error between the tracks only minimal difference to the approach using a global mean particle position error value would be expected. to provide some insight into the effect of individual track weights we extend the synthetic experiment shown prior by such an individual error value. as the particle positioning error there is simply prescribed by adding gaussian noise to the calculated particle positions, this switch simply requires modifying this noise source. instead of a random draw from a normal distribution with a fixed standard deviation for all tracks, we now draw vary this standard deviation for each particle and communicate this value together with the position result. this setup results in particles where for high reported error value it is likely that a larger amount of noise has been added than for a particle with a low reported error value. the approach was selected to avoid reporting the exact error value added to each particle, as such knowledge would never be possible to archive in a real experiment. with the such prepared error information the synthetic data is now processed using functional binning with individual track weight functions and the such calculated reynolds stresses then compared to the known ground truth data in a profile across the domain. as shown in the relative error plot in 7(b) there is an improvement when compared to the functional binning using a global mean particle positioning error. the regions where the improvement is visible are regions of lower absolute value of the analyzed reynolds stress and therefore more sensitive for the relative error value. a second different evaluation is included in this comparison where instead of directly utilizing the error value reported by the synthetic experiment we pretend that instead we only know for each particle a membership to one of three quality groups. one group containing particles with above average error, one for particles of about average error value, and one for those with a below than average error value. the motivation behind this is that such a rough classification might be more readily achievable for real measurement data. as seen in the figure this simpler approach already provides much of the improvement archived by the approach utilizing more detailed error information. with these results in mind we are currently working on a machine learning model to provide such error estimation classification for real world measurements in order to apply functional binning with such individual track weight functions. the model utilizes information from the shaking step of stb processing such as gradients and hessians from the optimization procedure this is a core portion of the processing where all the information about the camera images and particle positions comes together providing a wealth of condensed information to the learning process. originally this model was designed to provide a better filter for ghost particles than the currently used conventional filter and has shown some success on the test datasets provided by the lpt-challenge organizers (sciacchitano et al., 2021). extending the approach used for the machine learning model to provide a rough certainty classification instead seems feasible as the task is closely related, however this needs to be pursued further. x y z 0 0.2 0.4 coordinate direction pa rt ic le po si tio n er ro r[ px ] (a) particle position error estimation for multi-pulse stb based on measurement data. the separation into direction would also allow for utilizing individual error values for each of the coordinate directions 0 0.2 0.4 0.6 0.8 1 0 0.5 1 false positive rate tr ue po si tiv e ra te (b) performance comparison between the original filter and the machine learning model for identifying ghost particles in a synthetic measurement. ——conventional; ——machine learning model . figure 8: statistical evaluation on the measurement data allow for a posteriori uncertainty estimation to obtain a global particle positioning error. modifications to an existing machine learning model could provide a path towards particle individual position uncertainty estimation. 7 conclusion we have shown several applications of uncertainty quantification in functional binning and related approaches on lagrangian particle tracking data and illustrated the improvements over conventional approaches. functional binning uses uncertainty information of the measurement data as a core feature of the method to improve the calculation of statistics an provides a readily available way to introduce such information into the calculation of the various statistics. the determination of one-point statistics was demonstrated not just on the existing evaluation on synthetic data but for the first time on an actual multi-pulse stb dataset. while the lack of ground truth data does not permit a quantitative evaluation, the qualitative improvement visible when processing only a small subset of the data where the unconverged noisy profiles make any improvements immediately apparent is evident. this shows that an improvement in convergence speed is facilitated trough the functional binning approach not just for the synthetic experiment considered previously but also in a real-world multi-pulse stb measurement. the evaluation of two-point correlations is a natural extension of the one-point statistics shown so far, and the convergence improvement provided by the functional binning approach was demonstrated. we strengthen the link to the initial uncertainty analyses described in the publications relating to the two stb variants by emphasizing the reliance on an a posteriori uncertainty quantification of the particle positioning error provided by these as a basis on which all further error processing in functional binning is built on by propagation this error onwards. this also forms an interface for other lpt methods to utilize functional binning with no need to adapt its internals. as long as another method is capable of providing such particle positioning error these can then be propagated into the functional binning procedure. apart from the already more matured functional binning statistics mentioned above we also demonstrated an additional application in the form of the optimal point calculation for track-to-track comparisons. the advantage of error propagation was easy to see in this example and an optimal point was successfully determined. however, this approach still needs additional work as just a single optimal point calculation was demonstrated. the binning procedure surrounding this in order to be able to calculate statistics still needs to be completed so no actual statistical evaluations could be shown yet. still the core idea behind this approach was successfully demonstrated. the use and estimation of particle individual error values is similarly a topic were initial successes were presented but additional work is needed to fully utilize these concepts. conceptionally the functional binning approach is already prepared to utilize individual particle positioning errors for tracks and the presented synthetic experiment evaluation showed that there is value in such an extension. however, a more systematic evaluation of such an experiment is needed to gain a better understanding of the benefits depending on the amount of error variation in the measurement. to truly utilize this capability with real world measurement data it is necessary to extract such individual error estimation from the measurement data. we have described why this should be feasible with the available measurement data, especially with the reduction to just a classification into a limited number of groups. for initial work on a machine learning model to provide such classification we were able to present progress in a closely related task, putting this capability into reach but requiring further work. the presented evaluations and ideas highlight the large amount of opportunities that uncertainty quantification approaches provide in the improvement of oneand two-point statistics, especially in the context of functional binning which provides a readily available path to incorporate this uncertainty information into the calculation of statistics of lpt data. it is also apparent that while some approaches are relatively mature and ready for application to measurements, there are still many interesting ideas and extensions left to explore and further develop. acknowledgements the authors gratefully acknowledge the gauss centre for supercomputing e.v. (www.gauss-centre.eu) for funding this project by providing computing time on the gcs supercomputer supermuc at leibniz supercomputing centre (www.lrz.de). the project leading to this contribution has received funding in the frame of the project homer from the european union’s horizon 2020 research and innovation program under grant agreement no. 769237. references agüı́ jc and jiménez j (1987) on the performance of particle tracking. journal of fluid mechanics 185:447–468 agüera n, cafiero g, astarita t, and discetti s (2016) ensemble 3d ptv for high resolution turbulent statistics. measurement science and technology 27:124011 bhattacharya s and vlachos pp (2020) volumetric particle tracking velocimetry (ptv) uncertainty quantification. experiments in fluids 61:1–18 bogaert i (2014) iteration-free computation of gauss–legendre quadrature nodes and weights. siam journal on scientific computing 36:a1008–a1026 gesemann s, huhn f, schanz d, and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser and imaging techniques to fluid mechanics, lisbon, portugal. pages 4–7 gesemann et al (2021) trackfit: uncertainty quantification, optimal filtering and interpolation of tracks for time-resolved lagrangian particle tracking. in 14th international symposium on particle image velocimetry giordano m (2016) uncertainty propagation with functionally correlated quantities. arxiv e-prints arxiv:1610.08716 godbersen p, manovski p, novara m, schanz d, geisler r, mohan nkd, and schröder a (2019) flow field analysis of subsonic jets at mach 0.5 and 0.84 using 3d multi pulse stb. in conference proceedings of the 13th international symposium on particle image velocimetry. 202. pages 545–554 godbersen p and schröder a (2020) functional binning: improving convergence of eulerian statistics from lagrangian particle tracking. measurement science and technology 31:095304 hammond a and meng h (2021) particle radial distribution function and relative velocity measurement in turbulence at small particle-pair separations. journal of fluid mechanics 921:a16 manovski p, novara m, mohan nkd, geisler r, schanz d, agocs j, godbersen p, and schröder a (2021) 3d lagrangian particle tracking of a subsonic jet using multi-pulse shake-the-box. experimental thermal and fluid science 123:110346 mogensen pk and riseth an (2018) optim: a mathematical optimization package for julia. journal of open source software 3:615 novara m, schanz d, geisler r, gesemann s, voss c, and schröder a (2019) multi-exposed recordings for 3d lagrangian particle tracking with multi-pulse shake-the-box. experiments in fluids 60:44 novara m, schanz d, reuther n, kähler cj, and schröder a (2016) lagrangian 3d particle tracking in high-speed flows: shake-the-box for multi-pulse systems. experiments in fluids 57:128 ouellette nt, xu h, and bodenschatz e (2006) a quantitative study of three-dimensional lagrangian particle tracking algorithms. experiments in fluids 40:301–313 raiola m, lopez-nuñez e, cafiero g, and discetti s (2020) adaptive ensemble ptv. measurement science and technology 31:085301 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:70 sciacchitano a, leclaire b, and schröder a (2021) main results of the first lagrangian particle tracking challenge. in 14th international symposium on particle image velocimetry van gent p, michaelis d, van oudheusden b, weiss pé, de kat r, laskari a, jeon yj, david l, schanz d, huhn f et al. (2017) comparative assessment of pressure field reconstructions from particle image velocimetry measurements and lagrangian particle tracking. experiments in fluids 58:33 wieneke b (2008) volume self-calibration for 3d particle image velocimetry. experiments in fluids 45:549– 556 introduction functional binning uncertainty propagation application to measurement data further uses of uncertainty information individual uncertainty conclusion 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a kalman filtering approach to particle track filtering and track uncertainty quantification for 3d ptv measurements r. sethu viji, j. eshraghi, j. zhang, m. c. brindise, s. bhattacharya, p. p. vlachos∗ purdue university, department of mechanical engineering, west lafayette, in 47907, usa ∗ pvlachos@purdue.edu abstract three-dimensional particle tracking velocimetry (3d-ptv) is a non-invasive flow measurement technique that computes the velocity field by reconstructing 3d particle positions of individual tracer particles and by subsequently tracking those positions. the particle velocity measurement accuracy depends on the faithful reconstruction of 3d particle positions. the complex measurement chain in 3d-ptv involves several steps, from calibration to 3d position reconstruction and particle position tracking, each having its own source of error. additionally, higher seeding density increases the uncertainty in particle reconstruction and tracking, which in turn, increases the noise in the estimated tracks. a noisy track decreases the measurement accuracy and amplifies any noise in the ptv-derived quantities of interest, which includes acceleration, pressure and vorticity. thus, track filtering techniques are critical in a 3d-ptv measurement. track fitting using polynomial functions, filtering methods adopted from signal processing and object tracking are among the well-established techniques used to achieve smooth position, velocity estimates from reconstructed particle trajectories. the kalman filter is one such filtering technique that is widely used in various applications. the strength of the kalman filter lies in its ability to perform noise reduction that is informed by existing physical models and the uncertainty estimates of recorded measurements. however, the measurement uncertainty input to the kalman filter needs to be known at priori, which in many cases may not be available or could be difficult to estimate. in the literature on kalman filters and their variants applied to 2d-piv/ptv, the position uncertainty data fed to the filter is either user-defined or estimated based on global noise levels in the ptv measurements. but instantaneous position and velocity uncertainty quantification for individual particle positions/tracks has been challenging in the 3d ptv community. recent work by bhattacharya and vlachos (2020) provides an estimate of the uncertainty in the reconstructed particle positions for a 3d ptv measurement. this position uncertainty estimate dynamically updates the filter gain for each track and enables the evaluation of the performance of the kalman filter in 3d ptv track filtering. the kalman filter (kf) reconstructs smooth tracks from noisy experimental particle trajectories through a series of predictor-corrector steps. taking advantage of physical models that describe lagrangian particle tracking, kf internally evaluates the model prediction of a particle’s current state (xp). this is then fused with the recorded experimental data (yp) at the current frame to correct the prediction. the weighting applied on the two pieces of information, the model predictions and experimental data, towards the final estimate depends on the relative uncertainty associated with each experimental data point (r) and model prediction (p). this relative uncertainty is represented by the kalman gain factor (kg), defined as: kg = pp pp +r (1) for one-dimensional kf, also referred to as p-type kf filter (yagoh et al. (1992)). here pp corresponds to the uncertainty propagated through the predictor step. the filtered position estimate is computed as: x f = kg . yp +(1−kg) . xp (2) (a) noise 0% (b) noise 5% (c) noise 10% figure 1: cumulative distribution of rms error in track velocity estimates for a 3d synthetic vortex ring, generated at a seeding density of 0.025ppp. the improvement in kf filtered result is reported at 0.2 pixels/frame. equation 2 also represents the input to the physical model in the next iteration. hence, a given particle track measurement is reconstructed iteratively by taking into consideration the instantaneous position uncertainties associated with the experimental data. the filtered tracks are bound by a reduced set of position uncertainty values determined by kf. the investigation on the performance of the p-type kf applied to the 3d-ptv position and velocity measurements is twofold: one on the tracked particle positions and the other on particle velocity estimates. the performance assessment is based on a synthetic 3d vortex ring (wu et al. (2006)). more focus is directed towards analyzing the track velocity estimates, considering the wide dynamic range in the dataset chosen. for the velocity comparison, the filtered position estimates from kf are converted to particle velocities by applying a second-order central difference scheme, while the ptv velocity estimates are obtained from 3d-ptv nearest neighbor. the current results for the noisy synthetic data (fig.1) show more than 20% improvement in track velocity error compared to regular 3d ptv estimation when uncertainty informed kalman filtering is used. additionally, a gaussian smoothing (gs) filter can be used to compute velocities from the kf position estimates. the kf estimated track uncertainty would inform the gs on the level of velocity smoothing required. thus, the proposed kalman filtering approach provides an improved estimate of the particle trajectory from a noisy regular 3d ptv track and also quantifies the uncertainty in the filtered track. the current framework is further tested and validated for an experimental pipe flow case. the obtained results would be compared against velocity tracks estimated from flowfit (gesemann et al. (2016)). references bhattacharya s and vlachos pp (2020) volumetric particle tracking velocimetry (ptv) uncertainty quantification. experiments in fluids 61:1–18 gesemann s, huhn f, schanz d, and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser and imaging techniques to fluid mechanics, lisbon, portugal (pp. 4-7). wu jz, ma hy, and zhou md (2006) vorticity and vortex dynamics. pages 271–275. springer, berlin, heidelberg yagoh k, ogawara k, and iida si (1992) the particle tracking method using the kalman filter. in flow visualization vi (pp. 838-842). springer, berlin, heidelberg 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 tr-piv in highly pulsatile flow: pulsation frequency and wake dynamics case study i. a. carr1, m. w. plesniak2∗ 1division of applied mechanics, office of science and engineering laboratories, center for devices and radiological health, us food and drug administration, silver spring, md, usa 2 department of mechanical and aerospace engineering, george washington university, washington, dc, usa ∗ plesniak@gwu.edu abstract experimental study of highly pulsatile flows presents a number of challenges, primarily the inherently large dynamic range of velocities. herein, we use time-resolved particle image velocimetry processed with a technique known as pyramid sum-of-correlation to study highly pulsatile flow around a surface-mounted hemisphere. the frequency of pulsation is varied from low-frequency, quasi-steady pulsation to high frequency pulsation. we present a conceptual overview of the wake regimes observed and compare the flow physics of the high-frequency case to that of a vortex ring produced by a single impulse of fluid. 1 introduction surface-mounted obstacles produce a plethora of flow phenomena. herein we use time-resolved particle image velocimetry (tr-piv) to study the effects of a highly pulsatile freestream with variable pulsation frequency on the wake dynamics of a surface-mounted hemisphere. given the inherently large dynamic range of velocities in this flow field, both variation due to freestream pulsation and wake-to-freestream differential, attaining tr-piv data requires the use of multiple frames during correlation. in this study we discuss the tr-piv methods used and their applicability to highly pulsatile flow, as well as changes in the wake dynamics with changing freestream pulsatile frequency. these results are discussed in more detail in carr et al. (2020). 2 methods the studies were conducted in a small-scale, low-speed, pulsatile wind tunnel designed and constructed for these experiments, shown in figure 1. the pulsatile inflow velocity profile produced by the pulsatility generator depicted in figure 2 is roughly sinusoidal, varying from re = 0 to 2000, with an average re of 1000, as shown in figure 3 and figure 4. the reduced frequency of pulsation, k, varied from 0.01 to 0.1 as is shown in figure 3. 1 the tr-piv system was comprised of an photonics ind. nd:ylf laser (527nm, 10khz) and an idt motionpro y7 high speed camera (12k fps), and laser sheet forming optics from thorlabs. the piv processing was performed in lavision davis 8.4.0 software. to compute the flow velocity throughout the pulsatile cycle, an averaging process termed the pyramid sum-of-correlation from sciacchitano et al. (2012) was employed. this technique is particularly useful for flows with a large dynamic range of velocities. highly pulsatile flow such as the one studied herein is a particularly informative showcase of this technique. figure 4 shows the phases of the inflow waveform we will be using to examine the flow field. the phases shaded in red will be referred to as ”accelerating” and those in blue as ”decelerating”. from the velocity 1k = r f/ū where r is the hemisphere radius, f is the frequency of the pulsatility in hz, ū is the average streamwise velocity, and p is the period. flow conditioning contraction test section diffuser flow in from pulsatility generator flow redirection to seeding confinement tr-piv laser sph. lens cyl. lens high speed camera settling chamber figure 1: schematic of low speed pulsatile wind tunnel with tr-piv setup. 90 opposed butterfly valves programmable stepper motor fan flow to settling chamber flow diverted flow figure 2: schematic of butterfly valvebased pulsatility generator variation shown in figure 4 it is clear that traditional piv would require tuning the capture parameters for each phase to obtain usable data significantly increasing experiment time. using tr-piv in combination with the pyramid sum-of-correlation technique considerably reduces the complexity and time required to perform these experiments. instead of changing the time between frames, dt, corresponding to the value of freestream velocity at each phase, we were able to resolve the flow field keeping the time between frames at a constant dt = 164µs — which equates to 6khz framerate on the high speed camera. figure 3: idealized representation of the sinusoidal inflow waveforms of varying reduced frequency, k. figure 4: a pulsatile inflow waveform with markers indicating the position of the data displayed in figure 5. the region shaded red indicates the ”accelerating” phases and blue indicates the ”decelerating” phases. using the aforementioned techniques, we captured data at the phases shown in figure 4 for each inflow waveforms shown in figure 3 with the exception of the highest value, k = 0.2, due to limitations in the pulsatility generator. 3 results and discussion varying k results in regime changes in the wake dynamics. figure 5 shows four velocity fields taken throughout the inflow cycle for three of the values of k studied. the four phases are spaced evenly throughout the inflow profile as shown in figure 4. near the low end of the reduced frequency range the wake resembles that of a hemisphere in steady flow at the equivalent re (acarlar and smith, 1987). at the high end the wake dynamics are phased locked to the freestream forcing, producing only a single vortex structure per cycle. figures 5a-d represent the lowest value of k, in which hairpin vortices shed from a shear layer (highlighted in red) and there are no significant organized flow structures near minimum velocity (figure 5a). the hairpin vortices are produced from a kelvin-helmholtz instability near the downstream extent of the −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d minimum velocity −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d 50% acceleration −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d maximum velocity −0.5 0.0 0.5 1.0 1.5 2.0 x/d 0.0 0.5 1.0 1.5 y/ d 50% deceleration tr-piv k= 0.1flow sp an w ise v or tic ity −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d minimum velocity −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d maximum velocity tr-piv k= 0.05 −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d 50% accelerating −0.5 0.0 0.5 1.0 1.5 2.0 x/d 0.0 0.5 1.0 1.5 y/ d 50% decelerating −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d minimum velocity −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d maximum velocity −0.5 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 y/ d 50% accelerating −0.5 0.0 0.5 1.0 1.5 2.0 x/d 0.0 0.5 1.0 1.5 y/ d 50% decelerating tr-piv k= 0.01 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) 250 -250 figure 5: centerline velocity fields with spanwise vorticity contours from four positions in the pulsatile inflow cycle: maximum and minimum velocity along with times in the middle of inflow acceleration and deceleration. three of the values of k studied are shown. the axes are normalized by the diameter of the hemisphere, d. shear layer. for k = 0.01 the wake resembles that of a hemisphere in steady flow with the exception of the decelerating phases in which the shear layer lifts away from the surface and breaks up into small scale turbulence. figures 5e-h represents a transitional case which shares some characteristics with both the high and low cases. while there is a shear layer, the presence of the hairpin vortices is significantly reduced. in this case there is less time for the shear to develop and shed hairpins resulting in fewer, if any, hairpins released before deceleration begins and the shear layer is disrupted. figures 5i-l represents the high end of the range of k in which the wake is dominated by a single arch vortex which is phase-locked with the pulsatile freestream. the shear layer begins forming during acceleration and continues through maximum velocity. the time for the formation to take place is so short, the shear layer only extends roughly 1d downstream before it is rolled up into a single arch vortex during inflow deceleration. of most interest is the transition from a quasi-steady case in which the wake is characterized by a shear layer which sheds hairpin vortices downstream, to a single arch vortex produced once per pulse. to more clearly communicate the progression of wake regimes with increasing reduced frequency, figure 6 is a series of schematic representations of the primary wake structures observed at each of the reduced frequency. progressing from k = 0.01 to k = 0.2, the wake of the hemisphere changes from a quasi-steady case which is largely made up of the same structures seen in steady flow, to a highly pulsatile case in which each pulse produces its own vortex structure. as represented in figure 6 and in figure 5i-l, the transition from a 0.010 0.025 0.05 0.1 0.2 turbulent wake & k-h shedding smooth, phase-locked single structure turbulent wake only reduced frequency, k ragged, phase-locked single structure figure 6: schematic representations of the primary wake structures with increasing reduced frequency. wake resembling steady flow to a single flow structure per pulse occurs near k = 0.1. at k higher than 0.1 arch vortices will continuously form with each pulse though their intensity and size may change. at k lower than 0.01, the wake will continuously approach a steady flow configuration. flow flow vortex ring arch vortex image arch vortex figure 7: conceptual comparison of a vortex ring produced with the traditional, sharp-edged piston-driven vortex generator and the arch vortex in the wake of a hemisphere in pulsatile flow. in these higher frequency cases, k > 0.1, the pulsation so dominates the flow physics that they resemble that of a single impulse of fluid rather than a continuously flowing freestream. to demonstrate this, we draw the analogy between the arch vortex and a vortex ring produced from a sharp-edged piston-driven vortex generator, as depicted in figure 7. vortex rings have been extensively studied and in many of those studies the vortex ring is formed at the outlet of a sharp edged piston vortex generator. the vortex ring is formed and propagates in the same direction as the fluid ejection. at the high end of k, the arch vortex in the wake of the hemisphere is produced with the same mechanisms. interestingly, in this configuration, the direction of propagation in the arch vortex is counter to the freestream flow. this is, in part, what accounts for some of the vortex dynamics seen in deceleration — a more in-depth discussion can be found in carr and plesniak (2016). the series of flow fields measured herein has an inherently wide range of velocities both within one phase and throughout the pulsatile cycle. while traditional, more labor intensive techniques would allow measurement of these flow fields, the combination of tr-piv and the pyramid sum-of-correlation techniques made resolving these flow fields significantly quicker and less prone to experimental error. 4 conclusions in this study we investigated the effects of highly pulsatile flow with different pulsation frequencies on the wake dynamics of a surface-mounted hemisphere. to handle the inherently large dynamic range of velocities in these flow fields we used tr-piv and processed the data using the pyramid sum-of-correlation technique. these techniques produced high quality velocity data from which we can observe the changing wake regimes with increasing k. to better conceptualize these regimes we present schematic depictions of the primary flow structures in four regimes. we also compare the wake dynamics at high values of k to that of a vortex ring ejected from a piston driven vortex generator. this conceptual overview provides a framework for understanding the interaction between pulsatile flow and surface-mounted obstacles. moreover, it provides a useful example of employing tr-piv and pyramid sum-of-correlation processing and the utility of those techniques. references acarlar ms and smith cr (1987) study of hairpin vortices in a laminar boundary layer: part 2. hairpin vortices generated by fluid injection. journal of fluid mechanics 175 carr ia, beratlis n, balaras e, and plesniak mw (2020) effects of highly pulsatile inflow frequency on surface-mounted bluff body wakes. journal of fluid mechanics 904 carr ia and plesniak mw (2016) three-dimensional flow separation over a surface-mounted hemisphere in pulsatile flow. experiments in fluids 57:9 sciacchitano a, scarano f, and wieneke b (2012) multi-frame pyramid correlation for time-resolved piv. experiments in fluids 53:1087–1105 introduction methods results and discussion conclusions piv measurement of buffer and logarithmic layers with detached eddies which mimics the neutral atmospheric surface layer y. hattori1*, hitoshi suto1, keisuke nakao1, hiromaru hirakuchi1 1 central research institute of electric power industry, civil eng lab, abiko, japan yhattori@criepi.denken.or.jp motivation accurate comprehension of turbulence characteristics in the atmospheric surface layer (asl) under near neutral conditions, which is a lower part of the atmospheric boundary layer and a very high-re number flow, is critically required in view of the increasing and broadening use of numerical weather prediction models. the models need to estimate turbulence fluxes of momentum, heat and moisture in the asl as boundary conditions. on the other hand, observations (högström 1990, drobinski et al. 2007) have revealed that the fluxes under near-neutral conditions are often inconsistent with monin-obukhof theory, which has been widely used in models. the observations were conducted over flat surfaces with homogeneous roughness, and thus the violation from the theory might not be due to the underlying surface conditions. thus, aiming to investigate an origin of the violation from the theory, we have carried out a wind tunnel experiment on the logarithmic layer along a smooth flat wall with a larger-scale disturbance, which mimics the near-neutral atmospheric surface layer (hattori et al. 2010). in the present study, we especially examine a piv measurement with a long-distance microscope lens to discuss the interaction of turbulences structures between buffer and logarithmic layers, which must give a clue on reynolds number effects experimental apparatus and procedure we used the same experimental technique of our previous study (hattori et al. 2010), except velocity measurements. the experiment was conducted in an open-circuit wind tunnel at the central research institute of electric power industry (criepi). the test section is 1000 ×1000 mm2 in area and 6200 mm long, and the walls of the test section are made of smooth flat wood walls. an active turbulence grid (makita et al. 1987), installed at the front of the test section, was used to control the turbulence characteristics in the logarithmic layer; the active turbulence grid composed of rotating grid bars with attached triangular agitator wings, stepping motors located at the end of each grid bards outside the wind tunnel and a controller. the velocity at the centerline of the test section was set to 5 m⋅s-1 to obtain the fully-developed turbulence boundary layer at the measuring location, which was fixed at the downstream distance from the active turbulence grid of 4180 mm. the logarithmic layer height, hs, and the friction velocity, uτ, which are characteristic length and velocity for the logarithmic layer flow, were 70 mm and 0.2 m⋅s-1, respectively. in the present study, the velocity vectors were measured by using a piv technique with a long-distance microscope lens. olive-oil mists added to the wind field were illuminated by light sheet discharged from an yag laser system, the output of which is 200mj/pulse. particle-containing flow images in the streamwisevertical (x-z) plane were captured by a ccd camera (2k×2k pixels) with a long-distance microscope lens to ensure spatial resolutions for capturing small turbulence eddies, which are generated near the wall. the distance between the lens and the object plane was set to 800 mm, giving the physical size of measuring area was 10.8×10.8 mm2. the time interval between the two pulsed illuminations was set at 20µs to keep the maximum displacement of successive particle images below the half of the interrogation windows size. the velocity vectors were calculated using a cross-correlation method with interrogation windows of a size of 32×32 pixels. the overlap ratio was 50%, and the 16384 velocity vectors were obtained in each pair of images, which gives the spatial resolutions normalized with inner parameters of ∆+ = 1.12. 14th international symposium on particle image velocimetry − ispiv 2021 august 1−5, 2021 results figure 1 depicts an example of visualized flow fields with calculated velocity vectors. the particles are appropriately added in flow fields, and the velocity vectors are obtained even in the vicinity of the surface of the wall. the velocities become very small near the surface with the non-slip conditions, and become large with organized motions above the near-wall region. figure 2 shows the profile of time-averaged streamwise velocity normalized with inner parameters, with the lines for u+ = z+, = (1/0.41)lnz+ + 5.0. this profile shows the present piv firmly captures the velocity fields of buffer and logarithmic layers. the profile agrees well with that for logarithmic layer for z+ > 30 and approaches that for viscous sublayer for z+ < 30. more detailed experimental results on the structural characteristics will be presented in a presentation to understand fundamental characteristics of turbulence structure in the surface layer. such results also provide a deep insight into coherence structures of a wall turbulence under high reynolds number conditions; the asl mimicked in the present study easily yields turbulence flows, the reynolds number of which is much larger than those with wind tunnels. indeed, a renowned observation campaign at the surface layer turbulence and environmental science test facility (kunkel and marusic 2006) used to examine the turbulence structures under very high reynolds number conditions and have revealed the existence of very large-scale organized motions in the logarithmic layer (hutchins and marusic 2007, marusic et al. 2010). references drobinski, p, carlotti p, redelsperger j-l, banta rm, masson v and newsom rk (2007) numerical and experimental investigation of the neutral atmospheric surface layer. j atmos sci 64: 137-156 hattori y, moeng c-h, suto h, tanaka n and hirakuchi h (2010) wind-tunnel experiment on logarithmiclayer turbulence under the influence of overlying detached eddies. boundary-layer meteorol 134: 269-283 högström u (1990) analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions. j atmos sci 47: 1949-1972 hutchins n and marusic i (2007) evidence of very long meandering features in the logarithmic region of turbulent boundary layers. j fluid mech 579: 1-28 makita h, sassa k, iwasaki t and iida a (1987) evaluation of the characteristic features of a large-scale turbulence field (1st report, performance of the turbulence generator). trans jsme b 53: 3173-3179 (in japanese) marusic i, mathis r and huthins n (2010) predictive model for wall-bounded turbulent flow. science 329: 193-196 kunkel gj and marusic i (2006) study of the near-wall-turbulent region of the high-reynolds-number boundary layer using an atmospheric flow. j fluid mech 548: 375-402 (a) visualized image (b) instantaneous velocity vectors figure 1: example of image and instantaneous velocity vectors figure2: profile of time-averaged u 10 100 10 15 5 20 u+ z+ 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 bubble piv technique to measure the velocity field of a free-swimming california sea lion gino perrotta1, frank e. fish2, megan c. leftwich1∗ 1 george washington university, department of mechanical and aerospace engineering, washington, usa 2 west chester university, 2department of biology, west chester, usa ∗mleftwich@gwu.edu 1 introduction fish et al. (2014) adapted laboratory piv for safe use on larger animals. as opposed to seeding the entire flow with reflective particles and illuminating a plane of the flow with a laser, they produced a sheet of small bubbles and used sunlight for global illumination. underwater cameras imaged the flow in a method similar to traditional piv. this technique was used to measure the flow around a swimming dolphin and estimate the thrust produced during a tail stand maneuver (fish et al. (2014, 2018)). in the current work, we will extend the modification of piv of fish et al. to measure the flow produced by a swimming sea lion also using bubbles as seeding particles and sunlight as illumination. this is the first time that the flowfield of a swimming sea lion has been directly measured. we will present an extensive extension to the image processing required to measure flow under field conditions. finally, we will present the flow generated by propulsive strokes of an adult female (cali) sea lion freely swimming through a pool of stationary water. 2 methods data collection: measurements were taken at science learning and exploration with the help of sea lions (slewths) in moss landing, california. three adult california sea lions trained to follow an instructor?s target were guided to swim through a sheet of bubbles in front of a submerged camera. small bubbles were generated in a thin flat sheet by releasing compressed air through a porous irrigation hose placed on the floor of the pool. the motion of the bubbles was recorded by a submerged gopro hero 5 at 1920x1080 pixels and 120 fps. image processing: the raw images need extensive processing to yield clear velocity fileds. the process, and results are shown in fig. 1. the process involves xxx steps: image data reduction (fig. 1(b)), a sliding minimum subtraction (fig. 1(c)), a spatial median subtraction (fig. 1(d)), a heuristic refinement (fig. 1(e)), a two-dimensional piv calculation (fig. 1(f)), and a three-dimensional median subtraction (fig. 1(g)). this lengthy process is necessary largely due to the use of global illumination via sunlight and the resulting reflections throughout the large field of view. 3 results the flowfield measured in the bubble-plane was measured for 173 runs of three separate individuals. fig. 1(g) shows the velocity magnitude in a representative run. because the animals swim freely in the pool, ensuring in-plane motion and propulsive stroke timing necessitate a large number of runs, a feat made more challenging by the difficulties of working with marine mammals. from these data we are able to examine the full-scale flowfield produced by the swimming sea lion, and estimate the strength of the resulting fluid jet. overall, xxx flowfields were measured showing distinct flow features created by the sea lion at various points in the propulsive stroke. the method was repeated in a water channel at west chester university at known steady velocity. this allowed for validation of the technique by measuring a known flowfield in a controlled setting (something this is not possible in the field experiments). figure 1: each panel shows a step in the data processing from the raw data (a) to the measured flowfield (h). 4 conclusions the flowfield of swimming california sea lions was measured by adapting and advancing bubble piv techniques. these results not only illuminate this particular flow phenomenon, they also provide additional options for measuring flowfields in field settings where typical piv techniques are not feasible. acknowledgements finding for this study was provided by the office of naval research award n000141712312 (po tomas mckenna) to mcl and fef and award n000141712448 (po robbert brizzolera) to mcl. as well as the national science foundation award cbet 1604876 to mcl. references fish fe, legac p, williams tm, and wei t (2014) measurement of hydrodynamic force generation by swimming dolphins using bubble dpiv. journal of experimental biology 217:252–260 fish fe, williams tm, sherman e, moon ye, wu v, and wei t (2018) experimental measurement of dolphin thrust generated during a tail stand using dpiv. fluids 3:33 introduction methods results conclusions microsoft word ispivabstmurai.docx 1 color contamination matrix property assessment 1 for improvement of colored smoke piv 2 3 yuichi murai, yasufumi horimoto, hyun jin park, and yuji tasaka 4 5 laboratory for flow control, faculty of engineering, hokkaido university, n13 w8, sapporo 060-8628, japan 6 * corresponding author. tel./fax: +81(japan) 11 706 6372. e-mail: murai@eng.hokudai.ac.jp. 7 8 a single-camera color piv system that can acquire piv data of three separated layers has been re-9 designed, purposing improvement of wind tunnel applicability. we target smoke image that has 10 particle-per-pixel values higher than unity. the system constitutes of a high-power color-coding 11 illuminator and a digital color high-speed video camera. rgb values in recorded image involves 12 severe color contaminations due to five optical and digital sequences (fig. 1). to quantify this, a 13 snapshot calibration is proposed to describe the contamination matrix equation (eq. (1)). taking the 14 inverse matrix (eq. (2)) allows in-plane piv in each color layer to be accurately implemented. we 15 also derive mathematical limits to operate the colored smoke piv, which is explained by the matrix 16 property (eq (3)). feasibility of the proposed method has been demonstrated by application to a 17 turbulent wake behind a delta wing (fig. 2) and also to a boundary layer flow along heated chocolate. 18 19 20 fig. 1 color contamination property for a water mist in air projected by a sheet of color light 21 22 color contamination matrix equation: 23 3 5 1 1 6 2 2 4 3 1 1 1 l l l r a a r b g a a g b b a a b b                                        , (1) 24 2 inverse matrix equation for estimating smoke density in three colored layers 1 3 6 3 5 4 4 6 5 1 2 6 1 2 5 1 5 6 2 1 3 2 2 4 3 1 4 3 1 1 1 1 l l l r a a a a a a a a r b g a a a a a a a a g b k b a a a a a a a a b b                                       , (2) 2 determinant of the inverse matrix 3  1 3 5 2 4 6 1 4 2 5 3 61k a a a a a a a a a a a a      . (3) 4 5 6 fig. 2 flow velocity vector distribution obtained by inter-color 3-d cross correlation for a wake 7 behind a delta wing of 25 degree in angle of attack at which periodic stall occurred. 8 9 references 10 pick s, lehmann f (2009) stereoscopic piv on multiple color-coded light sheets and its application to axial flow in 11 flapping robotic insect wings. exp fluids 47: 1009-1023. 12 watamura t, tasaka y, murai y (2013) lcd-projector based 3d color ptv. exp thermal fluid sci 47: 68–80. 13 charonko j, antoine e, vlachos pp (2014) multispectral processing for color particle image velocimetry. microfluid 14 nanofluid 17: 729-743. 15 aguirre-palbo aa, alarfaj, mk, li eq, hernandez-sanchez jf, thoroddsen st (2017) tomographic particle image 16 velocimetry using smartphones and colored shadows. sci reports 7: 3714-3722. 17 xiong j, aguirre-pablo aa, idoughi r, thoroddsen st, heidrich w (2021) rainbow piv with improved depth 18 resolution – design and comparative study with tomo piv. meas sci tech 32: 025401. 19 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 gans-based piv resolution enhancement without the need of high-resolution input alejandro güemes1, carlos sanmiguel vila1, stefano discetti1∗ 1 universidad carlos iii de madrid, aerospace engineering research group, madrid, spain ∗ sdiscett@ing.uc3m.es abstract a data-driven approach to reconstruct high-resolution flow fields is presented. the method is based on exploiting the recent advances of srgans (super-resolution generative adversarial networks) to enhance the resolution of particle image velocimetry (piv). the proposed approach exploits the availability of incomplete projections on high-resolution fields using the same set of images processed by standard piv. such incomplete projection is made available by sparse particle-based measurements such as super-resolution particle tracking velocimetry. consequently, in contrast to other works, the method does not need a dual set of low/high-resolution images, and can be applied directly on a single set of raw images for training and estimation. this data-enhanced particle approach is assessed employing two datasets generated from direct numerical simulations: a fluidic pinball and a turbulent channel flow. the results prove that this data-driven method is able to enhance the resolution of piv measurements even in complex flows without the need of a separate high-resolution experiment for training. 1 introduction the enhancement of the spatial resolution in particle image velocimetry (piv) is a long-standing line of research. many efforts have been directed towards increasing both the dynamic spatial range (dsr) and the dynamic velocity range (dvr), defined as the ratio between the largest and smallest measurable length/velocity, respectively (adrian, 1997). an increase of the dsr can be achieved either by technological advances (enlarging the sensor size) or by algorithms capable of reducing the size of the smallest resolvable scale. along this line, it has been assumed for long that the mean interparticle spacing was the lowest bound for resolution, unless temporal information is used in the process. for time-resolved piv, this process has led already to several successful applications in 2d and 3d (see for instance hain and kähler 2007). the challenge of achieving higher resolution flow fields is critical in turbulent flows in which the spatial scales have a wide spectrum, being the ratio between the integral scale and the kolmogorov scale proportional to re−3/4 (pope, 2000), where re is the reynolds number based on the large-scale size and velocity. due to their presence in a large number of relevant fluid-flow problems, in recent years, applications based on ensemble-correlation (westerweel et al., 2004; scharnowski et al., 2012) and ensemble-particle-averaging (cowen and monismith, 1997; kähler et al., 2012; agüera et al., 2016) approaches have been employed to increase the resolution of flow statistics in standard two-frame applications. unfortunately, the outcome of these approaches is restricted to obtaining high-resolution turbulence statistics since, when it comes to obtaining instantaneous fields, the resulting outcome is a sparse sampling of the velocity field that does not provide enough information to study the flow features. to overcome these limitations, recently, a model-free fully-data-driven method to enhance the spatial resolution of two-frame piv fields has been proposed by cortina-fernández et al. (2020). the method is based on using sparse particle-tracking-velocimetry (ptv) data to build a high-resolution dictionary of proper orthogonal decomposition (pod) modes. the pod modes are then used to reconstruct velocity fields using a pod temporal basis obtained from low-resolution piv fields. this method has the main limitation of being based on linear projection on temporal modes obtained from low-resolution piv fields. consequently, it cannot resolve non-linear dependencies, especially for what regards features that are not resolved in the original low-resolution piv fields, which are recurrent in turbulent flows. convolutional neural networks (cnns) and generative adversarial networks (gans) are now offering new opportunities for super-resolution imaging, and have already been used for resolution enhancement of turbulent flow fields (fukami et al., 2019; deng et al., 2019; liu et al., 2020; fukami et al., 2021). gans for image super-resolution (srgans), in particular, have show promising resolution upsampling also for piv experiments. while the success of these works is undeniable, they are all limited by the need for a high-resolution target for training, i.e. a set of pairs of fields with low and high resolution are needed, which limits their applicability. it is indeed difficult to obtain from experimental data, and somewhat implies that high-resolution measurements are already available. while it is true that in piv experiments there is not a pair of low and high resolution fields, we always have available at least an incomplete projection of the low-resolution fields onto an high-resolution one. indeed, while piv fields are obtained from cross-correlation of groups of particle images, ptv provides vectors at the level of the single particle, without filtering effects. this corresponds to sampling the field in scattered location, thus providing an incomplete (“gappy”) view of the high-resolution field. the ansatz of the work presented here exploits the capability of gans to be trained with conditional data to generate high-resolution fields from piv fields using only this scattered information. being the great advantage of this work, the ability to achieve high-resolution fields without having a priori any high-resolution field. 2 methodology 2.1 piv-tailored gan generative adversarial networks are composed of two competing networks, a generator, in charge of producing an artificial output which mimics reality, and a discriminator, which oversees distinguishing between reality and artificial outputs. for this work, the architecture proposed in ledig et al. (2017) has been used. however, following the findings of wang et al. (2019) the batch-normalization layers have been removed to ensure a proper fitting of the deep layers in the architecture. the in-plane piv velocity components are fed to the generator, which applies a convolutional layer with filter size 9× 9 and 64 feature maps, followed by a parametric relu (prelu) activation function. after these initial layers, 16 residual blocks are applied with the layout proposed by gross and wilber (2016), i.e., a convolutional layer followed by a prelu activation function and a second convolutional layer, with 64 feature maps of filter size 3× 3 for both convolution operations. before increasing the resolution, a skipconnection sum is performed between the output of the residual blocks and the output of the initialization layers. the subpixel convolution layer proposed by shi et al. (2016) is used to increase the resolution up to the targeted-ptv one. finally, a convolution operation with linear activation function and filter size 9×9 is applied to recover the in-plane ptv velocity components as outputs. both the real and generated ptv fields are fed into the discriminator network. it must be noted that the real fields are sparse, while the entire information is provided by the gan approach. the initialization of the network is carried out by a convolution operation of filter size 3× 3 and 64 feature maps, followed by leaky relu (lrelu) activation function. after this, 7 discriminator blocks of successive increasing feature maps and are applied, where the discriminator blocks are composed of convolutional layers of 3×3 size and lrelu activation function. note that odd blocks applied a stride step larger than one to reduce the height and width of the feature maps. finally, the feature-map tensor is flattened into a vector, followed by a fully-connected layer of 1024 neurons with lrelu activation function and output fully-connected layer with one neuron and sigmoid activation function. this output gives a probability of whether the input is real (0s) or fake (1s). the generator loss is defined with weighted mean-squared error of the predicted output with respect to its target. the target is built from the scattered vector discretized in windows, from now on called “bins”. binned-ptv distributions are obtained by setting to 0 the velocity in empty bins, and to the average velocity of the vectors within the bin when one or more vectors are founds. the error is weighted to consider only those bins in the target where there are vectors. moreover, an adversarial contribution is added to the error. this adversarial loss, weighted with a factor of 0.001, is defined as the binary cross-entropy of the predicted fields, i.e., to check if the discriminator has defined as fake the generated fields. the discriminator loss is defined as the mean values between the binary cross-entropy of the predicted fields and the target ones. for the latter, the error checks if the discriminator has recognized those fields as reals. it is worth to mention that to increase the stability of the gan training all the cross-entropy errors have been perturbed with a random fluctuation of standard deviation 0.2. the different cases have been trained during 100 epochs with 8 samples per batch. the generator and discriminator states have been stored each 5 epochs to find later the optimum point before the gan starts overfitting. both networks’ weights have been updated using adam optimizer with learning rate 0.0001. a schematic view of the architecture is presented in figure 1. xlr yhr ỹhrgenerator (g) discriminator (d) d(ỹhr) d(yhr) figure 1: schematic illustration of gan architecture (adapted from kim et al. (2021)). the novel element is the use for training and testing of gappy high-resolution fields provided directly by binned ptv data. 3 validation the present method has been tested employing two different direct numerical simulation (dns) dataset that includes a fluidic pinball and a turbulent channel flow. using these numerical simulations, a combined set of pseudo-piv and psuedo-ptv fields have been generated and used to train the presented gan architecture. 3.1 dataset description the first test case is the fluidic pinball (deng et al., 2020) which is a two-dimensional wake flow around a cluster of three equidistantly-spaced cylinders with equal radius r = d/2, whose centres form an equilateral triangle with side length equal to 3r. the triangle is oriented with an upstream vertex and with the downstream side orthogonal to the freestream flow, located at x = 0 and centred with respect to the y axis. the wake of the pinball includes the interaction of the wakes of three bodies, a region of development and the final merging in a large-scale unique shedding wake. the dns data at re = 130 (referred as chaotic regime deng et al. (2020)) are used to generate synthetic piv images. the details of the simulation settings and flow behaviour can be found in deng et al. (2020). a set of 4737 synthetic piv images are generated with a custom-made code. the first 4000 are used for training, while the rest is used for testing. gaussian blobs with a maximum intensity of 100 counts and 3 pixels diameter are generated on 8-bit images. a domain ranging from −5d to 8.04d in the streamwise direction and from −3.84d to 3.84d in the spanwise direction is discretized with 25pix/d, thus resulting in images with 576× 192 pixels. particles are randomly distributed to achieve an image density of 0.02 particles per pixel. the images are processed with a custom-made multi-pass image deformation (scarano, 2001) piv algorithm developed at the university of naples (astarita, 2008). the interrogation window is set to 32×32 pixels with 50% overlap. for this first test case, the srgan seeks to achieve upsampling levels ranging from fu = 2−8, with fu being the upsampling factor. the window used to bin the vector fields has size equal to b = di/ fu, with b,di being the bin size of the binned ptv and the interrogation window size of the piv process, respectively. furthermore, the grid is refined by the same amount, thus maintaining the overlap between adjacent windows. it is important to remark that selecting a smaller bin increases the levels of gappyness of the distributions to be reconstructed. the level of gappyness is approximately 1%,29%,73% for fu = 2,4,8, respectively. the second test case is the turbulent channel flow available at the johns hopkins turbulence database (http://turbulence.pha.jhu.edu/). the channel has a dimension of 2 half-channel-heights h from wall to wall, 3πh in the span-wise direction and 8πh in the stream-wise direction. the dns database covers one channel-flow through time 8πh/ub (where ub is the channel bulk velocity) with a dns time step of δt = 0.0014h/ub. the details of the simulation settings and flow behaviour can be found in li et al. (2008). for our simulated experiments, subdomains are taken of size 2h× h in the streamwise and wall-normal directions, respectively. such domains have been discretized with 512pix/h and seeded with particles with a density of 0.01 particles per pixel. the particles have been randomly distributed in the subdomain and tracked for 10 time steps of the simulations to generate the position in the second frame. snapshots are http://turbulence.pha.jhu.edu/ −4 0 4 y / d −5 0 5 10 15 x/d −4 0 4 y / d −5 0 5 10 15 x/d −5 0 5 10 15 x/d −5 0 5 10 15 x/d −1.5 0.0 1.5 −0.7 0.0 0.7 figure 2: contour maps of instantaneous velocities for fluidic pinball case with upsampling factor fu = 8. top and bottom row denote horizontal and vertical velocity components respectively. from left to right, columns refers to piv, binned ptv, gan prediction and dns reference field. generated with time separation of 1 convective time to reduce correlation between snapshots. in order to obtain a sufficient number of snapshots, data are extracted in subdomains at different locations in the streamwise and spanwise direction. the streamwise and spanwise separation between domains was equal to 2h and 0.25h respectively. a total of 11856 snapshots has been generated, with 10000 of them used for training. the particle images are generated with the same parameters of the previous test case. the interrogation window is set to 64× 64 pixels with 50% overlap. here a relatively large window is selected on purpose to challenge the gans in presence of a modulated input with severe lack of information in the near-wall region. as for the case of the pinball, for this test case, upsampling factors up to 8 have been tested. this corresponds to a gappyness percentage of approximately 8%,47% for fu = 4,8 respectively, while for fu = 2 the percentage of gaps is negligible. 3.2 results for both validation cases, gan performance is assessed in terms of instantaneous visualizations of velocity fields. although complete high-resolution dns data is not used during the training procedure, it is shown for the sake of comparison. moreover, an instantaneous velocity-based squared error is computed for the gan predictions with respect to the dns data. it must be recalled that this error is not the same that has been used during the training, which was referenced with respect to the incomplete high-resolution ptv data. figure 2 reports an instantaneous flow visualization of the fluidic pinball case with upsampling factor fu = 8. it can be observed that in the near-cylinder region the gan performance allows to recover most of the small-scale details. for instance, the vertical-velocity details in the front of the cylinders are perfectly recovered, while this information was barely seen in the piv input field. similar performance is observed in the cylinder wake, where all velocity patterns are recovered. figure 3 shows the same instantaneous velocity visualization for the turbulent channel case with upsampling factor fu = 8. for this case, gan improves the small-scale details with respect to the piv input. it is remarkable the recovery of wall-attached vertical velocity fluctuations in the near-wall region. nonetheless, the comparison between gan prediction and dns reference shows that the smallest-scale details are not perfectly recovered. the instantaneous squared error for the fluidic pinball case is reported in fig. 4. the error is normalized with the bulk displacement (in this case set equal to 1). together with the error for upsampling factors fu = [2,4,8], the original piv error is reported with respect to the dns reference. it is shown that the piv error is significantly larger than in any of the gan predictions, thus proving that the proposed methodology is providing a resolution improvement. this error is more significant in the near-cylinder region, where the velocity shear rate is larger, and the small spatial wavelenght of the shear layers released by the cylinders cannot be capture with the resolution of the original piv analysis. for the gan, it is observed that a fu = 2 is already sufficient to recover with very high accuracy the fluctuations in the developed wake. however, small scale details in the near wake are still missed. with increasing upsampling, the gan progressively recovers also such details, without suffering for quality reduction due to the high level of gappyness of the 0 1 y / h 0 1 2 x/h 0 1 y / h 0 1 2 x/h 0 1 2 x/h 0 1 2 x/h 0.4 0.8 1.2 −0.1 0.0 0.1 figure 3: contour maps of instantaneous velocities for turbulent channel case with upsampling factor fu = 8. top and bottom row denote horizontal and vertical velocity components respectively. from left to right, columns refers to piv, binned ptv, gan prediction and dns reference field. −4 0 4 y / d piv fu = 2 fu = 4 fu = 8 −5 0 5 10 15 x/d −4 0 4 y / d −5 0 5 10 15 x/d −5 0 5 10 15 x/d −5 0 5 10 15 x/d 0.00 0.01 0.00 0.01 figure 4: contour maps of instantaneous error, defined as the squared difference between the dns reference and piv/gan prediction, for fluidic pinball case. top and bottom row denote horizontal and vertical velocity components respectively. from left to right, columns refers to piv, and predictions with fu = [2,4,8]. binned ptv distributions used for training. for the turbulent channel flow case, the instantaneous squared error is shown in fig. 5. for this case, the larger error values are bounded in the near-wall and logarithmic regions. it is observed a clear error reduction between fu = 4 and fu = 2 with respect to the original piv fields. this was expectable, due to the artificially large interrogation window used for piv. however, there is not a clear improvement for case fu = 8 with respect to fu = 4, which confirms the visual inspection of fig. 5. with respect to the difference between wall-normal and streamwise velocity components, it seems that the latter suffers from larger errors. however, this worse performance can be ascribed to the normalization of the data, since the wavelength range present in wall-normal velocities is smaller. in any case, the comparison between the instantaneous error and velocity fields shown in fig. 3 indicates that the error is located in regions with high velocity shear, which points out the interface between highand low-momentum regions. 4 conclusions a novel method to enhance the resolution of piv snapshots based on sparse particle-based measurements has been proposed. the working principle is based on exploiting the ability to retrieve information of the generative adversarial networks. pairs of standard “low-resolution” piv and high-resolution sparse particle-based snapshots are used for the training process, being not necessary to have a complete highresolution field as target. in this study, the high-resolution target is generated naturally by binning the scattered ptv vector distribution on a regular mesh, and withdrawing empty bins during the training. the results show that flow features that are not captured in the piv snapshots can be recovered by the gan 0 1 y / h piv fu = 2 fu = 4 fu = 8 0 1 2 x/h 0 1 y / h 0 1 2 x/h 0 1 2 x/h 0 1 2 x/h 0.00 0.01 0.00 0.01 figure 5: contour maps of instantaneous error scaled with the channel bulk velocity ub, defined as the squared difference between the dns reference and piv/gan prediction, for turbulent channel case. top and bottom row denote horizontal and vertical velocity components respectively. from left to right, columns refers to piv, and predictions with fu = [2,4,8]. through the incomplete projections provided by the ptv. a reasonably good reconstruction error can be achieved even at an upsampling factor fu = 8, which normally corresponds to large levels of gappyness of the binned distributions, with minimal effect of noise or discontinuities in the reconstructed distributions. the results presented here highlight the promising margin of improvement of the spatial resolution of piv using machine learning, without the need of additional high-resolution data for training. acknowledgements this project has received funding from the european research council (erc) under the european union’s horizon 2020 research and innovation programme (grant agreement no 949085). this document reflects only the author’s view and the agency and the commission are not responsible for any use that may be made of the information it contains. references adrian r (1997) dynamic ranges of velocity and spatial resolution of particle image velocimetry. meas sci technol 8:1393 agüera n, cafiero g, astarita t, and discetti s (2016) ensemble 3d ptv for high resolution turbulent statistics. meas sci technol 27:124011 astarita t (2008) analysis of velocity interpolation schemes for image deformation methods in piv. experiments in fluids 45:257–266 cortina-fernández j, sanmiguel vila c, ianiro a, and discetti s (2020) from sparse data to high-resolution fields: ensemble particle modes as a basis for high-resolution flow characterization. exp therm fluid sci 120:110178 cowen e and monismith s (1997) a hybrid digital particle tracking velocimetry technique. experiments in fluids 22:199–211 deng n, noack br, morzyński m, and pastur lr (2020) low-order model for successive bifurcations of the fluidic pinball. journal of fluid mechanics 884:a37 deng z, he c, liu y, and kim kc (2019) super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework. phys fluids 31:125111 fukami k, fukagata k, and taira k (2019) super-resolution reconstruction of turbulent flows with machine learning. j fluid mech 870:106–120 fukami k, fukagata k, and taira k (2021) machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows. j fluid mech 909 gross s and wilber m (2016) training and investigating residual nets. facebook ai research 6:3 hain r and kähler c (2007) fundamentals of multiframe particle image velocimetry (piv). exp fluids 42:575–587 kähler cj, scharnowski s, and cierpka c (2012) on the resolution limit of digital particle image velocimetry. experiments in fluids 52:1629–1639 kim h, kim j, won s, and lee c (2021) unsupervised deep learning for super-resolution reconstruction of turbulence. journal of fluid mechanics 910 ledig c, theis l, huszár f, caballero j, cunningham a, acosta a, aitken a, tejani a, totz j, wang z et al. (2017) photo-realistic single image super-resolution using a generative adversarial network. in proceedings of the ieee conference on computer vision and pattern recognition. pages 4681–4690 li y, perlman e, wan m, yang y, meneveau c, burns r, chen s, szalay a, and eyink g (2008) a public turbulence database cluster and applications to study lagrangian evolution of velocity increments in turbulence. journal of turbulence 9:n31 liu b, tang j, huang h, and lu xy (2020) deep learning methods for super-resolution reconstruction of turbulent flows. phys fluids 32:025105 pope s (2000) turbulent flows. cambridge university press scarano f (2001) iterative image deformation methods in piv. measurement science and technology 13:r1 scharnowski s, hain r, and kähler cj (2012) reynolds stress estimation up to single-pixel resolution using piv-measurements. experiments in fluids 52:985–1002 shi w, caballero j, huszár f, totz j, aitken ap, bishop r, rueckert d, and wang z (2016) real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network. in proceedings of the ieee conference on computer vision and pattern recognition. pages 1874–1883 wang x, yu k, wu s, gu j, liu y, dong c, qiao y, and loy cc (2019) esrgan: enhanced superresolution generative adversarial networks. in l leal-taixé and s roth, editors, computer vision – eccv 2018 workshops. pages 63–79. springer international publishing, cham westerweel j, geelhoed p, and lindken r (2004) single-pixel resolution ensemble correlation for micro-piv applications. exp fluids 37:375–384 introduction methodology piv-tailored gan validation dataset description results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 applications of particle tracking velocimetry to severe nuclear accident experimentation m. johnson1, c. journeau1∗ 1 cea, des, iresne, dtn, smta, leag, cadarache, 13115 saint-paul-lez-durance, france ∗ christophe.journeau@cea.fr abstract experimental research into severe nuclear accidents may entail the discharge of a very high-temperature lava-like molten fuel mixture, corium, either into a pool of less-dense, more-volatile coolant or onto a solid substrate where the corium will spread and cool. in both instances, remote, high-speed video imaging is usually required to interpret these transient interactions and ptv represents a powerful tool for the characterisation of the dynamic properties of discrete melt fragments or distinctive features in the surface of the melt during spreading. nuclear fuel-coolant interactions present particular challenges for ptv analysis as a molten jet and its fragments can exhibit high rates of inter-frame deformation and undergo fragmentation with a relatively high frequency. a ptv algorithm, adapted to these challenges, is presented whereby a user-defined tolerance in the evolution of certain particle properties is used to refine the potential candidate particles prior to particle matching. this candidate refinement step is used to distinguish between acceptable levels of deformation between successive sightings of a given particle, and more substantial changes consistent with fragmentation or coalescence, requiring the tracking of a new particle. implementation of the ptv algorithm is presented for (1) an x-ray video from the fcina-30-1 experiment between a jet of molten stainless steel and liquid sodium, conducted at the jaea’s melt facility, and (2) video imaging of the ve-u9-ceramic experiment of a molten corium-thermite mixture spreading on a zirconium substrate, conducted at the cea’s vulcano facility. the latter case-study enabled the characterization of > 70,000 local velocity vectors at locations corresponding to distinctive temperature heterogeneities in the surface of the spreading melt, providing extensive insight into the spreading dynamics for the validation of corium spreading models. 1 introduction during a hypothetical core disruptive accident (cda) in a nuclear reactor, nuclear fuel and core infrastructure would rapidly melt leading to the relocation of molten core material, a high-temperature lava-like substance referred to as corium. one possible progression of the cda concerns the discharge of coherent jets of molten nuclear fuel through core discharge tubes, designed to reduce reactivity in the core (bertrand et al. (2018)), or control rod guide tubes, to a pool of the less dense, more volatile coolant, leading to a fuelcoolant interaction (fci). this phase of the cda is of interest to nuclear engineers as the fine fragmentation of the molten fuel, sudden destabilisation of vapour films surrounding melt fragments and rapid heat transfer between melt and coolant raises the potential for vapour explosions (berthoud (2000)). a subsequent phenomenon of interest concerns the possibility that the reactor pressure vessel is breached by the high-temperature corium, resulting in corium discharge to the containment floor (dinh et al. (2000); journeau et al. (2003)). under these circumstances it is desirable to promote ex-vessel spreading over a broad surface area to enhance the dissipation of radioactive decay heat and preserve the integrity of the containment building (johnson et al. (2021a)). both of these hypothetical scenarios have been the subject of extensive experimental research. the jaea’s melt facility (matsuba et al. (2016); emura et al. (2019); johnson et al. (2021b)) and cea’s krotos facility (zabiego et al. (2010); tyrpekl et al. (2014)) have been used to investigate fcis for sodium-cooled and water-cooled reactor configurations respectively, using x-ray imaging to visualise the interactions within the optically opaque test vessels (berge et al. (2018); johnson et al. (2021b)). the cea’s vulcano facility has been employed to investigate the discharge of molten corium-thermite mixtures and their subsequent spreading on concrete or ceramic substrates (journeau et al. (2003, 2006); johnson et al. (2021a)). mutliple optical and infra-red cameras are used to observe the progression of the melt during spreading. particle tracking velocimetry (ptv) (crocker and grier (1996); brevis et al. (2011); ohmi and li (2000)) is a powerful tool for the interpretation of images acquired during fci and corium spreading experiments. particle-matching enables analysis of the population of melt fragments without the double counting bias of the multiple sightings of each particle. the estimated velocity of missile fragments and the rate of expansion of vapour clouds could also be used to infer the energetics of fragmentation events. the spreading velocity of an advancing melt front and local velocity distribution similarly provide crucial insight into melt spreading dynamics for the validation of severe accident codes (spindler and veteau (2006); wittmaack (2002)). each type of experiment presents unique challenges for ptv analysis. the hydrodynamic pre-mixing of a molten metallic jet in a less dense fluid represents a complex three-dimensional transient interaction, captured by a single two-dimensional projection of the attenuated fan-beam x-ray source. the interaction occurs within a timescale of a few seconds, during which the particle population evolves significantly. a fragmentation event generates multiple potential candidate particles in close proximity, the new trajectories of which may either be tracked as a continuation of the original particle or characterized as new particles depending on the rigidity particle-matching criteria. coalescence events present similar complications, particularly as these can be difficult to distinguish from quasi-coalescence whereby distinct particles temporarily by-pass each other at different depths in the x-ray photon path. different fci experimental facilities generate x-ray images with frame rates ranging from 100–1000 fps (zabiego et al. (2010); emura et al. (2019); johnson et al. (2021b)) and the size of imaging fields of view vary significantly, requiring that the ptv algorithm tolerates a wide range of particle densities and offers flexibility in the particle matching criteria to account for the different rates of inter-frame particle deformation. a ptv algorithm is presented whereby candidate particle pairings are assessed in terms of a weighted similarity index enabling the rejection of candidate particles of insufficient likeness to the paired sighting prior to particle matching. the application of this ptv approach is demonstrated for (1) the fcina-30-1 fci experiment (johnson et al. (2021b)) between a jet of molten steel and liquid sodium, performed at the melt facility, and (2) the ve-u9-ceramic experiment (johnson et al. (2021a)) of a corium-thermite melt spreading on a zirconium substrate, performed at the vulcano facility. 2 experimental methods 2.1 fuel-coolant interaction experiments fci experimental facilities, such as krotos and melt, consist, in simplest terms, of a crucible for the melting of metal and metal oxide nuclear fuel analogues, a funnel to discharge the melt as a coherent jet, a test section containing a pool of liquid coolant, and a radiographic imaging system to visualise the interaction within the optically opaque environment. to demonstrate the application of ptv to fci experimental images, the fcina-30-1 experiment (johnson et al. (2021b)) conducted at the jaea’s melt facility (matsuba et al. (2016); emura et al. (2019)) will be investigated. this experiment was conducted between a jet of molten stainless steel and a pool of sodium coolant. a detailed explanation of the melt facility and experimental procedure can be found in johnson et al. (2021b). the radiographic images were acquired at a frame rate of 1000 fps for a field of view in the order of ∼ 12cm in diameter (johnson et al. (2021b)). this fci research at the melt facility was performed under the framework of the current implementing arrangement of the france-japan collaboration on sodium-cooled fast reactors (sfrs) from 2020 to 2024. 2.2 ex-vessel corium spreading experiments the vulcano facility consists of a zirconium crucible with a discharge tube at its base, suspended above a spreading test section with boundary walls which diverge at an angle of 9.5°. the ve-u9 spreading tests discharge a ≈ 30kg molten corium-thermite mixture to spreading test sections with either a ceramic zirconium or sacrificial concrete substrate. the spreading is imaged from multiple perspectives using optical and infrared cameras stored in protective housings. complete details of the experimental procedure are presented in johnson et al. (2021a). figure 1: flow chart for the ptv algorithm. 2.3 image processing and analysis the images generated during fci and ex-vessel spreading experiments are processed and subsequently analysed using spectra (software for phase extraction and corium tracking analysis), a cea image analysis software developed using matlab 2021a (mathworks, usa) (johnson et al. (2021b)). spectra is used to (1) clean the images of artefacts, such as additive white noise, lens distortion and vignetting, (2) extract objects of interest for analysis, and (3) perform quantitative characterization of the detected objects, including the implementation of tracking by ptv. 2.3.1 particle tracking velocimetry the ptv framework implemented in spectra, presented as a flow chart in figure 1, is based on the algorithm proposed in crocker and grier (1996) for images of colloidal particles but uses an alternative approach for particle matching more specific to the requirements of fci experimental images. the objective of the alternative particle matching routine is to allow the user to define bespoke, video-specific criteria to distinguish minor particle deformations from more significant fragmentation or coalescence events which constitute the formation of a new particle. following image pre-processing and segmentation, all detected particle sightings are identified, labelled and characterized according to k digital particle properties, not limited to the centroid, area, perimeter, caliper dimensions, orientation, mean and maximum intensity, aspect ratio and circularity. the ptv algorithm proceeds with the pre-selection of candidate particles, which is performed by distance thresholding. the centroid coordinates of j candidate particles in frame i+ 1 (xi+1, j) will have an euclidean distance from a particle centroid in frame i of less than a defined maximum displacement, r, (ohmi and li (2000)) therefore satisfying the inequality: |xi+1, j− xi| ≤ r (1) candidate particle assessment is performed using the k properties of each digital particle. the corresponding kth property of the current frame particle and the j candidate particles are labelled yi,k and yi+1, j,k respectively. each property is assigned a weighting coefficient, ωk, to refine the array of particle properties to a single coefficient called a weighted similarity index, wsi, calculated according to eq. 2: wsi = 1 ∑ k k=1 ωk k ∑ k=1 ωk |yi,k− yi+1, j,k| yi,k ≤mwsi (2) the wsi diminishes with increased likeness between the current frame and candidate particle. if only a single property, such as the area, is assigned a non-zero weighting coefficient, the wsi represents the percentage change in that property between consecutive video frames, normalised by a factor of 100. the candidate particles are refined by eliminating those with a wsi greater than a threshold maximum weighted similarity index, mwsi. the mwsi defines an acceptable tolerance in the evolution in particle properties between consecutive frames. this mwsi coefficient should be set to allow for sufficient tolerance in both the real particle deformation between frames and the more artificial uncertainties in particle detection and characterization due to imaging artefacts. the candidate particle assessment and refinement steps can be performed iteratively using different ωk and mwsi values to eliminate candidate particles which fail to satisfy alternative similarity criteria. the remaining candidate particles, which have satisfied the requisite conditions of proximity and physical likeness, proceed to the particle matching stage. the current frame particle and candidate particle pair (a) (b) (c) figure 2: (a) an example x-ray image from the fcina-30-1 experiment (reproduced from johnson et al. (2021b)), (b) the same image following pre-processing and melt segmentation, cropped to a region of interest, and (c) a semi-transparent overlay of (b) and the subsequent frame with the centroids indicated as red circles (current frame) and blue crosses (subsequent frame). with the lowest wsi are assigned the same particle number and are subsequently removed from alternative candidate particle pairings. the process is repeated until no valid particle pairs remain within the two images under consideration. the algorithm repeats this process for the subsequent image pairs. on completion of the particle matching and labelling process, unlabelled particles and particles which present with fewer than the desired minimum sightings, are removed. particles are then renumbered sequentially, if preceding particle numbers have been eliminated, and the characterization data is sorted by ascending particle number and then by frame number. the final stage requires the estimation of velocity vectors. in most cases the velocity vectors are determined from the euclidean displacement of the centroid, or intensity weighted centroid, normalised by the frame interval. for objects cropped at the image border, such as a molten jet entering the imaging window from above, the centroid displacement does not provide an accurate measure of the trajectory. for these border objects, the compass points of a rectangular bounding box around the object are defined and the displacement of the coordinates opposite the cropped boundary (i.e. the southern coordinate of the bounding box for objects entering from the top of the image) are used to estimate the particle trajectory. 3 results and discussion 3.1 fuel-coolant interactions an example x-ray image from the fcina-30-1 experiment, reproduced from johnson et al. (2021b), is presented in figure 2a. the image suffers from some common x-ray imaging artefacts, such as loss of intensity towards the image border (vignetting) and considerable additive white noise. the images are denoised in two stages using a spatiotemporal video-block matching and 3d filter, v-bm3d, (danielyan et al. (2012)), followed by a non-local means, nlm, (buades et al. (2005)) filter to remove residual noise. the images are then normalised by a clean flat field image, acquired from the averaged frames prior to the arrival of the melt jet, and corrected for pincushion distortion. the pre-processed images are then dynamically thresholded and cropped to a region of interest below the initial surface of the sodium pool and within an internal cylinder within the test section. application of this image pre-processing and segmentation routine to the image in figure 2a generates the image in figure 2b. a compound image of the melt fragments in figure 2b with a semi-transparent overlay of those observed in the subsequent frame, with their centroids shown as red circles and blue plus signs respectively, is presented in figure 2c. these image data have a number of advantageous qualities for exploitation by ptv. the images are (a) (b) figure 3: (a) the segmented image from figure 2b overlaid with velocity vectors revealing the complete trajectories of each particle, and (b) a chronological montage of all sightings of the coherent jet (particle 79) prior to its fragmentation. high in resolution giving a relatively low particle density of ∼ 10−5 pixel−1. the particles are macroscopic, morphologically distinctive, and are often relatively simple to distinguish. the high frame rate dictates a relatively low inter-frame particle displacement, often significantly smaller than the particle dimensions, and so particle pairings are typically self-evident. the complexity in applying ptv arises from (1) high rates of particle deformation due their molten nature, (2) a high frequency of particle division and coalescence, (3) apparent or quasi-coalescence due to the flattening of the depth field in the 2d image projection, (4) the partial or total obscuration of some particles by vapour clouds, (5) the possible detection of false particles due to the significant additive white noise in the raw images, and (6) the fact that the interaction extends beyond the limits of the field of view, thereby cropping many sightings at the image border. figure 2c identifies seven distinct first frame melt sightings, with eight sightings observed in the subsequent frame. of the seven first frame particle sightings, two are cropped at the image border, entering and leaving the imaging window respectively, four sightings appear to coalesce to form two particles in the subsequent frame, one particle fragments into two daughter particles of similar dimensions, and two sightings in the second frame appear to be false particles detected due to the image noise. for these x-ray projections of melt fragments, the intensity profile of the particle is proportional to the particle dimension, or chord length, parallel to the photon flux (macovski (1983)), thus, small particles may present with a very low signal to noise ratio. despite the implementation of powerful image denoising filters, the detection of sub-millimetre particles will generally necessitate the detection of some false particles, corresponding to small pockets of residual noise. since these false particles present at random spatiotemporal locations, rather than in close proximity to previous sightings, an initial iteration of the ptv algorithm with a conservative (relatively large) maximum displacement and a minimum sightings threshold of at least 2 will eliminate the majority of false particles. these false particles can be effaced from the video in a ptv-segmentation step, prior to a second, more precise iteration of the ptv algorithm with more stringent tracking parameters. coupling the conventional intensity and size based thresholding of image segmentation with the distance and similarity thresholding of this ptv-segmentation step to eliminate false particles can thereby enable particle detection at a reduced signal to noise ratio. implementation of the ptv algorithm with a maximum displacement of 50 pixel and a minimum sightings threshold of 2, with no similarity threshold (mwsi→ ∞), eliminates 1398 false particles from the population of 10422. refining the tracking parameters to a maximum displacement of 35 pixel, allowing for a 20 % tolerance in the change in particle area between successive frames (this tolerance is relaxed for objects entering and leaving the imaging window) and a minimum sightings threshold of 5 identifies 338 particles with 4547 sightings. thus, roughly half the total number of objects detected in the video correspond to long-life particles presenting with, on average, 13 sightings per particle. all of the velocity vectors corresponding to the 7 particles observed in figure 2b, and one additional particle (particle 106) produced following a quasi-coalescence involving particle 76, are presented, overlaid on the segmented image, in figure 3a. the tracking history of particles 68 and 76 reveals a shared origin which implies particle 68 to be a daughter particle following the fragmentation of particle 76. the most interesting observation from figure 3a concerns the sudden reversal in the trajectory of particle 106 close to the bottom left corner of the image. closer inspection of the video revealed that the particle in question experiences an elastic collision with a thermocouple installed on the steel support rod observed in the left hand side of figure 2a. the elastic collision not only infers solid-like behaviour, confirming the formation of a solid outer crust at the melt-coolant interface, but indicates that within 90 ms of contact with the coolant, the melt crust grows to a sufficient thickness to withstand a ≈0.9 ms−1 collision with the thermocouple without fracturing. figure 3b presents a chronological montage of all sightings of particle 79, the coherent melt jet, prior to its fracture. the morphology of the jet similarly exhibits solid-like qualities within ≈ 20ms of contact with the sodium. after around 40 ms of entering the imaging window, the jet spans the height of the imaging window. while the ptv algorithm continues to recognise the image spanning jet as the same particle, the characterization of the velocity vectors ceases to function for the image-spanning sightings since the centroid, intensity weighted centroid and the coordinates of the bounding box all become misleadingly static and fail to accurately capture the inter-frame displacement. for objects which span the length of the imaging window an alternative method will be required for the spatial cross-correlation of adjacent sightings to determine the particle trajectory. a normalized 2d cross-correlation (lewis (1995)) approach is currently being implemented in spectra for the determination of the trajectories of these selected image spanning particles. 3.2 ex-vessel spreading figure 4a presents an example image from the ve-u9-ceramic melt spreading experiment (johnson et al. (2021a)). the melt is segmented from each image by dynamic thresholding and a mask of the spreading section floor is used to refine the melt to its footprint. corners of the squares in the checkerboard image in figure 4b are defined as control points, used to generate a transform function to correct the camera perspective to a bird’s-eye view of the melt. the product of these segmentation and transformation steps is presented in figure 4c. application of ptv to the melt footprint in figure 4c enables characterization of the velocity of the advancing melt front as presented in johnson et al. (2021a), however this provides only limited insight into the spreading dynamics. the melt surface appears highly heterogeneous in temperature, providing a distinctive pattern in the melt luminosity. convolution of the image with an 11× 11 pixel laplacian of gaussian (log) operator with a standard deviation of 2, highlights the features with a significant change in local luminosity, corresponding mainly to the outer melt contour and a series of local heterogeneities in the melt surface temperature, generally features of reduced luminosity implying cold-spots, as presented in figure 4d. size thresholding of the features to retain those comprised of 5-50 pixels isolates the localised cold-spots from the larger features. ptv is employed to track these surface features and reveal the evolution of the local surface velocity distribution with time and space. application of the log edge detection and size thresholding to the ve-u9-ceramic experimental images revealed a total of 96755 surface features. modeling of the ve-u9 spreading dynamics in johnson et al. (2021c) predicted surface velocities of up to around 0.25 ms−1. the maximum velocity, combined with a pixel resolution in the transformed image of around 1.6 mm and a frame rate of 50 fps, dictates that local surface features are unlikely to move more than 4 pixel between consecutive frames. this implies that many features will exhibit displacements of less than a pixel and so velocity vectors will need to be averaged over multiple frames for accurate representation. the ptv algorithm was employed with a maximum displacement of 6 pixel, allowing for a 20 % change in the area and mean intensity of features between consecutive frames, and a minimum sightings threshold of 5. a total of 71527 sightings were found for 4534 distinct features, enabling the characterization of local velocity vectors at 74 % of the locations where surface temperature heterogeneities were detected. the instantaneous local velocities are averaged over five frames (or 0.1 s intervals) to smooth the data and to detect sub-pixel displacements. the local velocities are presented for the frames at 2 and 5.7 s after the initial melt discharge to the spreading section in figures 4e and f respectively. while a maximum velocity, parallel to the principal flow direction, vx, was found to be 0.45 ms−1, 98 % of the velocity vectors in the principal (a) (b) (c) (d) 0.1 m/s (e) 0.1 m/s (f) figure 4: images of (a) corium-thermite spreading on a zirconium substrate during the ve-u9-ceramic test, (b) a checkerboard calibration image of 5× 5cm squares, (c) the segmented melt from (a), transformed to a birds-eye perspective, (d) a laplacian of gaussian transform of (c) revealing the melt contour and temperature heterogeneities in the melt surface, and (e-f) quiver plots of the ptv-determined velocity vectors after (e) 2 s and (f) 5.7 s; the images in (c-f) correspond to dimensions of 830×340mm. flow direction were less than 0.23 ms−1, which demonstrates good agreement with theoretical predictions from johnson et al. (2021c). 4 conclusions experimentation in the field of severe nuclear accident research often requires remote video imaging of hightemperature transient interactions. ptv represents a very powerful tool for the analysis of (1) radiographic images acquired during investigations of molten fuel-coolant interactions, and (2) optical and infrared images acquired of ex-vessel melt spreading. fuel-coolant interactions present particular challenges for ptv analysis as the molten fuel exhibits high rates of deformation and a high frequency of fragmentation. a bespoke ptv algorithm is presented whereby candidate particles are refined by user-defined similarity criteria prior to particle matching, enabling the distinction between the tolerable deformation of a molten fuel droplet and a more significant fragmentation event which constitutes the formation of new particles. application of the ptv algorithm to the fcina-30-1 fuel-coolant interaction experiment (johnson et al. (2021b)) between molten stainless steel and liquid sodium enabled the detection of 338 relatively long-life particles presenting with an average of 13 sightings each. one melt particle presented with a sudden reversal in its trajectory which revealed an elastic collision with a thermocouple installed within the test section. this distinctly solid-like behavior confirms that within 90 ms of first contact with the liquid sodium, the steel formed a solid crust at the melt-coolant interface of sufficient thickness to withstand a 0.9 ms−1 collision with the thermocouple, implying a crude lower limit for the rate of crust growth. certain of the tracked particles, representing large melt jet fragments with strong evidence of a frozen outer shell, spanned the height of the imaging window and inhibited the characterisation of velocity through the displacement of the centroid or the leading front. the ptv algorithm will require an alternative cross-correlation technique to estimate the motion of objects with dimensions greater than the field of view. a second application of the ptv algorithm to images acquired during the ve-u9-ceramic spreading test (johnson et al. (2021a)) enabled the tracking of distinctive surface temperature heterogeneities, or cold-spots, in the molten corium-thermite mixture during its spreading on a ceramic substrate. this enabled the characterisation of over 70,000 local velocities during the ≈ 10s spreading test, providing extensive data for the validation of ex-vessel corium spreading simulations. acknowledgements the authors would like to thank the jaea, in particular everybody from the melt team, for sharing their fcina-30-1 experimental data under the france-japan collaboration on the sfr severe accident studies. we also wish to thank mitsubishi heavy industries for their financing of the ve-u9 spreading tests in collaboration with the cea, and the cea’s plinius team for their management of the vulcano facility during the ve-u9 tests. references berge l, estre n, tisseur d, payan e, eck d, bouyer v, cassiaut-louis n, journeau c, tellier rl, singh s, and pluyette e (2018) fast high-energy x-ray imaging for severe accidents experiments on the future plinius-2 platform. ieee transactions on nuclear science 65:2573–2581 berthoud g (2000) vapor explosions. annual review of fluid mechanics 32:573–611 bertrand f, marie n, bachrata a, brun-magaud v, droin j, manchon x, herbreteau k, farges b, carluec b, poumerouly s, and lemasson d (2018) status of severe accident studies at the end of the conceptual design of astrid: feedback on mitigation features. nuclear engineering and design 326:55–64 brevis w, niño y, and jirka gh (2011) integrating cross-correlation and relaxation algorithms for particle tracking velocimetry. experiments in fluids 50:135–147 buades a, coll b, and morel jm (2005) a review of image denoising algorithms, with a new one. multiscale modeling simulation 4:490–530 crocker jc and grier dg (1996) methods of digital video microscopy for colloidal studies. journal of colloid and interface science 179:298–310 danielyan a, katkovnik v, and egiazarian k (2012) bm3d frames and variational image deblurring. ieee transactions on image processing 21:1715–1728 dinh tn, konovalikhin mj, and sehgal br (2000) core melt spreading on a reactor containment floor. progress in nuclear energy 36:405–468 emura y, isozaki m, matsuba k, and kamiyama k (2019) penetration behavior of molten stainless steel into a sodium pool. in proceedings of the 24th national symposium on power and energy systems (spes 2019). page 583 johnson m, denoix a, bouyer v, goda h, kamohara ss, takeuchi j, brissonneau l, and journeau c (2021a) high-temperature ex-vessel corium spreading. part 1: experimental investigations on ceramic and sacrificial concrete substrates. submitted to journal of nuclear science and technology johnson m, journeau c, matsuba k, emura y, and kamiyama k (2021b) characterization of hightemperature nuclear fuel-coolant interactions through x-ray visualization and image processing. annals of nuclear energy 151:107881 johnson m, schiano t, denoix a, bouyer v, and journeau c (2021c) high-temperature ex-vessel corium spreading. part 2: scaling principles for gravity-viscous spreading with slip at the melt-substrate interface. submitted to journal of nuclear science and technology journeau c, boccaccio e, brayer c, cognet g, françois haquet j, jégou c, piluso p, and monerris j (2003) ex-vessel corium spreading : results from the vulcano spreading tests. nuclear engineering and design 223:75–102 journeau c, haquet jf, spindler b, spengler c, and foit j (2006) the vulcano ve-u7 corium spreading benchmark. progress in nuclear energy 48:215–234 lewis jp (1995) fast template matching. in vision interface. pages 120–123 macovski a (1983) medical imaging systems. prentice-hall. 1st edition matsuba ki, isozaki m, kamiyama k, and tobita y (2016) distance for fragmentation of a simulated molten-core material discharged into a sodium pool. journal of nuclear science and technology 53:707– 712 ohmi k and li hy (2000) particle-tracking velocimetry with new algorithms. measurement science and technology 11:603–616 spindler b and veteau jm (2006) the simulation of melt spreading with thema code part 1 : model assessment strategy and assessment against analytical and numerical solutions. nuclear engineering and design 236:415–424 tyrpekl v, piluso p, bakardjieva s, and dugne o (2014) material effect in the nuclear fuel-coolant interaction: analyses of prototypic melt fragmentation and solidification in the krotos facility. nuclear technology 186:229–240 wittmaack r (2002) simulation of free-surface flows with heat transfer and phase transitions and application to corium spreading in the epr. nuclear technology 137:194–212 zabiego m, brayer c, grishchenko d, baptiste dajon j, fouquart p, bullado y, compagnon f, correggio p, françois haquet j, and piluso p (2010) the krotos kfc and serena/ks1 tests: experimental results and mc3d calculations. pages 1–11 introduction experimental methods fuel-coolant interaction experiments ex-vessel corium spreading experiments image processing and analysis particle tracking velocimetry results and discussion fuel-coolant interactions ex-vessel spreading conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 unsupervised recurrent all-pairs field transforms for particle image-velocimetry c. lagemann1∗, m. klaas1, w. schröder1 1 rwth aachen university, chair of fluid mechanics and institute of aerodynamics, aachen, germany ∗ c.lagemann@aia.rwth-aachen.de abstract convolutional neural networks have been successfully used in a variety of tasks and recently have been adapted to improve processing steps in particle-image velocimetry (piv). recurrent all-pairs fields transforms (raft) as an optical flow estimation backbone achieve a new state-of-the-art accuracy on public synthetic piv datasets, generalize well to unknown real-world experimental data, and allow a significantly higher spatial resolution compared to state-of-the-art piv algorithms based on cross-correlation methods. however, the huge diversity in dynamic flows and varying particle image conditions require piv processing schemes to have high generalization capabilities to unseen flow and lighting conditions. if these conditions vary strongly compared to the synthetic training data, the performance of fully supervised learning based piv tools might degrade. to tackle these issues, our training procedure is augmented by an unsupervised learning paradigm which remedy the need of a general synthetic dataset and theoretically boosts the inference capability of a deep learning model in a way being more relevant to challenging real-world experimental data. therefore, we propose uraft-piv, an unsupervised deep neural network architecture for optical flow estimation in piv applications and show that our combination of state-of-the-art deep learning pipelines and unsupervised learning achieves a new state-of-the-art accuracy for unsupervised piv networks while performing similar to supervisedly trained liteflownet based competitors. furthermore, we show that uraft-piv also performs well under more challenging flow field and image conditions such as low particle density and changing light conditions and demonstrate its generalization capability based on an outof-the-box application to real-world experimental data. our tests also suggest that current state-of-the-art loss functions might be a limiting factor for the performance of unsupervised optical flow estimation. 1 introduction particle-image velocimetry (piv) is one of the key techniques in modern experimental fluid mechanics used to determine the velocity components of flow fields in a wide range of complex engineering problems. current processing tools usually compute the most probable particle displacement of two consecutive particle images based on the cross-correlation between corresponding interrogation windows. this, in fact, always yields a spatially averaged optical flow output since a single displacement vector is estimated for an entire interrogation window. state-of-the-art algorithms additionally use a wide range of other elements including subpixel interpolation, multigrid correlation schemes, automatic outlier detection, and window deformation according to local velocity gradients. usually, these approaches fully compensate for the loss-of-correlation due to in-plane motion if the flow within the final interrogation window is homogeneous or linearly varying. however, if the displacement is more complex due to unresolved fluctuations, non-constant velocity gradients, or out-of-plane displacement, the correlation peak is broadened and its intensity is reduced.the estimated mean field matches the ground truth fairly well, but velocity fluctuations are usually underestimated. a similar bias error can be observed in cases of inhomogeneously distributed tracer particles which is typical for near-wall flows. motivated by the limitations of current, cross-correlation based approaches, piv analysis based on new ideas of deep learning in end-to-end optical flow applications was proposed to effectively learn dense displacement fields going far beyond the spatial resolution of the current gold-standard. in contrast to existing methods, these approaches are general, near-automated, and yield per-pixel flow estimates. these methods side-step the problem of manually designing an analytical pipeline by defining an end-to-end network whose output is the dense per-pixel optical flow field. thus, fine flow structures can be resolved which alternatively are smoothed due to the spatial averaging inherent to traditional cross-correlation based methods. the first end-to-end application using cnns for piv processing was introduced in rabault et al. (2017). they trained different shallow convolutional and fully connected neural networks to predict the particle displacement of various synthetic test cases. however, the proposed networks were only applied to relatively simple test flows and ultimately did not achieve a competitive accuracy compared to available state-of-theart piv algorithms. a different evaluation scheme called piv-dcnn was proposed in lee et al. (2017). it consisted of a four-level regression convolutional neural network where each level was trained to predict a velocity vector from two input image patches. the network was verified to achieve similar results compared to standard piv methods based on a single cross-correlation pass including window deformation. due to its stacked architecture, piv-dcnn suffers from large computational cost and low efficiency. in cai et al. (2019b) a dense particle motion estimator was developed, piv-flownets, which was mainly based on flownet, a deep optical flow architecture introduced in dosovitskiy et al. (2015). this motion estimator extracts feature maps of particle images and predicts a dense displacement field for synthetic and experimental particle images. it achieves a good accuracy with a higher spatial resolution compared to standard correlation-based piv algorithms. follow-up work adopted an advanced liteflownet architecture proposed in hui et al. (2018) which allowed to significantly improve the accuracy. recently, a new piv processing network called raft-piv was presented in lagemann et al. (2021) outperforming existing neural based piv methods significantly. the underpinning optical flow backbone of this approach are recurrent all-pairs field transforms (raft) proposed in teed and deng (2020). raft differs from other optical flow networks in that it operates at a single resolution using a large number of lightweight, recurrent update operators. first empirical results demonstrate clear improvements of raftpiv on challenging synthetic benchmark and experimental examples, relative to both classical approaches and existing optical flow learners. all these approaches share the main idea of using supervised training on labeled synthetic piv images. however, supervised learning of robust optical flow estimation requires a sufficiently large dataset of training images alongside ground truth optical flow information. the computation of reliable ground truth data for real image sequences within a reasonable time is almost impossible yielding invevitably the generation of synthetic datasets. however, the huge diversity in fluid flows and varying particle image conditions in experimental environments probably outmatch the data distribution which can be covered by artificially rendered piv images resulting in an inherent distribution mismatch between training and test time domain. one potential solution to tackle this mismatch is the application of an unsupervised loss objective. in general, unsupervised learning paradigms have a major advantage since the loss objective is purely based on geometric penalty terms and hence, no ground-truth is required. as a consequence, unsupervised networks can be trained directly on real experimental data and therefore, might remedy the need of a general synthetic dataset while boosting the inference capability of a deep learning model such that the neural method can deal with arbitrary challenging real-world experimental data. first, zhang and piggott (2020) exploited the unsupervised loss formulation of meister et al. (2017) and extended their unsupervised learning strategy to piv application using a liteflownet network design. their loss consists of a photometric loss between two consecutive image frames, a consistency loss in bidirectional flow estimates, and a spatial smoothness loss. it is demonstrated that this method achieves competitive results compared to classical piv algorithms and supervised architectures. however, a comprehensive application to various real-world experimental data is still missing. therefore, we study the effectiveness of unsupervised learning paradigms in the context of raft-piv and introduce an unsupervised raft model denoted uraft-piv. 2 method the baseline model of our approach is raft-piv introduced in lagemann et al. (2021). similar to the original architecture, raft-piv extracts per-pixel features, computes a 4 level multi-scale correlation volume for all pairs of pixels, and iteratively updates a flow field using a convolutional gated recurrent unit. details can be found in teed and deng (2020). compared to other optical flow networks, it is unique in the sense that it operates at a single resolution using a large number of lightweight, recurrent update operators. given a pair of grayscale particle images, i1,i2, optical flow estimation requires to predict a dense displacement field (f1, f2) mapping each pixel of i1 to its corresponding coordinates in i2. raft mainly backward flow 1st frame 2nd frame optical flow warp photometric loss smoothness loss 2nd frame 1st frame optical flow warp photometric loss smoothness loss consistency loss warp forward flow (i) (ii) (iii) (iv) (v) (i) (ii) (iii) (iv) (v) figure 1: schematic visualization of uraft-piv and its main components: a shared feature encoder (i) extracts per-pixel features from both input images. based on the all-pairs correlation (ii) a 4d correlation volume is computed and subsequently stacked to form a correlation pyramid (iii) by pooling the last two dimensions from level to level. the context encoder (iv) sharing the topology of the feature encoder computes a context map of the first image frame. the convolutional gru (v) takes context map and correlation volume as input and recurrently updates the optical flow estimation. the loss objective of uraft-piv comprises a photometric, forward/backward consistent, and smoothness oriented penalty term. the photometric loss penalizes the photometric difference between the initial and the subsequent image which is warped according to the local flow prediction. an individual forward and backward flow is estimated by reversing the order of the input images. the consistency loss penalizes differences between forward and backward flow. finally, a smoothness penalty term is applied to forward and backward flow separately. consists of three stages, a feature extracting block, the computation of a full correlation volume between all pairs, and iterative updates based on a convolutional gated recurrent unit (conv gru). a schematic visualization of uraft-piv can be found in fig. 1. furthermore, we introduced a cost volume normalization and waive the spatial downsampling within the feature extraction block. this allows a state-of-the-art performance while showing a strong generalization ability in direct real world applications. to achieve an unsupervised learning scheme, we apply a loss objective which comprises photometric, forward/backward consistent, and smoothness oriented penalty terms. the photometric loss encourages the optical flow network to align image patterns by penalizing the photometric difference between the initial and the subsequent image which is warped according to the local flow prediction. in fact, a bi-directional photometric loss based on the generalized charbonnier loss is used which simply can be achieved reversing the order of the input data. thus, an individual forward and backward flow is estimated. to account for occluded pixels, which by definition do not have a valid counterpart in the other image, we compute an occlusion mask based on a forward/backward flow check. the consistency loss penalizes differences between forward and backward flow, again applying a generalized formulation of the charbonnier loss to the difference between forward and backward flow. to address the aperture problem, e.g., motion estimation of regions with insufficient image structure as present in sections in-between particles, we apply an edge-aware first-order accurate smoothness function to forward and backward flow. extensive hyperparameter studies are performed to identify proper weights for the specific objective penalty terms. furthermore, the loss of each optical flow iteration is weighted exponentially forming the final sequence loss. the sequence loss reads l = n ∑ i=1 γ n−i (li photo +li con +li smooth ) (1) where li photo,l i con,l i smooth denote the photometric, forward/backward consistent, and smoothness oriented penalty term of the iteration i and γ is the exponential weight. similar to teed and deng (2020), we choose γ = 0.8. the evaluation metric is the averaged endpoint error (aee) representing the euclidean distance between the final estimated (es) of the n-th iteration and ground truth (gt) optical flow of the test case being averaged over all pixels and reads aee = ‖fes,n− fgt‖1. (2) the computational graph of uraft-piv is implemented in the open source framework pytorch (paszke et al. (2017)). during training, we apply an adam-optimizer (kingma and ba (2014)) starting at an initial learning rate ε0 = 0.0001. furthermore, the learning rate is reduced by a factor of five once the evaluation metrics stopped improving for 15 consecutive epochs. the minimum learning rate is set to εmin = 10−8. all computations are run on multiple gpu nodes simultaneously each equipped with four nvidia a100. we compare the test results of uraft-piv to our state-of-the-art inhouse code pascalpiv. to allow particle shifts greater than half the interrogation window size, the image evaluation uses a multi-grid approach with integer window shift to get an initial displacement field. then, the displacement field is refined using an iterative predictor-corrector scheme with subpixel accurate image deformation according to the procedure described in astarita and cardone (2005). the initial displacement is interpolated for each pixel of the image using a third-order b-spline interpolation. both images are deformed by half the displacement to get a second-order accurate estimate of the displacement field. the image interpolation uses lanczos resampling , i.e., lanczos windowed cardinal sine interpolation, incorporating the neighboring 8× 8px2. an integral velocity predictor is used to ensure convergence of the iterative scheme (schrijer and scarano (2008)). hence, the predictor is the weighted average of the per-pixel displacement over the interrogation window. the corrector is determined by evaluating the cross-correlation function between both exposures with a 3-point gaussian peak estimator (raffel et al. (2018)). the initial window size for the multi-grid evaluation is 128× 128px2 and the window size used for the iterative piv evaluation is 32× 32px2 with 75% overlap. the windows of the iterative piv evaluation are weighted by a gaussian window with σ= 0.4. between the iterations, outliers in the vector field are detected using a normalized median test and are replaced by interpolated values. a total of three multi-grid steps and five steps of the iterative evaluation are performed. 3 results in this section, we highlight the performance of uraft-piv based on two learning tasks representing different image and flow conditions. during the first task, we trained the network on a synthetic particle image dataset consisting of five categories which was introduced in cai et al. (2019b). while this data is interesting and serves as a benchmark, we note that experimental images barely achieve this idealised quality in realistic piv experiments. as a result, inference runs of networks trained on this dataset hardly predict correct displacements for real-world measurements, likely due to the strong mismatch between training and test time distribution. to study the performance using images like those obtained in many real-world applications, we trained our network of the second learning task on a more realistic dataset introduced in lagemann et al. (2021) and compare inference results of uraft-piv on synthetic and experimental piv images to neural piv processing competitors and our cross-correlation based algorithm pascalpiv. 3.1 learning task i: idealised piv database the networks were trained on synthetic particle image datasets consisting of five categories representing well-known and realistic flow cases: (1) direct numerical simulations (dns) of isotropic turbulence; (2) flows along a backward facing step; (3) two-dimensional flows past a cylinder; (4) dns of a turbulent channel flow; and (5) simulations of a sea surface flow driven by a surface-quasi-geostrophic (sqg) model. this data is from a public database and is used to benchmark neural piv processing methods. in total, the resource contains 15,050 particle image pairs with corresponding ground truth flow fields and is divided into 12,000 training and 3,050 test images across all flow categories. further characteristics include a very high particle density, a maximum particle displacement of±10px, and particle peak intensities ranging from 200 to 255 counts within an 8-bit grayscale resembling images in perfect experimental conditions. details can be found in cai et al. (2019b). table 1 illustrates inference results on the test dataset of learning task i for various neural network and cross-correlation based piv processing methods. in the context of unsupervised learning, uraft-piv can outperform its liteflownet based competitor in all test cases and achieves a slightly higher error compared to the supervised piv-liteflownet-en proving the effectiveness of this learning paradigma. however, it cannot match the performance of its supervised counterpart raft32-piv, most likely due the simple but yet effective supervised loss objective which is based on the l1-norm between ground truth and optical flow estimation. in contrast, the unsupervised loss of uraft-piv is entirely based on geometric penalty terms including a photometric, forward/backward consistency and smoothness oriented loss. we note that networks solely trained on photometric differences tend to predict highly inconsistent displacement fields which are mainly characterized by local extrema in the neighborhood of image patterns while regions of less visual image texture do not contribute to the optical flow estimation. considering the fact that optical flow estimators aim at matching extracted image features between subsequent images rather than learning the most probable, physical displacement which in fact is not possible, a single photometric loss will not necessarily converge to the physically correct minimum. in this light, piv images pose an even greater challenge on unsuspervised optical flow networks since they contain many, but tiny and almost identical image features the particles and hence, provide similar image patterns within the local neighborhood impeding the prediction of the physical correct displacement. from a high-level perspective, smoothness oriented losses target this ambiguity since they penalize the prediction of strong gradients and encourage colinearity of neighboring flows to achieve a more effective regularization. however, this also means that displacement fields characterized by physically correct, strong gradients are usually underestimated resulting in higher error values. to illustrate this drawback, fig. 2 compares the ground-truth and predictions of supervised and unsupervised networks for two flow fields sideby-side. especially in gradient dominated flows, uraft-piv under-/overestimates the local displacement compared to its supervised counterpart since the unsupervised loss objective encourages the network to regularize the optical flow. as a result, the endpoint error of uraft-piv is one order of magnitude higher methods back-step cylinder jhtdb channel dns turbulence sqg widim [1] 3.4 8.3 8.4 30.4 45.7 hs optical flow [1] 4.5 7.0 6.9 52.5 15.6 pivnets-noref [2] {13.9} {19.4} {24.7} {52.5} {52.5} piv-nets [2] {5.9} { 7.2} {15.5} {28.2} {29.4} piv-liteflownet [1] {5.6} {8.3} {10.4} {19.6} {20.0} piv-liteflownet-en [1] {3.3} {4.9} {7.5} {12.2} {12.6} raft32-piv [4] {0.4} {1.8} {1.1} {2.8} {2.1} unliteflownet-piv [3] 10.1 7.8 9.6 13.5 19.7 uraft-piv (present) 6.5 6.6 8.1 12.5 13.2 table 1: averaged endpoint error (aee) for all test cases of the synthetic piv database introduced in cai et al. (2019b) of learning task i. uraft-piv outperforms its unsupervised competitor in all test cases and achieves a similar performance compared to a supervised liteflownet based network (piv-liteflowneten). its supervised counterpart raft32-piv still achieves the lowest endpoint error by quite a margin. the error unit is set to pixel per 100 pixels for easier comparison. values in brackets correspond to supervised networks. references: [1] cai et al. (2019a), [2] cai et al. (2019b); [3] zhang and piggott (2020); [4] lagemann et al. (2021) compared to raft32-piv, but still achieves a higher accuracy than unliteflow-piv which additionally shows strong prediction noise. in contrast, if the underlying displacement field is more smooth, the endpoint error decreases significantly. these findings are in line with literature (jonschkowski et al. (2020)) and suggest that the loss functions currently used might be a limiting factor for the performance of unsupervised optical flow estimation. current state-of-the-art unsupervised loss objectives are useful, but by far not as effective as supervising the network based on a ground-truth, i.e., more sophisticated loss objective can significantly boost the accuracy of unsupervised optical flow estimation. figure 2: optical flow prediction of different network architectures and absolute error between ground truth flow and network predictions. each image depicts two individual flow fields characterized by medium and strong gradients. the first two rows illustrate the displacement and error distribution of the horizontal direction while the last two rows show estimates for the vertical axis. especially in flow fields dominated by strong gradients (right half), uraft-piv under-/overestimates the local displacement compared to its supervised counterpart since the unsupervised loss objective encourages the network to regularize the optical flow. however, uraft-piv still achieves a higher accuracies compared to unliteflownet-piv and a lower prediction noise. 3.2 learning task ii: realistic synthetic and experimental piv images while the data above are interesting and useful, we note that it is almost impossible to obtain images of this quality in practical applications since piv setups are very sensitive to external and internal sources of noise, e.g., reflections on side walls or surfaces, light refraction at glass surfaces, slight misalignments in the setup, or density gradients as present in supersonic flows. to study the performance using images like those obtained in many real-world applications, an additional database with an increased particle displacement up to ±24px, a reduced particle density and signal-to-noise-ratio (snr), an increased variance of the particle diameter, and camera noise was used to train the networks of learning task ii. details of this dataset can be found in lagemann et al. (2021). first, we study the performance of uraft-piv in evaluating synthetic images based on a dns of a laminar and a fully turbulent boundary layer. results are depicted in fig. 3 illustrating the displacement prediction of uraft-piv and its supervised counterpart alongside comparisons of displacement profiles at different positions. in case of a laminar boundary layer, barely any differences become visible between raft32-piv and uraft-piv. compared to the ground-truth, however, local flow feature appear to be smoothed and less sharp. we assume that this is directly related to the fact that the particle images of learning task ii comprise significantly less particles compared to learning task i and consequently, less information of the underlying flow can be evaluated while more regions with low texture occur. the displacement profile confirms these findings highlighting that the raft inspired approaches and our cross-correlation algorithm closely match the ground-truth. in contrast, unliteflownet-piv shows some slight deviations and a more noisy distribution similar to previous findings. test runs on a turbulent boundary layer confirm these results. overall, one notices that raft32-piv follows the ground-truth most accurately only deviating slightly in regions of local extrema. the unsupervised uraft-piv similarly matches the overall trend of the ground-truth, but cannot reach the accuracy of its supervised counterpart. however, it still matches the performance of our cross-correlation based method and proves its effectiveness in realistic particle and flow conditions. in our final test case, we apply our uraft-piv model trained on the dataset of lagemann et al. (2021) to real-world experimental piv data. this test case consists of experimental piv measurements dealing with a turbulent wavy channel flow as shown in rubbert et al. (2019). together with flow field predictions of unsupervised piv networks and our raft models, we analyze the images using our in-house code. generally, fig. 4 evidences that both raft-piv approaches supervised and unsupervised perform likewise state-of-the-art cross-correlation based piv methods and hence, can serve as direct substitute. however, we noted that the prediction results based on uraft-piv show some spurious estimations in the area of high displacements (≈ 12px). this is potentially based on the unsupervised loss formulation which might not be suitable for high displacements since similar patterns also occur for unliteflownet-piv, but further analysis is required. moreover, it is noteworthy that uraft-piv clearly reduces the prediction noise due to its recurrent nature compared to its liteflownet based competitor. please note that our raft based approaches do not involve any post-processing steps but nevertheless achieve at least an equal noise level compared to gold-standard piv algorithms. for instance, pascalpiv performs a spatial multigrid cross-correlation scheme in a first step before computing the local displacement field of the final interrogation window in 25 iteration steps. prior to every iteration step, several validation criteria are applied to detect outliers and spurious values are replaced using a lanczos interpolation scheme. thus, a smooth displacement field is finally achieved. in contrast, the raft model resembles a single-shot approach which solely operates on a fixed input window without taking further neighboring information into account. considering this key difference, the low noise level of raft-piv is quite astonishing and further proves for the first time that unsupervised learning is a viable alternative when processing arbitrary real-world piv images. especially the possibility of training respectively fine-tuning existing networks on real-world experimental data states a key advantage for unsupervised learning tasks. however, detailed studies on new loss objectives and their corresponding effect on the accuracy are necessary. 4 conclusions we studied uraft-piv, an unsupervised deep neural network architecture for optical flow estimation in piv applications. uraft-piv achieves a new state-of-the-art accuracy on a public piv database for unsupervised learning and performs likewise supervised liteflownet based piv networks. uraft-piv also performs well under more challenging flow field and image conditions such as low particle density and figure 3: comparison of displacement fields and profiles for a laminar and turbulent boundary layer. in case of a laminar boundary layer, raft based networks and pascalpiv match the ground-truth well. unliteflownet-piv follows the overall trend, but predicts noisy results. the turbulent case reveals some smoothing behaviour of our raft approaches, but still match the ground-truth very accurately as does the traditional piv algorithm. similar to the laminar flow field, unliteflownet-piv can roughly predict the ground-truth distribution but shows significant noise. figure 4: visual comparison of raft-piv models with state-of-the-art piv algorithms as well as existing piv networks. the left column represents the results of all available methods w.r.t. the horizontal optical flow component and the right column depicts the predictions of the displacement in the vertical direction. raft32-piv and uraft-piv perform likewise with our high-performance code pascalpiv while significantly increasing the spatial resolution of the displacement field. further note that these neural methods match the noise level of pascalpiv without interpolating spurious displacement vectors using neighboring data points and hence, resemble single-shot methods. changing light conditions that are important for many real-world applications. our tests show that uraftpiv accurately predicts displacements while significantly reducing the noise level, most likely due to its recurrent nature. we also noticed that our unsupervised model under-/overestimates the local displacement in regions dominated by strong gradients since the unsupervised loss objective encourages the network to regularize the optical flow. these findings suggest that the loss functions currently used might be a limiting factor for the performance of unsupervised optical flow estimation. current state-of-the-art unsupervised loss objectives are useful, but by far not as effective as supervising the network based on a ground-truth meaning that more sophisticated loss objective can significantly boost the accuracy of unsupervised optical flow estimation. applying uraft-piv in an out-of-the-box fashion to experimental piv data demonstrates its generalization capabilities and its ability to significantly improve the spatial resolution while otherwise matching state-of-the-art piv algorithms. future work will incorporate further studies targeting the development of more suitable penalty terms. acknowledgements the authors gratefully acknowledge the gauss centre for supercomputing e.v. (www.gauss-centre.eu) for funding this project by providing computing time on the gcs supercomputers hawk at höchstleistungsrechenzentrum stuttgart (www.hlrs.de) and juwels at the forschungszentrum jülich (www.fz-juelich.de). references astarita t and cardone g (2005) analysis of interpolation schemes for image deformation methods in piv. experiments in fluids 38:233–243 cai s, liang j, gao q, xu c, and wei r (2019a) particle image velocimetry based on a deep learning motion estimator. ieee transactions on instrumentation and measurement 69:3538–3554 cai s, zhou s, xu c, and gao q (2019b) dense motion estimation of particle images via a convolutional neural network. experiments in fluids 60:73 dosovitskiy a, fischer p, ilg e, hausser p, hazirbas c, golkov v, van der smagt p, cremers d, and brox t (2015) flownet: learning optical flow with convolutional networks. in proceedings of the ieee international conference on computer vision. pages 2758–2766 hui tw, tang x, and change loy c (2018) liteflownet: a lightweight convolutional neural network for optical flow estimation. in proceedings of the ieee conference on computer vision and pattern recognition. pages 8981–8989 jonschkowski r, stone a, barron jt, gordon a, konolige k, and angelova a (2020) what matters in unsupervised optical flow. arxiv preprint arxiv:200604902 1:3 kingma dp and ba j (2014) adam: a method for stochastic optimization. arxiv preprint arxiv:14126980 lagemann c, lagemann k, mukherjee s, and schröder w (2021) deep recurrent optical flow learning for particle image velocimetry data. nature machine intelligence lee y, yang h, and yin z (2017) piv-dcnn: cascaded deep convolutional neural networks for particle image velocimetry. experiments in fluids 58:171 meister s, hur j, and roth s (2017) unflow: unsupervised learning of optical flow with a bidirectional census loss. arxiv preprint arxiv:171107837 paszke a, gross s, chintala s, chanan g, yang e, devito z, lin z, desmaison a, antiga l, and lerer a (2017) automatic differentiation in pytorch rabault j, kolaas j, and jensen a (2017) performing particle image velocimetry using artificial neural networks: a proof-of-concept. measurement science and technology 28:125301 raffel m, willert ce, scarano f, kähler cj, wereley st, and kompenhans j (2018) particle image velocimetry: a practical guide. springer rubbert a, albers m, and schröder w (2019) streamline segment statistics propagation in inhomogeneous turbulence. physical review fluids 4:034605 schrijer f and scarano f (2008) effect of predictor–corrector filtering on the stability and spatial resolution of iterative piv interrogation. experiments in fluids 45:927–941 teed z and deng j (2020) raft: recurrent all-pairs field transforms for optical flow. in european conference on computer vision. pages 402–419. springer zhang m and piggott md (2020) unsupervised learning of particle image velocimetry. arxiv preprint arxiv:200714487 https://www.gauss-centre.eu https://www.hlrs.de https://www.fz-juelich.de introduction method results learning task i: idealised piv database learning task ii: realistic synthetic and experimental piv images conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 moving surface actuation, effects of frequency-based shear layer excitation on the response of a bluff body wake m. r. singbeil1∗, c. ghiroaga1, c. morton1, r. j. martinuzzi1 1 university of calgary, mechanical and manufacturing engineering department, calgary, canada ∗ mrsingbe@ucalgary.ca abstract the effect of actuation frequency, using moving surface actuation, is investigated for a square cylinder bluff body wake. pressure sensor data are used to optimize actuation characteristics through the implementation of an nsga-ii evolutionary algorithm. velocity field data are obtained using particle image velocimetry (piv) for baseline and optimized actuation cases. a proper orthogonal decomposition (pod) analysis shows that the vortex shedding frequency shifts between frequencies associated with the actuation, moving between regions of lock-on and quasi-periodicity. additionally, the pod shows that the energy contained in the coherent shedding motion is reduced through actuation, while the total energy in the velocity field stays relatively constant. a reconstruction of the first 10 pod modes indicates that the coherent contribution to the reynolds stresses significantly decreases compared to the non-actuated case. the mechanism for drag reduction is investigated using the shed circulation flux and kochin’s drag formulation model. the drag obtained using piv measurements and kochin’s formulation is consistent with trends observed for the base pressure as a function of actuation frequency. 1 introduction vortex shedding is a common phenomenon caused by the interaction of two opposing shear layers in the wake of a bluff body. these interactions give rise to coupled instabilities leading to the quasi-periodic shedding of vortices (williamson, 1996). these vortices induce fluctuating loads which are major contributors to drag forces acting on high-speed vehicles and cyclic loading associated with flow-induced vibrations of structures. these forces are proportional to the strength of the shed vortices (i.e. circulation) and the rate at which they convect (kochin, 1964); both of which depend on the rate at which circulation is generated and advected from the body’s surface. due to the importance of circulation on the shedding process, actuation methods for manipulating the vorticity flux is vital for its control. hence, the work focuses on how frequency-modulated moving surface actuation affects the formation and shedding of vortices to control wake dynamics. shear layer excitation has potential to manipulate the circulation generation and transport to exploit flow instabilities to alter the shedding process (xu et al., 2017). the square cross-sectional prism was selected to isolate the influence of actuation by fixing the separation point and avoiding downstream shear layer reattachment. separation at the leading edge reduces the reynolds number sensitivity of aerodynamic characteristics (okajima, 1982) such as drag which is strongly correlated to the shed circulation flux in the wake (kochin, 1964). actuating at the inception of shear layer separation is achieved with a symmetric pair of moving surface actuators (rotating cylinders) at the leading edges. previous work with moving surface actuation, such as munshi et al. (1997), note very high surface velocity to free-stream ratios (vs/u∞) on the order of 3 times to achieve authority on the wake. these studies focused on boundary layer control through the addition of significant momentum resulting in delayed separation. in contrast, frequency based actuation methods exploit the frequency dependent nature of a bluff body wake achieving authority with less input energy (wu et al., 2007). the rotating cylinders experience a whirling motion which introduces a forcing frequency and cascading harmonics at integer multiples of the rate of rotation ( fw = n/60) where n is the revolutions per minute, rpm, of the motor (baek and sung, 2000). in this study, the effects of frequency-based moving surface actuation on the base pressure and wake dynamics are investigated. pressure on the obstacle’s surface is complemented by velocity data obtained using piv. results are investigated using fourier analysis and pod. 2 methodology the experiments were performed in a small-scale suction type wind tunnel shown in figure 1. air is drawn through four conditioning grids at the inlet before undergoing a 9:1 contraction down to the square test section with a wetted cross-sectional area of 203.2 mm × 203.2 mm and is 508.0 mm long. the obstacle is a square cross-section prism with a characteristic length d =25.4 mm (fig 2). the obstacle is mounted wall to wall with an aspect ratio of 8:1 and results in a blockage of 12.5% when installed 127.0 mm downstream of the test section inlet. figure 1: side view of wind tunnel facility the actuators are two 10 mm-diameter rotating cylinders driven via two brushless dc servo-motors mounted external to the test section. six differential pressure transducers are used to obtain pressure at locations p1 to p6 indicated in fig. 2. on the top/bottom surfaces, transducers p1 and p2 are 1-inch water column (all sensors d-4v) and on the leeward face p3 to p6 are 5-inch (all sensors dx-4v mini) transducers. �∞ �2 �3 �4 �5 �6 �1 figure 2: obstacle with surface mounted pressure taps and origin of the piv domain on the leeward surface a modified multi-objective nsga-ii sorting algorithm (deb et al., 2002) was used to explore the space of actuation parameters and reduce the dimensionality of the search space. multiple trials were performed first optimizing the direction and rate of symmetric cylinder rotation (r(t) = d×n), then introducing sinusoidal modulation of the motor control signal (r(t) = asin(2π f t)+n), followed by asymmetric actuation with a phase difference between motors (r(t) = asin(2π f t +φ)+n). over all trials the rate of rotation was limited to 0 < n < 3000 rpm, the oscillation amplitude varied between 5 and 50 rpm with a frequency of 0 to 4hz, and the phase difference ranging from 0 to π radians. these limits were chosen due to the stability margins of the servo-motor apparatus. the fitness functions prescribed to the genetic algorithm were set to maximize the average leeward face base pressure (cpb = 1 4 [cp3 +cp4 +cp5 +cp6]), and minimize the rms of the top and bottom pressure fluctuations (c′pl =c′p1 + c′p2) in order to maintain diversity of solutions. the non-dominating set of individuals within the final pareto front for each trial indicated that the base pressure was highest with symmetric actuation at a constant rpm in the positive sense of rotation with respect to the flow; thus reducing the search to a single parameter, n. as such, a grid search was performed gathering pressure data from 0 to 3000 rpm in increments of 5 rpm. planar piv was performed to gather instantaneous two-dimensional velocity data in the x and y directions. n = 0, 2000, 2180, 2200, and 3000 rpm were selected in order to investigate lock-on, desynchronization, and the quasi-periodic states. a single cavity photronics industries laser with a wavelength of 527 nm was operated in dual-pulse mode. each pulse of the laser was synchronized with a phantom miro lab 340 high-speed camera using a lavision high-speed controller. the laser beam was reflected through a cylindrical lens to illuminate the area six diameters downstream at the mid span of the obstacle. the inlet was seeded with atomized olive oil particles which are entrained uniformly into the test-section. an area of 6d × 6d was captured immediately downstream of the obstacle. a sampling rate of 600 frames per second was chosen to capture 10 instantaneous velocity fields per shedding cycle. la vision davis 8.3 image processing software was used to process the raw images into instantaneous two-dimensional velocity data. the fluctuating image field is processed with a multi-grid window deforming algorithm to produce the velocity field for each image pair. the first pass used a window size of 32 × 32 pixels and an overlap of 50% whereas the final pass used a window size of 16 × 16 pixels with no overlap to result in equal resolution of both the spatial and vector fields. the resulting vector field had a resolution of 0.0638d in both x and y directions. fourier analysis of the pressure data is performed to investigate the wake response to the actuation (fig. 3b). from the velocity field data gathered a pod analysis is performed to isolate changes in the spectra associated the vortex shedding, redistribution of total kinetic energy (tke) amongst the modes, and reductions in the reynolds stress associated with coherent fluctuations. the average circulation flux in the shear layer and shed vortices is then extracted using a phase average and formulation for the mechanism of drag reduction presented. 3 results 3.1 pressure measurements over the range of 0 to 3000 rpm, the pressure coefficient on the obstacle base was found to increase from -1.27 to -1.04 with regions of significant change followed by plateaus, indicated with red lines in fig. 3a. figure 3: a) the base pressure coefficient computed from the 4 pressure taps on rear face of the obstacle versus the actuation rate, n; b) flooded iso-contours of the psdf computed from signal x = c′p3−c′p6 at each actuation rate, n. the iso-contours of the power spectral density function (psdf), in fig. 3b, show the energy associated with frequencies in the wake. below n ≈ 1250 rpm, the highest energy is concentrated near the baseline shedding frequency (st = 0.184). surpassing 1250 rpm, concentrations of energy (or rays) form, corresponding to the harmonics of the actuation frequency ( fw). changes in the intensity of the psdf suggest regions of vortex lock-on, which shift with respect to these harmonics. in fig. 3a the first plateau in cpb occurs from ≈ 1250 to 1500 rpm as the ray associated with the third harmonic (3 fw) first appears near the unactuated shedding frequency. from 1500 to 2000 rpm a cloud of dispersed spectral energy is observed between the second and third harmonic rays. from 2000 to approximately 2400 rpm a second plateau in cpb can be seen in fig. 3a, while the results in fig. 3b suggest that the shedding frequency locks-on to the second harmonic of actuation (2 fw)(i.e., the cloud of dispersed spectral energy between 2 fw and 3 fw vanishes while the second harmonic appears near the unactuated shedding frequency). continuing past 2500 rpm the base pressure continues to trend upward as the shedding frequency desynchronizes from the second harmonic ray. the results indicate that the plateaus in cpb are linked to the state of the wake as the shedding frequency is either modulated by the nearby harmonics or experiences lock-on as the rays cross the unactuated shedding band. 3.2 pod analysis and coherent contributions to the reynolds stress performing a pod analysis, the distinct shedding frequencies for each piv data set are extracted from the spectra of the first temporal coefficient (fig. 4) and gathered in table 1. from 2000 to 2200 rpm the spectral peak associated with the shedding frequency is seen to coincide with the second harmonic of the actuation further supporting lock-on over this range. at 2350 rpm the shedding frequency begins to desynchronize from the actuation as the harmonic peak approaches the edge of the unactuated shedding band and by 3000 rpm is fully desynchronized experiencing modulation by the neighbouring actuation harmonics and in a state of quasi-periodicity as outlined by baek and sung (2000). these regimes match the behaviour seen in fig. 3b supporting that the distinct changes in the base pressure shown in fig. 3 are associated with the vortex shedding frequency transitioning between states of lock-on and quasi-periodicity with respect to the actuation harmonics. (a) n = 0;vs/u∞ = 0 (b) n = 2000;vs/u∞ = 0.119 (c) n = 2180;vs/u∞ = 0.130 (d) n = 2200;vs/u∞ = 0.131 (e) n = 2350;vs/u∞ = 0.140 (f) n = 3000;vs/u∞ = 0.178 figure 4: spatial modes (ψ1) with the spectra of their respective temporal coefficients (a1) for each piv case n fw 2 fw fvs 0 0 0 0.188 2000 0.0097 0.194 0.194 2180 0.1055 0.211 0.211 2200 0.1060 0.212 0.212 2350 0.1130 0.226 0.208 3000 0.1445 0.289 0.222 table 1: non-dimensional frequency ( f ∗ = f d/u∞) of the first and second harmonics of the actuation along with the shedding frequency from each piv case figure 5 shows the distribution of tke among the first 100 pod modes for each piv set. a reconstruction from the first 10 modes is performed in order to isolate changes in the fluctuating velocity field associated with coherent motions. this reconstruction captures approximately 62% of the tke in the baseline case (fig. 5b) and resolves 90% of the u′v′ field with only minor discrepancies in the shear layer due to incoherent fluctuations. from the reconstructed field, iso-contours of the reynolds stress with overlaid mean streamlines are presented in fig. 6 for each piv case. from the baseline to the actuated cases, the streamwise position of max[u′2] is seen to shift upstream along with the recirculation foci. this shift increases the relative distance from the foci to the maxima for both u′v′ and v′2 indicating that v′ fluctuations occur further downstream from the recirculation nodes. this behaviour along with the vanishing concentrations of u′v′ within the recirulation bubble indicate a change in the vortex formation. as n increases, the recirculation length (lr) is seen to decrease supporting a change in the mean wake structure. the distribution of reynolds stress over the domain shows a reduction in strength of both the fluctuating velocity field within the shear layer (u′2) as well as downstream of the recirculation length (v′2). these reductions indicate a reduced energy associated with both the formation and shedding of vortices, supporting a link with the observed trend in cpb. figure 5: a) percentage of the tke captured for each of the first 100 modes b) cumulative sum of the modal energies for the first 100 modes (a) n = 0;vs/u∞ = 0 (b) n = 2000;vs/u∞ = 0.119 (c) n = 2180;vs/u∞ = 0.130 (d) n = 2200;vs/u∞ = 0.131 (e) n = 2350;vs/u∞ = 0.140 (f) n = 3000;vs/u∞ = 0.178 figure 6: iso-contours of reynolds stress components u′2c , u′cv′c, and v′2c with overlaid mean streamlines in plots a, b, and c from the 8 mode reconstructed velocity field for each piv case to investigate changes of the reynolds stresses with n, the maximum values for each component of the reynolds stress are compared in figure 7 for both the rans and reconstructed fields. matching the trends observed in figure 6, reductions are noted in both u′ and v′ from the baseline to the actuated cases. however, as n increases, reductions are observed in u′v′ and v′2 indicating a less energy associated with the shed vortices. figure 7: maximum coherent contribution to the reynolds stress from the reconstructed field u′2c , u′cv′c, and v′2c (shown in red) and maximum of the reynolds stress u′2, u′v′, and v′2 (in blue) with respect to the rate of rotation, n. values for the baseline (n = 0) case are shown as dashed lines. from the pod analysis reductions in the tke associated with the first harmonic pair are observed. comparing the baseline and first actuated case (n = 2000) a reduction from 54 to 16% is seen in the first harmonic pair in fig. 5. in order to quantify the significance of reductions in tke associated with the vortex shedding, the tke within the domain and tke from the first harmonic pair are plotted with respect to n in fig. 8. as the rate of actuation increases, the tke associated with the first harmonic pair is reduced by a greater percent than changes in the tke of the domain. it can be inferred that the decrease in fluctuations seen in the reynolds stress are therefore likely associated with energy moving away from the shedding motion and exciting other coherent motions (or modes). figure 8: a) absolute tke captured the piv domain and the shedding pair for each case b) percent change in tke from baseline values for the total, shedding pair computed from [ case−baseline baseline ×100% ] 3.3 circulation flux in the wake to investigate how circulation in the wake varies with the observed changes in the reynolds stress both the flux along the shear layer and within the shed vortices are estimated. the circulation flux along the shear layer may be computed by finding the streamwise maximum of dγsl(x)/dt = ∫ y|umax y|umin uiωidy for each case and are shown as functions of n in figure 9. next, a conditional average is performed using the phase computed from the temporal coefficients from the pod a1 and a2 (θ = tan−1( a1√ 2λ1 / a2√ 2λ2 )). the vortex core is then identified (as a connected regions of q > 0) and the contained vorticity integrated for each frame. this value is an estimate of the circulation flux contained in a shed vortex (severed from the shear layer) which is multiplied by the respective shedding frequency and plotted in figure 9. figure 9: circulations flux in the shear layer, circulation flux in the shed vortices, and the ratio of these two quantities for each piv case. from fig. 9 the circulation flux in the shear layer is seen to drop by roughly 18% from n = 0 to 2000 rpm, minimally vary in the range of lock-on from 2000 to 2200, and further decrease from 2350 to 3000 rpm aligning with the reductions in u′ and v′ noted in fig. 7 while the flux in the shed vorticies is only seen to trend downward slightly over the range. the ratio of circulation flux in the shed vortices to that in the shear layer is then computed to quantify if the circulation supplied to the domain and that captured by the shed vortices is changing as a result of the actuation. from the values in fig. 9 no clear trend is observed as the changes in γvs/γsl do not match the increase in cpb. thus, it is speculated that the actuation is not just reducing the energy associated with the shedding motion but also altering the structure of the vortex shedding. as such in the following section, kochin’s derivation for the drag due to a vortex street is shown and how coupled changes in the vortex trajectories and circulation affect the drag on a bluff body are presented. 3.4 drag formulation due to the vortex street to understand the mechanism associated with the increased base pressure, contributions to the drag due to the shed vortices are considered. following kochin (1964), in the presence of a semi-infinite vortex street, the contributions to the form drag can be decomposed into three terms as given in eq. 1. each of these terms can be estimated from the velocity field obtained with piv. the contribution to the drag, expressed in non-dimensional form, is: cd = 2 [ γ2 vs fvs 2πuc +γvs(h/d) fvs− γvs fvs(h/d)(1−uc) uc ] , (1) where γ2 vs fvs/2πuc accounts for the balance of momentum due to the fluid within the domain at an instant, while both γvs(h/d) fvs and γvs fvs(h/d)(1−uc)/uc account for the change in momentum due to the fluid entering and exiting the domain over the period 1/ fvs due to the freestream and the motion of vortices respectively. the shedding frequency fvs may be determined directly from the spectra of the velocity fluctuations or pod temporal coefficients (fig. 4). the circulation of the vortices γvs is established in table 9 and the lateral spacing h/d and convective velocity uc are computed from the average trajectories of the vortex centroids over the shedding cycle. the location of the cores are computed using the q-criterion and second area moment of the z-vorticity where q > 0 before exiting the piv domain. the convective velocity pf the vortices is estimated by performing a linear regression of the streamwise position of the centroids versus phase once the vortices reach a constant velocity. the slope (m = ∆x/d ∆θ ) is then used to calculate an average velocity as uc = m×360 fvs and gathered in table 2. n h/d ∆x/d ∆θ fvs uc γvs 0 1.020 0.01243 0.188 0.841 2.60 2000 0.938 0.01039 0.194 0.726 2.19 2180 0.685 0.01028 0.211 0.781 2.16 2200 0.892 0.01026 0.212 0.779 2.10 2350 1.158 0.01096 0.208 0.821 1.96 3000 0.876 0.00800 0.222 0.639 1.55 table 2: summary of important quantities extracted from the average vortex trajectories substituting the values from table 2 into kochin’s formulation (eq.(1)) an estimate for the average coefficient (cd) is computed and summarized in table 3. the coefficient of drag for the baseline flow (cd = 1.16) is in agreement with values from the literature being reported at cd = 1.2 for a square cylinder with rounded leading edges (heddleson et al., 1957). figure 10: estimate of the coefficient of drag from piv measurements and base pressure based on kochin’s formulations for the drag due to a vortex street. n −cpb cpiv d 0 1.299 1.162 2000 1.141 0.891 2180 1.144 0.864 2200 1.121 0.945 2350 1.119 0.893 3000 1.096 0.558 table 3 the downward trend in estimated cd from kochin’s formulation aligns with the observed increase in the base pressure noted by figure 3a. it is worth noting that as kochin’s formulation is based on a potential flow solution it does not account for the dissipation due to turbulence and skin friction on the body; as such the slightly under reported values for the baseline are to be expected. figure 10a shows a significant decrease from the baseline, a plateau while synchronized with the second harmonic of the actuation, followed by another decrease from 2350 to 3000 rpm as the shedding desynchronizes and becomes quasi-periodic. to gain insight into the observed changes in drag and base pressure, the terms of the formulation may be separated into two major contributors, balance of projected momentum by the fluid within the domain plus the fluid entering/exiting the field of view over a period (1/ fvs) as the sum of t 1+t 2, and the projected momentum of the fluid leaving the domain due to motion of the vortices, t 3. these contributions are shown in figure 10b. the difference between these two values estimates the drag related to the strength and trajectory of the vortices. from the baseline to actuated cases, t 1+t 2 steadily decreases matching the reduced circulation whereas t 3 varies over the range with a local maxima at 2000 and 3000 rpm. these maxima match the lowest convective velocities and widest lateral spacing. these changes indicate that as the actuation harmonics shifts the shedding between states of lock-on and quasi-periodicity the mechanism associated with the decreased drag is not simply a reduction of the shed circulation but changes related to the convection rate of the vortices and, in particular, their trajectories. 4 conclusions the effects of frequency based moving surface actuation were investigated for a square cylinder bluff body wake. it was observed through the pod results that the vortex shedding frequency shifts between the actuation frequency harmonics as the rpm increases, moving between regimes of lock-on and quasi-periodicity. the amount of the tke and magnitude of the reynolds stresses associated with shedding were found to decrease as the actuation rate increased. conversely, the tke in the entire piv domain was found to remain relatively constant as actuation increases and therefore the energy associated with shedding is redistributed to other coherent motions. kochin’s formulation for the drag due to an infinite vortex street was evaluated and seen to be in agreement with the trend observed in the base pressure. differences in the drag formulation as the rate of actuation n increased were isolated to the effect of the vortex impulse as the primary mechanism for drag reduction. references baek sj and sung hj (2000) quasi-periodicity in the wake of a rotationally oscillating cylinder. journal of fluid mechanics 408:275–300 deb k, pratap a, agarwal s, and meyarivan t (2002) a fast and elitist multiobjective genetic algorithm: nsga-ii. ieee transactions on evolutionary computation 6:182–197 heddleson c, brown d, and cliffe r (1957) summary of drag coefficients of various shaped cylinders. technical report. general electric co cincinnati oh kochin ne (1964) theoretical hydrodynamics. international publications pages 214–218 munshi s, modi v, and yokomizo t (1997) aerodynamics and dynamics of rectangular prisms with momentum injection. journal of fluids and structures 11:873–892 okajima a (1982) strouhal numbers of rectangular cylinders. journal of fluid mechanics 123:379–398 williamson c (1996) vortex dynamics in the cylinder wake. annual reviews of fluid mechanics 28:477– 539 wu cj, wang l, and wu jz (2007) suppression of the von kármán vortex street behind a circular cylinder by a travelling wave generated by a flexible surface. journal of fluid mechanics 574:365 xu f, chen wl, bai wf, xiao yq, and ou jp (2017) flow control of the wake vortex street of a circular cylinder by using a traveling wave wall at low reynolds number. computers and fluids 145:52–67 introduction methodology results pressure measurements pod analysis and coherent contributions to the reynolds stress circulation flux in the wake drag formulation due to the vortex street conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 3d pressure field reconstruction from time-resolved stereoscopic piv measurements by relaxation of taylor’s hypothesis d. fratantonio1∗, j. j. charonko1 1 los alamos national laboratory, physics division, los alamos, nm usa ∗ dfratantonio@lanl.gov abstract this work presents reconstructions of 3d pressure fields starting from 2d3c stereoscopic-piv (spiv) measurements. in fratantonio et al. (2021), we presented a new reconstruction algorithm, the “instantaneous convection” method, capable of producing 3d velocity fields from time-resolved spiv measurements. for reconstructions in flows with strong shear layers and high turbulence intensity, this method is able to provide time-resolved 3d velocity volumes that are more accurate than those that can be obtained from the more frequently employed reconstruction method based on the taylor’s hypothesis and on the use of a mean convective field. here we investigate the possibility of reconstructing the 3d pressure field from the timeresolved series of reconstructed 3d velocity data. a pseudo-tracking method is employed for computing the velocity material derivative, and the pressure field is then reconstructed by solving the 3d poisson equation. the velocity and pressure reconstructions are validated on the direct numerical simulation data of the turbulent channel flow taken from the john hopkins turbulence database (jhtdb), and an application to experimental spiv measurements of an air jet flow in coflow carried out at the turbulent mixing tunnel (tmt) facility at los alamos national laboratory is presented. 1 introduction the last two decades have seen a fast development and improvement of tomographic piv/ptv techniques (elsinga et al., 2006; novara and scarano, 2013), and, with the increasing availability of time-resolved 3d3c velocity data, the existing algorithms for 2d pressure reconstruction (charonko et al., 2010) have been extended to the 3d case and further improved to increase accuracy (wang et al., 2016) and computational efficiency (huhn et al., 2016). although tomographic piv/ptv are now established techniques for performing 3d velocity measurements in fluid flows, the required experimental setup is still considered complex and expensive, since it requires at least 4 cameras and high-repetition, high-power laser systems in timeresolved measurements. therefore, any alternative methods capable of providing accurate time-resolved 3d velocity and pressure fields from less complex or expensive techniques are of great interest for the scientific community. in this perspective, several authors exploited the taylor’s hypothesis of frozen turbulence for converting time-correlation information of single-point or 2d measurements into missing spatial-correlation information. in applications of the taylor’s hypothesis to spiv measurements (ganapathisubramani et al., 2008), the time-resolved 2d3c velocity data uuu(x,y) at the spiv measurement plane is converted into a 3d velocity volume by application of the following hyperbolic operator, ∂uuu ∂t +w(x,y) ∂uuu ∂z = 000, with w(x,y) being the local mean out-of-plane velocity. we refer to this type of 3d velocity reconstruction as the “mean convection” (mc) method. it has been practically demonstrated, however, that the taylor’s hypothesis breaks down in highlyturbulent and/or shear flows (lin, 1953; dennis and nickels, 2008; zaman and hussain, 1981). large-scale turbulent structures cannot be considered “frozen” in a shear layer since they deform under the effect of the transverse spatial gradients of the mean velocity profile, and velocity fluctuations might convect the turbulent patterns with convective speed and direction different from those given by the local mean velocity. in this context, we recently proposed a new algorithm of 3d velocity reconstruction from spiv data (fratantonio et al., 2021), which we called the “instantaneous convection” (ic) method and which we demonstrated providing large 3d velocity volumes in shear flows that are more accurate than those provided by the mc method. the ic method is a step-by-step lagrangian-eulerian reconstruction that (i) convects the 2d3c velocity data in the 3d space with the local instantaneous velocity vector uuu = (u,v,w) and that (ii) “unfreezes” the 3d flow through an iterative poisson regularization of intermediate velocity reconstructions. it is the combining effect of these two new features in the reconstruction process that produces the key difference between the ic method and the mc method. since the convective field used in the ic method for transporting the flow properties in the 3d space corresponds to the local instantaneous velocity, enforcing the divergence-free condition through the poisson equation does not provide a simple regularization of the 3d field, but also introduces a temporal and spatial development of the convective field itself, thus recovering those non-linear fluid deformation mechanisms that would be otherwise lost when convecting the flow with a “frozen” mean velocity profile. a brief description of the ic algorithm is provided in section 2.1. our next goal is to investigate the possibility of recovering 3d pressure fields from time-resolved series of 3d velocity fields reconstructed from spiv measurements. the pressure field can be reconstructed by integration in the spatial domain of the pressure gradients. at present, there are two major classes of integration methods, i.e., direct line integration of the pressure gradients or poisson-based pressure solver (van oudheusden, 2013). both reconstruction strategies first require measurements of the material flow acceleration, duuu dt , which can be obtained with different approaches, depending on what type of velocity data is available (van gent et al., 2017). from time-resolved ptv measurements, the particle trajectories are directly measured and can locally provide duuu dt data, which can then be interpolated on a cartesian grid and integrated in space for pressure reconstruction by means of sophisticated processing tools, such as flowfit (gesemann et al., 2016) and vic+ (schneiders and scarano, 2016). in this context, the recently proposed “shake-thebox” method (schanz et al., 2016) enabled applications of tomographic-ptv with particle seeding densities comparable to that of tomographic-piv, thus providing accurate and dense material acceleration data able to enhance accuracy of pressure reconstruction. our reconstructed 3d3c velocity data resemble more what can be obtained from time-resolved tomographic-piv measurements, from which the material acceleration can be evaluated either with an eulerian approach, where duuu dt is computed in a stationary reference frame from the temporal and spatial velocity derivatives (jakobsen et al., 1997), or with a pseudo-tracking method, where imaginary particles are distributed in the domain and their trajectories are computed by forward and backward integration in time (liu and katz, 2006; pröbsting et al., 2013). other approaches that can approximate duuu dt from a single 3d3c snapshot exist, such as the taylor’s hypothesis approach of laskari et al. (2016) or the ivic method proposed by schneiders et al. (2016), but the ic or the mc methods can provide time-series of velocity volumes with the same temporal resolution used in carrying out spiv measurements, and we can therefore rely on time-resolved 3d data for performing pressure reconstructions. the application of these techniques to reconstructed spiv velocity volumes has not been performed to date, not even for velocity volumes reconstructed by the common mc method. to the best of our knowledge, the work of de kat and ganapathisubramani (2012) is the only one that has tackled the problem of evaluating the accuracy of pressure fields reconstructed from spiv velocity data in conjunction with the taylor’s hypothesis, but they limited the analysis to the reconstruction of 2d pressure fields by means of a 2d poisson equation derived from the residual between the taylor operator and the full navier-stokes equations. they did not perform reconstructions of 3d pressure fields directly from large 3d reconstructed velocity fields. in section 3, both the ic and the mc method are validated by application to a direct numerical simulation (dns) dataset of the turbulent channel flow taken from the john hopkins turbulence database (jhtdb), and an error analysis in terms of reconstructed 3d velocity and pressure fields is presented. section 4 demonstrates an application of the reconstruction algorithms to an experimental dataset of spiv measurements of an air jet flow in co-flow performed in the turbulent mixing tunnel (tmt) facility at los alamos national laboratory. 2 reconstruction algorithms 2.1 velocity reconstruction the way the ic method performs the reconstruction has direct effects on the resulting 3d velocity and, consequently, on the resulting 3d pressure field. although all the details of the ic method can be found in fratantonio et al. (2021), in this section we briefly describe the main structure of the algorithm, which will help in understanding the origins of eventual differences between the true fields and the reconstructed fields. starting from a set of spiv measurements taken over a x,y-plane with a sampling time step ∆ts, the ic method processes the 2d3c velocity planes through an iterative scheme. at each reconstruction iteration, the flow system is evolved forward/backward in time for a time step ∆trec = n∆ts, which is chosen as an integer multiple n of the spiv sampling time step, during which a subset n of spiv planes is introduced in the system and is processed by the following steps: 1. data convection: each data point of the 2d3c velocity planes are convected in the 3d space by the local instantaneous velocity uuu(x,y); 2. 3d interpolation: the resulting velocity data scattered in the 3d space are interpolated on a rectangular, regular cartesian grid; 3. poisson regularization: the poisson equation for the velocity ∇ 2uuu =−∇×ωωω, (1) is applied on the intermediate 3d velocity field, thus recovering a divergence-free flow; 4. planes re-initialization: new 2d3c velocity planes are re-defined from the interior of the regularized 3d velocity field. at the next algorithm iteration, the re-initialized planes along with new ones from the spiv database are processed by the same 4 steps above. the temporal evolution of the flow system happens during the convection step, where virtual fluid particles are associated to each node of the 2d3c velocity plane. because the spiv data do not provide any information on the flow structure in the out-of-plane direction, it is not possible to know how the particle trajectories vary in time and space as soon as the particles leave the spiv measurement plane. therefore, during the convection step of the ic method, the virtual particles are convected in the 3d space at a constant-in-time local velocity, thus forming linear trajectories. the hyperbolic operator that governs the velocity field of this phenomenon is duuu dt = 0, which implicitly corresponds to enforce zero pressure-gradients, ∇p = 0, (2) during the dynamical evolution of the flow. this does not necessarily mean that the pressure integration performed on the reconstructed 3d velocity volumes will provide a pressure field with zero fluctuations, since the right form of the navier-stokes equation is used for pressure reconstruction. however, as it will be shown in section 3, the approximation introduced during the convection step produces evident signatures on the velocity and pressure fields, and represents the most important source of errors introduced by the ic reconstruction. this reconstruction error is, however, limited by the prompt application of the poisson equation on the intermediate 3d velocity field, a regularization that emulates the application of pressure gradients that exist in a divergence-free flow. the mc algorithm consists, instead, in simply convecting the 2d3c velocity data forward and backward in space by means of the out-of-plane component of the mean velocity profile, w(x,y), and then interpolating the final velocity data on a regular 3d cartesian grid. a comparison of the resulting hyperbolic operator, i.e., ∂uuu ∂t +w(x,y) ∂uuu ∂z = 000, with the navier-stokes equations also reveal that the implicit pressure-gradient field applied to the flow during the mean flow convection is (see also laskari et al. (2016)): ∇p =− [uuu−w(x,y) ẑzz] ·∇uuu (3) as for the ic method, the distortions introduced by the pressure field of eq. 3 has direct effects on the accuracy of the reconstructed 3d velocity and pressure fields. the final result of both reconstruction algorithms is a series of velocity volumes on a 3d cartesian grid with a time separation equals to ∆ts, i.e., the sampling time step used for performing spiv measurements. 2.2 pressure reconstruction the reconstruction of the instantaneous pressure field requires first the evaluation of the pressure gradients, which can be inferred from the temporal and spatial evolution of the 3d velocity field: ∇p =−ρ duuu dt =−ρ ∂uuu ∂t +uuu ·∇uuu. (4) in eq. 4, the viscous term has been neglected since its contribution is relevant only in flow regions very close to the wall (schneiders et al., 2016). computations of the viscous term showed it was 2-3 orders of magnitude smaller than the material acceleration term, and including it in the evaluation of the pressure gradient did not provide any visible difference. the evaluation of the velocity material derivative from the time-series of velocity volumes is performed by means of the pseudo-lagrangian approach, which has been shown to be more precise than the eulerian approach when dealing with convective flows (violato et al., 2011). at the initial time t0, virtual particles are distributed at each node of the 3d velocity cartesian grid. each particle trajectory is then reconstructed by evaluation of the particle location at times t±i = t0± i∆ts for i = 1,2, ...,m, with m the number of forward or backward time steps. the particle position at the new time ti+1 = ti±∆ts is produced by using the predictor-corrector method reported in yu et al. (2012), in which the predictor step provides a first estimate of the particle location, xxx∗p (ti±1) = xxxp (ti)±∆tsuuu(xxxp (ti) , ti) , (5) and the corrector step provides the final particle position, xxxp (ti±1) = xxxp (ti)±∆ts 1 2 [ uuu(xxxp (ti) , ti)+uuu ( xxx∗p (ti±1) , ti±1 )] . (6) the material acceleration is then computed with a least squares approach, as proposed by pröbsting et al. (2013). the velocity uuup (t±i) of the particles at time t±i along the reconstructed trajectory is calculated by spline interpolation of the 3d3c velocity data. the material acceleration could be estimated using finite differences by considering any possible time difference ∆ti = ti− t0 with respect to the starting time t0 and the corresponding velocity variation ∆uuu(∆ti) = u j (xxxp (ti))−u j (xxxp (t0)) . this results in an over-determined algebraic linear system for each component j of the material acceleration of the form ∆ttt du j dt = ∆uuu j, (7) with ∆ttt a vector gathering all time differences, and ∆uuu j gathering all corresponding velocity differences for the j-component. the least squares solution of eq. 7 finally provides an estimation of the material acceleration at each node of the original 3d cartesian grid: du j dt = ( ∆tttt ∆ttt ) ∆tttt ∆uuu j (8) at the volume boundaries, the forward/backward advection can move the virtual particles outside of the domain, where velocity information is inaccessible. the pressure gradients computed at the boundaries are therefore cropped out, so to provide more accurate boundary conditions for the pressure integration step. the omni-directional integration method introduced by liu and katz (2006) is capable of efficiently minimizing the influence of local errors in the material acceleration on the final reconstructed pressure field. the poisson-based pressure integration is instead known to be more prone to error propagation, especially when pure neumann conditions are used in large domain (pan et al., 2016). nevertheless, the extension of the original 2d path integration method to 3d domains makes the number of required integration paths so large that a computational parallelization is necessary to make this pressure integration strategy affordable in terms of computational time (wang et al., 2019). we, therefore, opted for a pressure integration based on the simpler and more computationally efficient poisson equation. by taking the divergence of the momentum equation, the poisson equation for the pressure reads: ∇ 2 p =−∇ · ( ρ duuu dt ) , (9) which is completed by applying neumann boundary conditions at each boundary face of the rectangular domain: ∂p ∂n =−ρ duuu dt , (10) with n the spatial coordinate normal to the boundary. the laplacian operator is discretized by second-order centered differences, and the neumann boundary conditions are discretized by adding a ghost point out of the domain. the resulting algebraic linear system is then solved by spectral decomposition, in which virtual particles tracking fft-based poisson solver ∇2𝑝 = −∇ ⋅ 𝜌 𝐷𝒖 𝐷𝑡 3d3c velocity 𝒖𝒓𝒆𝒄 𝑥, 𝑦, 𝑧, 𝑡 material acceleration 𝐷𝒖 𝐷𝑡 𝑥, 𝑦, 𝑧 3d pressure 𝑝𝑟𝑒𝑐 𝑥, 𝑦, 𝑧 least squares estimation 𝒖(𝒙𝑝 𝑡2 , 𝑡2) 𝒖(𝒙𝑝 𝑡3 , 𝑡3) 𝒖(𝒙𝑝 𝑡1 , 𝑡1) particle trajectories planes convection 𝐷𝒖 𝐷𝑡 = 𝟎 2d3c velocity 𝒖𝑆𝑃𝐼𝑉 𝑥, 𝑦, 𝑡 3d interpolation poisson regularization ∇2𝒖 = −∇ × 𝝎 planes re-initialization velocity reconstruction pressure reconstruction figure 1: schematic of the algorithm for 3d pressure reconstruction starting from spiv velocity measurements. the projection of the right hand side onto the matrix eigenspace is performed by means of the fast fourier transform (fft). in order to be able to employ the fft for the projection, the eigenvector matrix has to be orthogonal and composed of cosine and sine functions. to mantain the eigenspace form as such while treating the neumann boundary conditions with ghost points, the poisson equation is solved on a staggered grid instead of the original cartesian mesh. finally, the resulting 3d pressure field is re-interpolated on the original grid, and the spatially averaged pressure over the entire volume is set to zero. the resulting overall procedure for reconstructing 3d pressure fields from spiv data is sketched in figure 1. 3 numerical validation the velocity and pressure 3d reconstructions provided by the ic and the mc methods are validated on the dns data of the turbulent channel flow available on the jhtdb (kim et al., 1987). in the following, all variables are non-dimensional, with the half-height channel h being the reference length and the bulk velocity wb being the reference velocity. the cartesian coordinate system is defined so that the z-axis is oriented towards the main flow direction, the y-axis represents the wall normal coordinate, and the x-axis is oriented in the spanwise direction of the channel. synthetic spiv 2d3c velocity data are sampled on a x,y-plane perpendicular to the main flow direction in a flow region close to the wall, i.e., in the range 150< y+ < 250, which is at the outskirt of the log-law region (pope, 2001). since the jhtdb provides the dns data on an inertial frame of reference moving in the flow direction at speed of 0.45, the synthetic spiv velocity measurements are also taken on the same moving reference frame. this does not pose any particular problem for the purpose of validating the reconstruction algorithms. it reduces the separation between the lagrangian time scale, τη, and the eulerian time scale, which is defined by the convected kolmogorov length scale as τeul = η/w , with w the average speed of the flow in the region under consideration. for a given spiv sampling time step ∆ts, this provides in turns a better resolution of the eulerian spectrum and, thus, a higher spatial resolution of the reconstruction in the flow direction (see fratantonio et al. (2021) for a more in-depth discussion of these aspects). the synthetic spiv measurements are performed at a non-dimensional sampling time step of ∆ts = 0.0065, thus resolving the smallest eddy turn-over times but under-resolving the highest frequency of eulerian spectrum, which is what commonly happens in real spiv measurements. table 1 summarizes the most important flow characteristics, including the kolmogorov time and length scales, estimated from the largest turbulent dissipation rate ε computed from the 3d dns velocity, and the ratio of the spiv sampling time step to the characteristic flow time scales. by defining the velocity fluctuations as uuu′′′ = uuu− uuu, the turbulence intensity is computed from u′rms = √ u′2 + v′2 +w′2. the presence of a shear layer (dw/dy ≈ 1) and of a relatively-high turbulence intensity (u′rms/w ≈ 20%) enhances the improvements provided by the ic method over the mc method, the latter being expected to fail in accurately reconstructing large-scale structures. reb = 2hwb/ν w u′rms w dw dy η = ( ν3 ε )1/4 τη = ( ν ε )1/2 τη = η w ∆ts τη ∆ts τeul 40000 0.49 0.2 1.16 0.0014 0.042 0.0026 0.155 2.5 table 1: non-dimensional flow characteristics. the non-dimensional kinematic viscosity is ν = 5 ·10−5. 3.1 velocity and pressure reconstructions from synthetic spiv data for the velocity reconstruction, each volume is generated from 500 synthetic spiv planes. for reducing the computational time of each reconstruction, the ic algorithm processes n = 10 planes at each iteration, thus the flow reconstruction evolves forward/backward in time with time steps of ∆trec = n∆ts = 0.065. the reconstruction starts from z = 0, the spiv measurement location, and extends downstream, in the z > 0 direction, i.e., the direction of the channel flow, and upstream, in the z < 0 direction. for the pressure reconstruction, the virtual particle tracking is performed with m = 3, by advancing the particles position 3 time steps forward and 3 time steps backward, for which 7 velocity volumes have been used. (a) (b) (c) figure 2: 3d pressure fields reconstructed from: (a) dns velocity; (b) reconstructed ic velocity; (c) reconstructed mc velocity. the spatially averaged pressure is set to zero for all volumes. the reconstructed 3d velocity fields are not shown here, but very similar results in terms of reconstructed 3d vorticity fields can be found in fratantonio et al. (2021). figure 2 reports isosurfaces of the reconstructed 3d pressure fields. the 3d pressure field in figure 2a is reconstructed from the exact dns velocity volumes. the dns pressure field directly available from the jhtdb is in very good match with that of figure 2a, thus validating the pressure reconstruction tools (the material derivative computation and the poisson solver) developed for this work. figures 2b and 2c show the pressure fields reconstructed by, respectively, the ic method and the mc method. in general, neither of the reconstruction methods are able to fully reproduce the pressure field correctly, especially on top and bottom of the volume, which are flow regions that are the furthest from the measurement plane location, z = 0, where the reconstruction errors on the reconstructed velocity are the highest ones. the ic method seems providing a reconstructed pressure field that does not recover all small scale pressure fluctuations, but well reproduces large structures such as the two large negative pressure lobes in the upstream region, −0.2 < z < 0. in contrast, the pressure field reconstructed by the mc method show the same large structures in the wrong location, being convected with the wrong speed and distorted by the mean shear layer profile ∂w ∂y . however, the 3d pressure fields shown in figure 2 allow us to visualize only the results at the domain boundaries, where the reconstruction errors are the largest both for the velocity and pressure reconstructions. for a better and more meaningful comparison of the ic and mc reconstructions, we reported in figure 3 the 2d maps of the vorticity and of the pressure fields at a x,z-plane cutting the 3d volumes of figure 2 at the center, at about y = 0.73. the vector fields on top of the 2d pressure maps correspond to the inplane velocity fluctuations (u′,w′). a qualitative comparison of the 2d maps of figure 3 demonstrate that the ic method provides better reconstruction than the mc method, both in terms of vorticity and pressure fields. with reference to figure 3c, the mc method tends to distort the flow field. the mean velocity u′ w′ ‖ωωω‖ p ic 0.973 0.996 0.887 0.898 mc 0.626 0.965 0.565 0.871 table 2: correlation coefficients computed on the 2d maps of figure 3 for different flow properties. profile w(x,y) moves the vortical structures with the wrong speed, so that they end in the wrong position and stretched by the mean shear layer. for instance, by considering the two strong vortices in the upstream region (−0.2< z<−0.1) indicated by the arrows in figure 3, one of them is stretched in the flow direction, while the second one is not even present in the flow field, being convected too far upstream. the ic vorticity is instead in much better match with the exact vorticity field, with all vortical structures located in the right spot, and no distortion is present. the higher reconstruction accuracy of the ic method is further corroborated by the correlation coefficients reported in table 2, which have been computed over the same 2d plane for different flow properties. it is, however, evident that the ic method tends to reduce the intensity of the strongest vortices in the field, as it happens for the intense vorticity regions indicated by the arrows in figure 3. as also discussed in fratantonio et al. (2021), these features are a direct consequence of how the 2d3c velocity data are convected in the 3d space. with the implicit zero-pressure gradients enforced on the flow during the convection step of the ic method, there is no pressure gradient field that would keep a vortex together as it happens in divergence-free flow. there are no pressure forces that would prevent those fluid portions at the vortex center that rotate faster to crash on and to compress outer fluid layers that rotate slower. this results in an expansion of the vortices, with a consequent weakening of their intensity. in the reconstructed pressure field, the amplitude of the negative pressure fluctuations at the center of the weakened vortices is, consequently, smaller. (a) (b) (c) figure 3: instantaneous enstrophy (top row) and pressure (bottom row) fields over a 2d plane cutting the volumes of figure 2 at y = 0.73: (a) dns data; (b) ic reconstruction; (c) mc reconstruction. the 2d pressure map in (a) is extracted from the 3d pressure field reconstructed from the dns velocity volumes. the vector fields on top of the pressure maps represent the in-plane velocity fluctuations (u′,w′). the arrows indicate the same vortices and the corresponding negative pressure fluctuations regions across the various reconstructions. 3.2 reconstruction error analysis for a more quantitative analysis of the reconstruction accuracy, we analyzed the error between the exact dns fields and the reconstructed ones. for the velocity reconstruction, we define the relative error εu = ‖uuurec−uuuex‖2 ‖uuuex‖2 . (11) in figure 4a, we reported the average value of εu computed over x,y-planes cutting the reconstructed 3d velocity field at different z-positions along the flow direction. in figure 4b, we also reported the correlation coefficient between the dns vorticity and the reconstructed vorticity fields computed on the same 2d cuts as a function of z. as expected, the relative error εu increases as a function of the distance from the spiv measurement plane location, i.e., z = 0, where the error is identically zero, since the reconstructed volume is centered on the synthetic spiv velocity plane extracted directly from the dns data. while the mc method provides 3d velocity fields with reconstruction errors that go up to more than 15%, the ic method is able to provide reconstructions with about half the errors, with maximum values of less than 10%. the improvements provided by the ic method are even more evident by looking at the results of figure 4b, showing an evident drastic drop in the correlation between the dns vorticity and the mc vorticity fields, even for reconstructed volumes as small as z = [−0.05;0.05], and a much better match of the ic reconstruction with the exact vorticity field, with correlation cofficients of about 0.9 even for reconstructed volumes as large as z = [−0.15;0.15]. although not shown here, curves very similar to those of figure 4b can be obtained for the turbulent dissipation rate ε. (a) (b) (c) figure 4: (a) average velocity reconstruction error εu as a function of z; (b) correlation coefficient between exact enstrophy field and reconstructed enstrophy field as a function of z; (c) absolute value of the average pressure reconstruction error εp as a function of z. the square, blue symbols refer to the ic reconstruction, and the circle, brown symbols to the mc reconstruction. the average errors and the correlation coefficient are computed over x,y-planes at each z-location, with z = 0 corresponding to the position of the spiv measurement plane. defining a relative error for the pressure reconstruction similar to that of eq. 11 gives error values that are very high, as high as 1000% in regions of the flow where the pressure value is close to zero. nevertheless, the errors in the reconstructed 3d velocity fields are in the range 5-15%, and, for such error levels in the velocity data, similar high relative errors on the reconstructed pressure has been observed even in application of the poisson-based integration method to 2d flows (charonko et al., 2010). for the same amount of errors in the velocity data, it has been observed that the omni-directional integration method is more efficient to average out the local errors in the pressure gradients computed from noisy velocity data, although the relative errors on the reconstructed pressure can still be very high in flow regions where the pressure is close to zero. for having a more meaningful comparison between the ic and the mc methods in terms of pressure reconstruction accuracy, we consider instead a definition of the pressure error similar to that proposed in wang et al. (2019), in which the pressure error difference is normalized by the turbulent kinetic energy: εp = prec− pex t keex . (12) in eq. 12, we defined t keex = 1 2 ρ ( u′2ex + v′2ex +w′2ex ) as a spatially-averaged turbulent kinetic energy of the dns velocity fluctuations, and we considered as reference pressure pex the 3d pressure field reconstructed from the dns velocity volumes. figure 4c reports the average error εp computed as a function of z. since the errors in the velocity reconstructed by the mc method are higher, the ic algorithm performs in general better even in terms of pressure reconstructions, except in the region −0.1 < z < 0, where the ic errors are slightly higher than the mc ones. as for εu, the average error εp is almost zero close to z = 0 and increases with the distance from the spiv measurement plane location, which indicates how the accuracy of the pressure reconstruction is directly affected by the local errors in the velocity data and the computed material acceleration. an analysis of the local error distribution can provide a better insight on the exact origin of the errors in the velocity and pressure reconstructions. with reference to the 2d maps of figure 3, the local value of the pressure error εp is shown in figure 5, where the vector field represents the error on the reconstructed in-plane velocity fluctuations. the average value of the error distributions of figure 5 are 0.004 and 0.0194 respectively for the ic and the mc pressure reconstructions. with reference to figure 5, the local pressure error given by the mc reconstruction is almost everywhere higher than that given by the ic method. more precisely, the largest velocity and pressure errors in the ic reconstruction are localized at the center of the strongest vortices in the flow. as discussed in the previous section, the inherent expansion of the strong vortices that occurs during the convection step of the ic method results in weakening the intensity of the vortices and, consequently, in a lower magnitude of the depressions at the center of the same vortices. (a) (b) figure 5: local pressure reconstruction error εp given by (a) the ic method and (b) the mc method for the 2d pressure field shown in figure 3. the vector field represents the error on the in-plane velocity fluctuations, i.e., (u′rec−u′ex,w ′ rec−w′ex). 4 velocity-pressure reconstruction from spiv measurements the reconstruction algorithms are applied to real experimental spiv measurements performed in the turbulent mixing tunnel facility at los alamos national laboratory. the tunnel has a cross section area of 0.524×0.524 m2, inside which an air jet is issued downward from a circular copper pipe with inner diameter d = 11 mm, and a coflow is generated by a fan located downstream. spiv measurements are carried out at a sampling frequency of fs = 2 khz by using two high-speed phantom® veo 640s cameras working in dual-exposure mode, and a dual head nd:yag laser delivering 20 mj/pulse at 532 nm. the spiv measurement plane is perpendicular to the jet flow direction and is located at a distance 16d downstream from the pipe outlet. currently, the experimental facility does not include simultaneous, alternative diagnostic techniques for providing measurements of pressure or velocity, and, therefore, we cannot directly assess the accuracy of the velocity-pressure reconstructions. we limit the following analysis to a comparison of the reconstructions provided by the ic and the mc methods. for this experimental test, we considered an air jet with an average speed of 6.3 m/s at the pipe outlet, which corresponds to a reynolds number re = 4250, and a coflow speed of about 0.8 m/s. at the measurement location, the average speed at the jet centerline is 2.2 m/s. figures 6a and 6b show the 3d vorticity and pressure fields reconstructed by, respectively, the ic method and the mc method. the appearance of more vortical structures in the mc reconstruction is partly due to the vortex-expansion issue affecting the ic convection and partly due to the smoothing effect of the iterative poisson regularization. the vorticity and pressure reconstructions around the spiv measurement plane are very much alike for the ic and mc methods, corroborating the error analysis of section 3.2. however, as the reconstruction develops in the upstream and downstream directions, the two reconstructions become qualitatively different in terms of position, orientation, and magnitude of the pressure and velocity fields, for which the numerical analysis of the previous section suggests that the ic reconstruction is more accurate than the mc one. (a) (b) figure 6: reconstructed 3d velocity and pressure fields from experimental spiv data: (a) ic reconstruction; (b) mc reconstruction. the brown isosurfaces correspond to the z-component of the vorticity with value |ωz| = 400s−1. the green isosurfaces correspond to the azimuthal component of the vorticity with value |ωθ|= 500s−1. the countour maps and lines correspond to the reconstructed pressure field. 5 conclusions in this work, we numerically and experimentally investigated 3d pressure reconstructions starting from 2d3c spiv velocity measurements. we numerically demonstrated that the ic method introduced in fratantonio et al. (2021) is more accurate than the mc method in reconstructing 3d velocity and pressure fields in turbulent flows with shear layer. in section 4, we presented a practical demonstration of the reconstruction algorithms on real spiv measurements of an air jet in coflow. as for the mc method, the ic method can be applied only to convective flows, in which the flow is crossing the spiv measurement plane in one direction only. this guarantees the existence of a main flux of flow information filling the reconstruction domain. for this reason, the presence of a coflow around the main jet is required for extending the volumetric reconstruction to outer flow regions. the error analysis presented in section 3.2 also revealed that the largest reconstruction errors introduced by ic method are mainly localized in the regions of strong vorticity. currently, we are working in improving the ic algorithm from this point of view, thus further improving both 3d velocity and pressure reconstructions. the ic algorithm is, therefore, a promising processing tool for obtaining accurate 3d velocity and pressure fields from time-resolved spiv measurements. references charonko jj, king cv, smith bl, and vlachos pp (2010) assessment of pressure field calculations from particle image velocimetry measurements. measurement science and technology 21:105401 de kat r and ganapathisubramani b (2012) pressure from particle image velocimetry for convective flows: a taylor’s hypothesis approach. measurement science and technology 24:024002 dennis dj and nickels tb (2008) on the limitations of taylor’s hypothesis in constructing long structures in a turbulent boundary layer. journal of fluid mechanics 614:197 elsinga ge, scarano f, wieneke b, and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 fratantonio d, lai cc, charonko j, and prestridge k (2021) beyond taylor’s hypothesis: a novel volumetric reconstruction of velocity and density fields for variable-density and shear flows. experiments in fluids 62:1–25 ganapathisubramani b, lakshminarasimhan k, and clemens n (2008) investigation of three-dimensional structure of fine scales in a turbulent jet by using cinematographic stereoscopic particle image velocimetry. journal of fluid mechanics 598:141 gesemann s, huhn f, schanz d, and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser and imaging techniques to fluid mechanics, lisbon, portugal. pages 4–7 huhn f, schanz d, gesemann s, and schröder a (2016) fft integration of instantaneous 3d pressure gradient fields measured by lagrangian particle tracking in turbulent flows. experiments in fluids 57:1–11 jakobsen m, dewhirst t, and greated c (1997) particle image velocimetry for predictions of acceleration fields and force within fluid flows. measurement science and technology 8:1502 kim j, moin p, and moser r (1987) turbulence statistics in fully developed channel flow at low reynolds number. journal of fluid mechanics 177:133–166 laskari a, de kat r, and ganapathisubramani b (2016) full-field pressure from snapshot and time-resolved volumetric piv. experiments in fluids 57:44 lin cc (1953) on taylor’s hypothesis and the acceleration terms in the navier-stokes equation. quarterly of applied mathematics 10:295–306 liu x and katz j (2006) instantaneous pressure and material acceleration measurements using a fourexposure piv system. experiments in fluids 41:227–240 novara m and scarano f (2013) a particle-tracking approach for accurate material derivative measurements with tomographic piv. experiments in fluids 54:1–12 pan z, whitehead j, thomson s, and truscott t (2016) error propagation dynamics of piv-based pressure field calculations: how well does the pressure poisson solver perform inherently?. measurement science and technology 27:084012 pope sb (2001) turbulent flows. iop publishing pröbsting s, scarano f, bernardini m, and pirozzoli s (2013) on the estimation of wall pressure coherence using time-resolved tomographic piv. experiments in fluids 54:1–15 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:1–27 schneiders jf, pröbsting s, dwight rp, van oudheusden bw, and scarano f (2016) pressure estimation from single-snapshot tomographic piv in a turbulent boundary layer. experiments in fluids 57:53 schneiders jf and scarano f (2016) dense velocity reconstruction from tomographic ptv with material derivatives. experiments in fluids 57:1–22 van gent p, michaelis d, van oudheusden b, weiss pé, de kat r, laskari a, jeon yj, david l, schanz d, huhn f et al. (2017) comparative assessment of pressure field reconstructions from particle image velocimetry measurements and lagrangian particle tracking. experiments in fluids 58:33 van oudheusden b (2013) piv-based pressure measurement. measurement science and technology 24:032001 violato d, moore p, and scarano f (2011) lagrangian and eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic piv. experiments in fluids 50:1057–1070 wang j, zhang c, and katz j (2019) gpu-based, parallel-line, omni-directional integration of measured pressure gradient field to obtain the 3d pressure distribution. experiments in fluids 60:1–24 wang z, gao q, wang c, wei r, and wang j (2016) an irrotation correction on pressure gradient and orthogonal-path integration for piv-based pressure reconstruction. experiments in fluids 57:1–16 yu h, kanov k, perlman e, graham j, frederix e, burns r, szalay a, eyink g, and meneveau c (2012) studying lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database. journal of turbulence page n12 zaman k and hussain a (1981) taylor hypothesis and large-scale coherent structures. journal of fluid mechanics 112:379–396 introduction reconstruction algorithms velocity reconstruction pressure reconstruction numerical validation velocity and pressure reconstructions from synthetic spiv data reconstruction error analysis velocity-pressure reconstruction from spiv measurements conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 pressure reconstruction of a planar turbulent flow field within a multiply-connected domain with arbitrary boundary shapes x.liu1∗, j. r. moreto1 1 san diego state university, department of aerospace engineering, san diego, california, usa ∗ xiaofeng.liu@sdsu.edu abstract figure 1: (a) the original rotating parallel ray omni-directional integration method for a simply-connected domain; (b) illustration of implementation of the rotating parallel ray omni-directional integration algorithm in a multiply-connected domain. over the past two decades, it has been demonstrated that the instantaneous spatial pressure distribution in a turbulent flow field can be reconstructed from the pressure gradient field non-intrusively measured by particle image velocimetry (piv). representative pressure reconstruction methods include the omnidirectional integration (liu and katz, 2006; liu et al., 2016; liu and moreto, 2020), the poisson equation approach (violato et al., 2011; de kat and van oudheusden, 2012), the least-square method (jeon et al., 2015), and most recently, the adjoint-based sequential data assimilation method, which also essentially utilizes the poisson equation to reconstruct the pressure(he et al., 2020). most of these previous pressure reconstruction examples, however, were applied to simply-connected domains (gluzman et al., 2017) only. none of these previous studies have discussed how to apply the pressure reconstruction procedures to a multiply-connected domain (gluzman et al., 2017). to fill in this gap, this paper presents a detailed report for the first time documenting the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply-connected domain that has arbitrary inner and outer boundary shapes. the pressure reconstruction algorithm used in the current study is the rotating parallelray omni-directional integration algorithm, which, as demonstrated in reference (liu and moreto, 2020) based on simply-connected flow domains, offers high-level of accuracy in the reconstructed pressure. while preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. validation of the multiply-connected domain pressure reconstruction code is conducted using the dns (direct numerical simulation) isotropic turbulence field available at the johns hopkins turbulence databases, with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. for further validation, the code is also applied for pressure reconstruction from the dns pressure gradient in the ambient flow field of a shock-induced non-spherical bubble collapse in water (johnsen and colonius, 2009). the successful implementation of the parallel ray pressure reconstruction method to multiply-connected domains paves the way for a variety of important applications including, for example, experimental characterization of pressure field changes during the process of cavitation bubble inception, growth and collapse, non-intrusive unsteady aerodynamic force assessment for an arbitrary body shape immersed in flows, and multi-phase flow investigations, etc. in particular, as an immediate follow-up effort, the parallel ray pressure code will be used for the instantaneous pressure distribution reconstruction of the turbulent flow surrounding cavitation inception bubbles occurring on top of a cavity trailing corner based on high-speed piv measurements. the original rotating parallel ray omni-directional integration method for simply-connected domain is illustrated in figure 1(a). this method utilizes parallel rays as guidance paths for line integration of pressure gradient. by rotating the parallel rays, effectively omni-directional paths with equal weights coming from all directions toward the point of interest at any location within the computation domain can be generated. to reduce the effect of erroneous pressure along the boundary, the parallel ray omni-directional integration algorithm utilizes iterations of boundary pressure values in the integration process. initially, integration along the perimeter of the measurement domain gives the initial boundary pressure values, but since each boundary node is crossed by numerous paths, the initial boundary values can be corrected/replaced with the results of the omni-directional integration. the integration process is then repeated using the new boundary values and the iterations proceed until the results converge within an acceptable threshold level, thus achieving accurate dirichlet conditions for boundary pressure values. the convergence of the boundary pressure calculation follows an exponential decay fashion, as demonstrated theoretically in liu and moreto (2020). once the accurate boundary pressure values are achieved, the pressure values over the entire domain can then be determined by invoking the final round of the omni-directional integration across the domain. the aforementioned key features of the rotating parallel ray omni-directional integration are preserved during the implementation of the same algorithm in a multiply-connected domain with arbitrary domain boundary shapes, as shown in figure 1(b). a bold parallel ray serving as guidance for the line integration penetrates the planar domain at boundary point a. along the way it encounters the inner void boundaries at points b, c, d and e, respectively, and finally leaves the entire domain at boundary point f. pressure values at all the boundary points identified in this way, including both the inner and the outer domain boundary points, will then go through the boundary value iteration process, as outlined in the procedures described in liu and moreto (2020). after achieving convergence, the pressure at inner nodal points within the multiplyconnected domain will then be calculated. please note during the entire pressure reconstruction process, nodal points within the void areas are not involved in any form of calculations. sample results for pressure reconstruction within multiply-connected domains based on the hopkins isotropic turbulence database are shown in figure 2. performance assessment based on the 1000 statistically independent pressure gradient field realizations with the added random noise (will show in the presentation) indicates that, like the simply-connected domain case demonstrated in liu and moreto (2020), the parallel ray algorithm outperforms the poisson equation approach in terms of the reconstructed pressure accuracy. as an example of further validation, figure 3 shows one sample comparison of the instantaneous dns pressure and the corresponding reconstructed pressure using the parallel ray code. the 2-σ deviation of the pressure difference between the reconstructed and the original dns pressures shown in the figure 3(d) is 0.03% of the maximum pressure (i.e., the shock pressure ps) in the field. please note that the procedures described in this paper can be readily extended to 3d applications. acknowledgements this work has been sponsored by the office of naval research grant no. n00014-21-1-2392 (dr. k.-h. kim is the program officer). the authors would like to thank professor tim colonius for his permission of the use of his shock-induced non-spherical bubble collapse dns data in this research. the help from mr. jose rodolfo chreim in retrieving the bubble collapse dns data, and the help from dr. minping wan and professor charles meneveau in retrieving the isotropic turbulence dns data from jhtdb are all gratefully acknowledged. both authors contributed equally to this paper. figure 2: sample pressure reconstruction results using the parallel ray code for a multiply-connected domain with arbitrary boundary shapes based on a dns isotropic turbulence database. (a) and (b), pressure gradient distributions; (c) reconstructed pressure distribution; (d) difference between the reconstructed and the original dns pressure fields; (e) histogram of the difference between the reconstructed and the dns pressure fields. references de kat r and van oudheusden b (2012) instantaneous planar pressure determination from piv in turbulent flow. experiments in fluids 52:1089–1106 gluzman s, mityushev v, and nawalaniec w (2017) computational analysis of structured media. academic press he c, liu y, and gan l (2020) instantaneous pressure determination from unsteady velocity fields using adjoint-based sequential data assimilation. physics of fluids 32:035101 jeon yj, chatellier l, beaudoin a, and david l (2015) least-square reconstruction of instantaneous pressure field around a body based on a directly acquired material acceleration in time-resolved piv. in symp. part. image velocim.-piv15 johnsen e and colonius t (2009) numerical simulations of non-spherical bubble collapse. journal of fluid mechanics 629:231–262 liu x and katz j (2006) instantaneous pressure and material acceleration measurements using a fourexposure piv system. experiments in fluids 41:227–240 liu x and moreto jr (2020) error propagation from the piv-based pressure gradient to the integrated pressure by the omnidirectional integration method. measurement science and technology 31:055301 liu x, moreto jr, and siddle-mitchell s (2016) instantaneous pressure reconstruction from measured pressure gradient using rotating parallel ray method. in 54th aiaa aerospace sciences meeting. page 1049 violato d, moore p, and scarano f (2011) lagrangian and eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic piv. experiments in fluids 50:1057–1070 figure 3: sample instantaneous pressure reconstruction from the dns pressure gradient of a shock-induced non-spherical bubble collapse in water. (a) the dns pressure from johnsen and colonius (2009); (b) the reconstructed pressure; (c) the difference between the reconstructed and the original dns pressure fields, normalized by the maximum pressure i.e., the shock pressure ps; (d) the probability density function (pdf) of the relative pressure difference. the white region in the plots indicates the deformed bubble during the collapse process. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 analysis of the contribution of large scale motions to the skin friction of a zero-pressure-gradient turbulent boundary layer using the renard-deck decomposition b. sun1∗, m. shehzad1, d. jovic1, c. cuvier2, c. willert3, y. ostovan2, jm. foucaut2, c. atkinson1, j. soria1 1 laboratory for turbulence research in aerospace & combustion (ltrac), department of mechanical and aerospace engineering, monash university, victoria 3800, australia 2 université lille nord de france, lmfl laboratoire de mécanique des fluides de lille, fre cnrs 2017, centrale lille, ensam, onera, villeneuve d’ascq, france 3 institute of propulsion technology, german aerospace center (dlr), cologne, germany ∗ bihai.sun@monash.edu abstract coherent flow structures in turbulent boundary layers have been an active field of research for many decades, as they might be the key to reveal the mechanics of turbulence production and transport in turbulent shear flows. renard and deck (2016) proposed a theoretical decomposition for the mean skin-friction coefficient based on the mean kinetic energy budget in the streamwise direction. this decomposition, referred to as the renard-deck (rd) decomposition, decomposes the mean skin friction generation into three physical mechanisms in an absolute reference frame, namely, direct viscous dissipation, turbulent kinetic energy production, and spatial growth. in this study, the large scale motions (lsms) are extracted using a proper orthogonal decomposition (pod) of the velocity field based on high-spatial-resolution two-dimensional – two-component particle image velocimetry (hsr 2c-2d piv) of a zero-pressure-gradient turbulent boundary layer (zpg-tbl), and their effect on the skin friction via rd decomposition. the high reynolds number turbulent boundary layer experiment was performed at the laboratoire de mécanique des fluides de lille (lmfl) in the lmfl high reynolds number boundary layer wind tunnel. the measurement took place in the streamwise – wall-normal plane along the centreline of the wind tunnel, where the zpg-tbl at the measurement location has a free-stream velocity of 9m/s, a reynolds number based on the momentum thickness of reθ = 8,120, a boundary layer thickness of δ ≈ 103mm and a viscous length of l+ ≈ 40µm. the piv images were captured with a 47mp imperx tiger t8810 camera which has a 57mm-diagonal array of size 8,864× 5,288 pixels. this results in a field of view of 255mm×152mm, or 2.46δ×1.45δ in terms of the boundary layer thickness, with a spatial resolution of 21.7 wall units in the streamwise direction and 5.42 wall units in the wall-normal direction. a more detailed description of the experiment, as well as an analysis on the method to correct for the lens distortion introduced by the large sensor size, can be found in sun et al. (2021). the lsms present in the zpg-tbl are extracted from the velocity field using pod by the snapshot method (sirovich, 1987). due to the limited field of view of the acquired data, the lsms in the present study are defined as the flow structures that have a wall-normal extent of approximately the full boundary layer, which are identified by the most energetic pod mode as shown in figure 1a. this mode accounts for 16% of the turbulent kinetic energy in the flow. velocity field snapshots containing stronger lsms than others are identified using the time coefficient of the most energetic pod mode, φ1, whose distribution is presented in figure 1b. the distribution of φ1 is gaussian-like, with its absolute value representing the strength of the lsm present in each snapshot. therefore, the following criterion is used to determine the snapshots containing strong lsms, |φ1,n| ≥ kσφ1 , (1) where φ1,n represents the time coefficient of the most energetic pod mode for snapshot n, and σφ1 represents the standard deviation of the time coefficient for all snapshots. a higher k value represents a tighter selection criterion. 0 1 2 x/ 0 1 y / (a) 200 0 200 time coeffcients 0 500 1000 1500 n u m b e r o f sn a p sh o ts (b) all 0.5 1.0 1.5 2.0 2.5 k 0.3 0.4 0.5 0.6 s tr e a m w is e a v e ra g e d c f b /c f (c) figure 1: (a) a vector plot of the fluctuating velocity of the most energetic pod mode. the colours of the vectors represent the velocity fluctuation magnitude. the red dashed line represents the boundary layer thickness. (b) distribution of the time coefficient of the most energetic pod mode, φ1. the red dashed line represents ±2.5σ, ±2σ, ±1.5σ, ±σ, ±0.5σ and the mean value of φ1. (c) streamwise averaged c fb/c f for different k values. the error bars in c fb/c f represents its standard deviation along the streamwise direction. renard and deck (2016) decomposition (rd decomposition) of the skin friction coefficient based on the mean kinetic energy budget of the fluid motion in an absolute frame of reference, which is given by c f = 2 u3 e ∫ ∞ 0 µ ( ∂u ∂y )2 dy︸ ︷︷ ︸ c fa + 2 u3 e ∫ ∞ 0 −〈u′v′〉∂u ∂y dy︸ ︷︷ ︸ c fb + 2 u3 e ∫ ∞ 0 (u−ue) ∂ ∂y ( τ ρ ) dy︸ ︷︷ ︸ c fc , (2) where τ = µ(∂u/∂y)−〈u′v′〉, u denotes the mean streamwise velocity, ue denotes the free stream velocity, 〈u′v′〉 denotes the reynolds shear stress, µ denotes the dynamic viscosity and ρ denotes the density. the rd decomposition decomposes the skin friction into physically interpretable terms that are local at each streamwise position. the first term, c fa represents the viscous dissipation of the mean streamwise kinetic energy, and it depends only on the mean values of the fluid field therefore has no direct contribution from the lsms. the second term, c fb , represents the production of the turbulent kinetic energy extracted from the mean streamwise kinetic energy and is the term of relevance in the analysis of the contribution of lsms. the last term, c fc , accounts for the growth of the boundary layer effect, as the growth of the boundary layer is slow for a zpg-tbl, this term is negligible. a conditional statistics analysis is performed by calculating the c fb term using the snapshots containing strong lsms as identified by equation 1. the resulting streamwise averaged value of c fb/c f for different threshold value k is presented in figure 1c. this results show that lsm dominated snapshots results in an increase of c fb , indicating that the lsms are a significant contributor to the turbulent production term in the rd decomposition of the skin friction. acknowledgements this research was supported by the australian government through the australian research council’s discovery projects funding scheme. the research was also benefited from computational resources provided by the pawsey supercomputing centre and through ncmas, supported by the australian government. the computational facilities supporting this project included the nci facility, the partner share of the nci facility provided by monash university through an arc lief grant and the multi-modal australian sciences imaging and visualisation environment (massive). daniel jovic and bihai sun are supported by a research training program (rtp) scholarship provided by the australian government. references renard n and deck s (2016) a theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer. journal of fluid mechanics 790:339–367 sirovich l (1987) turbulence and the dynamics of coherent structures. i. coherent structures. quarterly of applied mathematics 45:561–571 sun b, shehzad m, jovic d, cuvier c, willert c, ostovan y, foucaut jm, atkinson c, and soria j (2021) distortion correction of two-component – two-dimensional piv using a large imaging sensor with application to measurements of a turbulent boundary layer flow at reτ = 2,386. experiment in fluids microsoft word ispiv-2021-abstract-pressure-uncertainty_v4.docx 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 | chicago, il usa uncertainty of piv/ptv based pressure, using velocity uncertainty jiacheng zhang1, sayantan bhattacharya1, and pavlos p. vlachos1,2* 1 school of mechanical engineering, purdue university, west lafayette, in 47907, usa 2 weldon school of biomedical engineering, purdue university, west lafayette, in 47907, usa *pvlachos@purdue.edu abstract pressure reconstruction from velocity measurements using particle image velocimetry (piv) and particle tracking velocimetry (ptv) has drawn significant attention as it can provide instantaneous pressure fields without altering the flow. previous studies have found that the accuracy of the calcualted pressure field depends on several factors including the accuarcy of the velocity measurement, the spatiotemporal resolutions, the method for calculating pressure-gradient, the algorithm for pressure-gradient integration, the pressure boundary condition, etc. therefore, it is critical and challenging to quantify the uncertainty of the reconstructed pressure field. the recent development of the uncertainty quantification algorithms for piv and ptv allows for the local and instantaneous uncertainty estimation of velocity measurement, which can be used to infer the pressure uncertainty. in this study, we introduce a framework that propagates the standard velocity uncertainty defined as the standard deviation of the velocity error distribution through the pressure reconstruction process to obtain the uncertainty of the pressure field. the uncertainty propagations through the calculation of the pressure-gradient and the pressure-gradient integration were modeled as linear transformations, which can reproduce the effects of the spatiotemporal resolutions, the numerical schemes, the integration algorithms, and the pressure boundary condition on the accuracy of the resulting pressure fields. the proposed uncertainty estimation approach also considers the effect of the spatiotemporal and componentwise correlation of the velocity errors in common piv/ptv measurements on the pressure uncertainty. the method was firstly validated with synthetic flow fields for the reconstructions by solving the pressure poisson equation (ppe) and using the least-squares methods (ols, wls, gls) [1]. the synthetic flow fields were generated from a 2d pulsatile channel flow and were contaminated with varying levels of artificial noise that were correlated in space, time, and between components. the root-mean-square (rms) of the pressure error and uncertainty normalized by the characteristic pressure are compared in figure 1 as functions of the velocity noise level (𝛼). for ppe and ols, the rms uncertainty matched the rms error for cases with 𝛼 <10% but overestimated by about 10% for cases with greater noise. at low noise levels (𝛼 ≤5%), the rms uncertainty of wls and gls reconstructions were underestimated by 40-60%, while the rms uncertainty was within 10% of the rms error for the other noise levels. at high noise levels (𝛼 >10%), the rms uncertainty was overestimated by about 3% for wls while underestimated by 5% for gls. figure 1 the rms of pressure error and uncertainty from velocity fields with different noise level the method was then applied to the experimental velocity measurement of a vortex ring acquired using plannar piv [2]. to account for the effect of the interrogation window overlap on the spatial autocorrelation of velocity errors [3], the autocorrelation coefficient was approximated using a gaussian function of the spatial separation as: 𝜌 = exp*ln*𝑤!". × 𝑟#., (1) where 𝑤!" is the window overlap, and 𝑟 represents the spatial separation normalized by the grid resolution, thus, 𝜌 = 𝑤!" between neighboring velocity measurements. the streamwise velocity field is shown in figure 2(a). the histograms of velocty error and uncertainty quantified by the moment of correlation (mc) method [4] are presented in figure 2(b). the histograms of the pressure error and the estimated uncertainty for the reconstruction using ppe are compared in figure 2(c). as indicated by the rms values, the velocity uncertainty underestimated the velcoity error by 27%, while the pressure uncertainty was 21% lower than the pressure error. as suggested in figure 2(d), the pressure uncertainty showed a similar trend across field as the pressure error but was underestimated around the vortex cores, resulting in more uniform spatial distributions. the method was further applied to the volumetric ptv measurement of a laminar pipe flow [5]. the errors and estimated uncertainties are compared in figure 3(a) for the velocity fields obtained with an iterative particle reconstruction (ipr) based 3d reconstruction [6] and nearest-neighbor tracking, and the pressure fields reconstructed using ppe. as suggested by the rms values, the velocity uncertainty was 10% higher than the velocity error, while the pressure uncertainty was 7% higher than the pressure error. as shown in figure 3(b), the spatial distribution of the pressure uncertainty was consistent with the pressure error as they were both lowest at the center point of the inflow plane (at x=0 mm and r=0 mm) where the reference pressure was imposed. efforts are ongoing to estimate the uncertainty of pressure reconstructed from velocity measurements using volumetric piv. references [1] zhang j, bhattacharya s and vlachos p p 2020 using uncertainty to improve pressure field reconstruction from piv / ptv flow measurements exp. fluids 61 1–20 [2] kähler c j, astarita t, vlachos p p and sakakibara j 2016 main results of the 4th international piv challenge exp. fluids 57 1–71 [3] sciacchitano a and wieneke b 2016 piv uncertainty propagation meas. sci. technol. 27 084006 [4] bhattacharya s, charonko j j and vlachos p p 2018 particle image velocimetry ( piv ) uncertainty quantification using moment of correlation ( mc ) plane meas. sci. technol. 29 115301 [5] bhattacharya s and vlachos p p 2020 volumetric particle tracking velocimetry (ptv) uncertainty quantification exp. fluids 61 [6] wieneke b 2013 iterative reconstruction of volumetric particle distribution meas. sci. technol. 24 024008 figure 2 (a) the streamwise velocity field (b) the histograms of velocty error and uncertainty (c) the histograms of the pressure error and uncertainty with the rms values indicated by the vertical lines. (d) the spatial distributions of the normalized pressure error and uncertainty. figure 3 (a) the histograms of the normalized errors and uncertainties in the velocity and reconstructed pressure fields. the rms values are indicated using the vertical lines. (b) the spatial distributions of the pressure error and uncertainty from the ppe reconstruction. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 highly accurate optical flow method based on volumetric segmentation for 3d piv hua yang1∗, hang shi1, jin lu1, menggang kang1, zhouping yin1 1 huazhong university of science and technology, state key laboratory of digital manufacturing equipment and technology, wuhan, china ∗ huayang@hust.edu.cn abstract in this study, we present a new three-dimensional optical flow method based on volumetric segmentation for the velocity estimation of fluid flow. the proposed method uses a segmented smoothness term that is designed on the assumption that the particle velocity varies continuously in each segmented volume and discontinuously on the surfaces of the segmented volumes. subsequently, the data term is proposed on the basis of the segmented volumes and the fluid mass conservation equation, which is derived from the reynolds transport equation. in addition, the robust local level-set method is applied to segment the particle volume according to the velocity distribution of fluid flow. the proposed method is evaluated quantitatively on synthetic data and qualitatively on experimental data, and the velocity results are compared to the advanced 3d velocity estimation methods. the results indicate that the proposed method can obtain velocity fields with greater measurement accuracy for tomo-piv. 1 introduction as a non-contact velocity measurement technique, particle image velocimetry (piv) has a very wide range of applications such as aerodynamics, biological fluid mechanics, micro-scale complex flow, etc (raffel et al., 2018). with the development of laser lighting technology and image acquisition technology, piv has been extended from 2d velocity measurement to 3d velocity measurement (lasinger et al., 2020). tomographic particle image velocimetry (tomo-piv), as a 3d three-component velocity measurement technology developed from 2d piv, has been studied by many researchers (scarano, 2013). in tomo-piv measurement, the tracer particles are first seeded into the fluid flow. then, a thick laser slice is used to illuminate a measurement volume, which is observed by multiple cameras distributed in different views. subsequently, the particle distribution in the region of interest is reconstructed by the multiplicative algebraic reconstruction technique (mart) from the multi-view image in each frame (elsinga et al., 2006). finally, the 3d velocity field within a chosen interrogation volume is obtained by 3d cross-correlation method (discetti and astarita, 2012). among the various technical problems of tomo-piv, improving the accuracy and resolution of the velocity field estimated from the particle volume has received the most attention (scarano, 2013). after decades of development, the velocity estimation methods in tomo-piv can be divided into crosscorrelation-based methods and optical flow-based methods. in 3d cross-correlation methods, the particle volumes are divided into several fixed-size interrogation volumes, the correlation coefficient of two interrogation volumes in two successive particle volumes is calculated through the fast fourier transform, then the velocity vector in each interrogation volume is determined by the position of the correlation peak (lu et al., 2021). because of its strong robustness, the 3d cross-correlation methods have been widely used in tomopiv. discetti and astarita (2012) presented a 3d cross-correlation method based on voxel binning for quick estimation of the predicted displacement field. a 3d cross-correlation method based on gradient iterative volume deformation was proposed by cheminet et al. (2014). although these 3d cross-correlation methods have achieved significant improvements in accuracy, they still cannot achieve accurate velocity field measurement. the velocity vector obtained by the 3d cross-correlation methods can be interpreted as the spatial average velocity in the interrogation volume. the resolution of the estimated velocity field is restricted by the size of the interrogation volume, which makes it unsuitable for flow field measurement with a rapidly changing velocity field. alternatively, the global optical flow method, which can provide velocity fields with pixel-level resolution, has been verified in 2d piv and extended to tomo-piv (ruhnau et al., 2005). the 3d global optical flow methods use a global energy function composed of a data term and smoothness term to replace the interrogation volume in the 3d cross-correlation methods, in which the data term assumes that the given points retain the same intensity in the particle volume along their trajectories, and the smoothness term assumes that all neighboring points have similar motions. alvarez et al. (2009) first introduced the global optical flow method to the research field of tomo-piv, which includes the incompressibility of the flow as a constraint to the minimization problem. lasinger et al. (2017) presented a 3d version of the global optical flow model, augmented with a physically based smoothness term for incompressible fluids. although these 3d global optical flow methods are constantly improving the measurement accuracy of the velocity field in tomo-piv, they still cannot obtain results with higher accuracy because of global energy function constraints (lu et al., 2019). because the global energy function constraints will make the rapidly changing velocity field too smooth, and the fine structure cannot be preserved. therefore, improving the accuracy of 3d global optical flow methods for rapidly changing velocity field measurement is an urgent problem to solve. in this study, we propose a volumetric-segmentation-based optical flow (vs-of) method for highly accurate tomo-piv measurements. a segmented smoothness term is designed on the assumption that the velocity varies continuously within each segmented volume and discontinuously on the surfaces of the segmented volumes. subsequently, the data term is proposed on the basis of the segmented volumes and the fluid mass conservation equation, which is derived from the reynolds transport equation. in addition, the robust local level-set method is applied to segment the particle volume according to the velocity distribution of the fluid flow. the rest of the present paper is organized as follows. in section 2, the proposed vs-of method is described in detail. experimental analysis is given in section 3. conclusions drawn from the present work are summarized in section 4. 2 the proposed vs-of method 2.1 framework of the vs-of method in tomo-piv measurement, the accurate measurement of the velocity field is of great significance for the subsequent in-depth analysis of the flow structure. in this study, a volumetric-segmentation-based optical flow method is proposed. the main process of the vs-of method is shown in fig. 1. an initial velocity field (u0,v0,w0) is first estimated by the 3d optical flow of the vs-of method. subsequently, the initial velocity field is provided as an initialization for the next velocity field segmentation task. according to the segmentation results of the velocity field, the next step of optical flow calculation is guided. after several iterations, the final finer velocity field (u,v,w) is obtained. in traditional 3d global optical flow methods, due to the global energy function constraints, the velocity field is smoothed in the iterative calculation of optical flow. therefore, in order to avoid smoothing, the vsof method segments the 3d velocity field calculated in the previous step in each optical flow iteration. it should be noted that the segmentation operation is implemented on the three components of the velocity field rather than on the velocity magnitude, as shown in fig. 1. then, the particle volumes e (t) and e (t +dt) are segmented according to the segmentation result of the velocity field, and the segmented velocity field is taken as the initial value of the next optical flow iteration. the above process is repeated to obtain an accurate 3d velocity field. the proposed vs-of method has excellent comprehensive performance in terms of flow velocity estimation due to the process of velocity field segmentation. the segmented smoothness term and data term in the vs-of method will be presented and discussed in the following subsections. 2.2 a segmented smoothness term inspired by the level set segmentation method (li et al., 2007), a segmented smoothness term is designed on the assumption that the velocity varies continuously within each segmented volume and discontinuously on the surfaces of the segmented volumes. in addition, the segmented smoothness term can segment the particle volume according to the 3d velocity distribution of the fluid flow. without loss of generality, we simplify the smoothness term to consider only the u component—that is, to minimize eq. 1:∫ ωu kσ|∇u|2dx+ ∫ ωc u kσ|∇u|2dx+µ |su| (1) figure 1: concept of the proposed vs-of method. where u = (u,v,w)t is the velocity vector at location x, ωu denotes the segmented volumes in the u component, ωc u is the complement of ωu, su is the closed parameterized surface of the segmented volumes ωu, |su| is the area of surface su, µ is a parameter constraining the surface of a segmented volume to be as smooth as possible, and kσ denotes a gaussian kernel with standard deviation σ. drawing lessons from the idea of (li et al., 2007), the unknown evolution surface is replaced with the level set function φu(x) : φu(x) > 0 if x is inside the closed surface su, φu(x) < 0 if x is outside su, and φu(x) = 0 if x is on su. we can approximate |su| = ∫ ω |∇h(φu)|dx = ∫ ω δ(φu) |∇φu|dx, and eq. 1 can be rewritten as follows:∫ ω ( h(φu)kσ|∇u|2 +(1−h(φu))kσ|∇u|2 ) dx+ ∫ ω µδ(φu) |∇φu|dx = ∫ ω ( kσ|∇u|2 +µδ(φu) |∇φu| ) dx (2) where h(φ) is the heaviside function, which is equal to 1 if φ ≥ 0 and to 0 if φ < 0; δ(φ) is the dirac function, and δ(φ) = h ′(φ). generally, the heaviside function h(φ) in eq. 2 is approximated by a smooth function defined by: h(φ) = 1 2 [ 1+ 2 π arctan(φ) ] (3) the dirac function δ(φ), the derivative of h(φ), is the following smooth function: δ(φ) = h ′(φ) = 1 π 1 1+φ2 (4) we now extend the segmented smoothness term to three components, and eq. 2 can be expressed as follows: ev s smooth = ∫ ω ( kσ|∇u|2 +µδ(φu) |∇φu| ) dx+ ∫ ω ( kσ|∇v|2 +µδ(φv) |∇φv| ) dx + ∫ ω ( kσ|∇w|2 +µδ(φw) |∇φw| ) dx (5) 2.3 a segmented data term define a new segmentation surface s0 based on the segmented surface su, sv and sw:s0 = su ∪ sv ∪ sw = {(x,y,z)|φu(x,y,z) = 0,φv(x,y,z) = 0,φw(x,y,z) = 0}, and ω0 denotes the segmented volume surrounded by s0. consistent with the smoothness term, we replace the segmented surface s0 with the level set function φ0. therefore, we propose the segmented data term on the basis of the fluid mass conservation equation, which is derived from the reynolds transport equation: ∫ ω0 ( ∂e ∂t +∇e ·u+e divu )2 dx+ ∫ ωc 0 ( ∂e ∂t +∇e ·u+e divu )2 dx (6) in addition, for the segmented volumes, the material density in the fluid remains constant, and the divergence of the velocity is zero: divu = ∇ · u = 0. in other words, the fluid is incompressible in each segmented volume ω0. we can derive a simplified segmented data term by constraining divu = 0: ev s data = ∫ ω h(φ0) ( ∂e ∂t +∇e ·u )2 dx+ ∫ ω (1−h(φ0)) ( ∂e ∂t +∇e ·u )2 dx = ∫ ω ( ∂e ∂t +∇e ·u )2 dx (7) where ω is the entire particle volume. based on eqs. 5 and 7, the model of the proposed vs-of method is as follows: ev s=αev s data +ev s smooth =α ∫ ω ( ∂e ∂t +∇e ·u )2 dx+ ∫ ω ( kσ|∇u|2+µδ(φu) |∇φu| ) dx + ∫ ω ( kσ|∇v|2+µδ(φv) |∇φv| ) dx+ ∫ ω ( kσ|∇w|2+µδ(φw) |∇φw| ) dx (8) where α is a parameter controlling the balance between the data term and smoothness term. finally, the multiscale technique and image warping operation are implemented in the segmented particle volumes to avoid falling into local optimal solutions and obtain an accurate velocity field. 3 experimental analysis 3.1 experimental setup in order to make a quantitative comparison with the proposed vs-of method, we extend the multiple-pass cross-correlation method provided by thielicke and stamhuis (2014) and the global optical flow method proposed by ruhnau et al. (2005) to three dimensions. in terms of numerical evaluation indicators, the root mean square error (rmse) and average angle error (aae), which are often used to verify accuracy in the field of optical flow (alvarez et al., 2009; lu et al., 2019), are used to quantitatively evaluate the experimental results: rmse = √ 1 n n ∑ i=1 |ut i −ue i | 2 (9) aae = 1 n n ∑ i=1 arccos ( ut i ·ue i |ut i| |ue i | ) (10) where ut and ue denote the ground truth and the estimated velocity field, respectively. n is the total number of voxels in the estimated particle volume, and the subscript i represents the voxel coordinates. method synthetic particle volume reconstructed particle volume rmse aae rmse aae 3d cross-correlation 0.46 9.77 0.62 13.38 3d global optical flow 0.24 6.68 0.47 12.57 the proposed vs-of 0.21 5.76 0.39 10.49 figure 2: left: velocity contours of the ground truth in the u component. right: rmse and aae errors of the velocity fields for the synthetic and reconstructed particle volumes estimated by different methods. figure 3: velocity contours estimated from the synthetic particle volumes (top) and reconstructed particle volumes (bottom) in the u component on the z = 0 plane. left to right: contours estimated by the 3d cross-correlation method, the 3d global optical flow method, and the proposed vs-of method, as well as the ground truth. 3.2 synthetic data in the synthetic data, the ground truth velocity field from the johns hopkins turbulence database provided by li et al. (2008) is used to quantitatively evaluate the proposed vs-of method. the velocity field comprises a numerically generated 3d isotropic turbulent flow with an average velocity of 1.3 voxels and a maximum velocity of 2.9 voxels. a synthetic particle volume of 640×640×300 voxels is generated with a random seed density of approximately 0.1 particles per pixel. the particles are projected onto four cameras with 1024×1024 pixels at viewing angles of ±35◦ with respect to the x = 0 plane and ±18◦ with respect to the y = 0 plane. then, the particle volume is reconstructed using the reimplementation of mart proposed by scarano (2013) with a quality factor q = 0.79. to distinguish the influence of mart, the synthetic particle volume (without mart) and the reconstructed particle volume (with mart) are used to evaluate the different methods. the results for the synthetic and reconstructed particle volumes estimated by the different methods are presented in fig. 2. due to the influence of mart, the rmse and aae errors of the reconstructed particle volume are larger than those of the synthetic particle volume, but the errors of the proposed vs-of method are smaller than those of the other two methods on both the synthetic and the reconstructed particle volumes. the velocity contours in the u component on the z = 0 plane estimated by the proposed vs-of method exhibit behavior similar to the ground truth, as shown in fig. 3. figure 4: left: real experiment scene of cylinder wake (michaelis et al., 2006). right: spectrum analysis of the velocity fields for the experimental data. figure 5: velocity contours in the xy-slice of the flow on the z = 203 plane. top to bottom: reference flow field in u, v, and w components provided by michaelis et al. (2006); estimated flow field in u, v, and w components by the proposed vs-of method. 3.3 experimental data in this subsection, we present qualitative results of the experimental data in the water flow (michaelis et al., 2006). the experimental data package contains of two particle volumes of 2107×1434×406 voxels. it is a karman vortex street behind a cylinder with a diameter d =12mm, which is positioned to the left of the volume, with water flowing to the right, as shown in fig. 4. the velocity contours in the xy-slice of the flow on the z = 203 plane estimated by the proposed vs-of method are shown in fig. 5. in addition to our own results, we also show the reference flow field provided in the experimental data package, which is processed by the 3d cross-correlation method (elsinga et al., 2006). the results indicate that our method can better preserve the flow field structure with a rapidly changing velocity field compared to the reference flow. to better investigate the performance of the proposed vs-of method, spectrum analysis is performed for the two processing methods, as shown in fig. 4. the spectrum obtained by the proposed vs-of method is closer to the -5/3 spectrum slope. from this experiment, we can conclude that the proposed vs-of method is suitable for velocity field estimation in experimental data. 4 conclusions in this study, we propose a novel 3d optical flow method based on volumetric segmentation for the velocity estimation of fluid flow. the proposed vs-of method uses a segmented smoothness term designed on the assumption that the particle velocity varies continuously in each segmented volume and discontinuously on the surfaces of the segmented volumes. the data term is proposed on the basis of the segmented volumes and the fluid mass conservation equation, which is derived from the reynolds transport equation. in addition, the robust local level-set method is applied to segment the particle volume according to the velocity distribution of the fluid flow. to verify the performance of the proposed vs-of method, we evaluate it quantitatively on synthetic data and qualitatively on experimental data. it can be seen from the synthetic data that compared with the 3d cross-correlation method and 3d global optical flow method, the proposed vs-of method can obtain velocity fields with greater accuracy. finally, we demonstrate the good performance of the proposed vs-of method in a real cylinder wake flow experiment. acknowledgements this work was supported by the national natural science foundation of china (grant no. 51875228), the national key r&d program of china (grant no. 2020yfa0405700), and the national defense science and technology innovation special zone project (grant no. 193-a14-202-01-23). references alvarez l, castano c, and garcı́a m (2009) a new energy-based method for 3d motion estimation of incompressible piv flows. computer vision and image understanding 113:802–810 cheminet a, leclaire b, and champagnat f (2014) accuracy assessment of a lucas-kanade based correlation method for 3d piv. in 17th international symposium on applications of laser techniques to fluid mechanics, lisbon, portugal, july 7-10 discetti s and astarita t (2012) fast 3d piv with direct sparse cross-correlations. experiments in fluids 53:1437–1451 elsinga ge, scarano f, and wieneke b (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 lasinger k, vogel c, and pock t (2020) 3d fluid flow estimation with integrated particle reconstruction. international journal of computer vision 128:1012–1027 lasinger k, vogel c, and schindler k (2017) variational 3d-piv for incompressible fluid flow estimation. in 12th international symposium on particle image velocimetry, busan, korea, june 18-22 li c, kao cy, and gore jc (2007) implicit active contours driven by local binary fitting energy. in ieee conference on computer vision and pattern recognition, minneapolis, mn, usa, june 17-22 li y, perlman e, and wan m (2008) 3d fluid flow estimation with integrated particle reconstruction. journal of turbulence 9:1–29 lu j, yang h, and zhang q (2019) a field-segmentation-based variational optical flow method for piv measurements of nonuniform flows. experiments in fluids 60:142 lu j, yang h, and zhang q (2021) an accurate optical flow estimation of piv using fluid velocity decompositions. experiments in fluids 62:78 michaelis d, poelma c, and scarano f (2006) a 3d time-resolved cylinder wake survey by tomographic piv. in 12th international symposium on flow visualization, göttingen, germany, september 10-14 raffel m, willert ce, and scarano f (2018) particle image velocimetry: a practical guide. springer ruhnau p, kohlberger t, and schnörr c (2005) variational optical flow estimation for particle image velocimetry. experiments in fluids 38:21–32 scarano f (2013) tomographic piv: principles and practice. measurement science and technology 24:012001 thielicke w and stamhuis e (2014) pivlab–towards user-friendly, affordable and accurate digital particle image velocimetry in matlab. journal of open research software 2:e30 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 application of simultaneous time-resolved 3-d ptv and two-colour lif in studying rayleigh-benard convection sina kashanj and david s. nobes∗ university of alberta, department of mechanical engineering, edmonton, canada * dnobes@ualberta.ca abstract to study the flow topology and temperature distribution of rayleigh-benard convection in a highly slender cell, measurement of the simultaneous velocity and temperature in the 3-d domain is required. for this aim, implementing a simultaneous time-resolved 3-d ptv and two-colour plif is planned. as a part of this development, for both ptv and two-colour plif techniques, the experimental setup has been implemented separately to measure time-resolved 2-d velocity and temperature and is presented in this paper. for ptv, a scanning system is also utilized to scan the flow field to capture the planar velocity in different depths of the flow domain. progress on calculation of the out-of-plane velocity component including the theory is discussed. finally, results of the time-resolved 2-d ptv and plif systems are presented. 1 introduction buoyancy-driven flow in an enclosure heated from below and cooled from above is known as rayleigh-benard convection, (rbc) adrian (2013). rbc is an idealized flow system to study the flow and heat transfer of a wide spectrum of phenomena and applications from engineering to geophysical subject matter couston et al. (2019). different parameters such as the temperature of the heat source and sink, working fluid and geometry of the cell can affect the convective heat transfer coefficient in rbc zwirner et al. (2020). it is also shown that the number of large scale circulations (lscs) which is dependent on the geometry itself can affect the heat transfer zwirner et al. (2020). measuring the temperature of the flow field in rbc is crucial in experimental studies, since it is almost accepted that the kinetic and thermal energy both are added to the flow by the rise and fall of the thermal plumes adrian (2013). there are different techniques to measure the temperature such as thermocouples, liquid crystal thermography, phosphorescent thermography, and fluorescent thermography. planar laserinduced fluorescence (plif) is a non-intrusive fluorescent thermography technique that can be applied for measurement of the temperature of liquid and gaseous flow fields sakakibara and adrian (1999). to reduce the effect of uncertainty sources such as laser fluctuation and increase the temperature sensitivity, two-colour plif technique has been developed. rhodamine b and rhodamine 110 are a common pair of fluorescent dyes for two-colour plif in aqueous flow kim and kihm (2001), song and nobes (2011). it is shown that by pairing other fluorescent dyes such as fluorescein-rhodamine b, fluorescein-kiton red, and fluorescein-rhodamine 101 the temperature sensitivity can be enhanced up to around ~7 % ℃⁄ for high temperatures (~50 ℃) sutton et al. (2008). it is also shown that for low temperatures, 𝑇 < 20 ℃ the temperature sensitivity decreases significantly behshad et al.(2010). the highest temperature sensitivity obtained in the range of 5 < 𝑇 < 20 ℃ is around ~4.2 % ℃⁄ behshad et al.(2010). to visualize the flow field of rbc and investigate the effect of the flow structures, measurement of the velocity of the flow field is required. particle tracking velocimetry (ptv) which is a non-intrusive velocity measurement technique can be applied to measure the velocity with high spatial resolution raffel et al. (2018). to capture the out of plane velocity and obtain all three velocity components, scanning 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 has been used with particle image velocimetry (piv), and ptv in a variety of cases with steady or low velocity conditions such as in microfluidics (by applying confocal microscopy) bown et al. (2007) and in natural convection studies fujisawa et al. (2005), kazemi et al. (2016). since the scanning technique can be applied in cases with small geometries and can be applied simultaneously with other techniques such as plif, it is an advantageous technique in comparison to other 3-d velocity measurement techniques such as tomographic piv or 3dptv. a simultaneous time-resolved 3-d ptv and two-colour plif system is under development by the authors. the aim of this paper is to investigate the approach to develop such a system to measure the velocity and temperature of a large aspect ratio square cross-section rbc cell. furthermore, the next steps to achieve the 3-d simultaneous measurement such as the theory of calculating the out-of-plane velocity component is discussed. 2 experimental setup the slender cell of the rbc with dimensions of 5×5×50 mm3 and aspect ratio, 𝛤 = 𝑊 ℎ⁄ equal to 0.1 is shown in figure 1(a). windows are made from acrylic sheet with a thickness of 6.35 mm that has a low thermal conduction coefficient of 0.2 w mk⁄ . based on the described test cell, the temperature boundary condition which is shown in figure 1(a) can be described as a temperature constant at the top and bottom and adiabatic at the side walls. the field of view (fov) of the imaging systems where the temperature and velocity investigation was carried out is also shown in figure 1(a). a rendering of the physical set of the slender cell used for this experiment is shown in figure 1(b). two heat exchangers contain a base and a copper plate is connected to the two water baths. the base is fabricated by additive manufacturing (form3, formlabs inc.) using a clear resin material with a low thermal conduction coefficient (0.15 w mk⁄ ). (a) (b) figure 1: (a) a schematic of the dimensions and boundary conditions of the test cell and (b) a rendering of the solid model of the slender rectangular rbc cell and a schematic of the optical measurement system set to apply 3-d ptv and two-colour plif is shown in figure 2(a) and (b) respectively. a diode pump laser with a maximum power of 2 w and wavelength of 532 nm was used to illuminate the seeding particles and excite the fluorescent dyes. two scanning mirrors (thorlabs inc.) are used to make the laser sheet (scanning mirror-y) and scan the laser sheet in the depth of the channel, z-direction (scanning mirror-z). as can be observed in figure 2(a), a double convex lens with a focal length of 80 mm after the scanning mirrors makes the laser sheet parallel to the x-y plane in each z. to apply 3-d ptv, an 8-bit high-speed cmos cameras (flare 12m125, io industries inc.) with a maximum frame rate of 220 fps and resolution of 2048 pixels × 2048 pixels is utilized. the optical system used to apply two-colour plif, shown in figure 2(b), is the same as the 3-d ptv optical system, but instead of one camera, two cameras, one for each colour of fluorescent dye is used with an appropriate filter used used to capture the signal of each dye separately. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) (b) figure 2: schematic of the optical measurement system used for (a) 3-d ptv and (b) two-colour lif a two-channel function generator is used to control the frequency and amplitude of the scanning mirrors. a signal generator also is utilized to synchronize the cameras and the two scanning mirrors. a timing plot of the signals generated to control the scanning mirrors and synchronize them with the cameras is illustrated in figure 3. in this figure, signal a is the waveform that scan the laser sheet in depth of the test section. the initial voltage of this waveform defines the initial position of the laser sheet in the z-direction (by the voltage-space calibration). for this experiment 50 slices with 0.1 mm space are used to scan the depth of the channel in 12.5 s, which is significantly faster than the time scale of motion for this flow which is on the order of minutes. the laser sheet thickness is equal to ~150 mm which makes the scans with 50 % overlap. signal b in figure 3 is set to scan the laser beam in the y-direction to make the laser sheet. signal c is a ttl signal generated to control the framerate of the cameras and synchronize the cameras with the scanning mirrors. for each plane, five ttl signals were generated to capture five frames at each plane. ptv processing is applied to each captured five frames for each plane since scanning is used only after establishment of the steady fully-developed flow. figure 3: schematic diagram of the three signals produced to synchronize the two scanning mirrors and the cameras. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 3 two-colour plif to apply the two-colour plif, sodium fluorescein (fl) and kiton red (kr) were chosen as the fluorescent dyes. properties of the two fluorescent dyes is shown in table 1. a schematic of the variation of the absorption and emission spectra of the dyes with wavelength is illustrated in figure 4 along with the location of the illumination laser at 532 nm. though the absorption wavelength of fl has a limited interface with the 532 nm light, it still can be excited with sufficient power. to avoid receiving the signal of the laser, a notch filter (edmund optics) with central wavelength (cwl) of 532 nm and full width at half maximum (fwhm) of 17 nm is utilized which is shown with light gray in figure 4 the fl signal (which is shown with light green in figure 4) was collected using a bandpass filter (edmund optics) with cwl of 525 nm and fwhm of 50 nm. the 532 nm laser light is also used to excite kr and the emitted signal has a maximum temperature sensitivity in the range of 560 to 620 nm bown et al. (2007). therefore, to capture the kr signal with maximum temperature sensitivity and to avoid receiving the fl emitted signal, a bandpass filter (edmund optics) with cwl of 607 nm and fwhm of 36 nm is used, shown in light orange in figure 4. table 1: properties of the fluorescent dyes used in two-colour lif fluorescent dye empirical formula molecular weight 𝜆𝑎𝑏𝑠 at peak (nm) 𝜆𝑒𝑚 at peak (nm) fluorescein c20h10na2o5 376.27 586 490 kiton red c27h29n2nao7s2 580.65 565 514 figure 4: a plot of the absorption and emission signal variation with wavelength of fl and kr (after behshad et al. (2010) ). different colours show the different filter wavelength range and the laser wavelength as can be seen in figure 5, fl has a positive temperature sensitivity that is equal to ~ + 1.7 % ℃⁄ . kr has the temperature sensitivity of ~ − 1.6 % ℃⁄ which makes it a good pair with fl to have a maximum temperature sensitivity under a ratiometric condition. the intensity-temperature calibration graph which shows the linear relation between the emitted signal intensity and the temperature of each fluorescent dye can be seen in figure 5(a). the intensity-temperature calibration of the fluorescent dyes which lead to figure 5(a) has been done using a dye calibration cell (lavision gmbh) with the same conditions of the experiments and in the range of 15 ℃ < 𝑇 < 40 ℃. the ratiometric intensity-temperature graph, figure 5(b), shows the temperature measurement with the maximum temperature sensitivity of ~ 4.9 % ℃⁄ . 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) (b) figure 5: normalized intensity-temperature calibration graph. (a) one colour, fl and kr calibration, 𝐼𝑟𝑒𝑓 = 𝐼(𝑇 = 40 ℃) (b) ratiometric intensity-temperature, 𝑅(𝑇) = 𝐼𝐹𝑙(𝑇) 𝐼𝐾𝑟(𝑇)⁄ 4 time-resolved ptv to apply ptv, hollow glass spheres with a diameter of 18 μm were used as seeding particles. a raw image of the fluid domain with seeding particles is shown in figure 6(a). the ability of the seeding particle following the fluid flow is crucial in buoyancy-driven flows and specifically for this work because the density of flow is changing. the experiment starts from a stationary condition with no flow and the flow field was captured over the long time scale (3000 seconds) of the flow with the flow pattern became steady. seeding particles rising velocity due to the buoyancy force can be described by: 𝑉𝑟𝑖𝑠𝑒 = 2𝜌𝑔𝐷𝑝 2∆𝜌 9𝜇𝜌 (1) which is derived from stokes drag force of a spherical particle. here, 𝑉𝑟𝑖𝑠𝑒 is the rising velocity, 𝜌 is the density of the fluid, ∆𝜌 the density difference of the particle with the fluid, 𝑔 is gravitational acceleration, 𝐷𝑝 is the diameter of particles, and 𝜇 is the dynamic viscosity of the fluid. considering this equation, the maximum of 𝑉𝑟𝑖𝑠𝑒 is estimated at 30 μm s⁄ which is deemed a significantly low value for this experiment. also, a relaxation time of 30 minutes is implemented before the start of the experiment to ensure that the flow has achieved a stationary condition. the piv result after the relaxation time shows that the motion of the seeding particles is negligible and it can be considered stationary. ptv processing was applied using a commercial software (davis 10.0.5, lavision gmbh) after background subtraction was applied to enhance the seeding particle intensity contrast with the background to improve their detectability, as shown in the example figure 6(a). particle detection criteria are defined as the seeding particles with the size in the range of 2 to 5 pixels and with an intensity higher than 20 counts. the camera frame rate is set to 30 fps, so the seeding particle’s motion with the lowest velocity (at the start of the convection) to the highest velocity (developed flow) can be captured time-resolved. the depth of focus of the camera’s lens is set to cover the whole 5 mm depth of the field. calibration results show that the magnification change in the depth can be neglected. the velocity vectors obtained from the ptv processing are shown in figure 6(b). as can be observed the velocity vectors are dispersed base on the motion and location of each detected seeding particle. to plot the velocity contour from the calculated velocity vectors, the dispersed data of the velocity is interpolated onto a structured grid with the size of 16 pixels. the results of the non-dimensional velocity contour, 𝑉∗ = 𝑉 𝑉𝑚𝑎𝑥⁄ can be observed in figure 6(c). 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) (b) (c) figure 6: ptv procedure to calculate velocity vectors. (a) image of the field of view showing the seeding particles image before and after background subtraction, (b) velocity vectors obtained from ptv at 𝑡 = 1391 s, (c) velocity contour and streamline obtained from interpolation on the structured grid at 𝑡 = 1391 s the described procedure of the velocity calculation was applied on each plane at different depths of the test cell (z-direction) and results in the calculation of the velocity component in x-y plane, 𝑉𝑥 and 𝑉𝑦. to calculate the out-of-plane velocity component, 𝑉𝑧, the continuity equation: 𝜕𝑉𝑧 𝜕𝑧 + 𝜕𝑉𝑥 𝜕𝑥 + 𝜕𝑉𝑦 𝜕𝑦 = 0 (2) can be applied. the first order discretized form of this equation can be expressed as: ( 𝜕𝑉𝑥 𝜕𝑥 )𝑖,𝑗,𝑘 = 𝑉𝑥𝑖+1,𝑗,𝑘 − 𝑉𝑥𝑖,𝑗,𝑘 ∆𝑥 (3) ( 𝜕𝑉𝑦 𝜕𝑦 )𝑖,𝑗,𝑘 = 𝑉𝑦𝑖,𝑗+1,𝑘 − 𝑉𝑦𝑖,𝑗,𝑘 ∆𝑦 (4) ( 𝜕𝑉𝑧 𝜕𝑧 )𝑖,𝑗,𝑘 = 𝑉𝑧𝑖,𝑗,𝑘+1 − 𝑉𝑧𝑖,𝑗,𝑘 ∆𝑧 (5) considering the nonslip boundary condition in which 𝑉𝑥 = 𝑉𝑦 = 𝑉𝑧 = 0, equation(3) to (5) can be solved implicitly on the structured grid for all the 50 planes captured by scanning the flow domain. in these 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 equations, 𝑖, 𝑗, and 𝑘 represent the discretization in 𝑥, 𝑦, and 𝑧 direction with ∆𝑥, ∆𝑦, and ∆𝑧 distance. this calculation results in obtaining the out-of-plane velocity distribution for the whole fluid domain. 4 results temperature measurement, 𝑇∗ = (2𝑇) ((𝑇𝑚𝑎𝑥 + 𝑇𝑚𝑖𝑛))⁄ , for the onset of convection are shown in figure 7(a) to (d). in this case, the temperature of the bottom and top surfaces are equal to 45 ℃ and 5 ℃ respectively. before the onset of convection, the fluid is at the stationary condition and the temperature of the fluid is constant and equal to 𝑇∗ = −0.35. as can be observed in the figure, the convection starts by rising and falling a hot and cold plume respectively. figure 7(c) shows the first interaction between the two plumes which leads to temperature moderation of each part of the flow (hot and cold) and formation of two columns of the flow, a hot column at the right-hand side and a cold column at the left-hand side shown in figure 7(d). the result of the temperature distribution shows a significant temperature variation during the 3000 seconds of the experiment for this regime, 𝑅𝑎 = 5.5 × 108. the temperature distribution after 1391 seconds is shown in figure 7(e). despite of figure 7(c) which has two thermal zones, in this figure the temperature distribution is more complex. (a) (b) (c) (d) (e) figure 7: temperature variation at the different times (a) 𝑡 = 8 s, (b) 𝑡 = 19 s, (c) 𝑡 = 34 s, (d) 𝑡 = 54 s, (e) 𝑡 = 1391 s for the same experimental conditions, the results of the ptv, 𝑉∗ = (2𝑉) ((𝑉𝑚𝑎𝑥 + 𝑉𝑚𝑖𝑛))⁄ is shown in figure 8(a) to (d). though the results are taken in two separate experiments, the velocity vectors describe the same phenomenon at the onset with a small time difference visualized with the temperature distribution. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 from figure 8(a) and (b), the rise and fall of the hot and cold plumes can be observed. figure 8(c) shows the first interaction between these plumes and figure 8(d) shows the flow structure in which two thermal zones were described, figure 7(d). comparing figure 7(d) and figure 8(d) it can be observed that the hot zone is the rising zone and the cold zone is the falling zone. (a) (b) (c) (d) (e) figure 8: velocity variation at the different times (a) 𝑡 = 8 s, (b) 𝑡 = 20 s, (c) 𝑡 = 36 s, (d) 𝑡 = 64 s, (e) 𝑡 = 1391 s the results of the velocity visualization during onset of the flow shows that this regime is unsteady. the velocity of the flow field at 𝑡 = 1391 s, is shown in figure 8(e) which three lscs can be observed. though the time of this ptv result is same as what was shown for the temperature in figure 7(d), the flow topology is much more complex rather at onset, which makes it more difficult to compare the thermal plume dynamics with the velocity. this observation shows the importance of collecting simultaneous measurements of the temperature and velocity to fully characterize the flow. as an example of the in-plane flow structure evaluation in different elevenation in the z-direction, is shown in figure 9 for five different depths of the test cell. this shows the evaluation of the flow structure from 𝑧∗ = −0.041 to 𝑧∗ = 0.041 where 𝑧∗ = 𝑧 𝐻⁄ . the series of 50 planes from 𝑧∗ = − 0.05 to 𝑧∗ = 0.05 is going to use to calculate out-of-plane velocity component. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) (b) (c) (d) (e) figure 9: velocity distribution on the different planes (in z-direction). (a) z* = 0.041, (b) z* = 0.033, z* = 0, z* = 0.033, z* = 0.041 conclusion the methodology of applying time-resolved 2-d ptv and two-colour plif on studying the rbc in a highly slender cell with an aspect ratio of 0.1 was discussed. for time-resolved two-colour plif, the procedure of the fluorescent dye selection and calibration were discussed. furthermore, the result of the temperature measurement for different times were shown. regarding the velocity measurement, implementation of a scanning system to apply 2-d ptv at different depths of the flow domain was shown with presenting the results of the different depths. all the presented work was a part of a procedure for applying these two techniques simultaneously in the future. acknowledgement the authors acknowledge financial support from future energy systems (fes) and the natural sciences and engineering research council (nserc) of canada. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 references b. adrian (2013) convection heat transfer. john wiley and sons, inc. jeffrey a sutton, brian t fisher, and james w fleming. (2008) a laser-induced fluorescence measurement for aqueous fluid flows with improved temperature sensitivity. experiments in fluids 45:869–881 behshad, m, shafii, chee, l lum, and manoochehr m koochesfahani (2010) in situ lif temperature measurements in aqueous ammonium chloride solution during uni-directional solidification. experiments in fluids 48:651–662 bown, m. r., j. m. macinnes, and r. w.k. allen. (2007) three-component micro-piv using the continuity equation and a comparison of the performance with that of stereoscopic measurements. experiments in fluids 42: 197–205 couston, louis alexandre, daniel lecoanet, benjamin favier, and michael le bars. (2019) shape and size of large-scale vortices: a universal fluid pattern in geophysical fluid dynamics. physical review research 2: 23143 fujisawa, n., s. funatani, and n. katoh. (2005) scanning liquid-crystal thermometry and stereo velocimetry for simultaneous three-dimensional measurement of temperature and velocity field in a turbulent rayleigh-bernard convection. experiments in fluids 38: 291–303 kazemi, mohammad amin, janet a w elliott, and david s nobes. (2016) determination of the three components of velocity in an evaporating liquid from scanning piv. in 18th international symposium on applications of laser techniques to fluid mechanics. kim, h. j., and k. d. kihm. (2001) application of a two-color laser induced fluorescence (lif) technique for temperature mapping. in american society of mechanical engineers, heat transfer division lohse, detlef, and ke qing xia. (2010) small-scale properties of turbulent rayleigh-benard convection. annual review of fluid mechanics 42: 335–64 miroshnichenko, i. v., and m. a. sheremet. (2018) turbulent natural convection heat transfer in rectangular enclosures using experimental and numerical approaches: a review. renewable and sustainable energy reviews 82: 40–59 raffel, markus, willert, christian e., scarano, fulvio, kähler, christian j., wereley, steve t., kompenhans, jürgen (2018) particle image velocimetry: a practical guide. springer sakakibara, j, and r j adrian. (1999) whole field measurement of temperature in water using two-color laser induced fluorescence. experiments in fluids 26: 7-15 song, xudong, and david s. nobes. (2011) experimental investigation of evaporation-induced convection in water using laser based measurement techniques. experimental thermal and fluid science 35: 910–19. lukas zwirner, andreas tilgner, and olga shishkina. (2020) elliptical instability and multiple-roll flow modes of the large-scale circulation in confined turbulent rayleigh-benard convection. physical review letters 125, 05402 https://link.springer.com/journal/348 https://link.springer.com/journal/348 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 development of optical techniques for large volume ptv measurements h. abitan1,2∗, y. zhang1, s. l. ribergård1, j. s. nielsen2, c. m. velte1 1 turbulence research laboratory, technical university of denmark, department of mechanical engineering, kgs. lyngby, denmark 2 instrument group, technical university of denmark, department of mechanical engineering, kgs. lyngby, denmark ∗ haiab@mek.dtu.dk abstract measurements of 3d volumetric velocity fields are of great theoretical interest with numerous practical applications. these measurements are essential for studying volumetric flows that do not exhibit inherent flow symmetry, such as turbulence or vortex breakdown. in the past decade, several technological innovations facilitated the emergence of 3d-ptv techniques for measuring velocity fields at khz rate with volumes of interest up to 104 cm3 that contain 300 µm helium-filled soap bubbles. however, when a commercial laser beam with millijoule pulse-energy is expanded and shaped to fill volumes above 102 cm3 for 3d-ptv experiments with 15 µm air filled soap bubbles, one finds that the power density of the laser source is insufficient to generate a signal image. this is because the power density of the laser beam falls inversely with respect to its cross-section area and due to the quadratic dependence of mie-scattering on the particle diameter. here, we report of the analysis and development of two optical techniques for extending the volume of measurement in volumetric ptv. in particular, when a volume about 103 cm3 is seeded with 15 µm air-filled soap bubbles and a laser with a pulse energy of few single mj illuminates it. the first technique uses multi reflections between two opposing parallel mirrors. the second technique is a development of laser scanning piv for volumetric scanning: the potential to increase the scanned volume is examined by experimenting with an acousto-optic modulator for fast scanning. furthermore, by employing an off-axis parabolic mirror, we obtain parallel beam scanning, which increases the efficiency and quality of the scanning. 1 introduction in the past decade, techniques for volumetric velocimetry of fluid flows have been rapidly evolving. brücker and althaus (1992) developed the laser-sheet scanning-piv technique already three decades ago. it was actually the first attempt to conduct 3d-piv volumetric flow measurement. three years later brücker (1995) used laser scanning with time laps to obtain temporal 3d-piv. elsinga et al. (2006) reported of a volumetric piv, which they named “tomographic piv”. in this method, images from 3-4 tilted cameras were obtained simultaneously and analysed with triangulations to calculate the location of particles. since 2012 and till date computational capacity grew, the responsivity of cmos detectors improved and also algorithms to calculate the velocity field from images became more efficient. in particular, the algorithm coined ’shake the box’ (stb) by schanz et al. (2016) reduced significantly the required calculations. recent 3d ptv methods use several cameras to acquire simultaneous images from a volume of interest that is illuminated by a laser beam or by leds. a survey, reported by barros et al. (2021) shows that at sub khz repetition rate the volume of interest is typically up to the order of 102 cm3 using 1µm oil droplets, up to 104 cm3 using 300 µm helium filled soap bubbles, or up to about 103 cm3 using 15 µm air filled soap bubbles (henceforth ’soap bubbles’). however, for some investigations of turbulent flows, it is essential to extend further the size of the volume of interest and work at high laser repetition rate. for example, investigation of turbulence jet flow with millimetre spatial resolution requires a volume of interest about 103 cm3 with 15µm soap bubbles as tracer particles at 4 khz repetition rate zhang et al. (2021). in ptv measurements with a laser and tracer particles with a diameter larger than the laser wavelength, the image signal of a particle depends linearly on the optical intensity of the laser beam and quadratically on the diameter of the scattering particle. since the optical intensity depends inversely on the cross-section area of the laser beam, one finds that as the laser beam cross-section increases with volume size, the optical power density from available high-power commercial lasers (few mj pulse energy at few khz repetition rate) is not sufficient for generating a detectable image signal. the low signal problem becomes significantly noticeable when 15µm soap bubbles are used, due to four orders of magnitude drop in mie scattering signal from 15µm soap bubbles, compared with 300 µm helium-filled soap bubbles. here we report of the development of two optical techniques for overcoming the problem of low image signal in large volumetric 3d-ptv measurements. in particular when a 532 nm laser with pulse energy of few single millijoule is illuminating 15 µm soap bubbles tracer particles. the strategy underlining the two techniques is to shape the cross-section area of the laser beam into a collimated elliptic beam with a crosssection area that is tested to have the required power density flux for generating a detectable image from 15µm soap bubbles. then, a collimated elliptic laser beam is shaped to have the required power density flux and it is used multiple times. in the first technique, the laser beam is incident onto two parallel opposing mirrors and it goes multiple reflections while filling the volume between the mirrors with sufficient optical power density. in the second technique, we examine the reuse of a laser beam by fast transverse scanning with an acousto-optic modulator. the rotated laser beam that is outgoing from the acuosto-optic crystal is reflected by an off-axis parabolic mirror to obtain parallel beam scanning over the volume. since the scanning rate of acousto-optic modulators is larger by three orders of magnitudes compared with mechanical methods (such as galvanic mirrors), it has the potential to scan larger volumes per image frame. our present acousto-optic scanner is far from being suitable for the final system. however, it taught us of the great potential it holds. figure 1.(a) is a top-view sketch of a set-up for multi-reflection between two parallel mirrors. a collimated elliptic laser beam is shaped to have the required power density flux. the laser beam is incident onto the left-hand side of the rear mirror. then, the incident beam is reflected towards the opposing parallel front mirror and vice versa multiple times until it exits the right-hand side of the volume between the two parallel mirrors. both mirrors are highly reflective with appropriate dimensions. the angle of incidence of the laser beam is set to optimize the filling of the volume of interest with optical power density while minimizing losses at the entrance into the volume and at the exit from the volume. figure 1.(b) shows a laser beam that is transmitted through an acousto-optic modulator (aom). placing the aom at the focal point of an off-axis parabolic mirror as is shown in figure 1.(b) results in parallel beams scanning over a volume. (a) the set-up for multi-reflections (b) the set-up for acousto-optic scanning figure 1: fig.1 (a) is a top-view sketch to illustrates the idea of multi-reflections. fig.1 (b) is a top-view sketch to illustrate the idea of fast scanning with an acousto-optic modulator and an off-axis parabolic mirror. 2 multi-reflection ghaemi and scarano (2010) reported on a method called multi-pass amplification for volumetric piv measurements. in this method, a laser beam is reflected between two opposing mirrors that are almost parallel. the small angle between the two mirrors is set so that the incident laser beam at one edge of the mirror will propagate by reflections toward the edge at the other end of each mirror with decreasing distances between sequential reflections. the closer the laser beam progresses toward the other end of a mirror, the more dense are the reflections. the small angle between the planes of the mirrors is set so that when the beam reaches the opposite end of the mirrors, it starts to reverse its direction backward. the resulting optical power density between the two opposing mirrors is inhomogeneous. the power density is rarefied where the beam is initially incident and it is highly dens at the opposite side of the mirrors. this is not ideal for generating large scale volumes with roughly homogeneous optical density for volumetric ptv measurements. in multi-pass amplification, volumetric imaging is done at the part of the volume where the power density flux is large enough to generate a detectable image of the mie scattering particle. in this method, the power of the laser beam is not used efficiently to generate a maximal volume with the required power energy flux. front mirror rear mirror beam diameter 2 incoming beam (a) top-view sketch of multi-reflections (b) 3d visualization of multi-reflections figure 2: fig.2 (a) is a top-view sketch showing two parallel mirrors with offset. fig.2 (b) illustrate that the laser beam has an elliptic cross-section area with noticeable dimensions compared with the rectangular mirrors here, we analyse and experiment with multi reflections between two parallel rectangular mirrors for volumetric 3d-ptv measurements as shown figure 2.(a). the parallel mirrors have a slight off-set, in order to minimize the angle of incidence. the incoming laser beam is reflected from the rear mirror toward the reflective side of the front mirror and vice versa. the reflections points are equidistant. the laser beam is shaped to have an elliptic and collimated cross-section area as illustrated in figure 2.(b). the minor and the major beam waists are set by requiring that the corresponding power density flux (i.e., the laser intensity) will generate an acceptable image signal. the required power density flux was found experimentally: a pulsed laser with an expanding gaussian beam was transmitted through a volume containing the 15µm soap bubbles. a satisfactory image signal with snr ratio of 15 (figure 3) was generated from the soap bubbles floating in air when they where illuminated by a laser pulse with a duration of τ = 220 ns and an energy pulse ep = 2.8 mj at 4khz repetition rate (532 nm blizz laser, innolas photonic gmbh). the minor and major waists of the elliptical laser beam at 900 mm from the laser output mirror were calculated (by the method of abcd gaussian beam analysis) to be 1 mm and 40 mm, respectively . images of the 15µm soap bubbles were acquired at 90◦ with a phantom camera (v2640) with a 60mm lens at 1000mm working distance. the optical minification was 16.6. by using the minification with image analysis of figure 3, we measured that the size of the major waist is close to 40 mm, confirming our abcd matrix analysis for gaussian beams. figure 3: image from phantom v2640 camera when an elliptic laser beam propagates through 15 µm soap bubbles. the image analysis confirmed our abcd gaussian beam analysis for the size of the major beam waist. we deduced from this image and from the laser parameters that the required optical power density flux for snr=15 is 10 [kj] [s][cm2] the required power density flux is calculated by using the equation for the intensity of a pulsed laser: i = ep πωaωbτ (1) inserting into eq.1 the laser pulse-energy, pulse-duration and the laser cross-section area, the required power density flux for detecting 15 µm soap bubbles is calculated to be 10 [kj] [s][cm2] . in the aforementioned measurement, the camera focal lens was f = 60 mm and the working distance was 1000 mm. it means that if we use the same aperture diameter but we change the camera lens to 35 mm and configure a working distance at 350 mm (for keeping the same field of view), we would be able to use a beam cross-section with π×5×50 mm2 and maintain snr ratio of about 20. equipped with the required power density flux (10 [kj] [s][cm2] ) and the corresponding cross-section area of the laser source (π×5×50 mm2), the expected field of the optical power density between the two opposing mirrors can be calculated numerically. this field depends on several factors of the design: the cross-section area of the laser beam (π×5×50mm2) for 35mm lens, the angle of incidence of the laser beam, the fresnel reflection loss, the dimensions of the reflecting mirrors compared with the cross-section area of the laser beam; and the distance between the two mirrors. the field of the optical power density in the volume between the two opposing mirrors depends on the angle of incidence of the laser beam and on propagation and reflection losses of the beam. the propagation loss is negligible. this is due to the very small mie scattering coefficient (∼ 10−16 1 cm2 ). thus the power level of the laser beam is virtually unchanged as it propagates through air with relatively low soap bubble density. however, the laser beam power drops at each reflection. the power drops due to fresnel reflection rf from the mirror’s surface and due to the finite size of the reflecting mirrors (and the infinite extension of the elliptic gaussian beam). in order to fill the volume of interest with a useful optical power density, the power of the beam, just before it exits the volume of interest, needs to be above the required power density for an acceptable snr of 10. i.e. the power density flux of the exiting beam needs to be above 10 [kj] [s][cm2] . figure 4 shows the drop of the predicted power of a 532 nm laser beam after consecutive fresnel reflections from three different coatings of mirrors: aluminium, silver and dielectric. fresnel reflection at 532 nm is 0.95,0.975 and 0.998 for aluminium (thorlabs), silver (thorlabs) and dielectric coated mirror (laser-optik gmbh, respectively. the calculation in fig.4 considers only fresnel reflection losses (the losses due to the finite size of the mirrors will be considered later below). examining fig.4, we note that aluminium coated mirrors will be effective for 7 reflections. silver coated mirrors will be effective for 27 reflections and dielectric mirrors will be effective for at least 200 reflections. at 2.8 mj pulse energy of our laser source, 350 mm working distance and with minor axis ωa = 5 mm and major axis ωb = 50 mm, the laser power density is about 2 times the required power density. large volumes can be filled with such a beam if it is reflected effectively. as long as the power density of our laser beam in fig.4 is above 0.5, the snr will be above 10 and the signal will be detectable. accordingly, aluminium coated mirrors could cover a volume of interest with a cross-section area of approximately π× 2.5×7 cm2 =∼ 5.4×10 cm2 . silver coated mirrors could fill a volume of interest with a cross-section area 0 20 40 60 80 reflection number 0 0.2 0.4 0.6 0.8 1 p o w e r d e n s it y f lu x [ a .u ] laser power vs. reflections number al ag dielectric 0.5 figure 4: the power of a reflected beam vs. number of reflections. it can be seen that a dielectric mirror with 0.998 fresnel reflectivity keeps the power of the collimated beam above the required power even after 300 reflections (the loss due to the finite size of the mirrors and the infinite size of the elliptic gaussian beam was not consider in this calculation) of π× 2.5× 27 cm2 =∼ 2.1× 102 cm2; and dielectric mirror could fill a volume of interest with a crosssection area of π×2.5×150 cm2 =∼ 1.1×103 cm2. this cross-section area could be used over a length of at least 10 cm. it means that we could fill volumes, at least of the order of 104 cm3. this is a rough estimation. in order to evaluate realistically the field of the optical power density between the two parallel mirrors, we must consider the loss due to fresnel reflection at the mirrors and evaluate numerically the loss due to the finite size of the mirrors (and the infinite extension of a gaussian beam). in order to calculate the reflectivity of an elliptic gaussian beam from a finite size rectangular mirror we recall from hawkes and latimer (1995) that the intensity of an elliptic gaussian beam is given by: i = i0 exp ( − x2 ω2 a − y2 ω2 b ) (2) the total power in such an elliptic gaussian beam is: ptotal = i0 ∞∫ 0 e − x2 ω2a dx ∞∫ 0 e − y2 ω2 b dy (3) since the rectangular mirrors has a finite size, only the part of the incident gaussian beam that will fall on the mirror will be reflected according to fresnel reflection law. for the purpose of clarity, let’s assume that the center of the elliptic beam coincides with the center of the rectangular mirror. then, since the beam is reflected only from the mirror, the reflected power is given by: pf = rf × +w 2∫ −w 2 e −2x2 ω2a dx + h 2∫ − h 2 e −2y2 ω2 b dy (4) where rf , w and h represent fresnel reflection, width and height of the mirrors, respectively. the effective reflected power is thus: re f f = pf ptotal (5) (a) (b) figure 5: (a) shows the cross-section of an elliptic gaussian beam with ωa = 5 mm and ωb = 50 mm that is incident at the center of a rectangular mirror 200× 100 mm. the effective reflectivity for these mirror dimensions and beam shape is calculated numerically to be 0.963. (b) illustrates the same elliptic gaussian beam incident on a rectangular mirror with dimensions of the mirror 200×160mm. the effective reflectivity is calculated to be 0.9974. the integrals of ptotal and pf can be calculated analytically. ptotal = i0 π 2 ωaωb and the integral for pf results in expressions that involve er f (x) and er f (y). it turned out to be much more convenient to calculate the effective reflectivity re f f by writing a matlab program with a graphical user interface to change mirrors and beam dimensions at will. figure 5.(a) shows a simulation where an elliptic gaussian beam with a crosssection area of π× 5× 50 mm2 is incident at the center of a rectangular dielectric mirror with dimensions 200 mm×100 mm. the beam suffers about 4% reflection loss. on the other hand, when the dimensions of the rectangular mirror were set to 200 mm× 160 mm, the effective reflection loss dropped to 0.26%. this example demonstrates that one needs to consider a rectangular mirror with a height that is at least 3 times larger than the major waist ωb. since the loss due to the finite height of the mirror will occur at each reflection, it is a critical design rule. it is also necessary to calculate the effective reflectivity re f f due to the finite width of the mirrors and the infinite extension of the width of the minor waist of the gaussian beam. this loss is negligible at the inner area of the rectangular mirror but significant at the edge of the mirror where the laser beam enters the volume of interest. a similar numerical calculation (using matlab) as was explained above, showed that when the beam center is 1.1ωa away from the edge of a mirror, the power loss is about 0.86%. the closer the entering beam would be to the edge of the front mirror, the smaller angle of incidence could be achieved. a small angle of incidence will result in a dense filling of the volume between the two mirrors by the reflected beams, which is a desired feature. however, the closer the elliptic beam is to the edge of the front mirror, a larger loss will occur due to blocking by the back side of the front mirror. the beam that enters the two parallel mirrors will have a loss from the back of the front mirror, from the edge of the rear mirror and from the edge at the reflective side of the front mirror. this happens only three times at the entrance and two times at the exit from the volume. it is important to track this ’entrance’ and ’exit’ losses. it boils down to selecting an angle of entrance so that it would generate an optimal fill of the volume of interest with adequate optical power while minimizing ’entrance’ and ’exit’ loss. the numerical simulations showed that if the laser beam is a distance of 1.1ωa from the edge of the front mirror; and 1.1ωa from the edge of the reflective rear mirror, the effective reflectivity would be 0.9926%. it gives about 3% ’entrance’ loss and 2% ’exit’ loss. when 1.1ωa is taken to be the edge distance, the angle of incident of the laser beam θi upon the mirrors can be evaluated from tanθi = 1.5 ωa d . where d is the distance between the two mirrors. this relation can be used to evaluate the required width of the mirrors for a given minor waist of the elliptic gaussian beam. the width of the mirror should equal an integral number of 1.5 ωa cosθi . practically, it is more convenient to use mirrors with a given width and then adjust the distance d between the mirrors so that the beams entrance and exit into the volume will be at a small angle of incidence θi and with minimal reflection losses at the edges. figure 6.(a) shows a side view (in an x-y plane) of the field of the optical intensity on the reflective surface of one rectangular mirror. the green rectangle marks an area of 100 mm by and 200 mm. the equidistant spacing between two reflected beams is 2.2ωa at the mirror surface. this distance falls the closer one gets toward the opposite mirror (where the beams overlap). figure 6.(b) shows a side view of the approximated field of the optical intensity at the midpoint between the two mirrors. the equidistant between the nearly parallel beams is 6mm. the green rectangle mark the area where there is adequate optical density (recall that the average intensity of the laser is 2 times the required power density). a top view on the field gives a better insight into the power density field between the two mirrors. figure 7 is a top view of the intensity field. it demonstrate the field at the x-z plane when y=80 mm. (a) (b) figure 6: (a) shows a side view of the field of the optical intensity on the surface of the mirrors. the green rectangular represents the mirror surface. the equidistant between reflected beams is 12 mm at the mirror surface. (b) shows a side view of the field of the optical intensity at the midpoint between the two mirrors. the green rectangular marks an area of 100 mm by and 200 mm. the equidistant between the nearly parallel beams is 6 mm the two mirrors are parallel but they oppose each other with a slight off-set. the off-set facilitates a minimum angle of incidence θi while keeping the entering beam a distance 1.1ωa from the mirror edges. i.e. the equidistant between reflected beams is 2.2ωa at the mirrors surface. the field of the optical power density is seen to be suitable for generating a sufficient signal over a large volume. the angular propagation of the gaussian beam was achieved by rotation of the cartesian coordinates system according to x → xcos(θi)+ ysin(θi). it is apparent that there are volumes where the power density is larger than snr= 20 (due to overlapping) and volumes where the power density is bellow the level required for imaging with snr = 10. present algorithms of volumetric 3d-ptv can handle such variations. by reflecting the exiting beam backward with a slight angle, the power variations can be decreased. figure 8 shows the experimental set-up that was built in order to investigate multi-reflections: a continuous wave laser (cni dragon laser) was used, two aluminium coated mirrors (height 100 mm and 150 mm width) which are 800 mm apart. the translator at the front mirror, allows to control the offset between the two mirrors. the mirrors are attached to a rail, so that their separation distance can be easily adjusted. this systems confirmed our model. replacing the silver coated mirrors with dielectric mirrors would generate a volume with similar features to those in the simulations. figure 7: a top view (x-z plane,y=80 mm) of the optical intensity in the volume between the two parallel mirrors. laser front mirror rear mirror figure 8: the experimental set-up: a laser source pass by the front rectangular mirror towards the rear mirror. it is reflected from the rear mirror towards the front mirror then back to the front mirror and vice versa. 3 acuosto-optic scanning with off-axis parabolic mirror laser scanning piv was first demonstrated by brücker and althaus (1992) and brücker (1995) where phenomena with flow velocities of single cm s were measured. in those early reports, a laser sheet was scanned over a volume in a time of about 0.75s. the relatively large time scale of the volume scan in those experiments limited the application of laser scanning to phenomena with slow velocities or to phenomena within a small volume. since then, laser scanning advanced: velocities improved and more cameras were added to obtain more accurate tomographic analysis of the volume flow. sun and c.brücker (2016) measured rotational flow fields where the full volume scan was done in 8 ms (10 scans per volume) and three cameras were used for tomographic reconstruction of the volumetric flow. scanning piv measurements are usually done by mechanical scanning devices (rotating mirror or galvanic mirrors). the mechanical nature of a rotating mirror has the advantage of having a large angular deflection at the cost of relatively low angular-velocity and compromised repeatability due to inertia. as one aspires to increase the scanning volume, another challenge appears: the laser beam is rotated about a fixed rotation axis and pointed towards a large cylindrical lens. the limited size of commercial cylindrical lenses and spherical aberration means that only a small scanning angle can be used for transmittance of parallel beams. here, we investigated the feasibility for using an aom for volumetric ptv. an aom is made of a piezoelectric crystal that is electrically induced to vibrate (fig.9.(a)).the piezoelectric crystal is coupled to an optically transparent crystal that transmits the acoustic vibrations generated by the piezoelectric crystal (quartz is a transparent crystal that is commonly used for deflecting lasers in the visible band). physically, the acoustic wave that passes through the optical crystal is made of planes of high and low densities of the crystal’s atoms. these planes scatter the incoming laser beam. bragg angles are the direction (angles) where the scattering interfere constructively. these angles are given by θb = sin−1(m λ 2λ ) known as bragg equation, where θb is the bragg diffraction angle, λ is the laser wavelength, λ is the acoustic wavelength, and m is an integer denoting the order of the diffraction. outgoing laser beam first orderbragg diffracting beams incominglaser beam acoustic wavelength � piezoelectric transducer density waves in the optical crystal (a) acousto-optic modulator off-axis parabolic mirror laser (b) figure 9: (a) illustrates the principle of bragg diffraction from an aom. (b) shows the experimental set-up of laser beam scanning by an aom. the exit aperture of the aom is placed at the focal point of the off-axis parabolic mirror the experimental set-up consists of a 532 nm laser source (cni dragon), an aom (coherent model 305) and an off axis parabolic mirror. the laser beam enters the aom. the exit aperture of the aom was placed at the focal point ( f = 306 mm) of a 101 mm diameter off-axis (30◦) parabolic mirror (aluminium coated) from edmund optics as is shown in figure 9.(b). the aom is controlled by a driver (isomet model no.2211a-2). both aom and the aom driver are outdated components. their technical specs and manuals could not be obtained from the manufacturers. however we managed to operate them (not optimally), and characterise their operation and appreciate the potential of using an aom. we measured the bragg angle of the first order by measuring the distance between the zero order to the first order to be 8 mm at a distance of 1450 mm. this means that our aom has a deflection angle of 5.4 millirads. the focal length of the off-axis parabolic mirror is 306 mm. it gives a beam scanned over 1.68 mm. this is not much, but it was useful enough to observe that the scanned beam was reflected by the off-axis parabolic mirror in parallel motion. the power efficiency was measured to be 32%. i.e. only 32% of the initial power was deflected. in this experiment we managed to conduct only feasibility tests. the results convinced us that there is a potential in using aom with off-axis parabolic mirror for effective volumetric ptv (or just 2d ptv). 4 summary and outlook the strategy behind the two techniques presented in this report is to reuse a collimated beam by reflections (multi-reflection between two parallel mirrors) or by fast transverse shifting of the beam (laser scanning with an off-axis parabolic mirror). when the pulse energy is limited, it is an ideal approach to extend the volume of the measurement. our simulations and experiments suggests that multi-reflections between two reflecting mirrors is a promising technique. it can facilitate large volumetric ptv (up to 104 cm3) with a collimated laser beam with few single mj pulse energy. the only drawback of this technique is that it requires periodical cleaning of the mirrors surfaces. the experiments for laser scanning with aom and off-axis parabolic mirror had also shown promising results. although, the scanned volume seems limited in the present experiment, this volume can be greatly increased by optical methods. for example, by using an off-axis mirror with larger focal length and adding 45◦ reflectors. modern aom has about 40 times max scanning angle compared with the aom we tested, and angular velocity at sub microsecond rate. the authors believe that computerized and programmed control of the position of parallel beams from aom with sub microsecond speeds, could lead to development of more flexible and elaborated 2d and 3d ptv techniques. acknowledgements financial support from the poul due jensen foundation (grundfos foundation) for this research is gratefully acknowledged. references barros dc, duan y, troolin dr, and longmire ek (2021) air-filled soap bubbles for volumetric velocity measurements. experiments in fluids 36:933–947 brücker c (1995) digital-particle-image-velocimetry (dpiv) in a scanning light-sheet: 3d starting flow around a short cylinder. experiments in fluids 19:255–263 brücker c and althaus w (1992) study of vortex breakdown by particle tracking velocity (ptv). experiments in fluids 13:339–349 elsinga ge, scarano f, and b wieneke bwvo (2006) tomographic particle image velocimetry. experiments in fluids 13:933–947 ghaemi s and scarano f (2010) multi-pass light amplification for tomographic particle image velocimetry applications. meas sci technol 21:339–349 hawkes j and latimer i (1995) lasers theory and practice. prentice hall schanz d, gesemann1 s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 70:1–27 sun z and cbrücker (2016) investigation of the vortex ring transition using scanning tomographic piv. experiments in fluids 58:1–12 zhang y, abitan h, ribergård sl, and velte cm (2021) a novel volumetric velocity measurement method for small seeding tracers in large volumes. in 14th international symposium on particle image velocimetry piv21, chicago, illinois, usa, august 1-4 introduction multi-reflection acuosto-optic scanning with off-axis parabolic mirror summary and outlook 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 super-large-scale flow visualization using natural snowfall for the study of utility-scale wind turbine flows a. abraham1,2, j. hong1,2∗ 1 university of minnesota, department of mechanical engineering, minneapolis, minnesota, usa 2 university of minnesota, st. anthony falls laboratory, minneapolis, minnesota, usa ∗ jhong@umn.edu with the rapid growth of wind turbine installation in recent decades, fundamental physical understanding of the flow around wind turbines and farms is becoming increasingly critical for further efficiency increases. however, the effort to develop this understanding is hindered by the significant challenges involved in modelling such a complex dynamic system with a wide range of relevant scales (blade boundary layer thickness at ∼ 1 mm to atmospheric scales at ∼ 1 km). additionally, conventional methods used to measure air flow around wind turbines in the field (e.g., lidar) are limited by low spatio-temporal resolutions. to meet the need for a high-resolution field-scale atmospheric flow measurement technique, hong et al. (2014) developed super-large-scale particle image velocimetry (slpiv) using natural snowflakes as flow tracers. when illuminated at night and captured on video, the snowflakes provide sufficient signal for flow visualization and slpiv in an area even above a scale of 100 m. moreover, due to the inertia of snow particles, they tend to be expelled from the centers of strong vortices, forming regions of low snow concentration, or voids, which become effective markers of coherent vortical structures in a turbulent flow field. when implemented in the near wake of a utility-scale wind turbine, the snow particle images are able to provide unprecedented visualization of all characteristic coherent flow structures (fig. 1). figure 1: sample images of snow particle patterns used for flow visualization and slpiv measurements of (a) the bottom blade tip vortices, (b) turbine nacelle wake, (c) tower vortex tubes, (d) atmospheric flow approaching the turbine, (e) near-wake flow at the tower plane, and (f) near-wake flow at the plane normal to the flow direction. for measurements in the plane parallel to the flow, quantitative flow information is extracted using cross-correlation between consecutive video frames, as in conventional piv. for the relatively small field of view (∼ 10 m) measured in hong et al. (2014), individual snow particles provide the signal for the crosscorrelation, enabling sufficient resolution to capture the velocity field around individual vortices shed from the turbine blade tips (fig. 2a). for a large field of view on the order of 100 m, the correlation used in slpiv relies on the movement of large-scale patterns formed by the voids and clusters of snow particles, rather than individual snow particles, as described in detail by dasari et al. (2019) and shown in fig. 2(b). for measurements in the plane normal to the flow direction, additional image enhancement techniques are applied to snow particle images for robust extraction of the snow voids associated with helical blade tip vortices (fig. 1f). the change of the near-wake blade tip vortices over time reveal the corresponding largescale wake movement in response to changes in atmospheric conditions and turbine operation, shown in fig. 2(c) and described in detail in abraham and hong (2020). figure 2: (a) a sample instantaneous velocity vector field around the bottom blade tip vortices superimposed with velocity magnitude contours. (b) a sample instantaneous velocity vector field with velocity magnitude contours (1:2 skip applied for clarity). (c) sample time series of the top portion of the wake envelope extracted from snow particle images recorded in the plane normal to the flow direction. these measurements have revealed several interesting behaviors of near-wake flows (e.g., wake contraction, dynamic wake modulation, enhanced momentum flux at the ground surface, etc.), and their connections with constantly-changing inflow and turbine operation, which are unique features of utility-scale turbines. these findings have demonstrated that near wake flows, though highly complex, can be predicted with substantial statistical confidence using information readily available from current utility-scale turbines. such knowledge can be potentially incorporated into wake development models and turbine controllers for wind farm optimization in the future. additionally, the slpiv technique used for these measurements can be applied to the investigation of a wide variety of atmospheric flows. it has been implemented to analyze characteristics of large-scale boundary layer flow (heisel et al., 2018) and the interactions between snowflake settling and atmospheric turbulence (nemes et al., 2017). in the future, it can be further utilized to study other atmospheric flows, such as the wakes behind tall buildings and the flow through urban environments. references abraham a and hong j (2020) dynamic wake modulation induced by utility-scale wind turbine operation. applied energy 257:114003 dasari t, wu y, liu y, and hong j (2019) near-wake behaviour of a utility-scale wind turbine. journal of fluid mechanics 859:204–246 heisel m, dasari t, liu y, hong j, coletti f, and guala m (2018) the spatial structure of the logarithmic region in very-high-reynolds-number rough wall turbulent boundary layers. journal of fluid mechanics 857:704–747 hong j, toloui m, chamorro lp, guala m, howard k, riley s, tucker j, and sotiropoulos f (2014) natural snowfall reveals large-scale flow structures in the wake of a 2.5-mw wind turbine. nature communications 5:4216 nemes a, dasari t, hong j, guala m, and coletti f (2017) snowflakes in the atmospheric surface layer: observation of particle-turbulence dynamics. journal of fluid mechanics 814:592–613 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 towards the closure of collar’s triangle by optical diagnostics g. gonzález saiz1*, a. sciacchitano1, f. scarano1 faculty of aerospace engineering, delft university of technology, delft, the netherlands *g.gonzalezsaiz@tudelft.nl abstract an experimental methodology is proposed for the study of aeroelastic systems. the approach locally evaluates the forces involved in collar’s triangle, namely aerodynamic, elastic, and inertial forces. the position of flow tracers as well as of markers on the object surface is monitored by a volumetric piv system. from the recorded images, the flow tracers and surfare markers are separated based on their optical characteristics. the resulting images are then analysed by lagrangian particle tracking. the inertial and elastic forces are obtained solely analysing the motion and the deformation of the solid object, whereas the aerodynamic force distribution is obtained via the pressure-from-piv technique. experiments are conducted on a benchmark problem of fluid-structure interaction, featuring a flexible panel installed at the trailing edge of a cylinder. a polynomial fit of the markers’ positions is carried out to determine the panel’s instantaneous shape, from which the inertial and elastic forces are evaluated. the pressure loads on the panel are determined via solution of the poisson equation for pressure, imposing adaptive boundary conditions that comply with the panel. the simultaneous measurement of the three forces allows to assess the equilibrium of forces, and in turn to close collar’s triangle. 1 introduction aeroelastic phenomena occur frequently in nature as well as in a wide number of engineering applications, most notably in civil engineering (sarkar et al., 1994), energy production (abdelkefi, 2016, marshall et al., 1996), and in the transport sector (wright and cooper, 2008). in the aeroelastic regime, a flexible body immersed in a flow is subjected to the aeroelastic system of forces, namely aerodynamic, elastic, and inertial. their mutual relationship was sketched by collar in 1946 in the so-called collar's triangle of forces. still nowadays, fluid-structure interaction (fsi) problems are difficult to study both from the computational as well as from the experimental viewpoint. from the computational perspective, the one of the main challenges consists of the coupling between the simulation of the fluid flow mathematically with time-varying structural boundaries. computational aeroelasticity often makes use of simplified geometries (schuster et al., 2003) to increase affordability. the numerical coupling of independent fluid and structural solvers, while improving the computational efficiency, poses new challenges at the fluidstructure interface, especially for highly non-linear phenomena, such as for unsteady separated flow regimes. this situation justifies the need to advance experimental approaches as a necessary component for the validation of computational tools. from the experimental perspective, the first challenge is given by the problem of scaling. while mach and reynolds numbers are the most relevant parameters for aerodynamic scaling, for fsi problems, one needs to consider the ratio of fluid and structure inertia alongside the relative stiffness of the latter (friedmann, 2004; wan and cesnik, 2014). even when the problem is scaled to a satisfactory extent and the experiment is realised, monitoring the fluid flow and structure behaviour is hindered by the technical complexity of the needed instrumentation. most of the works carrying out simultaneous measurements of flow and structure have been reported only in the last decade, often by combining optical techniques. many studies have approached the flow measurements by planar particle image velocimetry (timpe et al., 2013; hortensius et al., 2017; kalmbach and breuer, 2013; giovannetti et al., 2017; bleischwitz et al., 2017), and only a few have employed volumetric measurements (kalmbach and breuer, 2013; mitrotta et al., 2019). the measurement of the structural motion was performed either by digital image correlation (timpe et al., 2013; bleischwitz et al., 2017; giovannetti et al., 2017) or based on multiple-point laser triangulation (kalmbach and breuer, 2013). moreover, timpe et al. (2013) directly measured the inertia forces on the structure with a force balance. furthermore, mitrotta et al. (2019) used the lagrangian particle tracking technique (schanz et al., 2016) to determine simultaneously the flow velocity and the structural motion. optical diagnostics for fsi investigation has nowadays advanced to a level that it compares with techniques based on installed instrumentation aboard the structural model. the combined use of piv techniques (adrian et al., 2011) and optical diagnostics like digital image correlation or alike (dic, chu et al., 1985; image pattern correlation technique or ipct, boden et al., 2014) to perform both tasks is currently under development. pressure from 3d-piv enables the evaluation of the fluid flow pressure both in the fluid domain as well as in close proximity of the solid object surface (liu and katz, 2006; van oudheusden, 2013). a pioneering work that applies pressure from piv to fsi problems with generic three-dimensional and flexible structures has been conducted by percin et al. (2017). finally, the evaluation of inertia forces, traditionally performed by means of accelerometers (as in ground vibration tests, peeters et al., 2009; or under in-flight conditions, kehoe, 1995), has also been surrogated by optical diagnostic methods. for example, the videogrammetric model deformation (vmd, burner et al., 2001) measurement technique captures the attitude of wings by tracking rows of markers on the model. similarly, a new sensing approach (de figueiredo et al., 2020) measures natural frequencies of aeronautical structures using a computer vision system. the present work paves the way towards the closure of collar’s triangle experimentally, that is, determining simultaneously all agents of the dynamic fsi interaction. in order to do so, an experimental methodology is proposed to extract aerodynamic, elastic and inertial forces from lpt measurements of flow tracers and surface markers from a single tomographic system. 2 fsi measurement working principle let us consider a flexible object, such as a panel of length l, width w and thickness t (𝑇 << 𝐿, 𝑊) subject to aerodynamic forces from an air flow as illustrated in error! reference source not found.. the aerodynamic loads consist of pressure p and friction 𝜏. the object opposes deformation by its stiffness, and acceleration motions by its inertia. considering a square tile of such panel, i.e. a small element of side length l (see figure 1), the equilibrium of forces acting on such element reads as: ∑ 𝑭 = 𝑭𝑖 + 𝑭𝑒 + 𝑭𝑎 = 0 (1) where 𝑭𝑖 , 𝑭𝑒 and 𝑭𝑎 stand for the inertia, elastic, and aerodynamic forces, respectively. figure 1: schematic of a flexible foil immersed in a flow with cross-sectional view of a tile element. inertia force when the net external forces are non-zero, the tile will accelerate and as such an inertial force 𝑭𝑖 can be defined in the direction opposite to the acceleration a of the element, 𝑭𝒊 = −𝑚 𝒂 (2) where m is the tile’s mass. the local measurement of the object motion is typically performed by means of optical markers applied onto the surface of the panel. the marker’s position in time is recorded, while velocity and acceleration are obtained as time derivatives of the position. the inertial force is thus computed by knowledge of the tile’s mass (from the material’s density and the tile’s volume). elastic force elastic forces arise as a reaction of the object opposing deformation. in the present discussion, deformation is assumed to occur in the linear elastic regime. the force is hypothesized to act normal to the surface and tensional forces (e.g. arising from aerodynamic skin friction) are neglected. in the above conditions, the whole elastic force reduces to the bending stress only. considering the thinness of the deformable body under study, a 1-d simplification of the kirchhofflove plate theory provides a relation between the physical attributes of a tile of material and the elastic forces due to a z-deformation h(x), illustrated in figure 1. according to such theory and derived from the compatibility relations (strain-displacement) and the stress-strain relations, the stress along the body reads: 𝜎𝑥 = − 𝐸 1 − 𝜈2 𝑧 ( 𝜕2ℎ 𝜕𝑥2) = 𝐸 1 − 𝜈2 𝑧 ℎ′′ (3) where e is the young modulus and 𝜈 the poisson ratio. the linear dependence on z (with respect to the neutral axis) agrees with the tensile and compressive stresses at opposite faces of the panel. the nonuniform normal stress distribution gives rise to a moment reaction. finally, from moment equilibrium for a tile and considering the internal shear forces the normal force acting on the surface and producing such displacement can be inferred: 𝑭𝒆 = 𝐸 𝑙2 𝑇3 1 − 𝜈2 ( 𝜕4ℎ 𝜕𝑥4) 𝒆𝒛 = 𝐸 𝑙2 𝑇3 1 − 𝜈2 ℎ′′′′𝒆𝒛 (4) the complete derivation of the theory can be found in the work of panc (1975). once the material properties are known, the experimental evaluation of such force relies on the assessment of the 4th spatial derivative of the deformation, which in turn could be determined from a dense, yet discrete, description of the deformed foil by a pattern of surface markers. aerodynamics force aerodynamics loads are usually decomposed into normal (pressure) and shear (friction) stresses. friction is negligible in most aeroelastic regimes. moreover, the pressure loads on a thin panel reduce the discussion to the pressure difference ∆𝑝 at its opposite sides. the aerodynamic force acting on the tile reads as: 𝑭𝒂 = ∆𝑝 𝑙2 𝒏 (5) where n is unit vector in the normal direction to the surface. the pressure field can be determined from the velocity field information invoking the momentum equation, in turn requiring the solution of the poisson equation for pressure (van oudheusden, 2013). such force is less straightforward to obtain from fluid flow measurements as it typically requires high-quality time-resolved 3d measurements (beresh, 2021). moreover, the choice of boundary conditions can largely affect the evaluation of the pressure field (neeteson et al., 2016). furthermore, the surface pressure is typically estimated extrapolating the pressure from the flow domain towards the solid surface (jux et al., 2020). it should be stressed that for evaluating the surface pressure distribution over a generic surface, curved and in motion, time-resolved three-dimensional flow field measurements are required that surround such surface. collar’s equilibrium of forces equation 1 can be rewritten combining the explicit terms obtained in eq. 2, 4 and 5. the resulting equilibrium of forces is expressed as: 𝐸 𝑙2 𝑇3 1 − 𝜈2 ℎ′′′′𝒆𝒛 + ∆𝑝 𝑙2 𝒏 − 𝑚 𝒂 = 0 (6) from such equation, we can identify some describing parameters of the structural element considered: size (l, t), mass (m) and material properties (young modulus, e, and poisson ratio, 𝜈). instead, the remaining elements in the equation, such as the pressure difference ∆𝑝, the element acceleration 𝒂, orientation 𝒏, and derivatives of the deformation ℎ′′′′, must be measured to address the problem. in the present study, state-of-the-art optical diagnostics based on piv techniques is employed for the above purpose. the fluid flow velocity is obtained over an extended three-dimensional domain by tracking large tracers (helium-filled soap bubbles, hfsb) along their trajectories. this data is used to ultimately determine the flow pressure in the vicinity of the body. the acceleration of the panel is measured by tracking the motion of surface markers with the same algorithm as for the fluid tracers. finally, the orientation and the deformation of the panel can be inferred from the analysis of the 3d position of the markers and their relative displacement, respectively. section 3 details the complete description of the experimental approach to measure these unknowns (∆𝑝, 𝒂, 𝒏, ℎ′′′′) with such methodologies. 3. experimental setup flow facility and model the experiments are conducted at the aerospace engineering laboratories of tu delft, with an open-jet open-return wind-tunnel of 60𝑥60 cm2 exit cross-section. a black solid cylinder (𝐷 = 90 𝑚𝑚) is located vertically with a flexible transparent foil attached along the rear mid-plane. the see-through characteristic of the foil allows to track flow tracers at both sides of the body even when looking from only one side. the foil size (105 𝑥 200 𝑚𝑚2) is such that the foil undergoes a 2d motion following the karman wake of the cylinder at 𝑈∞ = 2.25 𝑚/𝑠 (𝑅𝑒 = 1.35 × 104). for the measurement of the foil kinematics, a regular pattern of bright surface markers (see fig. 2c) is speckled on the foil by hand. the markers had an average diameter 𝑑𝑚 = 0.8 𝑚𝑚 and a pitch 𝑝𝑚 = 1 𝑐𝑚. the overall experimental setup is provided in figure 2a. figure 2: experimental setup (a) showing the model (foil attached to a cylinder), the led units. raw snapshots of foil markers with hfsb (b) and without (c). table 1: physical properties of the flexible foil and tile thickness, t [mm] 0.25 length, l [mm], l [mm] 95, 10 width, w [mm], w=l [mm] 200, 10 density of material, 𝜌 [kg/m3] 1290 young modulus of material, e [gpa] 1.0 poisson ratio of material, 𝜈 [-] 0.3 tracers measurement the flow is seeded with neutrally buoyant sub-millimetre (𝑑 ≈ 350𝜇𝑚) helium-filled soap bubbles (hfsb, scarano et al., 2015), released by an in-house developed 200-generator seeding rake installed in the settling chamber. the nominal production rate of flow tracers is 6x106 bubbles/s distributed over a section of 120 × 50 cm2, resulting in a seeding concentration of ~10 bubbles/cm3 for a freestream velocity 𝑈∞ = 2.25 𝑚/𝑠 at the test section. for the current experiment, only half seeder was operated to keep the seeding concentration below the optical limit of 0.05 particles per pixel (ppp) for 4-camera tomographic systems (elsinga et al, 2006; scarano, 2013). a seeded volume of 22 × 40 × 20 𝑐𝑚3 is illuminated vertically by two lavision flashlight 300 led banks located under the test section. the imaging system consisted of four high-speed cameras (1024x1024 pixels,12-bit, 20 m pixel pitch) mounted in a tomographic configuration as shown in figure 2. the cameras subtended an aperture of approximately 30 degrees. the image acquisition and processing is conducted with the lavision davis 10.0.5 software. sets of 5000 images are recorded at a rate of 1 khz. for the calibration process, a geometrical calibration (soloff et al. 1997) is followed by the volume self-calibration (wieneke 2008) and optical transfer function determination (otf calibration, schanz et al 2012). surface markers are visually distinguished from flow tracers based on their distinct optical characteristics. in order to track the most fluid tracers (3d bubbles) and the most structural markers (2d flat bright circles), the volume self-calibration and the otf calibration are performed independently with a clean run of each tracers. the flow tracers’ velocity is evaluated by means of the shake-the-box algorithm (schanz et al., 2016) to the overall measurement domain. as for the flow tracers, the motion of the markers is determined by means of the stb processing. the analysis volume is reduced to the bounded moving foil to avoid retrieving flow tracers. in addition, given the periodic 2d nature of the foil motion, velocity limits within the tracking algorithm aid to discard flow particles with a stream-wise motion. table 2: optical system information. tomographic system illumination 2 x lavision flashlight 300 led cameras 2 x photron fastcam sa1.1 (1024x1024 pixels, 5400 fps) 1 x photron fastcam sa5 (1024x1024 pixels, 7000 fps) 1 x highspeedstar 8 (1024x1024 pixels, 7000 fps) imaging 3 x objectives nikkor 50 mm f# 1/11 1 x objectives nikkor 60 mm f# 1/11 acquisition frequency 1000 hz 4 data reduction for load estimation the following section describes the data reduction procedure to obtain the distribution of forces along the foil from the analysis of the tracers and markers motion. structural forces as introduced in section 2, inertial and elastic forces are determined via the computation time and space derivatives of the measured foil location. in order to avoid noise propagation through the derivation process, a spatio-temporal regularization is performed on the locations of the markers to fit a coherent surface. the fit is built upon a 5th order polynomial in space that comprises a time stencil of 17 samples (~10% of a cycle). the function is calculated on a finer grid with 0.5 cm spacing in x & y directions. therefore, the resulting tiles have a surface area of 0.25 cm2. the derivations in time and space to determine the acceleration and elastic force, respectively, are conducted analytically based on the polynomial description of the foil’s instantaneous shape. figure 3 compares the kinematics in time of a tracked surface marker with the kinematics of its projection on the reconstructed surface. figure 3-right illustrates a clear suppression of the noise in the foil’s acceleration. figure 3: kinematics of a measured surface marker (dotted blue) and projection at fitted surface (solid red) at the location (x=0.75 l, y=0.5 w). fluid load finally, for the determination of the aerodynamic forces, the surface pressure distribution along the foil needs to be evaluated. the volumetric pressure is computed based on the solution of the poisson equation for pressure for incompressible flows (van oudheusden, 2013), which results from the divergence of the equation of conservation of momentum: ∇2𝑝 = ∇ ∙ (− 𝜌 𝐷�̅� 𝐷𝑡 + 𝜇∇2�̅�) (11) the computation of the pressure field relies on the material derivatives of the velocity, 𝐷�̅� 𝐷𝑡 , and the viscous dissipation, 𝜇∇2�̅�. the latter is neglected due to the high flow reynolds number (𝑅𝑒 = 2 × 104). the material derivatives are directly extracted from the ptv measurements, in which particles are tracked along their trajectories in a lagrangian fashion. dense velocity reconstruction from particle tracks is performed with the vic# algorithm implemented in davis 10.1 (jeon et al., 2018). the approach is based on the vortex-in-cell method, which optimizes the vorticity field to best fit the velocity tracks via an optimization algorithm that minimizes a cost function j built upon experimental-computational variables disparities. pressure integration is performed simultaneously to the velocity reconstruction since the pressure is computed within the optimization algorithm and it is included in the cost function of vic# (jeon et al, 2018). pressure fields are computed by solving the poisson equation with neumann conditions at every boundary and a constant dirichlet condition at a free stream location. similarly to most fsi applications, the current case is characterized by unsteady fluid-solid boundaries. however, the application of the vic# methodology limits its applicability to cartesian domains, limiting the knowledge of the pressure field from the outer-most region of the measurement domain down to the limits of the foil motion (4 cm away from the neutral position of the unperturbed foil). the gap is such that the foil does not enter the fluid domain under consideration. thus, a cartesian mesh of fluid domain outside the range of motion of the foil is selected for fine-gridding the velocity field and computing the flow static pressure field. for the determination of the actual surface pressure, the pressure is extrapolated towards the foil location (from both sides) via a nearest neighbour approach, neglecting the change of static pressure across the wake. 5. results the flow velocity fields are analysed first. a full field x-z view of the velocity vectors is captured in figure 4, averaged along the y-direction. the foil location is given as a reference. the spanwise component of the velocity does not provide relevant information and so it is omitted. the fields show the wake of the cylinder as a low velocity region. from the streamwise component (top row in fig. 4), the wake undergoes an oscillatory behaviour with deflections of ±20° with respect to the x-axis. the vortex shedding phenomenon is also reflected in the transverse velocity component, which shows positive and negative velocity regions coincident with the upwards-downwards wake deflections respectively. the dominant frequency of the flow can be already inferred from the sequence, 𝑓 ≈ 5.6 𝐻𝑧. the latter agrees with the characteristic frequency for cylinder shedding wakes, 𝑆𝑡 ≈ 0.2 (williamson, 1996), showing no effect the existence of the flexible foil at the trailing edge of the cylinder. figure 4: sequence (left to right) of average (along the y-direction) flow velocity fields (u and w, top and mid rows respectively in [m/s]) and pressure field (bottom row in [pa]). the pressure fields, which are provided in the third column of fig. 4, give an insight of the forcing mechanism of the problem. focusing on the low pressure regions (dark blue), it is observed how the latter pull on the foil creating the oscillatory motion. in particular, the actual forcing appears to happen when the low pressure region convects from the foil mid-length (x=0.5 l) to the end of the foil (x=l). in this situation, both pulling force and velocity vector are aligned, and translates into a positive work performed by the flow on the foil. this mechanism is enhanced by the high pressure regions (redorange), which build up at the outer region when the foil is at the limit of the motion (when the foil is still) and aid to push the foil back within the oscillatory fashion. about the structural motion, the complete 4d description of the foil is provided in figure 5. contours of position, acceleration and elastic force for the spanwise direction (z-) are provided on the deformed state of the foil. the acceleration of the foil (centre column) follows the inverse trend to the motion itself, as expected from the second derivative a given periodic signal. similarly, the elastic forces oppose to the foil position, as the deformation promotes internal stresses and moments that act against it. this working mechanism is analogous to that of a mass-spring system under deformation. figure 5: sequence (top to bottom) of structural variables contours on the deformed foil: z-location (left column, in [m]), zacceleration (related to the inertia forces, centre column, in [m/s2]), and z elastic force (right column, in [n/cm2]). the time-evolution of the computed aeroelastic forces is extracted at a particular tile location (x=0.75 l, y=0.5 w) and presented in figure 6. the z-position of such tile is included as a reference as a purple dashed line. a first reading can be done on the relative phase of the forces with respect to the motion of the foil. it can be seen that the tile’s inertia is in-phase with its z-displacement. this result can be explained via the following reasoning. considering the z-position as a pseudo-sinusoidal signal, the second time derivative (tile acceleration) results in a counter-phase signal, i.e. a signal with π phaseshift. however, recalling eq. 2, the inertia (red line in fig. 6) has opposite sign to the acceleration, resulting in an in-phase signal with the foil deformation (dashed black in fig. 6). in fact, the inertia acts to maintain the motion of the foil, opposing to accelerations caused by other external forces. in contrast, the elastic forces (yellow in fig. 6) oppose the deformation, reacting to bring the foil back to the nondeformed state. therefore, the elastic forces are in counter-phase with the z-position. however, as indicated in the previous section, the computation of the latter forces relies on the 4th spatial derivative of the deformation, which causes measurement noise to affect the accurate evaluation of the elastic forces. last but not least, the aerodynamic force (blue in fig. 6) shows lower force levels and anticipates the foil’s motion by a phase shift of about π/2. this phase shift is caused by the structural and aerodynamic damping of the system . in order to perform work, and so induce the motion to the foil, the external force, i.e. aerodynamic pressure difference across the body, must align with the velocity of the body. the velocity and the position present a π/2 phase shift, thus a similar phase-shift occurs between the aerodynamic force and the z-location of the foil. finally, the closure of collar’s triangle, i.e. force equilibrium residual (eq. 1), is evaluated for the afore-analysed tile location (x=0.75 l, y=0.5 w) and provided in fig. 6 as black dash-dotted line. a priori, one could expect the residual to be incoherent in time and dominated by random noise. however, the signal presents the dominant frequency of the motion in-phase to the inertial forces. this behaviour possibly indicates an underestimation of the elastic and/or aerodynamic loads on the foil. figure 6: instantaneous time-evolution of aeroelastic forces: aerodynamic (blue), inertial (red), and elastic (yellow) for the location (x=0.75 l, y=0.5 w). the sum of forces is drawn in black dash-dotted. z-position (purple dashed) is given as reference (right y-axis). 7. conclusions a non-intrusive measurement methodology for aeroelastic experiments based on the lagrangian particle tracking technique is proposed to simultaneously estimate aerodynamic, elastic and inertial loads from a deforming model. the method relies on the tracking of flow tracers to characterize the flow, and of surface markers to describe the dynamics of the structure. an experiment was carried out to show the applicability of the proposed methodology. the measurements regarded a flexible transparent foil, attached to a solid cylinder, interacting with the wake of the cylinder. both flow tracers, hfsb, and surface markers, installed on the panel, were tracked in time with a single optical tomographic system. the results show the potential of measuring the surface markers position, velocity and acceleration via a tracking approach for load estimation. structural forces where successfully estimated on the flexible foil. for the current work, aerodynamic pressure on the surface of the moving body was extrapolated from the cartesian fluid domain via the nearest neighbour approach. a challenge to overcome in future works is the surface determination of the unsteady pressure for a deforming body in motion. nevertheless, the behaviour of the computed forces time-evolution are consistent with the hypothesized trends. yet, the noise propagation through the spatial derivation process affects the accuracy of the estimated elastic forces, precluding the closure of the aeroelastic triangle. to conclude, the proposed methodology offers a wide spectrum of information (flow fields, flow topology, fluid loads, structural deformations, and structural loads) based on non-intrusive optical measurements by lagrangian particle tracking. moreover, the simultaneous estimation of the main forces involved in an aeroelastic experiment implies the ability to close collar’s triangle, bringing promising advantages to the experimental study of the challenging aeroelastic regimes. references abdelkefi a (2016) aeroelastic energy harvesting: a review. international journal of engineering science 100:112-135 adrian l, adrian rj and westerweel j ( 2011) particle image velocimetry. cambridge university press. beresh s (2021) time-resolved particle image velocimetry. measurement science and technology bleischwitz r, de kat r and ganapathisubramani b (2017) on the fluid-structure interaction of flexible membrane wings for mavs in and out of ground-effect. journal of fluids and structures 70:214-234 boden f, kirmse t, poroikov ay, rinkevichyus bs, skornyakova nm and shashkova ia (2014) accuracy of measurement of dynamic surface deformations by the image pattern correlation technique. optoelectronics, instrumentation and data processing 50(5):474-481 burner aw and liu t (2001) videogrammetric model deformation measurement technique. journal of aircraft 38(4):745-754 chu tc, ranson wf and sutton ma (1985) applications of digital-image-correlation techniques to experimental mechanics. experimental mechanics 25(3):232-244 collar ar (1946) the expanding domain of aeroelasticity. the aeronautical journal 50(428):613-36 de figueiredo hv, castillo-zúñiga df, costa nc, saotome o and da silva rga (2020) aeroelastic vibration measurement based on laser and computer vision technique. experimental techniques, 1-13. elsinga ge, scarano f, wieneke b and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41(6):933-947 friedmann pp (2004) aeroelastic scaling for rotary-wing aircraft with applications. journal of fluids and structures 19(5):635-650 giovannetti lm, banks j, turnock sr and boyd sw (2017) uncertainty assessment of coupled digital image correlation and particle image velocimetry for fluid-structure interaction wind tunnel experiments. journal of fluids and structures 68:125-140 hortensius r, dutton jc and elliott gs (2017) simultaneous planar piv and sdic measurements of an axisymmetric jet flowing across a compliant surface. in 55th aiaa aerospace sciences meeting (p. 1886). jeon yj, müller m, michaelis d and wieneke b (2018) efficient reconstruction of flow field with pressure from particle tracks: vic. bulletin of the american physical society 63 jux c, sciacchitano a, scarano f (2020) flow pressure evaluation on generic surfaces by robotic volumetric ptv. measurement science and technology 31(10):104001. kalmbach a and breuer m (2013) experimental piv/v3v measurements of vortex-induced fluid–structure interaction in turbulent flow—a new benchmark fsi-pfs-2a. journal of fluids and structures 42:369-387 kehoe mw (1995) a historical overview of flight flutter testing. liu x and katz j (2006) instantaneous pressure and material acceleration measurements using a four-exposure piv system. experiments in fluids 41(2):227 panc v (1975) theories of elastic plates. springer science & business media. peeters b, hendricx w, debille j and climent h (2009) modern solutions for ground vibration testing of large aircraft. sound and vibration 43(1):8 percin m, vanierschot m and van oudheusden bw (2017) analysis of the pressure fields in a swirling annular jet flow. experiments in fluids 58(12):166 marshall jg and imregun m (1996) a review of aeroelasticity methods with emphasis on turbomachinery applications. journal of fluids and structures 10(3):237-267 mitrotta fm, sciacchitano a, sodja j, de r. and breuker bw (2019) experimental investigation of the fluidstructure interaction between a flexible plate and a periodic gust by means of robotic volumetric piv. in proceedings of the 13th international symposium on particle image velocimetry. universitat der bundeswehr munchen. neeteson nj, bhattacharya s, rival de, michaelis d, schanz d, schröder a (2016) pressure-field extraction from lagrangian flow measurements: first experiences with 4d-ptv data. experiments in fluids 57(6):1-8. timpe a, zhang z, hubner j and ukeiley l (2013) passive flow control by membrane wings for aerodynamic benefit. experiments in fluids 54(3):1471 sarkar pp, jones np and scanlan rh (1994) identification of aeroelastic parameters of flexible bridges. journal of engineering mechanics 120(8):1718-1742 scarano f, ghaemi s, caridi gca, bosbach j, dierksheide u and sciacchitano a (2015) on the use of heliumfilled soap bubbles for large-scale tomographic piv in wind tunnel experiments. experiments in fluids 56(2):42 schanz d, gesemann s and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57(5):70 schanz d, gesemann s, schröder a, wieneke b and novara m (2012) non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. measurement science and technology 24(2):024009 schuster dm, liu dd and huttsell lj (2003) computational aeroelasticity: success, progress, challenge. journal of aircraft 40(5):843-856 soloff sm, adrian rj and liu zc (1997) distortion compensation for generalized stereoscopic particle image velocimetry. measurement science and technology, 8(12), p.1441. van oudheusden bw (2013) piv-based pressure measurement. measurement science and technology 24(3):032001 wan z and cesnik ce (2014) geometrically nonlinear aeroelastic scaling for very flexible aircraft. aiaa journal 52(10):2251-2260 wieneke b (2008) volume self-calibration for 3d particle image velocimetry. experiments in fluids 45(4):549556 williamson ch (1996) vortex dynamics in the cylinder wake. annual review of fluid mechanics 28(1):477-539 wright jr and cooper je (2008) introduction to aircraft aeroelasticity and loads. john wiley & sons. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 determination of the near wall flow of a multi-stage tesla valve using piv and ptv yeganeh saffar, shadi ansari, reza azadi, jan raffel, david s. nobes* and reza sabbagh department of mechanical engineering, university of alberta, canada * dnobes@ualberta.ca abstract particle image velocimetry (piv) and particle tracking velocimetry (ptv) are two popular methods to measure the velocity in complex geometries such as the tesla valve. this paper provides an investigation on the application of a tessellation meshing method for interpolating non-uniform velocity vectors calculated using ptv. the procedure to apply this method containing mask generation and mesh study is described. the results are compared to the piv results particularly where the near wall results are important. the result of the flow field calculated by the application of the tessellation method on the ptv results are presented for a two-stage tesla valve operated in the range of re = 100 to 600 both in forward and reverse configuration. 1 introduction the tesla valve is a nonmoving mechanical flow control device used to restrict the flow preferentially in one direction tesla (1920). its geometry generates a higher pressure drop in the flow in one direction and a lower pressure drop when it is used in the reverse direction. the simplicity of its fabrication and the operation in comparison to the conventional valves makes it an appropriate choice for different applications porwal et al. (2018), wahidi et al.(2020). the efficiency of the tesla valve depends on the pressure drop of the flow in each direction which is related to the flow field inside the channel (gamboa et al. (2005). therefore, understanding the internal flow can lead to a better insight into the design and optimization of the tesla valve j. raffel (2019). particle tracking velocimetry (ptv) is a non-intrusive imaged based velocimetry method that follows a particle in two successive frames of images captured of the flow. in the cases of high velocity gradients, ptv provides a higher spatial resolution which is an advantage in comparison to particle image velocimetry (piv) m. raffel et al. (2007). these two methods are great candidates to study the flow field in mini and micro channels such as the tesla valve s. ansari et al. (2018) and j. raffel et al. (2021). however, both of these methods need additional corrections based on the geometry of the domain and the flow field conditions. unlike piv, ptv is highly dependent on the number of the seeding particles and their distribution in the flow field. this increases the possibility of having missing velocity values in regions with fewer particles such as the near wall region m. raffel et al. (2007). in this work, the flow behavior inside a tesla valve is studied applying piv and ptv and a method is proposed to improve the quality of results. the determination of the near wall flow characteristics in this complex channel flow geometry is affected by the type of particle analysis carried out to obtain the flow velocity. thus, this research focuses on how best to determine the near wall characteristics. the use of a tessellation meshing method to discretize the domain and assimilate the experimental data to calculate velocity in the wall region is discussed. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 2 experimental setup a transparent flow channel shown in figure 1, was fabricated using a 3d printer and a clear resin material. the top window is a laser cut acrylic sheet chosen to give optical access to the channel. the channel width, d = 2 mm and a two-stage tesla valve is used for this experiment. to ensure that a uniform flow is entering the tesla valve, a honeycomb is designed before each forward and reverse inlets. the same cell is used for both forward and reverse flow directions, by changing the direction of the flow stream. figure 1: the solid model of the tesla valve and the inlet and outlet of the flow stream for both forward and reverse flow direction a schematic of the experimental imaging setup is shown in figure 2 which is used to image tracer particles inside the tesla valve with the particle shadow velocimetry (psv) technique. a high-speed ccd camera is used to capture images for reynolds numbers between 100 ≤ re ≤ 300 with 2000 fps and the resolution of 1536 pixels × 768 pixels. for conditions of reynolds numbers of 400 ≤ re ≤ 600, 4000 fps and the resolution of 1280 pixels × 512 pixels is used. a green led is used to illuminate the channel from below to visualize the motion of the particles in a shadowgraph configuration. inside the channel, a mixture of water and glass bead particles with a different diameter of 10 μm and 20 μm (dynoseeds ts10, ts 20) for each experiment is used. figure 2: schematic of the optical setup showing shadowgraph configuration 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 3 image processing images of the flow are processed to obtain the velocity vectors in the flow field. this is undertaken by applying the tessellation meshing method before processing the images for piv/ptv. to generate a mesh for the tessellation, obtaining the boundary of the geometry is required. this provides the ability to distribute the nodes of the mesh on the channel walls. the raw images, however, need to be masked to eliminate unwanted shadow regions and their effect on image analysis. since this specific geometry cannot be simply generated using mathematical approaches, raw images of the flow field are alternative references that can be used in the masking process. the raw image shown in figure 3(a) is an instance which shows the geometry of the channel with seeding particles and other extra shadows. all of these additional shadows increase the difficulty in finding the channel walls. to overcome this problem, for each reynolds number, 1000 instantaneous frames containing flow and tracer particles are used to calculate the standard deviation of the images intensity. figure 3(b) shows the standard deviation of 1000 raw images. with the high contrast apparent between the channel and background, the edge of the channel walls can be detected using an image processing algorithm in matlab. figure 3(c) represents the final binarized mask of the geometry generated from the raw images. having a proper masked geometry allows only the region containing the particle data to be identified as in figure 3(d) which is for re = 600. the final images, similar to the processed image in figure 3(d), are used for both ptv and ptv combined with the tessellation meshing method. (a) (b) (c) (d) figure 3: image processing steps to obtain the wall boundaries of the geometry; (a) raw image showing the initial domain, (b) standard deviation of the intensities calculated from 1000 raw images, (c) the masked generated by image processing of the standard deviation of 1000 images, (d) result of masked image with seeding particles 4 tessellation combined with ptv preliminary results obtained from piv and ptv are compared to highlight the difference in the determined near wall flow. figure 4(a) displays the result of the flow processing using piv. vortices can be observed as a result of the flow separation and are also shown as zoomed-in streamlines. such vortices are observed near the merging and dividing areas where the flow is experiencing a negative pressure 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 gradient. the same trend can be observed in figure 4(b) where ptv is used to process the flow images. a rectangular grid is used to interpolate the velocity distribution in the flow domain calculated using the ptv approach. comparing the highlighted areas in figure 4, a major disagreement in the streamlines can be observed close to the wall region which is mainly due to the grid type used for calculating the velocity from ptv data. this highlights that the piv and ptv approaches should be used carefully in flow studies to ensure the proper interpretation of the flow physics. (a) (b) figure 4: the velocity field and streamlines of a reverse flow inside the tesla valve for re = 500 using (a) piv and (b) ptv method. the highlighted area shows the near wall streamlines important flow parameters such as pressure can be calculated after distributing the dispersed ptv velocity vectors, on a discretized domain azadi et al. (2021). the structured rectangular grids are mostly used for simple geometries. in cases with complex geometries, moving boundaries, or high curved regions such as the tesla valve geometry, generating a high-quality structured grid becomes more challenging azadi et al. (2021). to overcome this issue, a tessellation meshing method can be used. this method maps the dispersed ptv velocity data onto an optimized high-quality triangular node structure azadi et al. (2021). the mapping process starts with identifying the boundaries of the domain azadi et al. (2021). as the second step, a sufficient number of nodes is distributed on the boundaries. the tessellated domain forms from the inserted nodes and the specifications of the mesh depending on each case azadi et al. (2021). the delaunay triangulation algorithm used in this method, adjusts itself to the perfect position in order to make a high-quality mesh azadi et al. (2021). this adjustability results in generating a mesh which can be easily matched to the boundaries of the domain. as a result, a precise near wall flow can be determined using the dispersed velocity data from ptv. figure 5(a) shows the non-uniform vectors calculated from ptv for the forward flow condition for re = 100. the uniformly distributed velocity vectors and the velocity contour which are obtained from the tessellation method are shown in figure 5(b). 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) (b) figure 5: (a) non-uniform scattered ptv velocity vectors for the forward flow re = 600, (b) velocity field and uniform vectors after applying the tessellation for the forward flow re =100, |v| represents the velocity magnitude in the plot. three different mesh densities were used to study the effect of the mesh size on the tessellation results. table 1 contains the properties for each of these cases. it is noticeable that for each case the skewness is less than the recommended amount of 0.33 azadi et al. (2021). the tesla valve is made from multiple narrow channels and therefore, to generate a semi-uniform mesh maximum ℎ𝑚𝑎𝑥 and minimum ℎ𝑚𝑖𝑛 cell sizes are chosen such that ℎ𝑚𝑎𝑥 ≤ 2ℎ𝑚𝑖𝑛.the minimum cell size, ℎ𝑚𝑖𝑛 is used to distribute nodes on the boundaries and ℎ𝑚𝑎𝑥 dictates the maximum size for the cells further from the walls. table 1 mesh properties for three different mesh densities. case ℎ𝑚𝑖𝑛 (mm) ℎ𝑚𝑎𝑥 (mm) skewness 1 0.08 0.1 0.325 2 0.1 0.2 0.3104 3 0.3 0.5 0.308 the tessellation results for all 3 grids are investigated to find the optimum mesh size, and the results are shown in figure 6. the velocity field of the reverse flow condition with re = 100 is chosen and shown for all cases in figure 6(a). from the highlighted areas it can be realized that all of the cases represent the same velocity gradient. it is also notable that as the mesh becomes smaller, more details are provided by the tessellation. figure 6(b) represents the velocity profile for a certain location 𝑥 = 32 ± 0.05 mm. the velocity profiles for all cases start from zero at the walls, reach the maximum velocity and follow the same trend. case 3, the largest mesh size, diverges from the trend in some points which means that in some locations some of the velocity data points are neglected. on the other hand the profile for case 1, the smallest mesh, fluctuates in the region highlighted in figure 6(b). this fluctuation is an indicator for the lack of information. this means that the distance between dispersed values extracted from the ptv is too large and the velocity value is only the output of an interpolation regardless of the small mesh size. it can be concluded that for this data set, case 2 is an appropriate mesh size which provides a reliable velocity profile based on the ptv data. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) (b) figure 6: (a) representation of the mesh generated effect on the velocity field for 3 different mesh densities in tesla valve, (b) the comparison of the velocity profile calculated for these cases. 5 results and discussion this section discusses the results obtained using different techniques including standard piv, standard ptv, tessellated ptv, and ptv interpolated onto a structured grid. the discussion is mainly focused on the near wall velocity vectors where the difference between each technique is significantly distinguishable. near wall vectors for forward flow with re = 600 are shown in figure 7 comparing the effect of a structured grid and a tessellated grid on the velocity field generated using the ptv method. velocity vectors near the wall in figure 7(a) are pointing toward the walls when there is no tessellation. this means that a velocity component normal to the wall is added to the flow. the normal component indicates that flow passes through the solid channel walls contrasting the physics. figure 7(b) shows the same field of view with the velocity field discretized to the unstructured mesh using the tessellation method. unlike the velocity field from the structured mesh in figure 7(a), velocity components normal to the wall are eliminated in figure 7(b). furthermore, interpolated ptv data in figure 7(a) is not perfectly aligned with the channel wall. this misalignment generates extra small triangular regions outside the channel. these additional regions are corrected using the triangular grid generated and perfectly adjusted by tessellation. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 (a) (b) figure 7: (a) the velocity vectors coming out of the wall in forward flow at re = 600 using ptv, (b) near wall treatment of the ptv obtained velocity vectors using tessellation algorithm at re = 600 the effectiveness of the tessellation on dispersed ptv results is compared to disperse ptv, ptv interpolated on the structured grid, and piv results is shown in figure 8. velocity is extracted from a 1 mm range on the 𝑥-axis 4.5 mm ≤ 𝑥 ≤ 5.5 mm as shown in the top right corner of figure 8 on the geometry. this is to ensure sufficient data points are collected from all methods. figure 8 shows that all of the methods follow the same trend. in figure 8 regions (i) and (ii) show that dispersed ptv and interpolated ptv on the structured grid data do not indicate the near wall velocity values. despite having a similar trend, as it can be seen from figure 8, no velocity data is obtained near the wall from different techniques except for the tessellated ptv. tessellated ptv results shows a similar but smoother trend to piv results shown in figure 8. it is also observable in figure 8 regions (i) and (ii) that tessellated ptv provides the near wall results with velocity profile and trend similar to piv results. figure 8: (a) velocity magnitude for data points 4.5 mm ≤ 𝑥 ≤ 5.5mm calculated by piv and ptv distributed with structured and triangular mesh for tesla with reverse flow and re = 100 and the trend line to the tessellated ptv data; regions (i) and (ii) highlights the near wall areas 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 using the tessellated ptv approach, the effect of flow rate and flow direction are explored for the valve. the velocity field with uniform flow velocity for re = 100 is shown in figure 10 for forward and reverse flows. flow velocity near the wall is corrected using the tessellation method. the vortices in the reverse direction are observable in figure 10(a) which indicates that tessellation can distribute velocity without eliminating the vortices. figure 10(b) shows the flow in the forward direction where flow passes the tesla valve with maximum flow rate. as it is seen from figure 10(b) the flow in the branches in forward direction is almost stationary. (a) (b) figure 9: tessellated velocity field and uniform velocity vector distribution for flow at re = 100 in (a) reverse and (b) forward direction with increasing the reynolds number to 600 vortices start to grow more in areas where the flow is separated. as a result, the changes in the velocity value and components increases in all directions. this makes the velocity transportation from a dispersed state to the tessellated map more challenging. as shown in figure 10, velocity direction is treated using the tessellation method near the wall. for both flow directions shown in figure 10(a) and (b), a smooth velocity field is achieved. as shown in figure 10(a) flow in a reverse direction generates vortices which are responsible for the pressure drop and the reduction of the outlet flow rate. in figure 10(b) forward flow is presented in which the flow is passing through the tesla valve with minimum detaching on the loops joint. as a result, in the forward direction the flow inside the loops is almost stationary whereas in the reverse direction the flow stream is clearly detected inside the loops. (a) (b) figure 10: tessellated velocity field and uniform velocity vector distribution for flow at re = 600 in (a) reverse and (b) forward direction 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 conclusion a meshing methodology to apply tessellation in a complex geometry such as a multi-section tesla valve is investigated. four different approaches are compared to obtain the velocity profile including standard piv, standard ptv, tessellated ptv and ptv interpolated onto a structured grid. the results shows tessellated ptv provides more details and smoother results in certain regions where other techniques miss the data. the results also indicate that the tessellation method can be a reliable method for discretizing the dispersed results for complex geometries. since this method provides access to boundaries of the channel to set boundary conditions, the velocity field generated by the tessellation method can be used for calculating pressure. references azadi, reza, jaime wong, and david s. nobes. (2021) determination of fluid flow adjacent to a gas/liquid interface using particle tracking velocimetry (ptv) and a high-quality tessellation approach. experiments in fluids 62: 1–20. gamboa, adrian r., christopher j. morris, and fred k. forster. (2005) improvements in fixed-valve micropump performance through shape optimization of valves. journal of fluids engineering, transactions of the asme 127: 339–46. porwal, piyush r., scott m. thompson, d. keith walters, and tausif jamal. (2018) heat transfer and fluid flow characteristics in multistaged tesla valves. numerical heat transfer; part a: applications 73: 347–65. raffel, jan. (2019). influence of the reynolds number on the stationarity of the flow field in a tesla diode a bachelor thesis. leibniz university hannover. raffel, jan, shadi ansari, and david s. nobes. (2021) an experimental investigation of flow phenomena in a multi-stage micro tesla valve. journal of fluids engineering, 21-1079 raffel, markus, christian e willert, fulvio scarano, and christian j kähler. 2007. particle image velocimetry a practical guide. germany. tesla, nikola. 1920. patented feb. 3, 1920., issued 1920. wahidi, tabish, rajat arunachala chandavar, and ajay kumar yadav. (2020) stability enhancement of supercritical co2 based natural circulation loop using a modified tesla valve.” journal of supercritical fluids 166: 105020. ansari, shadi, michael bayans, faezeh rasimarzabadi, and david s nobes. (2018) flow visualization of the newtonian and nonnewtonian behavior of fluids in a tesla-diode valve. 5th international conference on experimental fluid mechanics – icefm 2018 munich, munich, germany. a novel streak velocimetry technique based on 2d fits of decaying phosphor particle images luming fan1,2,3, patrizio vena2, bruno savard3,4, guangtao xuan1, benoît fond1,* 1otto-von-guericke-universität magdeburg, universitätsplatz 2, 39106, germany 2national research council (nrc), 1200 montreal road, ottawa on k1a 0r6, canada 3university of ottawa, 75 laurier ave., ottawa, on k1n 6n5, canada 4polytechnique montréal, 2500 chemin de polytechnique, montréal, qc h3t 1j4, canada abstract a new 2d velocimetry technique based on streaks formed by individual phosphor particles, which are moving during their luminescence decay following pulsed excitation is proposed in this study. tin-doped phosphor particles (sr,mg)3(po4)2:sn2+ are dispersed into flows and excited by a pulsed uv light sheet. during the phosphor decay time (~27 µs), the emission streaks due to particle motion are recorded. a 2d fitting is then applied on each particle streak against the analytical expression of intensity distribution, to obtain the velocity information for each particle. unlike particle tracking velocimetry (ptv) this technique does not rely on any particle image searching procedure. introduction. near-wall velocity measurements still remain a great challenge to the velocimetry community today, because (a) laser reflection could easily damage the camera; (b) laser flare and reflection from the wall strongly deteriorates the vector detection probability; and (c) as a window-based technique, piv cannot resolve the fine length scales as required by boundary layer studies. to solve these problems, we propose a new velocimetry technique based on individual phosphor particle streaks in the present study. particle streak velocimetry (psv) is, however, not a new concept, but used as a very old expedient method before two-head pulsed lasers were available to researchers. in that method, particles were illuminated by a continuous light source and their trajectories were recorded on films by a camera with a fixed exposure time. the length of these streaks were then measured manually and converted to velocity vectors. this manual process is very onerous and time-consuming, and in particular, the accuracy cannot be guaranteed as the particle start and end position cannot be determined accurately due to light diffraction. later on, similar psv techniques based on fluorescent-dyed particles or quantum-dots were also introduced. however, soon after double pulse piv lasers and double-frame ccd cameras were invented and commercialised, psv was no longer popular, and instead piv became the state-of-the-art tool for planar velocimetry. however, 40 years since then, the computational capability of pcs and image processing tools have gone through tremendous progress. therefore, we revisit the particle streak velocimetry technique based on phosphor particle tracers, and use a 2d fitting to extract the initial particle position and the two components of velocity with sub-pixel accuracy. for near-wall measurement, in particular, the incident laser wavelength is rejected by phosphorescence spectral filter, so the problem of laser flare and damage to the camera can be avoided. the proposed technique relies on 2d parametric fitting, by which the contribution from background signal can be recognised and does not affect the extraction of velocity components. further, since the psv technique is based on individual particle tracking, and has subpixel resolution (< 10 µm) on particle position determination, velocity information within the near-wall boundary layer can be well resolved. in this study, we firstly introduce the theory of the phosphor streak velocimetry. then we demonstrate the psv technique in an air jet, and compare it with the piv result, conducted simultaneously using a green piv laser (fig.1). finally, we show some results obtained from a near-wall velocity measurement. methods. the psv setup is shown in figure 1. particles of (sr,mg)3(po4)2:sn2+ seeded into an air flow are imaged with a scmos camera at a magnification of 0.3 for a field of view of 2.7 x 2.3 cm2. the decay time is around 27 µs between 300-500 k [1], which provides a velocity dynamic range of 0.5-7 m/s. nevertheless, the psv technique can be easily extended to flows with higher/lower velocities by selecting a proper candidate that has a shorter/longer decay time from a long list of phosphor materials. the intensity distribution of a still particle image is expressed by the airy function, and is usually approximated as a 2d gaussian function. adding velocity components 𝑣𝑥 𝑎𝑛𝑑 𝑣𝑦, time 𝑡 and a decay constant 𝜏 to this 2d gaussian function reads: integrate this equation over 𝑡 from 0 to infinity yields a set function of 6 variables: 𝐼0 is the intensity constant, 𝑥0, 𝑦0 are initial particle position, 𝜎 is the particle image size constant. those parameters are extracted for each recorded particle streak by least square fitting. local background signals can be estimated from the intensity pdf in each streak window, or by applying a threshold to the intensity gradient. results. figure 2 shows the image processing method and an example streak fitting. figure 3 provides (a) an example single-shot, and (b) accumulated vector field in a re = 1500 open jet obtained by phosphor streak velocimetry. figure 3(c) and (d) show the comparison between the psv and piv results at different flow velocities. within 0.5-7 m/s velocity range, the psv results based on tin-doped phosphor matched well with those obtained by piv. figure 4(a) presents the accumulated near-wall vector field measured by psv, the closest vector measured is only 30 µm from the wall, as shown in figure 4(b). figure 4(c) shows the comparison between the measured velocity profile across the boundary layer and the theoretical blasius solution, which shows excellent agreement. conclusions. in this study, a new velocimetry technique is proposed, based on phosphor particle streaks and 2d least-square fitting to the analytical expression of the emission trajectory. the technique is first demonstrated in an open jet where results were compared to piv before being applied in a 200 μm thick boundary layer. experiments had very good agreement and showed that the new psv technique can be applied to characterise the flow field very close to the wall. further, considering the ratio-based thermometry that has been well established for phosphor particles, simultaneous temperature imaging can be implemented by adding another camera, which will be presented in future work. references [1] b.fond, c.abram, m, pougin, f, beyrau. investigation of the tin-doped phosphor (sr,mg)3(po4)2:sn2+ for fluid temperature measurements. opt. mat. express. 9 802-818 (2019). figure 1 schematic view of experimental setup figure 2 the image processing procedure and an example streak fitting figure 3 (a) single shot, and (b) accumulated psv vector field; (c) comparison of mean axial velocity profiles, and (d) comparison of psv and piv results in the square region at different flow velocities figure 4 near-wall boundary layer measurement, and a comparison with the blasius solution 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 multi-spectral imaging for thermochromic liquid crystal based particle image thermometry: a proof of concept t. käufer1∗, s. moller1, m.rosenberger2, g. notni2, c. cierpka1 1 technische universität ilmenau, institute for thermodynamics and fluid mechanics, 98693 ilmenau, germany 2 technische universität ilmenau, group for quality assurance and industrial image processing, 98693 ilmenau, germany ∗ theo.kaeufer@tu-ilmenau.de abstract in this contribution, a novel imaging approach for thermochromic liquid crystal (tlc) based particle image thermometry (pit) is demonstrated. in contrast to state of the art approaches, a multi-spectral camera was used to record the color response of the thermochromic liquid crystals seeding particles. an experiment with a transparent, water-filled, cylindrical cell as the central element was set up to investigate the novel approach. the temperature in the cell can be controlled by adjusting the temperature of the bottom and top plate. calibration images at eleven different temperatures ranging from 18 ◦c to 21.6 ◦c, as well as images of a stable thermal stratification, were recorded. 90 percent of the calibration data was used to train a neural network (nn) to predict the temperature. the remaining 10 percent of the calibration data and the data of the stable thermal stratification were used to test the nn. the tests show that the deviation between predicted and ground truth temperature is mostly below 0.1 k and that the linear profile of the stable thermal stratification can be predicted with a maximum deviation of ≈ 0.15 k. this shows that multi-spectral imaging with neural networks for data processing is feasible and a promising concept. 1 introduction to fully describe temperature-driven flows, quantitative knowledge of both velocity and temperature is of vital importance, which requires the measurement of both quantities. to measure fluid velocities, particle image velocimetry (piv) and particle tracking velocimetry (ptv) are well-established, sophisticated methods and are the go-to techniques for many experimental investigations when an optical access can be ascertained. likewise, for optical temperature measurements in fluids, several different methods have been developed and are applied depending on the field of application, expected temperature range, and required uncertainty. one approach is called laser induced fluorescence (lif). to perform lif, one or two temperature-sensitive dyes are added to the fluid. those dyes are then excited by a laser, and the fluorescence emission spectrum is observed from which the temperature can be derived. however, those dyes result in a slight opacity of the fluid of investigation, which decreases the signal-to-noise ratio of the particle images if particles are added for simultaneous piv measurements. in this case, the seeding particles required for the piv measurements also interfere with the temperature measurements, see funatani et al. (2004). an alternative approach is to use temperature-sensitive seeding particles for temperature measurement. the major advantage is that the seeding particles can often also be employed for the velocity measurements, and, therefore, both measurements do not interfere with each other. those temperature-sensitive particles may, for instance, have temperature-related luminescent (massing et al. (2016)), phosphorescent (abram et al. (2018)) or reflective properties (dabiri and gharib (1991)). this technique is called particle image thermometry (pit). commonly used seeding particles with temperature-related reflective properties are encapsulated thermochromic liquid crystals (tlcs). when tlcs are illuminated by white light, the reflected wavelength range and thus the color shade of the tlcs depends on the temperature and the observation angle. the combination of piv and pit has proven to be well-suited for the experimental investigation of heat and momentum transfer in large aspect ratio rayleigh-bénard convection where the temperature range to be considered is oftentimes moderate, see moller et al. (2021). for this application, uncertainties in the temperature measurements of 0.1 k and less are reported by moller et al. (2019). the current state of the art is to record the color response of the tlcs with an rgb (red, green, blue) color camera. after recording the rgb-images, the color information is then transformed into the hsv/i (hue, saturation, value/intensity) color space because the perceptible change in color appearance can be sufficiently described by the hue value only, which means that a bijective relation between hue value and temperature exists. however, neural networks (nn) were also successfully applied to estimate the temperature from the intensity data, see anders et al. (2020). the novelty of this work is the application of a multi-spectral camera instead of a conventional rgb color camera to record the color response of the tlcs. in general, multi-spectral cameras feature numerous different color channels with oftentimes smaller bandwidths. among other applications, multi-spectral cameras have already been successfully used for food quality assurance, see rosenberger and celestre (2016). when applied to capture the color response of the tlcs, the additional color channels allow for a more detailed spectral resolution of the tlcs compared to the three color channels of the rgb camera. furthermore, the multiple spectral bands might also allow capturing the reflection in the near-infrared (nir) range. this might increase the measurement range since it was shown by könig et al. (2019) that the tlcs reflect slightly in the nir range when the illumination spectrum also contains those wavelengths. hence, the scope of this work is to demonstrate the feasibility of multi-spectral imaging for pit. 2 experimental setup in order to test, the suitability of a multi-spectral camera for pit an experiment was set up. a schematic top view of the setup can be seen in figure 1(a). the central unit of the experiment is a water-filled, cylindrical cell with a height of h = 55 mm and an inner diameter of d = 110 mm, which is enclosed by two plates made of aluminum, as it can be seen in figure 1(b). the temperature of the bottom and top plate can be adjusted θ light source multi-spectral camera mounting rails rotation stage cylindrical cell (a) rotation stage top plate bottom plate cylindrical cellh d (b) figure 1: (a) schematic top view on the experimental setup (a). θ denotes the observation angle. (b) side view on the cylindrical cell with mounted rotation stage. h and d denote the height and the inner diameter of the cell, respectively. independently and can be measured by pt-100 temperature sensors. on top of the cell a rotation stage is fixed on which a mounting rail with the multi-spectral camera is mounted. thereby, the observation angle θ between camera and light source can be adjusted. the used multi-spectral camera is a filter wheel camera with twelve different color channels and a sensor resolution of 1024 pixel× 1160 pixel. a camera objective with a fixed focal length of f = 6 mm is mounted in front of the camera. for details on the camera the reader is referred to rosenberger and celestre (2016). the advantage of such a filter wheel is that the spectral bands of the color channels can be easily adjusted by exchanging the filters in the filter wheel. yet, the usage of a filter wheel has the disadvantage that the color channels are not recorded instantaneously but subsequently, in contrast to sensor-mounted filters. this restricts the range of application of a filter wheel camera to slowly changing or stationary temperature distributions. however, the scope of this work is to investigate the feasibility of multi-spectral imaging for pit rather than the quantification of a specific flow. therefore, the advantage due to the customizablitiy of the color channels surpasses the disadvantage of the non-simultaneous recording. as the light source an led array with integrated light sheet optics is used, that generates a light sheet with a thickness of ≈ 2.5 mm. the spectrum of the light source is depicted figure 2, where the relative intensity ir = i / imax is shown in dependency of the wavelength λ. one can see that the illumination spectrum of 400 500 600 700 800 λ [nm] 0.0 0.2 0.4 0.6 0.8 1.0 i r [] ir filter figure 2: illumination spectrum of the used light source. the optical filters used in the multi-spectral camera are shown as red lines in the plot. for a better visualization the vertical position of the lines is altered. the led ranges from a wavelength λ≈ 400 nm to λ≈ 800 nm with two intensity peaks at λ≈ 460 nm and λ≈ 560 nm. the red lines in the plot depict the filter selection mounted in the filter wheel of the camera. in table 1 the central wavelengths λc and the bandwidths ∆λ of the filters are listed. the bandwidth is defined as full width at half maximum (fwhm), which means that the transmission at the edges of the bandwidth is half of the maximum transmission. the bandwidth ∆λ is centered around the central wavelength λc of the filter. as seeding particles encapsulated tlcs of type r20c20w (lcr hallcrest) were used. there nominal table 1: this table shows the central wavelength λc and bandwidth ∆λ of the used filters. the filters are numbered ascending according to their central wavelength. 1 2 3 4 5 6 7 8 9 10 11 12 λc [nm] 425 450 475 500 550 575 600 625 675 725 775 825 ∆λ [nm] 50 25 25 50 25 25 25 50 50 50 50 50 temperature sensitivity starts at 20 ◦c and ends at 40 ◦c for an observation angle of θ = 0◦. however, for larger observation angles close to θ = 90 ◦, which is often beneficial for the investigation of fluid flows with optical measuring techniques, the sensitivity is increased while the temperature range is drastically decreased, as shown by moller et al. (2019). 3 results after setting up the experiment, calibration measurements were performed. the goal of the calibration measurements is to determine the relationship between the intensity distribution across the color channels and the related temperature. therefore, several isothermal states have been set inside the cell at eleven different temperature levels ranging from 18 ◦c to 21.6 ◦c by adjusting and measuring the temperature of the bottom and top plate of the cell. when the temperature sufficiently converged, a total of ten calibration sets were recorded for each individual calibration temperature. a set consists of twelve images, on for each filter. however, for further processing, only the ten filters with the central wavelengths in the range 425 nm≤ λc ≤ 725 nm were used since the absolute intensities for the filters λc = 775 nm and λc = 825 nm were too low to be meaningful. this is a consequence of the low emission of the light source at λ≈ 800 nm. figure 3 shows the filter-wise relative intensity if,r = if / if,max for the ten filters with the central wavelengths in the range 425 nm ≤ λc ≤ 725 nm in dependency of the temperature level. the images were recorded 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 t [◦c] 0.0 0.2 0.4 0.6 0.8 1.0 i f ,r [] 425 nm 450 nm 475 nm 500 nm 550 nm 575 nm 600 nm 625 nm 675 nm 725 nm figure 3: transition of the filter-wise relative intensity if,r across the calibration temperature range under an observation angle θ = 70◦ and the filter-wise intensities if were estimated by spatially averaging the intensities in a region that covers almost the full height of the cell but only a slim horizontal span at the center of the cell. thereby the change of the observation angle θ along the width and optical distortion caused by the cylindrical wall can be neglected. in vertical direction θ is constant. for a more extensive explanation, the reader is referred to the publication of moller et al. (2019). one can see that the relative intensities for all filters are small for the lowest temperature levels and that they rise until the curves reach their individual peak. the peak temperature of the filters is inversely related to the central wavelength of the filters. this means that the tlcs appear red for lower temperatures and continuously change their appearance through the visible spectrum until they appear blue at temperatures above 21.5 ◦c. by comparing the nominal starting point and the range of the tlc (start at 20 ◦c, range of 20 k) with the filter-wise relative intensities, it gets apparent that the nominal range can only be used as a qualitative indicator. thus, due to the influence of the illumination spectrum and the observation angle on the color appearance of the tlcs a calibration is required for every specific measurement arrangement. furthermore, the calibration has to be performed locally since the change of the observation angle across the field of view can not be neglected in this arrangement. therefore, the images are sliced into interrogation windows with a size of 32 pixel× 32 pixel that overlap by 16 pixel. due to the additional data provided by the multi-spectral camera, a hue-based calibration approach can not be easily applied. it could furthermore negate possible benefits through the increased spectral resolution. hence, a neural network was trained to estimate the temperature from the intensity data. the nn and the data processing pipeline were implemented in the python programming language. the nn is based on the multi layer perceptron (mlp) regressor provided by the scikit-learn software library (pedregosa et al. (2011)) and is designed as a feedforward nn. in the first step, the calibration images of the ten filters with the lowest central wavelength were cropped to the region of interest depicted in figure 4, then the images were sliced into interrogation windows and the mean intensity value of each interrogation window was calculated. based on the intensity data and the coordinates of the center of interrogation windows, a buffer was 0 1 1 x y figure 4: exemplary image of the stable thermal stratification recorded by the multi-spectral camera through the filter with λc = 550 nm. the white box denotes the region of interest. x and y denote the coordinate system used to visualize the results of the nn. created. by dividing the intensity data of each filter by the maximum occurring intensity of that specific filter, the intensity data were normalized. likewise, the interrogation window coordinates were normalized by the size of the region of interest. thereby all values are in the interval [0, 1] and had a similar scale which is beneficial for the nn. from this buffer, the data of nine sets were used for training and one set for testing purposes. the nn consists of the input layer that takes twelve inputs (ten intensities, two coordinates), six densely connected layers with 100 neurons each, and the ”relu” activation function and an output layer with a single neuron. for the optimization, the ”adam” optimizer was used. the nn configuration was optimized experimentally. for the final training, a split of ten percent of the training data was used to validate the progress during the training and to avoid overfitting, and the nn was trained for 44 iterations until both training and validation loss had converged sufficiently. to test the quality of the nn, a randomly sampled temperature distribution was used. this randomly sam0.0 0.2 0.5 0.8 1.0 x [ ] 0.0 0.2 0.4 0.6 0.8 1.0 y [] 18 19 20 21 22 t g [°c ] (a) 0.0 0.2 0.5 0.8 1.0 x [ ] 0.0 0.2 0.4 0.6 0.8 1.0 y [] 18 19 20 21 22 t p [°c ] (b) figure 5: (a) temperature field displaying the ground truth temperature tg of the randomly sampled temperature distribution. (b) temperature field showing the temperature predicted by the neural network tp. the x and y coordinates are the same as shown in figure 4. pled temperature distribution was created from the calibration data reserved for testing purposes. for each interrogation window, the intensity data was randomly selected from the eleven measured calibration temperatures. the corresponding field of the ground truth temperature tg is shown in figure 5(a). even though a temperature distribution like this is only of theoretical nature, it can be considered as a worst-case scenario to test if the nn is capable of predicting the temperature of each interrogation window independently, which is vital for the investigation of the temperature in fluid flows. the field of the predicted temperature tp is depicted in figure 5(b). by comparing the predicted temperature field and the ground truth temperature field, one can already see the quality of the prediction and that the nn is capable of predicting the temperature of each interrogation window independently. a more detailed view on the deviations tp tg is provided by the deviation field in figure 6(a) and the related histogram in figure 6(b). one can see that the deviation is small 0.0 0.2 0.5 0.8 1.0 x [ ] 0.0 0.2 0.4 0.6 0.8 1.0 y [] −0.10 −0.05 0.00 0.05 0.10 t p − t g [k ] (a) −0.2 −0.1 0.0 0.1 0.2 tp − tg [k] 0 25 50 c ou nt s [] (b) figure 6: (a) deviation field depicting the deviation tp tg of the temperature field depicted in 3. (b) histogram of the deviation tp tg. the gaussian shape indicates a normal distribution of the deviations. and almost randomly distributed across the field of interest. furthermore, the histogram shows that the vast majority of the deviation is in the range of -0.1 k to 0.1 k, which is comparable to the results reported in the literature by moller et al. (2019). the histogram in figure 6(b), which almost follows a gaussian shape, also indicates a normal distribution of the deviations. in addition to the randomly sampled temperature distribution, the nn was tested on a stable thermal stratification. therefore, the top plate of the cell was heated to ≈ 20.9 ◦c, while the bottom plate was cooled to ≈ 18.3 ◦c. thereby, fluid motion is inhibited, and heat is only transferred from the top plate to the bottom plate by means of conduction. as a result, a well-known linear temperature profile along the heights of the cell can be achieved. in addition to the well-known profile, the stratification is temporally stable, compensating the relatively long acquisition time of ≈ 4 seconds for a full set. the predicted temperature field can be seen in figure 7(a). the plot shows the smooth transition from the hot temperature at the top to cold temperatures at the bottom. at this point, it is important to mention that the perspective distortion present in the image due to the oblique observation angle is not compensated. this is noticeable in the slight change of the temperature gradient along the x-axis and. for quantitative analysis, the vertical temperature profile at the position x = 0.5 was extracted and is shown in figure 7(b). in this figure, the predicted temperature tp (solid, black line), the theoretical temperature of the linear profile tlin (dotted, black line) and the deviation tp tlin are plotted over the vertical position y . to determine the temperature of the linear profile tlin, the temperatures measured by the sensors in the plates were scaled according to the position of the region of interest. by comparing the curves for tp and tlin, it gets apparent that the linear profile is predicted accurately by the network, especially at the bottom and top of the region of interest. but by viewing the deviation tp tlin, a slight overestimation of the temperature profile with a maximum deviation of ≈ 0.15 k can be seen. however, this overestimation might also be traced back to an imperfect stratification or errors introduced by the scaling. nevertheless, the profiles show that multi-spectral imaging combined with a neural network for data processing is a promising approach for particle image thermometry that should be further investigated. 0.0 0.2 0.5 0.8 1.0 x [ ] 0.0 0.2 0.4 0.6 0.8 1.0 y [] 18.5 19.0 19.5 20.0 20.5 t [°c ] (a) 0.0 0.2 0.4 0.6 0.8 1.0 y [ ] 18.5 19.0 19.5 20.0 20.5 21.0 t [°c ] tp tp − tlin −0.05 0.00 0.05 0.10 0.15 0.20 t p − t li n [k ] (b) figure 7: (a) temperature field of the stable thermal stratification. (b) plot of the vertical temperature profile (solid, black line), the theoretical temperature of the linear profile (dotted, black line) and the deviation tp tg over the vertical position y at x = 0.5. 4 conclusions in this work, the feasibility of multi-spectral imaging for thermochromic liquid crystal based particle image thermometry was investigated. an experiment consisting of a transparent, cylindrical cell with adjustable temperature at the bottom and top side was set up. for the acquisition, a multi-spectral camera with twelve color channels was used, and a neural network was trained to predict the temperature from the intensity data. the suitability of the neural network was tested on a randomly sampled temperature distribution and a stable thermal stratification. the test on the randomly sampled temperature distribution showed that the predominant part of the deviations is below 0.1 k. the comparison between the predicted and the expected profile of the stable thermal stratification shows a maximum deviation of ≈ 0.15 k. both results demonstrate that multi-spectral imaging for pit combined with neural networks for data processing is promising and should be further investigated. therefore, the following improvements should be considered: at first, an illumination source with an extended wavelength spectrum at the edge between the visible wavelength range and the near-infrared wavelength range should be utilized. secondly, the illumination power of the light source should be increased to reduce the exposure time in order to speed up the time required for the recording of a full set of filters. the usage of a super-continuum laser can accomplish both, see könig et al. (2019). alternatively, a camera that simultaneously records all color channels can be employed. acknowledgements the authors are grateful to andrei golomoz, axel sichard and richard fütterer for their help with the camera configuration and the camera control. references abram c, fond b, and beyrau f (2018) temperature measurement techniques for gas and liquid flows using thermographic phosphor tracer particles. progress in energy and combustion science 64:93–156 anders s, noto d, tasaka y, and eckert s (2020) simultaneous optical measurement of temperature and velocity fields in solidifying liquids. experiments in fluids 61:1–19 dabiri d and gharib m (1991) digital particle image thermometry: the method and implementation. experiments in fluids 11:77–86 funatani s, fujisawa n, and ikeda h (2004) simultaneous measurement of temperature and velocity using two-colour lif combined with piv with a colour ccd camera and its application to the turbulent buoyant plume. measurement science and technology 15:983 könig j, moller s, granzow n, and cierpka c (2019) on the application of a supercontinuum white light laser for simultaneous measurements of temperature and velocity fields using thermochromic liquid crystals. experimental thermal and fluid science 109:109914 massing j, kaden d, kähler c, and cierpka c (2016) luminescent two-color tracer particles for simultaneous velocity and temperature measurements in microfluidics. measurement science and technology 27:115301 moller s, könig j, resagk c, and cierpka c (2019) influence of the illumination spectrum and observation angle on temperature measurements using thermochromic liquid crystals. measurement science and technology 30:084006 moller s, resagk c, and cierpka c (2021) long-time experimental investigation of turbulent superstructures in rayleigh-bénard convection by noninvasive simultaneous measurements of temperature and velocity fields. experiments in fluids 62:1–18 pedregosa f, varoquaux g, gramfort a, michel v, thirion b, grisel o, blondel m, prettenhofer p, weiss r, dubourg v, vanderplas j, passos a, cournapeau d, brucher m, perrot m, and duchesnay e (2011) scikit-learn: machine learning in python. journal of machine learning research 12:2825–2830 rosenberger m and celestre r (2016) smart multispectral imager for industrial applications. in 2016 ieee international conference on imaging systems and techniques (ist). pages 7–12. ieee introduction experimental setup results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 on the uncertainty of defocus methods for 3d particle tracking velocimetry c. cierpka1∗, r. barnkob2, s. sachs1, m. chen3, p. mäder3, m. rossi4 1 institute of thermodynamics and fluid mechanics, technische universität ilmenau, p.o. box 100565, d-98684 ilmenau, germany 2 heinz-nixdorf-chair of biomedical electronics, department of electrical and computer engineering, technical university of munich, translatum, 81675 munich, germany 3 group for software engineering for safety-critical systems, technische universität ilmenau, p.o. box 100565, d-98684 ilmenau, germany 4 department of physics, technical university of denmark, dtu physics building 309, dk-2800 kongens lyngby, denmark ∗ christian.cierpka@tu-ilmenau.de defocus methods have become more and more popular for the estimation of the 3d position of particles in flows (cierpka and kähler, 2011; rossi and kähler, 2014). typically the depth positions of particles are determined by the defocused particle images using image processing algorithms. as these methods allow the determination of all components of the velocity vector in a volume using only a single optical access and a single camera, they are often used in, but not limited to microfluidics. since almost no additional equipment is necessary they are low-cost methods that are meanwhile widely applied in different fields. to overcome the ambiguity of perfect optical systems, often a cylindrical lens is introduced in the optical system which enhances the differences of the obtained particle images for different depth positions. however, various methods are emerging and it is difficult for non-experienced users to judge what method might be best suited for a given experimental setup. therefore, the aim of the presentation is a thorough evaluation of the performance of general advanced methods, including also recently presented neural networks (franchini and krevor, 2020; könig et al., 2020) based on typical images. for the assessment of the uncertainty and the tracking probability in different imaging situations, the ground truth has to be known. for this reason, synthetic images were used which show a systematic variation of the imaging conditions, in this case, the degree of astigmatism (none, mild, strong), the noise level and the number of particle images per pixel (rossi, 2020). in addition experimental images were obtained using a typical defocus setup (m = 20), including a cylindrical lens ( fc = 250 mm). for further details the reader is refereed to barnkob et al. (2021) and may access the data soon1. three different methods to determine the depth position by evaluating certain features of the defocused particle images are compared. if a model function (mf) is known, the width and height of the particle images can be evaluated with classical image analysis and related to the depth position (cierpka et al., 2010). however, often such a model function is unknown or too complex. in this case the cross-correlation (cc) with a template image that is determined from a set of calibration images can be used (barnkob et al., 2015; rossi and barnkob, 2020). a high value of the correlation between template and particle image indicates the same depth position. another recently presented method is the use of image recognition by modern machine learning neural networks (nn) to determine the volumetric particle position (franchini and krevor, 2020; könig et al., 2020). the image aberrations serve as features in this case and the network can be trained to relate these features to a corresponding depth position. the uncertainty and the recall (i.e. the ratio between valid detected particles and total number of particles in the image) were evaluated to compare the different methods using synthetic and experimental images with different noise levels and particle image overlapping. in general, it can be stated that all three methods are able to determine the 3d position of particles. the mf algorithms require astigmatic aberrations of the images and show low uncertainties especially for mild astigmatism and low particle image concentration. as a model function (in this case a gaussian intensity distribution) was used, no image pre-processing had to be applied. cc methods worked for all cases and especially well in the case of large image overlap and noise 1https://defocustracking.com/datasets/ https://defocustracking.com/datasets/ levels. however, special care has to be given when the particle images differ strongly in different positions of the field of view. for both approaches, cc and mf the error in the depth direction never exceeded 3% of the whole measurement depth for typical experimental conditions. in the current study nn algorithms were not able to reach similar uncertainties as compared to the other techniques. especially as the synthetic data consists of the same intensity distribution per particle image shifted to different positions within the field of view, the amount of training data is too limited. if experimental images are used the algorithms work considerably better (könig et al., 2020). in the final presentation, the performance of the different algorithms will be shown. the reasons for the observed differences will be discussed together with guidelines for which algorithm may be used in which setup. acknowledgements cc and ss acknowledge financial support by the dfg under grant no. ci 185/8-1 within the pp 2045 mehrdimpart. mr acknowledges financial support by the villum foundation under the grant no. 00022951. pm and cc acknowledge financial support by the carl zeiss foundation’s grant: deepturb. the authors also want to thank dr thomas fuchs (unibw munich) for implementing the edge-detection algorithm. references barnkob r, cierpka c, chen m, sachs s, mäder p, and rossi m (2021) optimization of defocus particle tracking based on image recognition. measurements science and technology 32:094011 barnkob r, kähler cj, and rossi m (2015) general defocusing particle tracking. lab on a chip 15:3556– 3560 cierpka c and kähler cj (2011) particle imaging techniques for volumetric three-component (3d3c) velocity measurements in microfluidics. journal of visualization 15:1–31 cierpka c, rossi m, segura r, and kähler cj (2010) on the calibration of astigmatism particle tracking velocimetry for microflows. measurement science and technology 22:015401 franchini s and krevor s (2020) cut, overlap and locate: a deep learning approach for the 3d localization of particles in astigmatic optical setups. experiments in fluids 61:140 könig j, chen m, rösing w, boho d, mäder p, and cierpka c (2020) on the use of a cascaded convolutional neural network for three-dimensional flow measurements using astigmatic ptv. measurement science and technology 31:074015 rossi m (2020) synthetic image generator for defocusing and astigmatic piv/ptv. measurement science and technology 31:017003 rossi m and barnkob r (2020) a fast and robust algorithm for general defocusing particle tracking. measurement science and technology 32:014001 rossi m and kähler cj (2014) optimization of astigmatic particle tracking velocimeters. experiments in fluids 55 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 investigation of the shear-layer instabilities in supersonic impinging jets using dual-time velocity measurements t. sikroria1∗, j. soria2, s. karami2, r. sandberg1, a. ooi1 1 department of mechanical engineering, university of melbourne, parkville campus, melbourne, victoria 3010, australia. 2 laboratory for turbulence research in aerospace and combustion (ltrac), department of mechanical and aerospace engineering, monash university, clayton campus, melbourne, victoria 3800, australia. ∗ tsikroria@student.unimelb.edu.au 1 introduction motivated by applications in the propulsion industry, the fundamental study of phase-locked shear-layer instabilities in supersonic impinging jets has been of research interest for long time. while such flows have been experimentally investigated in various research studies using time-unresolved particle image velocimetry (piv) techniques, the understanding of the shear-layer dynamics is limited, due to the absence of temporal information. time-resolved piv measurements for high-speed flows require a large bandwidth, which is challenging to achieve with the current state of technology. an alternate approach using timeunresolved double-piv measurements is presented in the current study, which provides multiple samples of dual-time data, depicted in figure 1. such data can be obtained using two co-visual piv systems, triggered at a user-selectable time-offset, ∆t. as shown by sikroria et al. (2020), the application of techniques like dynamic mode decomposition (dmd) on time-unresolved dual-time data provides valuable information about the flow structures governing the shear-layer instabilities. the experimental setup for such measurements in supersonic impinging jets, followed by the determination of the relevant dynamical flow structures from the data, will be presented in the conference. 2 experimental measurements the experiments were conducted using the suband super-sonic jet facility in the laboratory for turbulence research in aerospace and combustion (ltrac), monash university, whose details have been reported in mitchell et al. (2013), weightman et al. (2019). the main challenge in double-piv experimental measurements was to ensure that the camera from the first piv system did not capture the illumination by the laser from the second piv system and vice versa. the principle of the difference in polarization between two laser systems was used for the measurements in the current study, which has been used previously in the work of christensen and adrian (2002). the optical setup used for the experiments is shown in figure 2. a high-power and high-frequency innolas spitlight dpss evo iv laser, which was a composite of two laser systems, the master and the slave, respectively, was used for the double-piv experiments. the master and the slave lasers had opposite polarization and this difference in the polarization formed the basis of the dual-time data acquisition. the images were captured using two cameras, mounted on a t-shaped plate. both the cameras were connected to a polarizing beam splitter, attached to the lens. the arrangement ensured that each of the two cameras could see the laser light corresponding to a particular polarization only. the timing was synchronized by programming the bbb (beagel bone black) controller (fedrizzi and soria (2015)) which provided the platform to specify a user-selectable time-shift, ∆t, between the two piv systems. multi-grid cross-correlation algorithm proposed by soria (1996) was used for the processing of images. following the work of sikroria et al. (2020), the double-piv measurements were carried out for moderately under-expanded jet at a nozzle pressure ratio (npr) of 3.4 and impinging distance of 5 nozzle diameters. acoustic measurements were additionally conducted for the selected test-case, for validation of figure 1: sampling of velocity fields in double-piv measurements showing ensemble of pairs of velocity fields. figure 2: schematic of the optical setup for double-piv measurements. the spectral information obtained from the double-piv data. g.r.a.s. 46be 1/4” ccp free-field standard microphone, having a frequency range of 4 hz 80 khz, was used for the acoustic measurements. the impingement tones were determined from the peaks observed in the spectrum obtained using the pressure signals from the microphone. acknowledgements the research is being funded by a discovery project grant from the australian research council (arc). references christensen k and adrian r (2002) measurement of instantaneous eulerian acceleration fields by particle image accelerometry: method and accuracy. experiments in fluids 33:759–769 fedrizzi m and soria j (2015) application of a single-board computer as a low-cost pulse generator. measurement science and technology 26:095302 mitchell dm, honnery dr, and soria j (2013) near-field structure of underexpanded elliptic jets. experiments in fluids 54:1578 sikroria t, soria j, karami s, sandberg rd, and ooi a (2020) measurement and analysis of the shear layer instabilities in supersonic impinging jets. in aiaa aviation 2020 forum. page 3070 soria j (1996) an investigation of the near wake of a circular cylinder using a video-based digital crosscorrelation particle image velocimetry technique. experimental thermal and fluid science 12:221–233 weightman jl, amili o, honnery d, edgington-mitchell d, and soria j (2019) nozzle external geometry as a boundary condition for the azimuthal mode selection in an impinging underexpanded jet. journal of fluid mechanics 862:421–448 introduction experimental measurements 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 investigation of smoothing operation in 3-d reconstruction for plenoptic piv b. sapkota1∗, d. kelly1, z. p. tan2, b. thurow1 1 auburn university, aerospace engineering, auburn, al, usa 2 national yang ming chiao tung university, department of mechanical engineering, taiwan ∗ bzs0084@auburn.edu this paper investigates the effect of smoothing operation in 3d reconstruction using a plenoptic camera. a plenoptic camera also known as light field camera features a commercial off the shelf camera with added microlens array (mla) behind the imaging lens, directly in front of the sensor. the main lens focuses the light to the mla plane, where each microlens then re-directs the light to small regions of pixels behind, each pixel corresponding to different angle of incident (t. fahringer (2015)) (adelson and wang (1992)). thus, mla encodes angular information of incident light rays into the recorded image that assist to acquire 4d information (u,v,s,t) of light-field including both position and angular information of light rays captured by the camera (ng et al. (2005)) (adelson and wang (1992)). four-camera tomographic particle image velocimetry (tomo-piv) is the current standard for 3d flow velocimetry. plenoptic piv represents an alternative velocimetry technique, with ability to perform 3d measurements with as few as a single camera, which is made possible as around ∼100 independent perspective views with mutual parallax can be decoded from a single plenoptic image hall et al. (2018). in addition, plenoptic piv also allows notable advantages like larger depth of field and suppressed propensity to ghost due to large number of perspectives available (tan et al. (2020)). thus, single camera plenoptic reconstruction is unique to the multi camera tomo reconstruction with large number of available perspective over small angular range. this paper analyzes the effect of smoothing in plenoptic reconstruction based on practices in multicamera tomo reconstruction. this includes 2d smoothing the image before reconstruction and 3d smoothing the volume during reconstruction. the image smoothing involves 2d convolution operator used as a point-spread function used to smear the pixel intensity. similarly, 3d smoothing involves the blurring the voxel intensity in 3d volume using a 3d gaussian convolution operator. the 3d smoothing is performed between each mart iteration. smoothing helps to obtain smooth solution, suppressing unwanted noise and ghosts while making the particle distinct (dav (2019)). first, the performance of plenoptic piv is compared against a multi-camera tomographic system. a simultaneous single camera plenoptic piv and 4-camera tomographic piv is set-up to observe a simplified flow-field of flow through a pipe in order to characterize the performance of plenpotic piv against tomo-piv 1(a). both camera were time-synchronized to observe the flow field simultaneously, and aligned in identical coordinate system. for the direct comparison of plenoptic and tomographic system, a 3d reconstruction code that can accommodate both types of images is required. a version of our in-house plenoptic piv processing code, called “dragon”, was used for this purpose. for this study, the code suite was modified such that four conventional non-plenoptic images could be fed into the algorithm for tomographic reconstruction. the plenoptic dragon and modified multicamera tomo dragon workflow is shown in figure 1(b). this modified version of dragon is also compared against the state of art multi-camera tomo-piv commercial software “lavision davis”. figure 2 shows the 3d particle field from dragon single camera plenoptic reconstruction, dragon 4camera reconstruction and davis 4-camera reconstruction. the davis particle field seems particularly smooth and distinct and is able to suppress the ghost formation efficiently. the particles from plenoptic reconstruction seems quite stretched along depth as compared to to particles from tomo-reconstruction because of low angular difference between end perspectives. the tomo reconstruction field has visibly noticeable ghost particle, which is diminished in plenoptic reconstruction. the large number of perspectives (a) (b) figure 1: (a) simultaneous 4-camera tomographic piv and single camera plenoptic piv setup (b)plenopticdragon workflow vs tomo-dragon workflow (a) (b) (c) figure 2: comparison of reconstruction using: (a) davis 4-camera tomo reconstruction, (b) dragon 4camera tomo reconstruction and (c) dragon plenoptic reconstruction available for plenoptic reconstruction suppresses the formation of ghosts. in order to improve the reconstruction in plenoptic particle field, the various smoothing operations were performed based on either smoothing the image or smoothing the volume between iterations. figure 3 shows the comparison of image based smoothing and volumetric smoothing on plenoptic reconstruction field. it is evident that, the both smoothing operation suppresses the formation of noise in the volume. however, the image based smoothing is observed to enhance the particle size significantly as compared to volume based smoothing. for quantitative analysis of the effect of smoothing on noise in reconstructed volume, a pair of synthetic plenoptic particle images representing a vortex ring flow was generated with 8500 particles and 10 percent gaussian noise added to it. this was then reconstructed to form a 261*261*261 cubic volume with different smoothing parameters. the effect of smoothing was then observed in terms of reconstruction quality and error in vector fields.from figure 4 it is inferenced that, both smoothing the image and the volume improves the reconstruction quality of plenoptic reconstruction. however, if the smoothing parameter is further increased, the reconstruction quality drops. this is in line with effects seen in multi-camera tomographic reconstruction. since the plenoptic reconstruction is unique in available information, further tests to identify best practices in plenoptic reconstruction based on general practices in multi-camera tomo reconstruction is desired. (a) (b) (c) figure 3: plenoptic dragon pipe-flow reconstruction with different smoothing operation: (a) normal mart (b) images smoothed with σ = 0.5 (c) volume smoothed with σ = 1.5 (a) (b) figure 4: synthetic vortex ring reconstruction quality for different smoothing operation: (a) volumetric smoothing with different σ (b) image smoothing with different σ. acknowledgements the material is based on the work supported by the national science foundation’s major research instrumentation program grant no. 1725929. references (2019) product manual-davis 10.0 software. technical report. lavision adelson eh and wang jy (1992) single lens stereo with a plenoptic camera. ieee transactions on pattern analysis and machine intelligence 14:99–106 hall em, fahringer tw, guildenbecher dr, and thurow bs (2018) volumetric calibration of a plenoptic camera. applied optics 57:914–923 ng r, levoy m, brédif m, duval g, horowitz m, and hanrahan p (2005) light field photography with a hand-held plenoptic camera. ph.d. thesis. stanford university t fahringer bt k lynch (2015) volumetric particle image velocimetry with a single plenoptic camera. measurement of science and tech 26:25 tan zp, alarcon r, allen j, thurow bs, moss a et al. (2020) development of a high-speed plenoptic imaging system and its application to marine biology piv. measurement science and technology 31:054005 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a stereoscopic piv system for the princeton superpipe l. ding∗, e. limacher, i. e. gunady, a. piqué, m. hultmark and a. j. smits department of mechanical and aerospace engineering princeton university, princeton, new jersey, usa ∗corresponding author: liuyangd@princeton.edu abstract herein, we describe the design and testing of a stereoscopic piv system uniquely adapted for the high pressure environment of the princeton superpipe. the superpipe is a recirculating pipe facility that utilizes compressed air as the working fluid to attain very high reynolds numbers. commercial piping is used as the pressure vessel to hold pressure up to 220 bars, and a test pipe is enclosed inside with a development length of 200 diameters that ensures a fully-developed condition at the test section. the highest achievable reynolds number (based on the bulk velocity and the pipe diameter) is 35×106, corresponding to a maximum friction reynolds number of 5×105. the unprecedented range of reynolds number has enabled a number of new insights in the behavior of high reynolds number wall-bounded turbulence (zagarola and smits, 1998; hultmark et al., 2013). however, past measurements in the superpipe have been primarily restricted to single-component, oneor two-point statistics of fully-developed pipe flows. the present work aims to expand the capability of the superpipe to study turbulent coherent structures and multi-point statistics by means of a new stereoscopic piv system. the high pressure environment and the confined space inside the pressure vessel pose challenges to both imaging and seeding, the solutions to which will be discussed. 1 imaging the imaging system has been designed so that only mirrors are contained in the high-pressure environment, and all cameras are located external to the test section. this configuration offers a significant benefit – its performance is nearly unaffected when the refractive index of compressed air changes with pressure. more specifically, the object plane is chosen to be the one determined by the axes of the test pipe and the access port of the test section (see figure 1). a laser light sheet is delivered into the test pipe through the sight windows on the sealing flange and the internal test pipe. an optical relay assembly consisting of two nearaxis and two off-axis mirrors is mounted directly to the test pipe and used to relay particle images to cameras placed outside the pressure vessel through the flange sight window. as indicated by the simulated light rays in figure 1, the mirrors on each side of the light sheet provide one view of the object plane, so the two pairs of mirrors constitute a stereoscopic system. by means of optical ray tracing, the imaging system is optimized in terms of the following aspects: (i) the angle between the two views in stereoscopic imaging is 90◦ to minimize the uncertainty in the azimuthal velocity component (lawson and wu, 1997); (ii) the field of view encompasses the region between the wall and the centerline of the pipe and spans at least one radius (r = 63.8 mm) in the pipe axial direction; (iii) the chief ray emanating from the center of the field of view (y = r/2 with y being the wall-normal distance) is perpendicular to the sight window on the sealing flange (#3 in figure 1) to minimize astigmatism. with the ray tracing analysis, we have also evaluated the images of point sources in the object plane. the image sizes across the field of view are smaller than 10 µm, as compared to the diffraction-limited spot size of 17 µm at the same magnification and f -number. 2 seeding the design of the flow seeding system must address the following challenges: (i) it must allow for the generation and injection of seeding particles at or near the desired test pressures; (ii) it must not foul the internal surfaces of the superpipe, which is difficult to clean; and (iii) it must produce a narrow distribution of particle sizes with a mean diameter around 1µm. our chosen design consists of a sealed, pressure-rated housing that serves as a liquid reservoir, with several laskin nozzles submerged in the liquid. compressed air at higher pressure is driven through the nozzles to generate an aerosol, which is then carried into the superpipe through a connecting tube. we have figure 1: the imaging system shown in a crosssection of the access port, with simulated light rays indicating the imaging paths. 1: test pipe with a thin sight window. 2: mirrors (two near-axis ones and two off-axis ones). 3: sealing flange with a sight window. 4: lens group of a 135-mm prime lens. 5: laser sheet. 0 200 400 600 800 1000 1200 0 1 2 3 4 5 figure 2: dp versus ∆p for all test cases run. filled circles denote purely seeded cases; empty squares represent cases with dry air mixed with seeded air. yellow-filled red stars are results from legrand et al. (2017) with no dry air added. opted for propylene glycol as the seeding liquid because it is inexpensive with a low vapor pressure – a desirable property keeping the surfaces of the test section free of liquid residue. a dantec pda system was used to characterize the size distribution of droplets produced by the seeder. the modal (peak) diameter dp is plotted in figure 2 versus the pressure difference, ∆p = p1 −p2, where p1 is the supply pressure, and p2 is the housing pressure. these results are for a nozzle with two 0.51mmdiameter holes; other configurations were also tested, but are omitted for brevity. in general, increasing the nozzle pressure difference tends to decrease droplet sizes, and adding dry air for a given configuration and ∆p tends to reduce the droplet size further, presumably due to evaporation. to confidently get a droplet size distribution with a modal diameter of 2 µm or less, one should maintain a pressure difference across the nozzle of about 500 psid, if purely seeded air is desired. mixing dry air is likely desirable to achieve seeding densities more appropriate to piv. however, it bears noting that these results and the above suggestion are sensitive to other system design parameters that are not fully understood. legrand et al. (2017), for example, managed to obtain smaller modal diameters than us at low pressure differences (yellow-filled red stars on figure 2). 3 system integration having designed, assembled and tested various subsystems, we have moved on to begin testing their integration. we will present preliminary results showing acquired particle images in the test pipe at ambient pressure, and we will discuss recently addressed and ongoing challenges such as background reflection and droplet condensation. acknowledgements this work is supported by onr durip grant no. n00014-19-1-2301 and onr grant no. n00014-17-12309. ieg was supported by the department of defense (dod) through the national defense science and engineering graduate fellowship (ndseg) program. references hultmark m, vallikivi m, bailey scc, and smits a (2013) logarithmic scaling of turbulence in smooth-and rough-wall pipe flow. journal of fluid mechanics 728:376–395 lawson n and wu j (1997) three-dimensional particle image velocimetry: error analysis of stereoscopic techniques. measurement science and technology 8:894–900 legrand m, nogueira j, rodriguez pa, lecuona a, and jimenez r (2017) generation and droplet size distribution of tracer particles for piv measurements in air, using propylene glycol/water solution. experimental thermal and fluid science 81:1–8 zagarola mv and smits aj (1998) mean-flow scaling of turbulent pipe flow. journal of fluid mechanics 373:33–79 imaging seeding system integration 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 cross-plane stereo-piv measurements in a refractive-index-matched environment of flow associated with barchan dunes immersed in a turbulent boundary layer n. r. bristow1, g. blois1, j.l. best2, k. t. christensen1,3∗ 1 university of notre dame, department of aerospace and mechanical engineering, notre dame, in, usa 2 university of illinois at urbana-champaign, departments of geology, geography and gis, mechanical science and engineering and ven te chow hydrosystems laboratory, urbana-champaign, il, usa 3 illinois institute of technology, department of mechanical, materials, and aerospace engineering, chicago, il, usa ∗ kenneth.christensen@iit.edu 1 introduction barchan dunes are crescent-shaped bedforms that form in aeolian (i.e., wind-driven) environments (including both earth and other planets, such as mars) as well as subaqueous environments. under the forcing of the aloft turbulent boundary layer, they migrate downstream at a rate inversely proportional to their size, which results in complex interactions between neighboring dunes of disparate scales. in particular, it has been observed that dunes will interact at a distance, causing changes in morphology without contacting each other, which is thought to be driven by the way dunes modify the local flow field bristow et al. (2018); assis and franklin (2020). in this study, the coherent structures formed in the wakes of barchan dunes are investigated using measurements of the flow over fixed-bed (i.e., solid) barchan models, both in the wake of an isolated barchan and the interdune region between interacting barchans (fig. 1(a)). furthermore, the interactions between the flow structures shed by the dunes and the structures in the incoming boundary layer are analyzed. 2 methods experiments are conducted in the large-scale refractive-index-matching (ls-rim) flume at the university of notre dame. transparent models of barchan dunes were fabricated using a combination of 3d printing and casting to obtain transparent acrylic models for configurations including a baseline isolated case and a series of dune–dune collision configurations (fig. 1(a)). the models were immersed in a turbulent boundary layer in the ls-rim, with reynolds number reτ ≈ 1800 and boundary layer thickness δ = 52.5 m such that h/δ ≈ 0.2. the rim approach involves using an aqueous solution of sodium iodide (≈63% by weight) as the working fluid, rending the models effectively invisible and thus facilitating unimpeded data collection around the bedform configuration. this technique minimizes reflections of laser sheet off the model and floor surfaces, allowing for higher accuracy measurements in these critical regions. the flow field was measured using high frame-rate stereo-piv in the y–z cross-stream plane at several streamwise positions. images were captured at 20, 350 and 700 hz with two 4mp phantom v641 cameras, equipped with schiempflug mounts, oriented at 45o relative to the test section side-wall (fig. 1(a)). due to the high refractive index of sodium iodide (≈1.49), solid acrylic prisms were mounted to the side-wall, with glycerin filling the air gap. the 20 hz measurements enabled well-converged measurements of the mean statistics, while the higher sampling rates captured in time-resolved dynamics. illumination was achieved with a northrop grumman patara dual-cavity nd:ylf laser capable of 50 mj per pulse at up to 1 khz. z/h x/h fl ow 0 -3 -6 3 6 0 3-3 z/h z/h z/h 0 0 03 3 3-3 -3 -3 -9 l/2 l/2 l/4 l/2 isolated collision a collision b collision c (a) f lo w z/h 2-2 0 z/h 2-2 0 -2 -4 -6 2 4 6 8 10 12 14 0 -2 -4 -6 2 4 6 8 10 12 -8 -t u c /h -t u c /h 0 x/h = 6.5x/h = 5 (b) figure 1: (a) dune model configurations with laser sheet positions indicated and experimental setup below. (b) pseudo-3d flow reconstructions from two different measurement planes in the isolated barchan wake. 3 results careful application of taylor’s hypothesis, using a uniform convection velocity, allowed for pseudo-3d volumes of the flow to be reconstructed over limited domains. an example of these results is shown in fig. 1(b), wherein isosurfaces of 3d swirling strength show evidence of hairpin-like vortices populating the wake of an isolated barchan. similar results are seen in the interdune region (not shown here). these results should not be mistaken for an instantaneous volume of the flow field, due to the limitations of taylor’s hypothesis here, but rather a time series of flow structures that have advected through the measurement plane. further analysis of vortex shedding dynamics associated with these structures using wavelet analysis and amplitude modulation indicates that they interact with large-scale motions in the overlying boundary layer, which impinge on the dune and excite the shear layer. 4 summary unique access to the high reynolds number flow field around a complex 3d bedform was achieved in a refractive-index-matched environment. high frame-rate measurements in the cross-plane elucidate the structures shed by barchan dunes, and provides important information about how these dunes not only interact with each other, but also the aloft boundary layer. work remains, however, to close the loop in terms of understanding sediment transport implications, as only fixed-bed models are used herein to model the flow field without particle loading. references assis wr and franklin edm (2020) a comprehensive picture for binary interactions of subaqueous barchans. geophys res lett 47:e2020gl089464 bristow nr, blois g, best jl, and christensen kt (2018) turbulent flow structure associated with collision between laterally offset, fixed-bed barchan dunes. j geophys res earth surf 123:2157–2188 introduction methods results summary 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 quantification of brownian motion under presence of flow using particle diffusometry d. lee1, s. t. wereley1∗ 1 purdue university, school of mechanical engineering, west lafayette, usa ∗ wereley@purdue.edu abstract particle diffusometry (pd), a quantification method for the brownian motion, is performed by recording temporally sequential images and using correlation analysis to obtain an ensemble diffusion coefficient for all particles captured in the imaging region (clayton et al., 2017). pd is proven to be successful in the detection of the waterborne pathogen v. cholerae in environmental samples using different imaging techniques, including an inverted fluorescence microscope as well as a handheld hardware device operated with a smartphone (clayton et al., 2019; moehling et al., 2020). although we intend to use pd to calculate diffusion coefficients in quiescent fluid, oftentimes unintentional fluid flows occur, creating measurement error when calculating the diffusion coefficient. in previous work, recordings under the presence of flow were discarded to avoid incorrect measurements of the sample. the diffusion coefficient is calculated as: d = s2 c −s2 a 16m2∆t (1) experimentally recorded image frames are obtained at an inter-frame time ∆t. these frames are then parsed into interrogation windows. interrogation windows from an image taken at ∆t is correlated with itself to obtain autocorrelation peak width sa. two separate image frames recorded at t and t+∆t are correlated to obtain cross-correlation peak width sc. the sc broadens compared to the sa due to the presence of brownian motion. the obtained peak widths can be then averaged spatially or temporally over number of image frames, to lower the random uncertainty of the measurement. the diffusion coefficient is then calculated using eq. 1 (olsen and adrian, 2000), where m is the total magnification of the recording setup. in this body of work, we modify our approach in measuring the diffusion coefficient in the presence of fluid flow. in the absence of flow, the correlation peaks described above produce axisymmetric gaussian profiles. however, in the presence of flow, the correlation peak center shifts to the direction of the flow—exactly the principle behind piv. if the flow also has gradients in it, the correlation peak stretches and rotates in the direction of shear, no longer axisymmetric. since the brownian motion along each axis is independent of others, proper identification of streamwise and cross-streamwise directions allow a generalized rotated two-dimensional elliptical gaussian function to be fit to the cross-correlation (chamarthy et al., 2009). the diffusion coefficient can be calculated from the cross-streamwise correlation peak width. in this work, simulated brownian motion images were generated with a frame rate of 15 frames per second with a diffusion coefficient of 1× 10−12m2/s with a variety of conditions: 0 to 80 degrees rotation with 10-degree increments, 1 to 10 pixel/∆t flow velocity with 10 pixel/∆t increments, and three different flow types (uniform, couette, and poiseuille flows). once the correlation peaks were calculated, all the peaks from each of the interrogation windows were averaged temporally over 100 frames image sets to reduce statistical random errors. a 3-point gaussian peak fit was applied in both xand y-directions to determine the sub-pixel maximum location for further flow analysis. to calculate the cross-streamwise peak width, a total of 11× 11 pixel2 areas were fitted (in contrast to the typical 5-point piv peak fit), and the ellipse equations at e−1 height is calculated using the fitted gaussian profile. resulting diffusion coefficient values of varying angles and velocities were averaged with respect to the induced velocity values. as shown in fig. 1(a), a 3-point gaussian sub-pixel fit on a single pass correlation poses no difficulty in estimating the flow velocity from the generated simulation videos. a larger measurement variation occurred in the low flow velocity region (i.e. 1-4 pixel/s), where distinguishing between the flow velocity and the brownian motion of particles presents a greater margin of error. for the case of measuring particle diffusion coefficient, presented in fig. 1(b), the diffusion coefficient calculated in the presence of uniform flow show minimal deviation from their simulated values, hence the smaller error. however, with non-uniform flows, we see greater deviations from theoretical values due to the gradient of the flow. overall, an increase in error is observed as the flow velocity is increased. analysis reveals that with the developed algorithm, analyzed diffusion coefficients show an error greater than 10% when the flow velocity exceeds 8 pixel/∆t. experimentally, flows were generated using a syringe pump through a rectangular channel. as the flow profile forms an elongated poiseuille flow along the wider dimension of the channel, the focal point is adjusted to ensure the recorded flow profile is that of a uniform flow. simulation parameter for the uniform flow is extended to 22 pixel/∆t to better compare the trend between the simulation and experiment results. due to the difficulty of obtaining even increment of volumetric flow, x-directional error bar is incorporated to account for the variation. the resulting fig. 1(c) shows the experimental data following the trend of the simulation results. the experiment shows the analyzed diffusion coefficients results in an error greater than 10% when the flow exceeds 18 pixel∆t with the developed algorithm. these 18 pixels account for 17% of overall interrogation window. in other words, the velocity is equivalent to 6.6µm/∆t, a significant movement if we take into account the particle size of 470nm that is used for the experimental verification. this current body of work shows a promising initial work toward measuring diffusion coefficients in the presence of fluid flow. (a) flow velocity (b) diffusion coefficient (c) experimental verification figure 1: comparison of simulation results with analyzed values (a,b), and with experiment values (c). references chamarthy p, garimella sv, and wereley st (2009) non-intrusive temperature measurement using microscale visualization techniques. experiments in fluids 47:159–170 clayton kn, lee d, wereley st, and kinzer-ursem tl (2017) measuring biotherapeutic viscosity and degradation on-chip with particle diffusometry. lab chip 17:4148–4159 clayton kn, moehling tj, lee d, wereley st, linnes jc, and kinzer-ursem tl (2019) particle diffusometry: an optical detection method for vibrio cholerae presence in environmental water samples. scientific reports 9:1739 moehling tj, lee d, henderson me, mcdonald mk, tsang ph, kaakeh s, kim es, wereley st, kinzerursem tl, clayton kn, and linnes jc (2020) a smartphone-based particle diffusometry platform for sub-attomolar detection of vibrio cholerae in environmental water. biosensors & bioelectronics 167:112497 olsen mg and adrian rj (2000) brownian motion and correlation in particle image velocimetry. optics & laser technology 32:621–627. optical methods in heat and fluid flow 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 mounting and support for pseudo biaxial scheimpflug focusing for unity-magnification, high-speed particle velocimetry s. l. ribergård1∗, p. j. olesen1, n. s. jensen1, j. s. nielsen1, c. m. velte1 1 turbulence research laboratory, technical university of denmark, department of mechanical engineering, kgs. lyngby, denmark ∗ silari@mek.dtu.dk abstract a camera mount that can support both heavy cameras and heavy optics allowing a total of seven degrees of freedom shared between them has been designed. this allows for scheimpflug focusing along one or two axes. a paper proposing a solution to two-axes scheimpflug focusing has been examined and a new nomer is proposed for two-axes scheimpflug focusing. the newly designed mounts allow for a broader range of solutions for combinations of positioning and alignment than traditional scheimpflug mounts. 1 introduction scheimpflug focusing has been widely applied in both scientific research and specialized photography when the desired object plane and focus plane do not coincide. this is particularly of interest when making experiments using particle image velocimetry with multiple cameras or single cameras with difficult optical access. stereoscopic and tomographic methods present challenges, as described in classical piv-textbooks, (raffel et al., 2018) and adrian and westerweel (2011), for which several commercial solutions have been made, which allows fulfillment of the scheimpflug criterion ensuring alignment of the image plane and the object plane. these solutions are all designed to sit between the camera and the lens, letting either the camera carry the weight of the adapter and lens, like the lavision manual scheimpflug mount, or letting the adapter carry both, like the pivtech single-axis scheimpflug camera adapter. this is fine when working with light-weight equipment or just a heavy camera, however, when attempting high-speed unitymagnification measurements both sides of the mount tends to increase in bulk and weight. for the setup being established at the turbulence research laboratory at dtu mechanical engineering in denmark, a solution was needed that could carry the heavy vision research phantom v2640 along with the lens setup consisting of the af-s nikkor 300mm f/4d if-ed with a af-s teleconverter tc-20e iii, all the while allowing for fulfillment of the scheimpflug criterion. the outcome is the design presented herein. a camera mount that, through its seven degrees of freedom, can reach complicated solutions for the scheimpflug criterion while carrying the heavy equipment needed for our desired experiments. 2 pseudo biaxial scheimpflug focusing already at the start of the previous century, theodore scheimpflug patented a method for what would become known as scheimpflug focusing in scheimpflug (1904). in this, he presents both the mathematical and intuitive backgrounds for achieving a focus coinciding with an object plane not parallel to the image plane of the camera. this method can be considered a single-axis, or monoaxial, scheimpflug focusing, as it only considers a single axis of rotation. in many cases, this is sufficient, assuming the ability to align the equipment such that the normals of the three planes (image, object and lens) are coplanar. this, however, is not always the most feasible approach, so in 2001, stephen walker published a paper in which he discuss biaxial scheimpflug focusing, walker (2001). he derives a mathematical solution resulting in a slanted scheimpflug line, i.e. the common line of the three planes. in our group, this approach was investigated, and while we came to similar results, we could not help feeling that this seemed artificial. as it turns out, we’re now convinced that there are no such thing as true biaxial scheimpflug focusing, only what we have dubbed “pseudo biaxial” scheimpflug focusing. as shown by euler, any one rotation can be decomposed into two or more rotations along different axes or vice versa. thus, what walker presented is “simply” a monoaxial focusing decomposed into two separate rotations. this, however, does indeed have its place, as rotating around the optical axis of the camera might not always be possible. for this reason, we found the nomer “pseudo biaxial” captures the principle better than “two-axes”. to achieve focus across the sensor, the same principle as for single-axis scheimpflug focusing still applies, understood as that the normals of the three planes must be coplanar. 3 design initial experimental designs complicated the camera setup, forcing the decision to design the camera mounts for flexibility. to accommodate the need for splitting up the rotation needed to satisfy the scheimpflug condition into two separate rotations, the mount needs to allow for rotations and translations of both camera and lens, independently. this solution can rotate the entire mount with both camera and lens at once, translate the camera along its optical axis and both rotate and translate the lens independently from the camera. the final design has a total of seven degrees of freedom, as seen in table 1. in figure 1 a kinematic sketch of the design principle can be seen, showing the translations and rotations relative to each other. table 1: list of degrees of freedom (dof). dof description r1 pitch of entire mount r2 pitch of lens r3 yaw of entire mount r4 yaw of lens t1 axial translation of camera t2 vertical translation of lens t3 horizontal traverse translation of lens figure 1: in this figure, a kinematic sketch of the seven degrees of freedom is shown. rotations are designated r# while translations are designated t#. after deciding on the necessary motions, a cad-model was constructed to determine what parts were necessary. the cad-model can be seen in figure 2. the mounts consist of the primary components found in table 2 with a number of bosch rexroth profiles cut to desired lengths and shapes. and lastly, in figure 3 photos of the final mount is shown. (a) side view (b) top view figure 2: (a) shows a cad-model of the camera mount in side view, while (b) shows the mount in a topdown view. table 2: components of each dof. dof type brand product no gear ratio r1 worm gear busck sb040 1:100 r2 worm gear busck sb025 1:60 r3 worm gear busck sb040 1:100 r4 worm gear busck sb030 1:80 t1 linear translation elesa-ganter gn 900-80-195-75-d-1 n/a t2 linear translation elesa-ganter gn 900-80-195-75-d-1 n/a t3 linear translation elesa-ganter gn 900-80-195-75-d-1 n/a 4 performance to quantify the range of motion and accuracy that this construction allows for, measurements have been done using a laser pointer mounted at the tip of the lens mounting point. the movement of the laser along a wall is measured for different inputs. each degree of freedom is subjected to one, two and three full rotations on the input axle making sure to always end with tension in the positive direction of rotation to minimize the effect of backlash. the range of motion is determined by turning or translating the relevant degree of freedom as far as the construction allows in both directions. the found values are presented in table 3. initial tests show that it is indeed possible to achieve focus across the sensor for combinations of rotations. 5 potential applications anywhere the image plane and object plane are not aligned, but desired to be, the scheimpflug angle can be applied. the general concept has near-limitless applications, but this specific mount allows solving the (a) side view (b) top view figure 3: (a) shows the actual camera mount in side view, while (b) shows the mount in a top-down view. table 3: performance metrics. dof increment per revolution range r1 3.6◦ [ 0◦ ; > 90◦ ] r2 6.0◦ [ −12.5◦ ; > 90◦ ] r3 3.6◦ [ <−90◦ ; > 90◦ ] r4 4.5◦ [ <−90◦ ; > 90◦ ] t1 1.0 mm [ 32.5 mm 32.5 mm ] t2 1.0 mm [ 32.5 mm 32.5 mm ] t3 1.0 mm [ 32.5 mm 32.5 mm ] scheimpflug focusing problem when using heavy equipment, both for the camera and the optics. this is especially relevant for optical measurement techniques, where high magnification and high temporal resolution is needed, as both increase the bulkiness of the equipment used. specifically, this setup allows the solution of the pseudo biaxial scheimpflug focusing mentioned previously, when geometric or practical limitations hinder the necessary freedom needed to reduce the focusing to a monoaxial problem. examples of situations in which this extra freedom of positioning can come in handy could be: a) stereoscopic piv when optical access to the plane of interest is limited. for example, imagine a wind tunnel in which the only viable camera position are on top, with optical access through a window, such as show in figure 4(a). in this case, even a single camera would need to correct for the misalignment of image and object planes. however, when going to multiple cameras, the solution to the scheimpflug focusing is less trivial, and with bulky equipment traditional mounts simply do not suffice. here, our design would allow the decomposition of the ideal rotation into two separate rotations. b) a pyramidal camera configuration for tomographic methods in which side-centered placement of the cameras is not possible, so they must be placed on the corners of the pyramid. this was the initial design for our setup, as seen in figure 4(b). 6 final considerations the notion of a 2-axes scheimpflug focusing has been reflected upon and the conclusion is that such a thing does not exist. at best, it is possible to talk about a pseudo biaxial scheimpflug focusing, which occurs when it is not readily possible to place camera and lens in a manner simplifying the rotation to a single axis. this is essentially just an decomposition of rotations using euler angles. to allow for this niche case of scheimpflug focusing, a camera mount that can carry both a heavy camera and a heavy optical (a) case a (b) case b figure 4: an example of stereoscopic piv with limited optical access. system has been designed, which allows independent control of the rotation of both camera and lens about their respective pitch and yaw axes. this is primarily useful when using high-speed equipment with highmagnification optical solutions in out-of-the-ordinary configurations. the mounts can, however, also easily handle monoaxial scheimpflug focusing, which could prove useful when using heavy and bulky equipment in simpler setups, such as our current side-centered pyramidal camera configuration. the range of motion and rough estimates on sensitivity have been determined and presented, the range typically offering way more range of motion than what would feasibly produce a useful image on the sensor due to vignetting and similar effects. acknowledgements this project has received funding from the european research council (erc) under the european unions horizon 2020 research and innovation program (grant agreement no 803419). furthermore, the author would like to acknowledge and thank dr. willert and his group at dlr köln for their generous hosting and help. references adrian rj and westerweel j (2011) particle image velocimetry. cambridge university press raffel m, willert ce, scarano f, kähler cj, wereley st, and kompenhans j (2018) particle image velocimetry a practical guide. springer. 3rd edition scheimpflug t (1904) improved method and apparatus for the systematic alteration or distortion of plane pictures and images by means of lenses and mirrors for photography and for other purposes. patent application. great britain patent number 1196 walker s (2001) two-axes scheimpflug focusing for particle image velocimetry. meas. sci. technol. 13:1– 12 introduction pseudo biaxial scheimpflug focusing design performance potential applications final considerations 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 velocity measurements of dilute suspensions over and through various porous media models e. a. haffner1, t. wilkie1, j. e. higham2, p. mirbod∗1 1 university of illinois at chicago, department of mechanical and industrial engineering, chicago, usa 2 university of liverpool, school of environmental sciences, liverpool, uk ∗ pmirbod@uic.edu abstract this study is focused on the motion of a dilute suspension containing rigid, spherical, non-brownian, noncolloidal particles flowing over and through porous media models. the flow is confined to very low reynolds numbers. to examine the velocity distribution particle image velocimetry (piv) was applied in conjunction with refractive index matching (rim) techniques. this study is the first of its kind analyzing the interaction between two common engineering systems: suspension fluid and porous media. 1 introduction porous media has been a prevalent structure in both the natural world as well as many manufactured systems. fluid motion over sediment beds goharzadeh et al. (2005) and coral reefs/ submerged vegetation ghisalberti and nepf (2009) have been investigated as natural forms of porous media. other studies have focused on using optical experimental techniques to investigate the properties at the interface of a porous media bounded on top by a free flow region. specifically, piv experiments were developed to identify the effect of the porous media characteristics and different porous media configurations on the overall flow structure and the properties at the interface, arthur et al. (2009); agelinchaab et al. (2006). these studies are limited to pure newtonian fluid over and through porous media. much like porous media, suspension flows are observed in natural systems, so they have been commonly utilized in engineering structures. because of this, optical experimental techniques were developed coupled with rim techniques to measure the velocity and concentration for suspension flow through various geometries. these piv experiments have been developed to study various phenomenon within the velocity profile for different types of suspensions, jesinghausen et al. (2016); medhi et al. (2011). by examining previous literature, it was clear that there was a fundamental gap in knowledge that describes how these two systems would interact to one another. these types of systems have been observed in pharmaceuticals, oil mining, and slurry transport. it is important to better understand how the properties of both systems would affect the flow structure. this study using piv to study how the velocity and interaction properties are effected by the porous media characteristics and the dilute suspension concentration. the suspension particles were monodispersed polymethyl methacrylate (pmma) with an average size of 82µm (cospheric, llc). the newtonian solvent was created based off of a solution presented by lyon and leal (1998a, 199b) lyon and leal (1998a,b). multiple dimensionless parameters such as particle reynolds numbers, stokes number, and pélect number were all checked to ensure the motion of the suspension particles was solely dependent on the fluid motion. the porous media was made up of rigid rods in a unit square and was created by a 3d printer. this was done so that we could control the various properties of the porous media. there were three dimensionless height parameters, δ = hp/l tested, δ = 4.54,1.37,0.74 and three permeability parameters σ = l/ √ k tested, σ = 2.2,3.46,6.09. in these relationships hp is the porous media thickness, l is half the free flow height, and k is the permeability. figure 1: (a) schematic of the experimental setup, and (b) an image of the experiments in mirbod’s lab. 2 results the velocity fields were extracted from two data collection planes, one plane within the rods of the porous media, p1, and one plane placed in the middle on top of the rods, p2. these two planes were area averaged together to get the full one-dimensional velocity profile for the flow through the porous media, arthur et al. (2009). these velocity profiles for the different δ values are shown in fig. 2. in each figure the three different permeability parameters are shown at each constant height ratio. in these figures, as the permeability parameter decreases the lower the velocity is within the porous media. for the largest height ratio, fig. 2(c), there is an observable effect on the velocity profile for the highest permeability parameter. for the other two height ratios there is not much of an effect at σ = 6.09. not only are the velocity profiles examined by also the properties at the interface between the free flow region and the top of the porous media. the slip velocity at the interface, us = |uave|(y/l=0), lauga and stone (2003), is normalized using two different methods. the first is using the maximum velocity in the free flow region, which is shown in fig. 3(a) for the three different delta values. the other method, known as the dimensionless slip parameter, uses local parameters such as the shear rate γ̇ = |du/dy|y=0 and the permeability. this parameter better describes the properties at the interface and is known and the dimensionless slip parameter. this is shown in fig. 2(b) for both data collection planes and the averaged profile. fig. 3(c) shows the slip length which is length between the actual location of the velocity profile and the location where the parabolic velocity profile would be if it were extrapolated to the interface. mathematically, this is defined as lslip = us/ |du/dy|y=0 . fig.3(a) and fig.3(c) shows that there is a negative trend as σ increases for all δ. fig. 3(b) shows that as δ increases so does the dimensionless slip parameters except for δ = 4.54 cases which show a negative trend. acknowledgements we would like to thank nsf cbet award #1854376 for funding this work. figure 2: the velocity profiles for various permeability parameters σ and different depth ratio (a) δ = 0.74, (b) δ = 1.37, and (c) δ = 4.54. figure 3: (a) the ratio of the slip velocity to the maximum velocity for the various test cases. (b) the dimensionless slip parameter for all test cases and the (d) slip length evaluated at the interface. the error bars were calculated using the velocity uncertainties and methods outlined by sciacchitano and wieneke (2016) and coleman and steele (1995) references agelinchaab m, tachie mf, and ruth dw (2006) velocity measurement of flow through a model threedimensional porous medium. physics of fluids 18:017105–11 arthur jk, ruth dw, and tachie mf (2009) piv measurements of flow through a model porous medium with varying boundary conditions. journal of fluid mechanics 629:343–374 coleman hw and steele wg (1995) engineering application of experimental uncertainty analysis. aiaa journal 33:1888–1896 ghisalberti m and nepf h (2009) shallow flows over a permeable medium: the hydrodynamics of submerged aquatic canopies. transport in porous media 78:309–326 goharzadeh a, khalili a, and jørgensen bb (2005) transition layer thickness at a fluid-porous interface. physics of fluids 17:057102–10 jesinghausen s, weiffen r, and schmid hj (2016) direct measurement of wall slip and slip layer thickness of non-brownian hard-sphere suspensions in rectangular channel flows. experiments in fluids 57:1–15 lauga e and stone ha (2003) effective slip in pressure-driven stokes flow. journal of fluid mechanics 489:55–77 lyon mk and leal lg (1998a) an experimental study of the motion of concentrated suspensions in twodimensional channel flow. part 1. monodisperse systems. journal of fluid mechanics 363:25–56 lyon mk and leal lg (1998b) an experimental study of the motion of concentrated suspensions in twodimensional channel flow. part 2. bidisperse systems. journal of fluid mechanics 363:57–77 medhi bj, kumar aa, and singh a (2011) apparent wall slip velocity measurements in free surface flow of concentrated suspensions. international journal of multiphase flow 37:609–619 sciacchitano a and wieneke b (2016) piv uncertainty propagation. measurement science and technology 27:084006 introduction results 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 validation of model-based correction for non-stokesian tracers joshua n. galler1∗, david e. rival1 1 queen’s university, department of mechanical and materials engineering, kingston, canada ∗ j.galler@queensu.ca abstract in-situ flow-tracking measurements at scales on the order of 10 m3 and larger remain a challenge. the large size of the tracers required for optical visibility results in an inertial lag and inherently low seeding density. for instance, natural snowfall, fake snow and soap bubbles on the order of 2 cm have been used as tracers for field measurements and extracted statistical quantities (nemes et al., 2017; wei et al., 2021; rosi et al., 2014). there is also growing interest in networks of sensors for remote-measurement where optical access is impossible (bolt et al. 2020; villa et al. 2016). onboard inertial measurement units (imu) are a promising tool for high-resolution measurements over large spatial domains without optical access. however, due to the intrinsic lag, a dynamic-model-based correction is required for the tracking of transient phenomena, sketched in figure 1. in the present study, the tracer-velocity correction is evaluated by quantifying the residual error in measured flow velocity after the method of galler et al. (2021) is applied. (a) non-ideal tracer response (b) inverse-model approach figure 1: a) sketch of a scenario in which sensor lag hinders the measurement of a coherent structure. error in local velocity and in fluid trajectories are a result of tracer inertia. b) sketch of the dynamic system in the laboratory-fixed frame of reference. the applied flow, u(t), causes aerodynamic drag, d, and results in a body response, u(t). with a robust model for d, u can be calculated using measured body velocity, u . to apply the dynamic-model-based approach to large tracers, the sensor response was captured in a gust flow. a spherical housing, pictured in figure 2(a), is used to carry the custom imu and simplify physical modelling. the sphere has a diameter of 10 cm and the system has a total mass of 12.3 g. experiments were performed in an open-jet gust wind tunnel with vertical configuration, seen in figure 2(b). the jet outlet has a cross-sectional area of 144 cm2. air was accelerated from rest to a terminal jet velocity of u f = 15 m/s. the sensor was optically tracked using a photron sa-4 high-speed camera and a python-based computer vision algorithm. figure 3(a) shows the agreement between imu and motion-tracking camera, validating the processing algorithm. figure 3(b) shows the agreement between the model correction and measured disturbance. despite the weak response of the body, in significant part due to its drag-to-weight ratio, the flow perturbation was extracted through dynamic modelling. the maximum residual velocity (error) was approximately 15%, a vast improvement over 95% error observed with the raw sensor output. in addition, while the sensor lagged behind the disturbance, never fully matching the prescribed velocity, the correction reduced the time-lag to approximately 30%. since the model correction relies on the sensor acceleration as input, the extracted time-scale is more sensitive to the magnitude of the aerodynamic response than the extracted velocity. in the present study, the feasibility of imu-based flow measurement is demonstrated using a nonstokesian sensor coupled with a dynamic-model-based correction. the working principle and proof-of(a) imu flow tracer system (b) wind tunnel setup figure 2: a) spherical sensor housing, imu and base station units. b) vertical open-jet gust wind tunnel facility showing the location of the sphere sensor, high-speed cameras, laser sheet and fields of view (fovs). sensor camera (a) imu validation (b) inverse model validation figure 3: (a) position and velocity time histories for the sensor and camera measurements. good agreement validates the sensor output. (b) modelled sensor correction against piv flow velocity measurements. good agreement suggests the model approach allows for the use of non-stokesian flow tracer and sensor systems. concept is presented through in-lab measurements of a rapid gust as a canonical flow perturbation example. minimum resolvable time scales are shown to be a function of the sensor aerodynamic response. references bolt m, prather jc, horton t, adams m et al. (2020) massively deployable, low-cost airborne sensor motes for atmospheric characterization. wireless sensor network 12:1 galler jn, weymouth gd, and rival de (2021) on the concept of energized mass: a robust framework for low-order force modeling in flow past accelerating bodies. physics of fluids 33:057103 nemes a, dasari t, hong j, guala m, and coletti f (2017) snowflakes in the atmospheric surface layer: observation of particle-turbulence dynamics. journal of fluid mechanics 814:592–613 rosi ga, sherry m, kinzel m, and rival de (2014) characterizing the lower log region of the atmospheric surface layer via large-scale particle tracking velocimetry. experiments in fluids 55:1736 villa tf, gonzalez f, miljievic b, ristovski zd, and morawska l (2016) an overview of small unmanned aerial vehicles for air quality measurements: present applications and future prospectives. sensors 16:1072 wei nj, brownstein id, cardona jl, howland mf, and dabiri jo (2021) near-wake structure of full-scale vertical-axis wind turbines. journal of fluid mechanics 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 lapiv using multi-resolution warping and proxy regularization yin yang1∗, dominique heitz1 1 inrae, ur opaale, f-35044 rennes cedex, france ∗ correspondent author: yin.yang@inrae.fr abstract the lagrangian particle image velocimetry (lapiv) method was firstly proposed in yang et al. (2019) as a prototype approach to achieve the goal of accurate and efficient reconstruction of 3d eulerian velocity field of fluid flow from multi-view particle images. after validating against synthetic datasets, the prototype has already shown significant advantages in revealing more small scale flow structures than other stateof-the-art eulerian velocity estimation methods, such as tomopiv (scarano, 2013) and vic# (jeon et al., 2019). however, at this early stage, lapiv can not be easily applied to other datasets. in the current work, we focus on extending lapiv to operational search by incorporating several essential and wellestablished paradigms: multi-resolution, warping, and proxy regularization. recent approaches, lasinger et al. (2019) and cornic et al. (2020), function in the same vein as lapiv, aiming at reconstructs the dense eulerian volumetric flow directly from multi-view particle-seeded images another pipeline consists of firstly reconstructing the lagrangian flow using the lagrangian particle tracking (lpt), then optimally interpolating the lagrangian flow to eulerian grids, taking into account the eulerian dynamics constraints as in flowfit (gesemann, 2020) and vic# (jeon et al., 2019). if eulerian flow is required, lapiv is the preferred approach due to its simplicity and ability to utilize the original rich image features. lapiv is built on the two pillars of local quasi-rigidity assumption and kernel method. for two-pulse double frame data, lapiv functions as follows: 1) reconstruct the particle field (position and intensity) of the first frame using ipr (wieneke, 2012); 2) prescribe the fixed eulerian grid with a resolution depending on the particle density. 3) for each grid point, find all particles in its neighborhood and assume those particles follows the same motion as the grid point; 4) solve for the velocity at the grid point by minimizing a cost function measuring the discrepancy in image space between the recorded image at the second frame and the projected image produced by an image model (transport equation + camera model + optical transfer function (otf)); 5) post-process. step 3 consists of finding particles in the ‘support region’ near the centering grid. we employ the word ‘support’ to denote that the transportation of the particles in the region can be contributed by the centering velocity. step 4 involves the kernel principle (yang and heitz (2021)). despite the nonlinear relationship between the projected image pixel intensity and the velocity at a given grid point, by finding a kernel function that can effectively match the projected particle image with the recorded image, we can train a function that maps the image features to the velocity from few generated samples. then the learned function can be applied on the recorded image to infer the real velocity. nevertheless, at the prototyping stage, the above algorithm has several drawbacks. first, convergence and precision of the algorithm can hardly be achieved simultaneously with one layer eulerian grid. estimated velocity on a coarser grid tends to converge better but at the risk of losing small scale information. on the other hand, working on a finer grid generally leads to lower local data discrepancy but not always more accurate velocity as wrong particle pairs are more likely to be matched. our strategy is to implement the multi-resolution technique and warping. we start the estimation at a coarser grid and gradually refine the estimation on a finer grid. the estimation process on the finer grid begins by inheriting an initial velocity field from the previous iteration on the coarse grid through warping instead of using zeros. second, holes are commonly presented in final velocity estimation resulting from a lack of particles at certain spots. inhomogeneous seeding is inevitable for real experiments. as a result, some interpolation schemes must be employed to fill velocity holes with meaningful values based on their neighbors. rather than treating the interpolation scheme naively in the post-processing step in the prototype stage, we formalize the optimal interpolation under variational settings using proxy regularization. we integrate a flow regularization step right after the proxy flow estimation is obtained at each grid level. here we use the term ‘proxy’ to denote the flow estimated from step 4 (kernel methods) of lapiv. the regularized flow respects various physical constraints and resembles the proxy flow as closely as possible. the resulting system to solve for the regularized flow remains light-weight compared to lasinger et al. (2019), or gesemann (2020), whose optimization methods are quite complex since they anchor either the image or the particle field as the data. as for lapiv, the regularized flow always occupies the same grid as the proxy flow. both are to be refined in agreement with the multi-resolution approach. we have participated in the 1st lpt challenge after a slight modification of the original algorithm, as the challenge emphasized lpt rather than the eulerian velocity reconstruction. as evaluated by the challenge, our method has achieved state-of-the-art performance at medium-high particle density levels both for twopulse datasets (ppp<= 0.08) and time-resolve datasets (ppp<= 0.12). we have also done quantitative tests against the same synthetic datasets depicting the wake flow of a turbulent cylinder at re=3900, produced by a large eddy simulation (parnaudeau et al., 2008). table 1 summarizes the rmse results of lapiv compared to tomopiv, stb-bin and vic# implemented in davis 10.0.5. lapiv yielded the minimum error among all methods. finally, we have applied lapiv to an impinging jet flow yang and heitz (2021) at re=1250. the q criteria of the instantaneous velocity field are shown in figure 1 with color-coded by the velocity magnitude. in this study, we have shown, after integrating those essential techniques such as multi-resolution and proxy regularization, lapiv can yield competitive, if not better, results compared to other state-of-the-art approaches facing versatile datasets. methods resolution rmse (nx,ny,nz) (uerr/u∞) tomopiv (145,45,24) 0.1517 stb-bin (145,45,24) 0.2439 vic# (145,45,24) 0.09141 lapiv (151,48,27) 0.07799 table 1: summary of results obtained by tomopiv, stb binning, vic# (all three methods are implemented in davis 10.0.5) and lapiv for datasets of wake flow behind cylinder at re=3900. figure 1: an isosurface of the q criteria criteria in an impinging jet flow at re = 1250, color coded by the velocity magnitude (mm/s). references cornic p, leclaire b, champagnat f, le besnerais g, cheminet a, illoul c, and losfeld g (2020) doubleframe tomographic ptv at high seeding densities. experiments in fluids gesemann s (2020) flowfit3: fast data assimilation for recovering instantaneous details of incompressible flows based on scattered data. in 3rd workshop and 1st challenge on da & cfd for piv and lpt jeon yj, müller m, michaelis d, and wieneke b (2019) data assimilation-based flow field reconstruction from particle tracks over multiple time steps. in 13th ispiv lasinger k, vogel c, pock t, and schindler k (2019) 3d fluid flow estimation with integrated particle reconstruction. international journal of computer vision parnaudeau p, carlier j, heitz d, and lamballais e (2008) experimental and numerical studies of the flow over a circular cylinder at reynolds number 3900. physics of fluids scarano f (2013) tomographic piv: principles and practice. measurement science and technology wieneke b (2012) iterative reconstruction of volumetric particle distribution. measurement science and technology yang y and heitz d (2021) kernelized lagrangian particle tracking. hal-03212696 yang y, heitz d, and mémin e (2019) lagrangian particle image velocimetry. in 13th ispiv 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 time resolved piv of the flow field underneath an accelerating meniscus m. ratz1,2, d. fiorini2, a. simonini2, c. cierpka1, m. a. mendez2∗ 1 technische universität ilmenau, institute of thermodynamics and fluid mechanics, ilmenau, germany 2 von karman institute for fluid dynamics, enviromental and applied fluid mechanics department, brussels, belgium ∗ mendez@vki.ac.be abstract we present an experimental analysis of the flow field near an accelerating contact line using time-resolved particle image velocimetry (tr-piv). both advancing and receding contact lines are investigated. the analyzed configuration consists of a liquid column that moves along a vertical 2d channel, open to the atmosphere and driven by a controlled pressure head. large counter-rotating vortices were observed and analyzed in terms of the maximum intensity of the q-field. to compute smooth spatial derivatives and improve the measurement resolution in the post-processing stage, we propose a combination of proper orthogonal decomposition (pod) and radial basis functions (rbf). the rbfs are used to regress the spatial and temporal structures of the leading pod modes, so that “high-resolution” modes are obtained. these can then be combined to reconstruct high-resolution fields that are smooth and robust against measurement noise and amenable to analytic differentiation. the results show significant differences in the flow topology between the advancing and the receding cases despite velocity and acceleration of contact lines are comparable in absolute values. this suggests that the flow dynamics are tightly linked to the shape of the interface, which significantly differs in the two cases. 1 introduction the dynamics of a gas-liquid interface moving along a solid wall plays an essential role in many wetting/dewetting processes (e.g. inkjet printing), coating applications (e.g. slot die coating) and capillary driven flows (e.g. liquid absorption in porous media or liquid pumping in microgravity). the capillary force plays a major role in these processes. this force depends on the curvature of the interface, which is linked to the angle formed at the contact line, known as contact angle. two main challenges exists in the modelling of these flows. first, the value of the contact angle cannot be predicted in the continuous fluid mechanics framework: on the contrary, this is a necessary boundary condition that must be imposed to solve for the interface shape, and hence for the fluid flows on both the gas and the liquid sides. the most common solution to the problem is the implementation of empirical and semi empirical correlations for the (macroscopic) contact angle as a function of the contact line velocity (hoffman, 1975; kistler, 1993). the limitations of these formulations are described in fiorini et al. (2021). the second challenge is that the very notion of moving contact line is at odds with the notion of no-slip boundary conditions that viscosity imposes to the liquid close to the contact line. this is the well known hydrodynamic paradox, which has motivated many theoretical and experimental works on the flow field near moving contact lines. a solution to this paradox has been proposed by huh and scriven (1971), who described the flow motion sufficiently close to the contact line as a creeping flow obeying the biharmonic equation. within this theory, the velocity fields compatible with advancing or receding contact lines for the case of wetting fluid configuration (θ < 90o) are characterised by a splitting streamline as sketched in figure 1. in an advancing contact line (see figure 1(a)), the fluid required to displace the interface is injected from the bulk (split injection configuration) while the opposite occurs in a receding contact line (split ejection configuration, see figure 1(b)). only few experimental investigation of these flow patterns have been presented (fuentes and cerro (2005); nasarek et al. (2008); zimmerman et al. (2010)) in the literature, mostly focused on quasi steady conditions. (a) (b) figure 1: schematic sketch of the stream lines in proximity of the contact line for a wetting configuration (θ < 90o) in case of an advancing contact line (left) and a receding contact line (right). the flow pattern on the left is known as stream line split injection, the flow pattern on the right is known as stream line split ejection. images are taken from fuentes and cerro (2005). while sufficiently close to the contact line the dominance of viscosity gives a sound theoretical justification to these patterns, it remains unclear what is their macroscopic impact on the dynamics of the interface and on the flow field far from it. at large reynolds number or in the presence of strong acceleration, i.e. when inertia becomes important, the flow field sketched in figure 1 might exist only very close to the interface but still have a strong impact to the flow at larger distances. the practical implications are numerous, especially considering that flow field and contact angle are intimately linked (see savelski et al. (1995)). in the classic capillary rise problem, for example, the most common models are based on the assumption that the flow field is fully developed (washburn, 1921; levine et al., 1976; quéré, 1997), but no theoretical nor empirical law can identify the distance from the interface below which this assumption ceases to be valid (see nasarek et al. (2008)). this work presents an experimental investigation of the flow field near a contact line moving at relatively high velocities and subject to large accelerations. the configuration of interest is a narrow rectangular channel in which a vertical column of liquid is driven into motion by a controlled pressure step. the gas liquid interface in contact with the walls produces two dynamic menisci which forces the interface to form two dynamic contact angles. both advancing and receding configurations are investigated. the flow field was measured via time-resolved particle image velocimetry (tr-piv), in a region of interest that follows the interface in its displacement. the measurement reveal the formation of two large counter rotating vortices with time-varying intensity. the estimation of the vortex intensity was carried out in terms of q-field (hunt et al., 1988). to accurately compute the required spatial derivatives, the velocity field is interpolated using a combination of proper orthogonal decomposition (pod) and radial basis function (rbf) regression. this approach was first proposed by (karri et al., 2009; raben et al., 2012) to compute spatial derivatives, and it is used here also for super-resolution. in particular, the rbf is used to smooth, filter and interpolate the spatial and temporal structures of the pod modes. the velocity field obtained from the reconstruction of the high-resolution pod modes enables super-resolution with robust outlier removal and analytic calculation of spatial and temporal derivatives. an adaptation of the tool for computing pressure field is currently in preparation (sperotto et al., 2021). the method is reminiscent of kriging enhanced gappy pod (gunes et al., 2006), but differs in the use of the rbf as opposed to the kernel-based kriging. section 2 shows the configuration of the narrow, two-dimensional channel in which the flow beneath the dynamic contact lines is observed. section 3 presents the data processing for the piv interrogation as well as the proposed regression tool. this algorithm is applied to a simple test case in section 4.1 and compared to traditional interpolation methods. the experimental results are discussed in section 4.2 and conclusions are given in section 5. (a) (b) figure 2: fig (a) sketch of the channel showing the area of the tr-piv measurements. fig (b) picture of the experimental setup with the camera (1), the channel (2), the reservoir (3), the release valve (4) and the pressure ports (5 and 6). 2 experimental setup and test cases a sketch of the experimental setup is shown in figure 2a. this consists of a rectangular channel with a width of δ = 5mm much smaller than its depth l = 250mm. the channel height is h = 150mm and is open to atmosphere. this channel is connected to a pressurized chamber in the bottom, sustaining the flow via a pressure difference ∆p. to reproduce an advancing contact line (i.e. interface moving upwards, along the y-axis), a positive pressure difference ∆p is suddenly introduced in the chamber by the opening of a fast release electronic valve connected to a pressure line. this valve opens linearly in 0.2 s. to reproduce a receding contact line (i.e. interface moving downward), the opposite procedure is followed: the chamber is initially at a ∆p= 1200 pa and the release valve is suddenly opened to the atmosphere, resulting in ∆p = 0 pa. a picture of the experimental setup is shown in figure 2b. the camera is placed perpendicularly to the channel’s flow cross section and illuminated with a laser sheet from the right side. the injection/removal of air during the pressurisation/depressurisation used in the advancing/receding experiments is performed on two sides of the chamber in order to ensure a symmetric flow and to minimise the entry effects. together with the camera (1), the picture shows the channel (2) and the pressurized chamber (3), the fast opening vale (4), and the two pressure ports (5 and 6). water is used as a fluid and the walls are made of plexiglass. the fluid is seeded with red fluorescent polymer microspheres from thermo fisher scientific with a diameter of 12 µs. the flow is observed with a tr-piv system from dantec dynamics. the particles are illuminated with the laser (dm40-527-dh nd: ylf from photonics industries) with a wavelength of 527 µm and a maximum pulse energy of 40 mj at a frequency of 1 khz. images are recorded with a speedsense ethernet m310 camera having a resolution of 1280×800 px at a maximum frame rate of 3260 hz. an objective lens with a focal length of 105 mm is used to get an optical magnification of 60 px/mm. the images are acquired in single frame mode using the dantec’s software dynamic studio. the exposure time of the camera is set to 250 s and the frame rate is set to 1200 hz. the time resolved configuration allows to capture about 60 snapshots during the rising/advancing experiment and about 100 during the descending/receding experiments for the rising interface, the flow is observed at the very top of the channel, close to the maximum height. in the first case, the reservoir is at an initial pressure of 0 pa and the pressure differce is 1500 pa. this is referred to as ‘test cases 1’. the second case, referred to as ‘test case 2’, has an initial pressure of 200 pa, the pressure difference is 1200 pa. these different initial conditions result in the same final height of the meniscus. the descending interface is observed at multiple positions inside the channel by changing the height of the camera between measurements. additionally, the release speed of the liquid is varied between cases to investigate the effects of different accelerations. the release speed is controlled by opening the release valve to the surrounding air at different speeds. 3 data processing: smoothing, super-resolution and q-fields the piv images are pre-processed using the pod-based background removal introduced by mendez et al. (2017). the piv interrogation is carried out using an in-house adaptation of openpiv (liberzon et al., 2020). in particular, due to the nature of the flow, two additional features were implemented. first, because of the large aspect ratio of the flow (the velocity component v, along y, is much larger than the velocity component u, along x), rectangular interrogation windows were implemented. this allows for a better sampling of the flow in the direction where the most substantial gradients are expected without deteriorating the signal-to-noise ratio in the cross-correlation maps. the second implementation is a dynamic region of interest (roi) to follow the gas-liquid interface across the available field of view (fov), as schematically illustrated in figure 2(a). at each image pair k at time tk, the velocity profile along the edge 1-2 (denoted as y1,2) is used to compute the average velocity vk = ∫ δ/2 −δ/2 v(x,y1,2, tk)dx and displace vertically the fov in the following image pair by v∆t. this allows focusing the processing always in the same region below the interface. adaptive iterative multigrid interrogation (scarano and riethmuller, 2000) is used to calculate the velocity fields. for the advancing contact line experiments, the initial window size is set to 256×64 px and reduced over two steps to 64×16 px. for the receding contact line experiments, the initial size is 64×64 px, and reduced to 24×24 px in two iterations. outliers are removed based on the signal-to-noise ratio measured in terms of peak to standard deviation in the cross-correlation map. the post-processing of the piv fields begins with a pod-based filter using a classic truncation ~u(x0, t0) = r ∑ i=1 σi~φi(x0)ϕi(t0) , (1) where r� nt is the truncation index, σi is the amplitude of the i-th pod mode having spatial structure ~φi(x0) and temporal structure ϕi(t0). note that x0 ∈rns×1 and t0 ∈rnt×1 here denote the spatial and temporal grids in which the piv field is available, reshaped as column vectors for computational convenience. because the flow fields here are bidimensional, given nx and ny the number of points along x and y, we have ns = 2nxny. the spatial structures~φ(x0) = (φu(x0),φv(x0)) collects the dominant velocity fields, computed by projecting the velocity field ~u = (u,v) on the pod temporal basis. the details of the pod computation can be found elsewhere (e.g. mendez et al. (2019, 2020a)) and are thus omitted here. the main idea behind the super-resolution strategy developed in this work is to perform radial basis function (rbfs, see fornberg and flyer (2015)) regression of the spatial and temporal structures of the decomposition, and then use a reconstruction of high-resolution pod modes to rebuild the velocity field. the rbf regression consists in writing both of these bases as linear combination of rbfs bases, i.e.: ~φi(x0) = nφ ∑ j=1 wφ i j γ φ j(x0|xi, j,σφ j) and ϕi(t0) = nϕ ∑ j=1 wϕ i, j γ ϕ j (t0|t j,σϕ j) , (2) where wφ i, j and wϕ i, j are the set of weights defining the regression functions, γ φ j(x0|x j,σφ j) are the nφ radial basis functions in space and γ ϕ j (t0|t j,σϕ j) are the nϕ radial basis functions in time. these have collocation points x j and t j and shape parameters σφ j and σϕ j . note that the coefficients wφ i, j must be defined as vectors, i.e. wφ i, j = (wφ u,i, j,w φ v,i, j) since the same radial basis γ φ j is used for both components (φu,φv). however, because every snapshot is reshaped as a column vector, regardless of whether this collects a vector or a scalar field, we keep the same notation as for the interpolation of the temporal structures. in this work, we consider gaussian rbf of the form: γ φ j(x0|x j,σφ j) = exp ( −(x0−x j) t ( 1/2σ2 x 0 0 1/2σ2 y ) (x0−x j) ) ; γ ϕ j (t0|t j,σϕ j) = exp (−(t0− t j) 2 σ2 t ) , (3) i.e. σφ j = diag(1/2σ2 x ,1/2σ2 y) and σϕ j = 1/2σ2 t . for both space and time regressions, the collocation point and the shape parameters are defined a priori and the regression is solved once the weights are identified. reshaping all bases functions as columns of matrices γφ(x0) ∈ rns×nφ and γϕ(t0) ∈ rnt×nϕ , collecting all the unknown weights into column vectors wφ ∈ rnφ×1 , wϕ ∈ rnφ×1 and collecting all the entries of~φi(x0) and ϕi(t0) into column vectors φ0 ∈ rns×1 and ϕ0 ∈ rnt×1, the weights are solution of classic least square problems. using a standard tikhonov regularization to mitigate the risks of overfitting (mendez et al., 2020b), the solution reads: ax = b → x = ( at a+αi )−1 at b, (4) where a = γφ(x0), x = wφ and b = φi for the regression in space and a = γϕ(t0), x = wϕ and b = ϕi for the regression in time. the regularization parameter α is taken as ε ||a||f , with ε = 1e− 11 and ||a||f the frobenious norm of a. note that the inverse in equation 4 can be precomputed and the system solved for all the modes in a single step. once the weights are computed, equation (2) can be used on any arbitrary mesh grid x and any time discretization t. then, the interpolated field reads ~u(x, t) = r ∑ i=1 σi~φi(x)ϕi(t) with { ~φi(x) = ∑ nφ j=1 wφ j γ φ j(x|x j,σφ j) ϕi(t) = ∑ nϕ j=1 wϕ j γ ϕ j (t|t j,σϕ j) (5) the derivatives of the flow can now be computed analytically by simply replacing the rbf with their required partial derivatives. for example, the spatial derivative ∂xu can be computed as: ∂xu(x, tk) = ∂x ( r ∑ i=1 σiφu,i(x)ϕi(tk) ) = r ∑ i=1 σi∂xφu,i(x)ϕi(tk) with ∂xφu,i(x) = nφ ∑ j=1 wφ j ∂xγ φ j(x|x j,σφ j) . (6) this derivative is analytically available because ∂xγ φ j is analytically available by differentiating eq.3. finally, as all derivatives can be accurately computed, the strength of the vortices detected in the piv fields can be measured in terms of q-field (hunt et al., 1988) q = 1 2 (||ω||2f −||s||2f) =− 1 2 ( (∂xu)2 +2∂yu∂xv+(∂yv)2 ) (7) where s = 1/2(∇v +∇v t ) and ω = 1/2(∇v −∇v t ) the symmetric and anti symmetric portions of the velocity gradient tensor. 4 results 4.1 synthetic test case before analysing the experimental data, we consider a simple synthetic test case to test the robustness of the implemented rbf regression against noise. the flow field chosen for the test is ~u = (u,v) = (sin(x) · cos(y),−cos(x) · sin(y)) over a domain x = [0,π]× [0,π]. this field is sampled on a cartesian grid with nx = ny = 11 points and is shown in figure 3(a). to simulate different noise levels, we add a white noise field ~w(x) ∈ [0,1] with relative intensity p, i.e. ~uδ(x) =~u(x)(1+ p~w(x)). the perturbed fields with p = 0.5 and p = 1 are shown in figures 3(b) and 3(c) respectively. the spatial regression is performed using a total of nφ = 40× 40 gaussian rbfs (see eq 3) with σx = σy = 2. the collocation points are uniformly distributed over a cartesian grid in the domain x. the rbf regression is then used to re-sample the velocity field onto a much finer grid, i.e. nx = ny = 22. the results for the three fields in figures 3(a), 3(b) and 3(c) are shown in figures 3(d), 3(e) and 3(f) respectively. in all these cases, the rbf regression removes the noise and reconstructs the flow field on the much finer grid. we close this subsection by comparing the performances of the rbf regression with two classic interpolants: a linear interpolation and a cubic spline interpolation, as available from the python’s library scipy. the performances were evaluated in terms of mean absolute error (mae), defined as: mae = 1 nx ny nx·ny ∑ i=1 |vgt,i− vi| (8) (a) (b) (c) (d) (e) (f) figure 3: illustrative synthetic test case to analyze the robustness of the rbf regression: a vortex field is sampled over a coarse grid. fig (a) (c): velocity field on the coarse grid with noise level (defined in the text) p = 0,0.5,1. fig (d)-(f): results of the re-sampling of the rbf regression on a much finer grid for the cases (a)-(c). where vi is the prediction of the interpolant and vgt,i is the analytic flow field. the results are shown in figure 4 as a function of the noise parameter p. while at low levels of noise the three approaches are comparable, the rbf is significantly more robust as p is increased. 4.2 piv fields the piv velocity fields were processed retaining a total of r = 25 pod modes in equation (1). the temporal structures of the modes were approximated with nϕ = 500 rbfs with σt = 0.01 while nφ = 900 rbfs were used for the spatial structures (see equation (3)). for the regression in space, the rbfs were collocated over a regular grid of nbx×nby = 60×15 and anisotropic kernels with σx = 10 and σy = 15 were selected. this allows to efficiently account for the high aspect ratio of the flow. no re-sampling was performed in the time domain since the available time resolution was sufficient for the scope of this work. the spatial resolution of the piv field, i.e. x0 in equation (1)-(3), has a resolution of ∆x = 0.12mm and ∆y = 0.48mm for the rising test cases and a resolution of ∆x = ∆y = 0.22mm for the descending test cases. the resulting rbf regression is used to re-sample the velocity field over a grid (x in equation (5)) with a resolution of ∆x = 0.04mm and ∆y = 0.16mm for the rising test casess, and ∆x = ∆y = 0.07mm for the descending test cases. figure 5 shows the results of the experiments with the rising interface, i.e. the advancing contact line problem. figure 5(a) and 5(b) show the acceleration and the maximum q-field within the roi as a function of the mean velocity within the channel. the labels correspond to the ones explained in section 2. the mean velocity is calculated by zero padding the velocity field at the walls and taking the mean of the average velocity of the bottom five rows and the acceleration is computed from the time derivative of the mean 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 p 0.0 0.1 0.2 0.3 0.4 m a e rbf linear cubic figure 4: mean absolute error after interpolation over the level of noise. ’rbf’ refers to the implemented interpolator, ’linear’ and ’cubic’ an interpolator using bivariate splines of first and third order. velocity. a clear trend is visible: the q-field is increasing with decreasing mean velocity. three instantaneous velocity fields are shown in figures 5(c) 5(e), corresponding to the three points marked in figure 5(a) and 5(b). for plotting purposes, the velocity fields are slightly high-pass filtered by using a gaussian filter with σx = σy = 15 and a truncation after 2.5 standard deviations. the quiver plot only shows every second column for the rising interface to avoid overcrowding the image. the q-field is also shown in each snapshot for quantitative analysis and the axis aspect ratio is set to one. the upper horizontal boundary of the roi is placed approximately 0.2 mm from the interface at the center of the channel, and this is the case for the three shown snapshots. however, because of light reflections and diffraction some of the rows close to the interface are sometimes considered invalid and hence this distance increases up to 1.5 mm. this might explain the noisy trends in figure 5(a) and 5(b). in each case, two counter rotating vortices are visible close to the walls. the one on the right is rotating clockwise and the one on the left counterclockwise. the vortices extends considerably along the vertical direction but only over a small distance in the cross-stream direction. at a distance of 1 mm from the wall, these have no appreciable influence on the velocity field. the initial pressure was high enough to produce a strong acceleration, as shown in figure 5(a). while the rolling motion of the flow is still present, the significant acceleration and high velocities push the stream-line split injection pattern and its vortices towards the wall. it is worth noticing that the velocity fields look similar even though figure 6(c) and 6(d) have largely different accelerations. referring to the expected theoretical flow field from figure 1(a), it appears that the stream-line split injection forms a small angle with the walls. as a result, the rolling motion expected by the viscous-capillary balance is confined to a narrow region of the flow. figure 6 shows the same results for the cases with the descending interface. the velocities and accelerations in figure 6(a) and 6(b) have a different sign because the interface moves downward. a similar trend as for the rising interface can be observed, with the magnitude of the q-field increasing as the velocity decreases. however, the reader should note that a decreasing velocity in this case means that the absolute value of the velocity is increasing. another observation is the increased strength of the q-field, with the maximum value being almost an order of magnitude above the maximum value for the rising interface. the vortices in figure 6(c) 6(e) show a different behaviour than the ones for the rising interface. besides the reversed rotation, as expected from the theoretical flow topology in figure 1, their centre is much closer to the centre of the channel, and the rolling motion extends much further in both the x and y-direction. in the case of the receding contact line, the stream-line split ejection (see figure 1(b)) forms a larger angle with the wall than for the advancing contact line. the large difference cannot be justified by the velocity of the contact line, which in the slowest rising test cases is comparable to the fastest falling test cases, nor by its acceleration, which are also comparable in the cases in 6(c) and the one in figure 5(e). 5 conclusions and perspectives time-resolved piv measurements of the flow field underneath a dynamic meniscus have been carried out in a two-dimensional channel. both advancing and receding contact lines were investigated. in both cases, two counter-rotating vortices were observed below the meniscus. in addition, super-resolution of the velocity 240 260 280 300 320 v [mm/s] −2500 −2250 −2000 −1750 −1500 −1250 a [m m /s 2 ] (c) (e) (d) test case 1 test case 2 (a) 240 260 280 300 320 v [mm/s] 0 200 400 600 q m a x [1 /s 2 ] (c) (e) (d) test case 1 test case 2 (b) −2.50 −1.25 0.00 1.25 2.50 x[mm] 0 100 200 (c) −2.50 −1.25 0.00 1.25 2.50 x[mm] 0 100 200 300 (d) −2.50 −1.25 0.00 1.25 2.50 x[mm] 0 100 200 300 (e) figure 5: results for the rising interface. fig (a) (b) acceleration and maximum q-field over the mean velocity for different test cases. the blue case corresponds to an initial pressure of 1400 pa and the orange one to 1500 pa. fig (c) (e) q-field contour with the high-pass filtered velocity field. the aspect ratio of the plot is set to one. fields was achieved using a regression scheme that combines an analytic approximation of the spatial and temporal structures of the leading pod modes using rbfs. this allowed analytical differentiation and accurate computation of the q-fields. in both advancing and receding cases, the strength of the vortices depends on the mean velocity and the acceleration of the flow, and whether the contact line is advancing or receding. the latter is especially important because the splitting stream-line forms a different angle with the wall and has the largest impact on the flow field. significant differences were observed between advancing/receding wetting configurations even when the modulus of velocity and acceleration of the contact lines were comparable. the main difference between the two cases was found in the interface’s shape (not shown here): this appeared nearly flat in the advancing cases and characterized by large menisci, with small contact angles, during the receding test cases. future work will complement the presented investigation with an analysis of the interface shape in both experiments. acknowledgments this project was funded by arcelormittal maizières research sa in the framework of the ‘minerva project’, and the authors thank jean-michel mataigne for many fruitful discussions on dynamic wetting. d. fiorini is supported by fonds wetenschappelijk onderzoek (fwo), project number 1s96120n. −200 −180 −160 −140 −120 −100 −80 −60 −40 v [mm/s] 0 200 400 600 800 1000 1200 a [m m /s 2 ] (c) (d) (e) 0 mm 40 mm 120 mm (a) −200 −180 −160 −140 −120 −100 −80 −60 −40 v [mm/s] 0 500 1000 1500 2000 2500 3000 q m a x [1 /s 2 ] (c) (d) (e) 0 mm 40 mm 120 mm (b) −2.50 −1.25 0.00 1.25 2.50 x[mm] −500 0 500 1000 1500 (c) −2.50 −1.25 0.00 1.25 2.50 x[mm] −200 0 200 400 600 800 (d) −2.50 −1.25 0.00 1.25 2.50 x[mm] −300 −100 100 300 500 700 (e) figure 6: results for the descending interface. fig (a) (b) acceleration and maximum q-field over the mean velocity for different test cases. the labels refer to the vertical position of the camera, where 0 mm refers to the part of the channel where it meets the reservoir. fig (c) (e) q-field contour with the high-pass filtered velocity field. the aspect ratio of the plot is set to one. references fiorini d, mendez am, simonini a, seveno d, and johan s (2021) a study on the effect of inertia on dynamic contact angles using an inverse method. to appear in journal of colloid and interface science fornberg b and flyer n (2015) solving pdes with radial basis functions. acta numerica 24:215–258 fuentes j and cerro r (2005) flow patterns and interfacial velocities near a moving contact line. experiments in fluids 38:503–510 gunes h, sirisup h, and karniadakis ge (2006) gappy data: to krig or not to krig?. journal of computational physics 212 212:358–382 hoffman rl (1975) a study of the advancing interface. i. interface shape in liquid—gas systems. journal of colloid and interface science 50:228 – 241 huh c and scriven l (1971) hydrodynamic model of steady movement of a solid/liquid/fluid contact line. journal of colloid and interface science 35:85–101 hunt j, wray a, and moin p (1988) eddies, streams, and convergence zones in turbulent flows. in studying turbulence using numerical simulation databases, 2. proceedings of the 1988 summer program, stanford, california, usa, june 27 july 22 karri s, charonko j, and vlachos p (2009) robust wall gradient estimation using radial basis functions and proper orthogonal decomposition (pod) for particle image velocimetry (piv) measured fields. measurement science and technology 20:045401 kistler sf (1993) hydrodynamics of wetting. in wettability. chapter 6, pages 311 – 430. crc press levine s, reed p, watson e, and neale g (1976) a theory of the rate of rise of a liquid in a capillary. in colloid and interface science. pages 403–419. academic press liberzon a, lasagna d, aubert m, bachant p, käufer t, jakirkham, bauer a, vodenicharski b, dallas c, borg j, tomerast, and ranleu (2020) openpiv/openpiv-python: added synthetic image generator mendez m, raiola m, masullo a, discetti s, ianiro a, theunissen r, and buchlin j (2017) pod-based background removal for particle image velocimetry. experimental thermal and fluid science 80:723– 729 mendez ma, balabane m, and buchlin jm (2019) multi-scale proper orthogonal decomposition of complex fluid flows. journal of fluid mechanics 870:988–1036 mendez ma, hess d, watz bb, and buchlin jm (2020a) multiscale proper orthogonal decomposition (mpod) of tr-piv data—a case study on stationary and transient cylinder wake flows. measurement science and technology 31:094014 mendez ma, pino f, and fiore m (2020b) machine learning for fluid mechanics: challenges, opportunities and perspectives. in optimization methods for computational fluid dynamics, vki lecture series. von karman institute nasarek r, wereley s, and stephan p (2008) flow field measurements near a moving meniscus of a capillary flow with micro particle image velocimetry (µpiv). in proceedings of the sixth international asme conference on nanochannels, microchannels and minichannels, darmstadt, germany, june 23-25 quéré d (1997) inertial capillarity. europhysics letters 39:533–538 raben sg, charonko jj, and vlachos pp (2012) adaptive gappy proper orthogonal decomposition for particle image velocimetry data reconstruction. measurement science and technology 23:025303 savelski m, shetty s, kolb w, and cerro r (1995) flow patterns associated with the steady movement of a solid/liquid/fluid contact line. journal of colloid and interface science 176:117–127 scarano f and riethmuller m (2000) pod-based background removal for particle image velocimetry. experiments in fluids 29:51–60 sperotto p, mendez m, and pieraccini s (2021) a meshless method to measure pressure fields via radial basis functions. to appear in experiments in fluids washburn ew (1921) the dynamics of capillary flow. physical review 17:273–283 zimmerman j, weislogel m, and tretheway d (2010) micro-piv measurements near a moving contact line. in proceedings of the asme 2010 international mechanical engineering congress & exposition, vancouver, british columbia, canada, november 12-18 introduction experimental setup and test cases data processing: smoothing, super-resolution and q-fields results synthetic test case piv fields conclusions and perspectives 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 piv measurement of complex flow characteristics in open-cell metal foam replica minsin kim1, youngwoo kim1, sajjad hosseini1, kyung chun kim1∗ 1 pusan national university, school of mechanical engineering, busan, south korea ∗ kckim@pusan.ac.kr abstract time-resolved 2-d particle image velocimetry was used to study on turbulent flow characteristics inside an open-cell metal foam under the laminar and turbulent inlet conditions. a study on the effect of reynolds number was conducted with different three channel reynolds numbers, 1000, 5000 and 10000. uniform upstream flow is divided by the pore network of metal foam and it is found that there are flow disturbances induced by metal foam structure even at a laminar inlet condition. it is confirmed that there is a similarity of the preferred flow path flows take regardless of reynolds number. 1 introduction metal foam is a metallic sponge which consists of many ligaments and nodes interconnect the struts. metal foam structures have been of interest because their geometrical characteristics like high porosity, large specific surface area. due to the great potential of applications, various studies have been conducted to understand the flow inside metal foam. however, flow characteristics inside metal foam are not fully understood because highly complex geometry of metal foam makes us difficult to observe flow inside metal foam. the characteristics of metal foam internal flow with a laminar flow inlet condition were studied by moon et al. (2018). in the present study, however, particle image velocimetry (piv) measurement was conducted to observe the turbulent characteristics of inside metal foam in detail when turbulent flow or laminar flow enters the metal foam replica. figure 1: experimental setup figure 2: contours of mean velocity magnitude of 6 view (a) re = 10,000 (b) re = 5,000 (c) re = 1,000 figure 3: contours of root-mean-squared temporal fluctuation velocities of streamwise component (upper row) and transverse component (lower row) (a),(d) re = 10,000 (b),(e) re = 5,000 (c),(f) re = 1,000 2 method the size of the replica is 80 mm × 80 mm × 200 mm and the cell diameter, pore diameter, strut diameter, and porosity of the replica are 36.08 ± 4.24 mm, 15.6 ± 1.32 mm, 3.2 ± 0.24 mm, and 0.92, respectively. the transparent metal foam model was placed inside a vertical water channel with same dimension. the experimental loop containing the test section is shown in fig. 1. 3 results and discussion fig. 2 shows the velocity magnitude fields. refractive index of metal foam and fluid could not be matched, however, it was possible to observe the flow in part due to the large size of the pore. it is found that there is similarity in the flow path regardless of reynolds number. this indicates that the preferred path the fluid takes through the metal foam structure is not different in the different flow regimes. this is similar result from lu et al. (2020). fig. 3 shows contours of the fluctuation velocities. when a turbulent flow with a turbulence intensity of 10% enters the metal foam, the turbulent intensity increases while passing through the metal foam replica. in the case of laminar inlet condition, the value of u ′ rms/ub of the upstream are near zero, but they increase to 0.1-1.4 inside the metal foam structure. this indicates there are flow disturbances induced by metal foam structure even at a laminar inlet condition. after passing through the metal foam structure, turbulent decays due to the shear-free uniform flow and all the enhanced turbulence recover to initial state. 4 conclusions further discussion about the turbulent characteristics such as vorticity and turbulent kinetic energy inside metal foam will be provided at the conference. acknowledgements this work was supported by the national research foundation of korea(nrf) grant funded by the korea government(msit) (no. 2020r1a5a8018822). references lu x, zhao y, and dennis dj (2020) fluid flow characterisation in randomly packed microscale porous beds with different sphere sizes using micro-particle image velocimetry. experimental thermal and fluid science 118:110136 moon c, kim hd, and kim kc (2018) kelvin-cell-based metal foam heat exchanger with elliptical struts for low energy consumption. applied thermal engineering 144:540–550 introduction method results and discussion conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 an experimental investigation on stall flutter over a vertically mounted rigid finite wing r. f. soares1*, i.karasu2, b. ganapathisubramani1 1 university of southampton, southampton, so17 1bj, united kingdom 2 adana alparslan turkes science and technology university, 01250, saricam, turkey ∗ r.f.soares@soton.ac.uk abstract as stall flutter has relevant engineering implications, such as in blades of wind turbine and hale (highaltitude long-endurance aircraft). this work presents the experimental investigation of rigid wing setup in a closed-circuit wind tunnel having 2.1 m × 1.5 m test section. the experimental campaign reached stable and symmetrical lco within the freestream range from 9 m/s up to 14 m/s (1.69 × 105 < re < 2.63 × 105). two techniques were used for position tracking: one mechatronic and one image-based. the latter used ‘shakethe-box’ method applied to a body, which has proven a successful approach as a non-intrusive tool. 1 introduction the experiments were carried out at the 7x5 wind tunnel; a closed-circuit facility with two test sections in serial. for this experiment, the setup was installed at the high-speed test section (2.1 m × 1.5 m). the wing is a naca0012 cross-section model of aluminium (.e. structure) and carbon-fibre composite (e.g. skin) of 0.3m chordwise and a span length of 0.77 m. a servo motor with cylindrical shield is the base for the wing, which was connected to a 6-axis delta ip65 load cell. in the heaving axis, the system was attached to a pair of linear-guided carriages, and the nominal rest position is found after two identical, counterbalance springs were linked, providing a spring constant (k) of 400 n/m. in the pitching axis, one pair of identical rubber bands were used on each side, connecting the wing leading edge to the cylindrical base. the image-based tracking solution involved particle tracking velocimetry (ptv) with ‘shake-thebox’ methodology, where 5 phantom v641 high-speed cameras recorded a scattered pattern of 8mm dots on the wing surface. experimental setup is illustrated in figure 1. figure 1: wing system and ‘shake-the-box’ hardware setup for structural analysis. 2 summary of results both position tracking tools were performed simultaneously and lately compared in order to assess the quality of the image-based technique as a surface tracking tool. the later were processed in two steps: (i) obtaining the time-resolved position tracking with ‘shake-the-box’ methodology, then (ii) reconstruction of the wing surface and estimation of the angular and heaving history. assuming the mechatronic position tracking results as baseline, the non-intrusive results are compared and presented in figure 2. a nominally harmonic dataset were found for each self-sustained lco, which allowed analysis in phaseaveraged format (figure 3), where the properties are averaged as a function of the angle of attack cycle (i.e. pitching motion) discretised within 1° resolution. figure 2: position tracking validation: mechatronicvs image-based systems. figure 3: phase-averaged lco’s. 3 conclusions the occurrence of a self-sustained lco were found of the system with a naca0012 rigid wing. an initial perturbation was required to trigger the phenomenon; however, the motion amplitudes were noticeably stable and reproducible for a same trigger input.the absolute minimum freestream able to sustain the motion was 8.5m/s with minor decay instabilities, and any freestream higher than 14 m/s would reach the physical end-stops. the ‘shake-the-box’ method applied as a body tracking solution has been successfully validated, allowing the use of this approach as a non-intrusive tool for further applications. acknowledgements we gratefully acknowledge the financial support from eu h2020 project homer (grant ref no: 769237). references [1] g. dimitriadis and j. li, “bifurcation behavior of airfoil undergoing stall flutter oscillations in lowspeed wind tunnel,” aiaa journal, vol. 47, no. 11, pp. 2577–2596, nov. 2009. [2] d. poirel and f. mendes, “experimental small-amplitude self-sustained pitch–heave oscillations at transitional reynolds numbers,” aiaa journal, vol. 52, no. 8, pp. 1581–1590, aug. 2014. 14th international symposium on particle image velocimetry intermittency effects in singleand multi-phase flow and anomalous transport in heterogeneous porous media zoë penko1, yaofa li1,2, diogo bolster1,3, and kenneth t. christensen1,3,4 1university of notre dame, department of aerospace and mechanical engineering 2now at montana state university, department of mechanical and industrial engineering 3university of notre dame, department of civil and environmental engineering and earth sciences 4now at illinois institute of technology, armour college of engineering introduction multi-phase flow and transport in porous media is prevalent in a wide range of challenging fluid mechanics problems related to sustainability, energy, and the environment. accurate prediction of the displacement and interaction of such flows is vital in addressing these problems. in particular it is critical to understand the smallor pore-scale flow and its spatial and temporal evolution, which can impact behaviors at system scales in a nontrivial manner. intermittency is a phenomenon currently observed in numerical and experimental studies of single-phase flow (anna et al., n.d.; morales et al., n.d.), but the case of multi-phase flow has yet to receive much study due to challenges faced in both simulations and experiments. the underlying physics of spreading, mixing, and interfacial processes must be understood for accurate predictions of transport in multi-phase flow systems. therefore, a comprehensive understanding of multi-phase flow at these very small scales is necessary in the development of accurate system-scale prediction models. we present results from a coordinated numerical and experimental study of intermittency effects over a range of viscous and inertial flow regimes in singleand multi-phase flows in 2d heterogeneous micromodels to quantify lagrangian flow statistics to better inform pore-scale models. the applicability of different modeling frameworks such as the correlated-continuous time random walk is tested by studying statistics of particle trajectories obtained by particle tracking velocimetry (ptv) measurements and lattice boltzmann simulations from singleand multi-phase flows. the results make particular note of the influence of the pore reynolds number (re) and inertial effects on intermittency, and compare these effects in the two flow regimes. methods experiments are conducted in the university of notre dame micropiv laboratory for energy and the environment. a ptv approach utilizing small, neutrally-buoyant (to serve as true tracers), and low-density seeded particles illuminated by laser light pulses synced to a camera by a synchronizer that captures images of the fluoresced light to reconstruct particle trajectories of single particles is used. volume illumination is employed to excite the fluorescent tracer particles seeded in the flow and the particle trajectories are imaged in a plane-defined 2d micromodel depth. figure 1 presents homogeneous and heterogeneous 2d porous models that are fabricated using established silicon microfabrication methods (kazemifar, 2020), where the top of the micromodel is formed by anodic bonding of a glass wafer to provide optical access to the flow in the 2d porous matrix. some limitations exist in collecting quality experimental data, as higher re flow experiments pose challenges due to the inherent trade-off between spatial resolution and the physical size of the field of view (fov), image acquisition rate limitation 1 figure 1: (top) homogeneous 2d porous micromodel; (bottom) heterogeneous 2d porous micromodel. by data transfer bandwidth, and the record length limitation by the on-board memory size for a given resolution. such limitations can be addressed by a lattice boltzmann method (lbm) simulation approach to numerically simulate multi-phase flow in the same porous media and complement experiments by broader parameter space exploration, an approach used on a 2d micromodel of water (wetting phase) being displaced by co2 (non-wetting phase) by li et al. (n.d.). future work a coordinated simulation and experimental study of intermittency effects in multi-phase flow spanning flow regimes from viscous to inertial in 2d and 3d porous media is underway in an effort to quantify lagrangian flow statistics and accurately model the pore-scale behavior, thereby advancing the fundamental understanding of such behavior. these data will be used to (1) calculate statistics of particle trajectories and intermittency for singlephase flow in 2d porous micromodels to test the applicability of different modeling frameworks, (2) study intermittency and dispersion with the addition of a second, immiscible fluid and the presence of trapped ganglia, (3) study the effect of re and inertia on intermittency in multi-phase porous media flow, and (4) compare these effects in singleand multi-phase flow in homogeneous and heterogeneous porous models. this analysis will form the basis of the final paper. the development of a more general and robust modeling approach that is fully validated by experiments and simulations will allow better prediction of the spreading, mixing, and interfacial processes that occur in natural and engineered environments. references anna, p. de, le borgne, t., dentz, m., et al. (n.d.). flow intermittency, dispersion, and correlated continuous time random walks in porous media. physical review letters 110, (), 184502. kazemifar, f. (2020). an experimental study of supercritical co2 flow in pipes and porous micromodels for carbon sequestration applications (). url: https://core.ac.uk/reader/29175208 (visited on 07/16/2020). li, y., kazemifar, f., blois, g., and christensen, k. t. (n.d.). micro-piv measurements of multiphase flow of water and liquid co2 in 2-d heterogeneous porous micromodels. water resources research 53, (), 6178–6196. issn: 00431397. morales, v. l., dentz, m., willmann, m., and holzner, m. (n.d.). stochastic dynamics of intermittent pore-scale particle motion in threedimensional porous media: experiments and theory. geophysical research letters 44, (), 9361– 9371. issn: 0094-8276. 2 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 uncertainty propagation and truncation errors in lpt kinematics l. chatellier1* 1institut pprime, upr3346, cnrs – université de poitiers – isae-ensma, france *ludovic.chatellier @univ-poitiers.fr abstract lagrangian particle tracking (lpt) has become a near-standard approach for performing accurate 3d flow measurements, thanks notably to the technical breakthroughs brought by the iterative particle reconstruction (ipr: wieneke, 2013) and shake-the-box (stb: schanz et.al, 2016) procedures. these decisive progresses have triggered a number of studies relative to the eduction of flow kinematics and dynamics based on particle trajectory analyses. novara & scarano (2013), and others, focused on polynomial approximations of the trajectories, which analytically provide the material derivatives used to estimate pressure gradients. in particular, approximations based on second order polynomials fits of a small number of particle positions are used in commercially available softwares and among research teams as a straightforward solution to obtain the first and second order derivatives with a limited effect of the measurement noise. additionally the analyses conducted during the 2020 lpt challenge (leclaire, 2020 ; sciacchitano, 2020) have addressed the performance of methodologies used by different groups with respect to second order trajectory fits for both multi-pulse and four-pulse (novara et. al, 2016) lpt cases. on more advanced theoretical grounds, geseman et. al (2016) have proposed the trackfit approach using penalized b-splines with considerations on the time-varying acceleration rate (i.e. jolt or jerk) and spectral content of noisy particle tracks. from a general point of view on function approximations, polynomial fit, taylor developments and finite differences schemes are absolutely equivalent ingredients of a unique framework in which discrete sets of ordered values are represented by continuous functions of a single parameter. this can be easily recalled using linear algebra applied to the construction of finite difference schemes and to the evaluation of their orders of truncation as well as their sensitivity to measurement noise. the present contribution provides a practical methodology that can be included in a global uncertainty quantification framework. examples illustrating a variety of schemes are presented, along with suggestions of analytical tests based on theoretical results. 1 introduction within the lagrangian particle tracking (lpt) framework, the time-history spatial positions of the individually identified particles are used to constitute discrete tracks and compute their trajectories as well as their kinematics. in pratice, acquisition sequences consist in two-, fouror multi-pulse exposures (resp. tp, fp and mp) resulting in two, four or multiple successive measured positions of a single particle in space, as depicted in figure 1. mailto:mohamed.larbi.kara.mostefa@univ-poitiers.fr mailto:mohamed.larbi.kara.mostefa@univ-poitiers.fr 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 δtt δtt δtt δtt δtt δtt δtt’ δtt δtt’ figure 1: typical distribution of two (green) four (blue) and multi-pulse (purple) lpt measurement time lags. in conventional ptv algorithms, tp measurements are used to derive central positions and velocities using second-order differentiation schemes, thanks to the symmetry properties of the 2point centered finite differences formulation. a minimum of three positions is needed to obtain acceleration using second order derivation schemes. for fp and mp (i.e more than two pulses) lpt measurements, higher order derivatives are accessible using second or higher order derivations schemes. apart from the jolt which is sometimes studied, the quantities of interest are most often limited to position, velocity and acceleration. it is also of common practice to model trajectories as piece-wise polynomials of degree ranging from 2 to a few units, from which these quantities are derived. while finite differences derivation schemes at various orders are long known, they are often presented as well-chosen linear combinations of taylor developments from which a particular derivative is obtained. elements of the richardson expansion are also sometimes used to build the linear combinations that can increase the truncation order of a given scheme. the formalism used below aims at rationalizing the practical writing of differentiation schemes with a view to ease the estimation of truncation errors, the propagation of measurement noise and uncertainty, and a direct correspondence with polynomial approximations. 2 taylor development and polynomial fit the estimation of derivatives using polynomial approximations or schemes based on taylor developments are perfectly equivalent approaches. this is recalled below in the context of discretized trajectories. given a set of particle positions xk belonging to the same trajectory γ as obtained from trptv or lpt, positions, velocities, accelerations and other derivatives can be educed from linear combinations of the measured positions using either finite differences or polynomial fits. given an instant of interest t and a distribution of time lags τk at which particle positions are measured, one writes : ∀ τk , xk=γ(t+τk)+ek , where ek is the measurement error on the particle position. within a set t m={t+τ1;…; t+ τm} of m measurement instants, the corresponding measured and true positions are respectively written as xm=[ x1 … xm] ⊤ and gm=[γ(t+τ1) … γ(t+τm)] ⊤ so that xm=gm+em . the taylor development of order n∈ℕ+ of the true positions around instant t then writes: 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 ∀n∈ℕ+ ,∀ τk ,γ( t0+τk )=γ(t) + τk γ̇ (t) + … + τk n γ (n) (t )/n! + o( τk n ) . yielding, for the set t m : gm=[ 1 τ1 … τ1 n ⋮ ⋮ 1 τm … τm n ] [ γ(t) ⋮ γ (n) ( t)/n!]+o( τ1 n ⋮ τm n ) . similarly, a polynomial p of degree n fitting positions gm according to a given norm can be defined from its coefficients (ak)k=0…n and written for the set t m as: [p( τp)]p=1…m=[ 1 … τ1 k … τ1 n ⋮ ⋮ 1 … τm k … τm n ][ a0 ⋮ an] . identifying coefficients (ak)k=0…n to the successive derivatives of p gives: ∀ k∈{0…n}, ak= p(k)(0) k ! . so that [p( τp)]p=1…m=[ 1 … τ1 k … τ1 n ⋮ ⋮ 1 … τm k … τm n ][ p (0) ṗ (0) ⋮ p(n)(0) /n ! ] . for the positions gm and derivatives (γ(k) ( t))k=0…n to be approximated by polynomial p , one therefore gets the same matrix formulation as the one provided by the taylor development of gm around instant t . the formal difference between the two approaches lies in the presence of truncation terms in the taylor development and, implicitly, of a possible fitting error in the polynomial approximation. 3 system inversion the linear relation between the positions and derivatives is fully contained in the full or truncated vandermonde matrix constructed from the time lags. for an equal number of positions and derivatives terms ( m=n+1 ), the matrix is complete and invertible provided that all time lags are distinct from each other. the polynomial therefore provides an exact fit of the measured positions. for reduced polynomial degrees or orders of truncation (i.e. m>n+1 ), the truncated vandermonde matrix is still left-invertible so that the generalized or the moore-penrose pseudoinverse can be used to identify the successive derivatives. in the following paragraphs, a reference time lag dt will be used in order to represent each time lag τk by τk=αk dt with ∀ k∈ℕ , αk∈ℕ , as represented in figure 2. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 dt dt rdt dt t dt dt t t rdt 3dt 3dt 2dt 2dtdt figure 2: definition of two (green) four (blue) and odd or even multi-pulse (purple) lpt measurement time lags referenced to a central measurement time, as used in finite difference schemes. the taylor development now writes: gm=[ 1 α1 … α1 n ⋮ ⋮ 1 αm … αm n ][ γ(t) ⋮ γ (n) ( t)dtn/n !]+o(dt n ) . for a square system, the m×m vandermonde matrix v (α1 ,… ,αm) will be denoted v m and its inverse wm . for m>n+1 , the m×(n+1) truncated vandermonde matrix will be denoted v mn and its (n+1)×m pseudo-inverse w nm , noticing that v m=v m m−1 and wm=wm−1 m . for the estimation of truncation errors, m× p ( p>n) matrices v mp will be used, which are either right-truncated, square or right-extended vandermonde matrices, depending on the values of m , n and p . defining am=[α1 … αm] ⊤ and dn=[γ(t) … γ (n ) (t)dt n/n! ]⊤ , the taylor development can also be formulated as: gm=v mndn+o (dt n )= [am 0 … am n ]dn+o (dt n ) . 3.1 exact fit for m=n+1 , the taylor development can be inverted to provide v m −1gm=dm+o(dt n ) , so that dm=w mgm+o(dt n ) . the differentiation schemes at all orders are therefore contained in the weighting matrix wm , modulated by the temporal and factorial terms, to provide an estimate of the derivatives as: [ ~ γ(t ) … ~ γ (n) (t )]⊤=diag ((k !/dt k )k=0…m−1 )wm xm=fmwm xm . formally, the order of truncation is equal to n=m−1 but can drop to lower values depending on the distribution of the time lags. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 3.1.1 error propagation: in the specific case of an exact fit, the taylor expansion at order n=m−1 and the polynomial fit of the same degree fall exactly on the measured positions xm , inducing no approximation error. it is then straightforward to educe the levels of error propagation due the differentiation schemes as: um=fmwm em . this formulation evidences the increasing sensitivity to measurement errors with increasing truncation orders, as a by-product of the well-known runge phenomenon occurring in increasing order polynomial interpolations 3.1.2 truncation error: the truncation error at order p>n+1 can be estimated using supplementary taylor terms : gm=[ am 0 am 1 … am p ] [ γ(t) ⋮ γ ( p) ( t)dt p/ p !]+o(dt m )=v mpdp+o (dt p )=[v m am n+1 … am p ]d p+o(dt p ) . inverting the system one obtains: wmgm=w m[v m am n+1 … am p ]d p+o (dt p )=wm[v m am m+1 … am p ][ dn+1 ⋮ γ ( p)dt p / p !]+o(dt p ) and dn+1=wmgm−wm [ am n+1 … am p ] [γ(n+ 1)dt n+1 /(n+1)! … γ ( p)dt p / p ! ] ⊤ +o(dt p) . hence, truncation errors at order m=n+1 and above are given by : ∀ p>n+1 , fmwm [ am n+1 … am p ] [γ(n+1)dt n+1 /(n+1)!… γ ( p)dt p / p ! ] ⊤ +o(dt p)=fmw m am n+1→ pdn+1→ p+o(dt p ) . considering the derivation terms (including the 0th order term), the remaining truncation error terms can be different for each derivation order depending on the distribution of time lags. 3.2 approximate fit extending this approach to lower order estimates in which n<m−1 is almost identical, although the vandermonde matrix will not be fully obtained and an over-constrained system will be defined. however, as right-truncated vandermonde matrices are always left-invertible, their pseudo-inverse writes: w nm=(v mn ⊤ v mn) −1 v mn ⊤ so that w nmv mn=1n+1 . 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 the pseudo-inverse w nm provides the differentiation scheme to be used to fit the trajectory and its n first derivatives, as gm=v mndn+o (dt n ) and w nmgm=dn+o (dt n ) . the derivatives are estimated using [ ~ γ(t ) … ~ γ (n) (t )]⊤=fn+1w nm xm . hence, the levels of error propagation due the differentiation schemes are: un+1=fn+1w nmem . the truncation error at order p>n+1 are given by : ∀ p>n+1, fn+1w nm am n+1→pdn+1→ p+o(dt p ) . the approximate fit therefore directly generalizes the exact fit using either the standard or pseudo-inverses of vandermonde matrices constructed from a taylor development. 3.3 examples the application of these procedures are easily illustrated using examples on common use. for tp measurements, the two-point centered derivation scheme leads to 3rd order truncation errors for the first derivative, although it is based on a first order development. for mp measurements, the three-point centered derivation schemes leads to the same stencil for the first derivative, although it is based on a second order development. acknowledging the fact that estimates are generally conducted on larger, centered, regular sets of instants in mp measurements, the three-point case is sufficient to identify which terms are to be taken into account for uncertainty and error estimates. a dedicated example is also given for the specific case of fp measurements, using a generic centered distribution of instants, and which illustrates the slight differences between exact and approximate fits of close orders. 3.3.1 exact fit two-point centered scheme (tp): for the two-point centered scheme built from instants t−dt and t+dt , the differentiation scheme is simply obtained from the taylor terms at order 1: g2=[1 −1 1 1 ][ γ(t )γ̇( t)dt ]+o(dt) ; v 2=[1 −1 1 1 ] ; w 2=[ 1/2 1/2 −1/2 1/2] . for this particular case, and more generally for centered distributions of an even numbers of instants, halving dt lightens the writing of the time lags surrounding the instant of interest (see figure 2). the central position and first derivative are estimated using [~γ(t ) ~ γ̇(t)]⊤=f2w 2 x2 , and the propagation of measurement errors is given by u2=f2w 2e2 : u2=[1 0 0 1/dt ][ 1/2 1 /2 −1/2 1 /2]e2=[ 1/2 1/2 −1/2dt 1/2dt ]e2 . 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 for uniform error levels, this yields error propagation terms of respective norms [1 1/dt ] ⊤ /√2 . the truncation error on both terms is obtained by right-extending the 2×2 vandermonde matrix to the 2×4 matrix v 23 and multiplying it by the finite difference scheme: w 2v 23=[ 1/2 1 /2 −1/2 1 /2] [ 1 −1 1 −1 1 1 1 1 ]=[ 1 0 1 0 0 1 0 1] , meaning that the central position is obtained with a 2nd order truncation error and the first derivative with a 3rd order truncation error. applied to the differentiation terms up to the 3 rd order, this explicitly yields: f2w 2v 23d3=[γ(t ) + γ̈ (t)dt 2 /2 γ̇(t ) + γ (3) ( t)dt2/6]+o(dt2) . three-point centered scheme (mp): for the three-point centered scheme built from instants t , t−dt and t+dt : g3=[ 1 −1 1 1 0 0 1 1 1 ][ γ(t) γ̇(t )dt γ̈(t )dt 2 /2]+o (dt) ; v 2=[ 1 −1 1 1 0 0 1 1 1 ] ; w 3=[ 0 1 0 −1/2 0 1 /2 1/2 −1 1 /2] . the propagation of measurement errors is given by u3=f3w 3e3 : u3=[ 0 1 0 −1/2dt 0 1 /2dt 1/dt 2 −2/dt2 1/dt 2 ]e3 , of norms [1 √2 2dt √6 dt2 ] ⊤ for uniform noise levels. the truncation error at order 4 is obtained from : w 3v 34=[ 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 ] . the central position is obtained with no truncation error, as it is measured prior to building the differentiation scheme. this property also distinguishes centered schemes based on odd or even numbers of instants. the first derivative is obtained with a 3 rd order truncation error, and the second derivative with a 4th order truncation error. one gets: 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 f3w 3v 34d3=[ γ(t) γ̇ (t) + γ (3 ) (t)dt2/6 + o(dt3) γ̈ (t) + γ (4) (t )dt 2 /12 + o(dt2)] . it can be noticed that the value of dt is doubled compared to the two-point scheme obtained with the same sampling, multiplying the error levels and truncation errors by factors 2±1…2 . generic four-point centered scheme (fp): for centered fp measurements, time lags are symmetrically defined as (τk /dt)k=1…4={−a ;−b ;b ;a } with a>b>0 . one can set b=1 and change dt accordingly without loss of generality to introduce the ratio r=a/b≠1 which is sufficient to describe any centered fp distribution. as for the tp case, halving dt lightens the writing of the time lags surrounding the instant of interest. the exact fit is obtained from a taylor development at the 3rd order in which: v 4=[ 1 −r r2 −r3 1 −1 1 −1 1 1 1 1 1 r r2 r3 ] . here, setting r=±3 or r=±1/3 transforms the generic fp case in a regularly distributed fourinstants mp case, which can be generalized to centered mp measurements based on an even number of instants. this yields the inverse matrix: w 4= 1 2r (r2 −1) [ −r r3 r3 −r 1 −r3 r3 −1 r −r −r r −1 r −r 1 ] , and gives the propagation error term u4=f3w 4 e4 : u4= 1 2 r (r2 −1) [ 1 0 0 0 0 1/dt 0 0 0 0 2/dt2 0 0 0 0 6/dt 3][ −r r3 r3 −r 1 −r 3 r3 −1 r −r −r r −1 r −r 1 ]e4 , of norms: 1 |r2 −1|[ √ r4 +1 √2 √r 6 +1 √2|r|dt 2 dt 2 3√2(r2 +1) |r|dt3 ] ⊤ . the corresponding truncation errors at order 5 are given by: 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 f4w 4v 45d5=[ γ(t ) − r2 dt 4 24 γ (4 ) (t) + o(dt5) γ̇(t ) − r2 dt 4 120 γ (5 ) (t) + o(dt 4 ) γ̈(t ) + (r2 +1) dt 2 12 γ (4) (t ) + o(dt2) γ (3) (t) + (r2 +1) dt 2 20 γ (5) (t) + o(dt2) ] . the central position and acceleration are obtained with a truncation error of 4 th order, respectively proportional to r2 and r2 +1 . velocity and jolt are obtained with a truncation error of 5th order, also respectively proportional to r2 and r2 +1 . 3.3.2 approximate fit for fp or mp measurements, the second order fit is mandatory but sufficient to obtain 2 nd order derivatives. it can be used to illustrate approximate fits at all orders below m . apart from the exact m=n+1=3 case illustrated above, it can be written from v m2=[am 0 am 1 am 2 ] whose pseudo-inverse is w 2m . error propagation is directly given by writing f3w 2m em and truncation errors from: w 2mgm=d2+w 2m am 3 γ (3)dt3/3 !+…+w 2m am ( p) γ (p )dt p/ p !o(dt p) . for odd mp distributions, the construction and analysis of the central finite differences scheme is similar to what is obtained for the exact m=n+1=3 case. for even mp distribution, the construction of the centered finite difference scheme can be illustrated by a second order approximate fit of the generic fp case. the corresponding taylor development is built as a restriction of v 4 used in the exact fp case: v 42=[ 1 −r r2 1 −1 1 1 1 1 1 r r2] , which results in the pseudo-inverse matrix: w 24= 1 2 [ − 1 r 2 −1 r2 r 2 −1 r2 r 2 −1 − 1 r2 −1 − r r2 +1 − 1 r2 +1 1 r2 +1 r r2 +1 1 r2 −1 − 1 r 2 −1 − 1 r2 −1 1 r2 −1 ] , 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 and in which only the first derivative weights differ from w 4 . the error propagation term is u4=f3w 24 e4 , of norms: [ √r4 +1 √2|r2 −1| 1 √2(r2 +1)dt 2 |r2 −1|dt 2 ] . the truncation error is given by: f3w 24v 44d4=[ γ( t) − r2 dt 4 24 γ (4 ) (t) + o(dt 4 ) γ̇( t) + r 4 +1 r2 +1 dt 2 6 γ (3 ) (t) + o (dt 2 ) γ̈( t) + (r2 +1) dt 2 12 γ (4 ) (t) + o (dt 2 )] . compared to the exact fp scheme, the estimates of the position and acceleration are identical. the difference between the two schemes only appear in the velocity estimates, which are obtained at order 3 in the approximate fit and order 4 in the exact fit. conversely, the error propagation on the velocity term is governed by: √r6 +1 √2|r||r 2 −1|dt for the exact fit, and 1 √2(r 2 +1)dt for the approximate fit. it is then clear that despite the lower truncation error, the 2nd order fit results in a significantly lower sensitivity to measurement errors, of at least a factor of the order of 3 depending on the chosen value for r . this result is also a by-product of the runge phenomenon. for the choice of an optimal value of r and an exact or approximate fit, some knowledge on the 3rd derivative can be obtained from the exact fit and compared with the propagation of measurement noise, however anticipating the choice of r before an experiment may not be straightforward unless numerical simulations or theoretical results can help estimate the balance between the two terms. for higher order schemes on mp measurement leading to long tracks, the orders of derivation needed to estimate the truncation error are accessible by simply increasing the order of the scheme of interest by a few units. thus, and accounting for the increased error propagation due to the runge phenomenon, all the needed terms can be estimated using: un+1=fn+1w nmem and ∀ p>n+1, fnw nm am n+1→pdn+1→p+o(dt p ) . in order to obtain higher order reference derivatives, trajectories may be approximated by alternative, non-polynomial functions. however, the large spectrum of possibilities doesn’t help 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 providing the most appropriate formulation. analytical flow solutions, though limited to idealized or approximate configurations, may provide the relevant results for a given situation. a few examples are proposed below. 3.3.3 error estimates from analytical trajectories finite difference schemes and error estimates as obtained from the above formulations may be benchmarked against known trajectories from which any order of differentiation can be expressed. apart for specific cases in which vanishing derivatives are a constitutive property, such as, e.g, resting, uniform or unidirectional flow, free fall, etc., non-polynomial analytic trajectories can provide the derivatives needed to qualify a given differentiation scheme. basic non-polynomial examples can be found from potential flows, such as the isolated vortex or normal stagnation points which provide trajectories as steady state streamlines. unsteady potential flows and the corresponding trajectories can also be obtained by imposing time-dependent parameters. stream-functions can also provide integrable analytical solutions for a variety of 2d viscous flows, including boundary layers (blasius, 1908) and non-orthogonal stagnation points (dorrepal, 1986). however, in many formulations, explicit time-dependent trajectories cannot be found and must be numerically integrated, leading to additional error terms, though the successive derivatives remain accessible. a universal illustration is provided by the isolated vortex for which trajectories are described by harmonic terms, with or without advection velocity, to provide circular or cycloid-like tracks. the truncation terms are therefore obtained from the harmonic terms around the measurement instant. for example, expanding ∀ τk ,γ(t+ τk)∝sin(ω(t+τk)) and applying the desired finite difference scheme, then substracting the taylor terms, will yield and exact expression of the truncated terms. similarly, the 2d inviscid flow normally impinging on a flat plate is represented by potential φ ∝ x2 − y2 , stream-function ψ ∝ xy or potential f (z)∝z2 in complex formulation, leading to exponential streamlines that can be expanded around the measurement instant using hyperbolic functions. despite its simplicity, this potential is representative of the flow in the close vicinity of stagnation or separation points on cylinders or wing profiles. for example, the 2d complex potential of the flow around a cylinder, yields near the stagnation point: f (z)=u 0( z+ a2 z−a ) : f (z) → z→0 −u 0 z2 a , locally leading to exponential trajectories. this can be extended to non-orthogonal impingement using a stream-function of type ψ ∝ 1 2 y 2 cosα+xy sinα to provide combinations of exponential trajectories of type: x=x0e t t sinα + 1 2 y0 cotα sh( tt sinα) ; y= y0 e − t t sinα . finally, in the close vicinity of a flat plate, the blasius boundary layer classically represented by the stream-function ψ( x , y )=δ(x )u f ( y / δ( x)) leads to power-law trajectories: x=x0 (1+ 5 4 u √re0 y0 x 0 2 α τ) 4/ 5 ; y= y0 (1+ 5 4 y0 x 0 2 u √re0α τ) 1/5 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 for f (η)=1 2 αη 2 +o(η5 ) and y≪δ( x ) . since ptv or lpt shall be preferred to piv measurements in order to resolve near wall velocity fields (kaelher, 2012), this last formulation may be used to predict uncertainty on a planned measurement, or to fit and qualify existing results. 4 conclusion although finite differences schemes are long known and widely used in the scientific communities for experimental and numerical studies, little attention is generally paid to their content in terms of error propagation and actual truncation terms, and to their relevance to data fitting. the present contribution provides a straightforward and practical mean to access and qualify these aspects using linear algebra, with the possibility of analytical quantification. additionally, the resulting formulations can be easily extended to 2d or 3d for post-processing dense, regular, spatial fields. in this perspective, the observations of, e.g., raffel et. al (1998) on the sensitivity of derivation results obtained from schemes based either on richardson expansion or least-square fits are formally explained by the balance between error propagation and truncation terms. acknowledgements this project has received funding from the european research council (erc) under the european union’s horizon 2020 research and innovation programme , project homer : holistic optical metrology for aero-elastic research (grant agreement no 648161). references acher g, thomas l, tremblais b, gomit g, chatellier l, david l, simultaneous measurements of flow velocity using tomo-piv and deformation of a flexible wing, 13th international symposium on particle image velocimetry, 2019 blasius h, the boundary layer in fluids with little friction (translation of grenzschichten in fliissigkeiten mit kleiner reibung, zeitschrift fixr mathematik und physik, band 56, heft 1, 1908), naca tm-1256, 1950 raffel m, willert m, kompenhans j., particle image velocimetry, a practical guide, springer-verlag berlin, heidelberg, 1998 dorrepal j m, an exact solution of the navier-stokes equation which describes non-orthogonal stagnation-point flow in two dimensions, j. fluid mech. 163:141-147, 1986 gesemann s, huhn f, schanz d, schröder a, from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties, 18th international symposium on the application of laser and imaging techniques to fluid mechanics, 2016 kähler c j, scharnowski s, cierpka c, on the uncertainty of digital piv and ptv near walls, experiments in fluids 52:1641–1656, 2012 leclaire b, challenge datasets generation: physical situation, numerical simulation and synthetic generation, 3rd workshop and 1st challenge on data assimilation & cfd processing for piv and lagrangian particle tracking, 2020 neagoe ve, inversion of the van der monde matrix, ieee signal processing letters 3:4, 1996 novara m, scarano f, a particle-tracking approach for accurate material derivative measurements with tomographic piv. exp.fluids 54:158, 2013 novara m, schanz d, reuther n, kähler cj, schröder a, lagrangian 3d particle tracking in high-speed flows: shake-the-box for multi-pulse systems, experiments in fluids 57(8), 2016 schanz d, gesemann s, schröder a, shake-the-box: accurate lagrangian particle tracking at high particle densities. exp.fluids 57:70, 2016 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 sciacchitano a, lpt challenge results, 3rd workshop and 1st challenge on data assimilation & cfd processing for piv and lagrangian particle tracking, 2020 wieneke b, iterative reconstruction of volumetric particle distribution. meas. science tech. 24,024008, 2013 1 introduction 2 taylor development and polynomial fit 3 system inversion 3.1 exact fit 3.1.1 error propagation: 3.1.2 truncation error: 3.2 approximate fit 3.3 examples 3.3.1 exact fit two-point centered scheme (tp): three-point centered scheme (mp): generic four-point centered scheme (fp): 3.3.2 approximate fit 3.3.3 error estimates from analytical trajectories 4 conclusion 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 noise canceling to compute second order statistic from spiv j-m. foucaut1∗, r. yuvaraj1, c. cuvier1 1 univ. lille, cnrs, onera, arts et métiers paristech, centrale lille, umr9014-lmfl-laboratoire de mécanique des fluides de lille-kampé de fériet, f-59000, lille, france, lille, france ∗ jean-marc.foucaut@centralelille.fr abstract stereoscopic piv (spiv) is performed near the wall in a turbulent boundary layer at high reynolds numbers (reτ = 2272, 3840) in the streamwise-wallnormal plane. a novel method for denoising the statistics is proposed by the use to two independent spiv systems to capture the same field of view, with the objective being that the random noise associated with the velocity fluctuations are not correlated between two independent piv systems. the derivatives in the third (spanwise) direction are obtained by axisymmetry assumptions [george and hussein (1991)] and continuity equation. the statistics are in agreement with that of dns at comparable reynolds number, from y+ = 25 for lower reτ experiment and from y+ = 40 for higher reτ experiment. 1 introduction stereoscopic piv (spiv) is a well recognized experimental method to study turbulent flow. many researchers also use this method to compute statistics of the flow such as mean velocity, reynolds stress tensor, probability density function or spectra [adrian et al. (2000), foucaut et al. (2011), herpin et al. (2013)]. spiv allows the measurement of the three components of the velocity in a plane with an accuracy of about 1-2% (0.1 pixel). for a turbulent flow, it opens up the unique capability of studying the organization of the turbulence. generally, due to the limited spatial resolution of piv, the smallest scales of the flow that can be investigated is limited. the piv random noise will also affect the statistics such as variance. in addition there is also the noise amplification that occurs when derivatives are computed [foucaut and stanislas (2002)]. nevertheless, the velocity gradient is necessary to determine the vorticity, the shear, the dissipation and specific criteria allowing the detection of vortices such as the q criterion which are useful tools to study the flow organization. in the present contribution we focus on statistics. the proposition here is to build an experiment of time resolved spiv in the near wall region of a turbulent boundary layer with a very good spatial and temporal resolution. this experiment is carried out in the lmfl boundary layer wind tunnel. it is setup with two spiv system in order to be able to characterize and to get rid of the noise. the measured velocity is considered ui = uit + uin where uit is the true value and uin is the noise (random error). the variance, then computed by 〈uiui〉 = 〈uit uit 〉+ 〈uin uin 〉 where 〈〉 corresponds to averaging in time and homogeneous direction (in streamwise direction for the present experiment), is affected by the variance of the noise and thus it could be overestimated. the solution is to use 2 independent piv systems to measure the same velocity at the same point. in that case the variance is computed as ui1 = uit +uin1 (1) ui2 = uit +uin2 (2) 〈ui1ui2〉= 〈uit uit 〉 (3) where the numbers 1 and 2 correspond to each piv system. the variance is free of noise because the noise of the two systems are not correlated. this allows the computation of denoised statistics and an estimation of the rms value of the noise by σ 2 uin = 〈ui1ui1〉−〈ui1ui2〉 (4) 2 experimental setup figure 1: schematic of the spiv experimental setup the measurement was done at 19.2 m from the inlet of the test section. at this station, the boundary layer thickness is of 0.273 m and 0.243 m for the reynolds numbers reτ of 2220 and 3840 for infinite velocities of 3m/s and 6m/s, respectively. figure 1 shows the two sets of stereoscopic piv (2d3c) employing 4 miro cameras to capture a field of view illuminated by a laser light sheet of 60.4 × 18.4 mm2 (503+×153+) for reτ = 2220 and 29.6 × 18.4 mm2 (493+× 306+) for reτ = 3840, both along the streamwise x and wall-normal direction y. the seeding for the experiment is 1 µm-size water-ethylene glycol mixture which is fully seeded in the wind tunnel. the cameras and the laser are synchronized by lavision’s high speed controller. the chip-size of the camera were reduced at 1280× 512 pixels to achieve 4.5 khz piv frequency and 640×512 pixels corresponding to 7.5 khz for the lowest and highest reynolds numbers, respectively and the lasers are triggered at same time with 10 mj/pulse. the images were acquired in a series of 5 images burst mode, up to a total of 1803 sets of time series images in order to offer possibility to make statistics on time derivative. this time-resolved spiv employed here is capable of producing a 2d-3c velocity field in a xy-plane, which provides all the derivatives in xand ydirections and time. with the help of continuity equation, it is possible to obtain the ∂w/∂z term. the experiment is calibrated by using an accurate calibration plate which has crosses at known places and are spaced equally by 1 mm distance, and this is in-turn captured by the cameras in 11 spanwise positions. the soloff method is used for the threecomponent reconstruction. this calibration procedure is followed by self-calibration [wieneke (2008)]. special care is taken to compute the velocity vectors at the same point for the two spiv system. to ensure that the velocities are computed at the same point the mesh is generated in the object plane and projected in the planes of the 4 cameras. the acquired data are then processed using a modified version of matpiv toolbox at lmfl. a multi-pass cross-correlation piv analysis is used with deformation at the last pass and with a final interrogation window size of 18 × 24 px which corresponds to 0.97 × 0.97 mm2 for the system 1 and 0.88 × 0.95 mm2 for the system 2, which are of the same order of magnitude corresponding to about 8+ for reτ = 2220, and 16+ for reτ = 3840. the small variation come from a little difference of angles and magnifications between the two systems. figure 2 shows the mean velocity profile in wall-units in spiv experiment at the two reτ, and is then compared with dns of tbl at reτ = 1989 [borrell et al. (2013)] and tcf at reτ = 4200 [hoyas and jiménez (2008)]. the ranges of accessible wall-distances from the spiv experiment are 10.25≤ y+ ≤ 157.13 (green vertical line) and 20.19≤ y+ ≤ 309.6 (red vertical line), for the lower and higher reτ datasets respectively. the mean velocity (u+) of the spiv experimental dataset at both the reynolds numbers shows a good agreement that of the dns datasets. figure 3 shows the comparison of variances computed from individual systems and denoised with that of dns datasets at nearest reτ. it is observed that the statistics of both the individual piv systems and denoised version from reτ = 2220 follows that of the dns at reτ = 1989 [borrell et al. (2013)]. however, as the wall 100 101 102 103 0 10 20 y+ u+ piv (reτ = 2220) piv (reτ = 3840) dns (reτ = 1989) dns (reτ = 4200) figure 2: comparison of average streamwise velocity normalised with inner co-ordinates u+ from the present piv experiments at reτ = 2220 and 3840 with dns datasets of tcf at reτ = 1989,3000,4200. the green vertical line shows the range of wall-distances for piv experiment with reτ = 2220, and the red vertical line shows the range of wall-distances for piv experiment with reτ = 3840 is approached one can observe that only the denoised statistics tend to follow that of dns down to y+ = 10. this result shows the advantages of using two spiv systems with the order of spatial resolution in present experiment for accurate measurement near the wall. the spiv with higher reτ = 3840 does approximately follow that of dns of tcf at reτ = 4200 [hoyas and jiménez (2008)] for u′, v′ and u′v′, and there is some discrepancy for w′. it is clear that the noise is very low in the present experiment, with the exception for the w component it is difficult to distinguish the noise. figure 4 gives a field of an estimation of rms value of the noise associated with the two systems for the streamwise component in pixels. it is observed that with the exception on the left side of the fields and near the wall, the noise is of the order of 0.06-0.08 px. the higher value on the left side is probably linked to a problem of vector validation at the border. figure 5 shows the same parameter but averaged along x for both spiv systems in pixels for reτ = 2220. the noise of the two systems stay under that 0.06 px which is remarkable. it is compared with the model of george and stanislas (2020) (denoted as ‘estimation george’) which is able to estimate the noise by taking into account the pixelisation error and the fluctuation of particle positions in the interrogation window due to the local turbulence. this noise from ‘estimation george’ is given by : σth = √ 1 n ( 〈u′21 〉vol + ∆2 12 ) w1(uδt) (5) where the first part of the right hand side of the equation correponds to the velocity fluctuation inside interrogation volume and the second part corresponds to the pixelisation error (∆ = 0.5) and n is the number of particles in the interrogation window. it is also compared with an estimation from spectral analysis as in foucaut et al. (2004) at distances of 45+ and 100+. the noise from george and stanislas (2020) is smaller compared to the noise from the present spiv experiment, which therefore shows that other sources of noise needs to be accounted in addition to the pixelisation error and fluctuation of particle positions. this model does not take into account other source of noise such as isolated particles or gradient in the interrogation window. the estimation from the spectra [foucaut et al. (2004)] is approximately of the same order as the noise estimated from the experiments. the spectra of the two systems and the subsequent noise estimation from them are very similar and of the same order as predicted by equation 4. figure 6 shows the dissipation which is composed by a sum of variances of spatial derivative of velocity, 101 102 4 6 8 10 y+ u′ 2 + 101 102 0 0.5 1 y+ v′ 2 + 101 102 1.5 2 2.5 3 y+ w ′2 + 101 102 −1 −0.5 0 y+ u′ v′ + figure 3: comparison of variances and covariances of streamwise, wall-normal and spanwise velocity components in the present piv experiments at reτ = 2220 and 3840 with dns of tcf datasets at reτ = 1989,3000 and 4200 200 100 0 100 200 x + 50 100 150 y + piv system 1 200 100 0 100 200 x + 50 100 150 piv system 2 figure 4: noise associated with spiv sys1 (left) and sys2 (right) in pixels obtained with individual system and denoised by the two systems. the derivatives are computed by a least squared method [foucaut and stanislas (2002)] which is based on second-order central difference scheme and is optimized to not amplify the noise. the missing variance of derivatives are obtained by the assumption of axisymmetry (see george and hussein (1991)). we can see the noise which is very small except close to the wall, and the effect of filtering for the highest reynolds number. this allows to evidence the filtering effect of piv for the highest reynolds number [atkinson et al. (2014)] which is mainly visible in the dissipation rate. the assumption of axisymmetry works down to y+ = 25 for the spiv experiment at figure 5: noise associated with spiv sys1, sys2 in pixels, compared with the noise estimation of george and stanislas (2020), and that of estimation from spectra foucaut et al. (2004) 101 102 0 5 ·10−2 0.1 0.15 0.2 y+ d + piv sys1 (reτ = 2220) piv sys1 (reτ = 3840) 15ν( du dx ) 2 (reτ = 2220) piv sys2 (reτ = 2220) piv sys2 (reτ = 3840) 15ν( du dx ) 2 (reτ = 3840) piv denoised(reτ = 2220) piv denoised(reτ = 3840) dns−t bl(reτ = 1989) figure 6: comparison of dissipation computed from individual piv systems 1, 2 and denoised at reτ = 2220 and 3840 with dns of tbl datasets at reτ = 1989. vertical green line shows the limit of axisymmetric assumption in the computation of dissipation reτ = 2220 which follows the explanation in foucaut et al. (2020). figure 7 shows the effect of denoise on the streamwise derivatives of two velocity components obtained from spiv experiment at reτ = 2220. it is observed for ( ∂u′ ∂x )2 + , the difference between the individual systems and that of denoised version are significant as the wall is approached, when y+ ≤ 25. and for ( ∂v′ ∂x )2 + , the difference between the denoised and individual system is small despite the denoised value being lower than that predicted by individual systems. so this method of denoising has the ablity to obtain accurate statistics especially near the wall. 101 102 0 0.5 1 1.5 ·10−2 ( ∂u′ ∂x )2 + 101 102 0.5 1 1.5 2 ·10−3 ( ∂v′ ∂x )2 + piv sys1 piv sys2 piv denoised figure 7: effect of denoise on the derivatives of streamwise and wall-normal velocities at reτ = 2220 3 conclusion a method to denoise the statistics of turbulent flow is proposed in the present paper. this method is based on the use of two independant piv systems. it allows the computation of the noise level of the order of 0.06 px. the derivative tends to amplify the noise (see foucaut and stanislas (2002)). this method allows also to denoise variances of velocity derivatives such as the terms of the dissipation rate. by using two different spatial resolutions we evidence that if the interrogation window size is of the order of 8 px it is possible to compute these dissipation with a very good accuracy. if the interrogation window size increases (doubled here) the filtering effect of piv is strongly observed in this parameter. if the interrogation window size is smaller than 4 kolmogorov length scale which is about 2 wall units, the dissipation will be computed with a good accuracy. acknowledgements this work was carried out within the framework of the cnrs research foundation on ground transport and mobility, in articulation with the elsat2020 project supported by the european community, the french ministry of higher education and research, and the hauts de france regional council. references adrian rj, meinhart cd, and tomkins cd (2000) vortex organization in the outer region of the turbulent boundary layer. journal of fluid mechanics 422:1–54 atkinson c, buchmann na, amili o, and soria j (2014) on the appropriate filtering of piv measurements of turbulent shear flows. experiments in fluids 55:1–15 borrell g, sillero ja, and jiménez j (2013) a code for direct numerical simulation of turbulent boundary layers at high reynolds numbers in bg/p supercomputers. computers & fluids 80:37–43 foucaut jm, carlier j, and stanislas m (2004) piv optimization for the study of turbulent flow using spectral analysis. measurement science and technology 15:1046 foucaut jm, coudert s, stanislas m, and delville j (2011) full 3d correlation tensor computed from double field stereoscopic piv in a high reynolds number turbulent boundary layer. experiments in fluids 50:839– 846 foucaut jm, george wk, stanislas m, and cuvier c (2020) velocity derivatives in a high reynolds number turbulent boundary layer. part iii: optimization of an spiv experiment for derivative moments assessment. arxiv preprint arxiv:201009364 foucaut jm and stanislas m (2002) some considerations on the accuracy and frequency response of some derivative filters applied to particle image velocimetry vector fields. measurement science and technology 13:1058 george wk and hussein hj (1991) locally axisymmetric turbulence. journal of fluid mechanics 233:1–23 george wk and stanislas m (2020) on the noise in statistics of piv measurements. arxiv preprint arxiv:201010768 herpin s, stanislas m, foucaut jm, and coudert s (2013) influence of the reynolds number on the vortical structures in the logarithmic region of turbulent boundary layers. journal of fluid mechanics 716:5 hoyas s and jiménez j (2008) reynolds number effects on the reynolds-stress budgets in turbulent channels. physics of fluids 20:101511 wieneke b (2008) volume self-calibration for 3d particle image velocimetry. experiments in fluids 45:549– 556 introduction experimental setup conclusion 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 using differential phase for 3d localization of tracer particles in digital inline holographic microscopy piv/ptv (dihm-piv/ptv) a. ahmed1∗, b. sun1, v. j. cadarso2, j. soria1 1 laboratory for turbulence research in aerospace & combustion (ltrac) 2 applied micro and nanotechnology lab (amntl) department of mechanical and aerospace engineering, monash university (clayton campus), vic 3800, australia ∗ asif.ahmed@monash.edu abstract digital inline holographic microscopy piv/ptv (dihm-piv/ptv) has the ability to provide 4-dimensional (4d), i.e. time-resolved, 3-component 3-dimensional (3c-3d) flow measurement with high spatial and temporal resolution, compact optical setup and minimal calibration sun et al. (2020) compared to most other volumetric techniques such as tomo-piv, defocusing piv, etc. despite all these advantages dihmpiv/ptv has not yet developed into a standard laboratory tool due to some major limitations such as the extended depth-of-focus (dof) problem and the virtual image effect which cause artefacts in the standard reconstruction volume limiting the seeding concentration and thus the achievable velocity spatial resolution. in order to mitigate the above-mentioned limitations we present a novel particle localization and extraction methodology which allows the minimization of these artefacts from the standard reconstruction and perform piv/ptv analysis on the particle volume fields only. the proposed algorithm is based on the differential phase, which is the axial phase shift of the object wave compared to the reference plane wave propagation. when micron-sized dielectric spheres are used as seeding particles (e.g. 1 µm polystyrene microsphere in the present study) illuminated with a plane reference wave, a spatially strong confinement of the electromagnetic field, known as a photonic nanojet heifetz et al. (2009), is observed on the shadow side of the particle as a result of mie scattering of the incident wave from the isolated microspheres. this spatial light confinement does not occur exactly at the centre of the microparticles and is observed at a certain axial distance from the centre that depends on the numerical aperture of the imaging system. this phenomenon makes it very challenging to determine the axial location of the seeding particles from the intensity of the reconstruction volume. however, due to this spatial light confinement the object wave goes through a transition from a converging to a diverging wavefront and thus, a transition from positive to negative differential phase, which can be easily obtained from the phase of the complex reconstruction volume. this phase change has been exploited in the present study to localize the seeding particles within the reconstruction volume and extract the particle fields eliminating all the artefacts. rigorous numerical simulations have been carried out using mie scattering theory including the effect of limited numerical aperture of the imaging system to generate synthetic holograms ahmed et al. (2020). the reconstruction volume obtained from the synthetic hologram shows excellent agreement with the one obtained from experiment, verifying the evolution of the photonic nanojet and transition in differential phase within the reconstruction volume. a flowchart of the proposed methodology for hologram processing and extracting the 3d particle field from the reconstruction volume for piv/ptv analysis is shown in fig. 1. first, we calculate a background image from a sequence of recorded holograms. then we use the background image to preprocess the raw recorded hologram that yields two new holograms, namely, the object hologram (using background subtraction) and the normalised hologram (using background division). background subtraction removes the dc reference wave from the raw hologram and therefore, the reconstruction volume generated using the object hologram will only have the scattered object field. thus, the object hologram is used to reconstruct the intensity volume which is then used to determine the (x,y) positions and diameter of the particles within the volume. however, this intensity volume does not provide the accurate z position of the seeding particles due to the above-mentioned fact that the peak intensity of the particle occurs at an axial distance away from the median image calculation recorded hologram background object hologram normalised hologram isolate object term division by background intensity volume differential phase volume measure (x, y) position and diameter measure z position collate centroid position and radius segment particles for piv/ptv figure 1: flowchart of the proposed methodology for hologram processing and extracting the 3d particle field for piv/ptv analysis particle centre because of the evolution of the photonic nanojet. hence, the normalised hologram is used to reconstruct the differential phase volume which is used to determine the z position of the seeding particles. background division improves the snr of the hologram, however, it does not remove the dc reference wave. therefore, the resulting reconstruction volume generated using the normalised hologram has both the reference wave, as well as the scattered object wave. as a result, the constructive and destructive interference of these two waves causes the change in differential phase which allows the determination of the accurate z position of the seeding particles. in this new proposed method, the differential phase volume obtained from the experimental hologram is cross-correlated with the one is obtained from the simulated hologram of known particle position for the accurate localization of the seeding particles in the axial direction. finally, the (x,y) positions and the diameter obtained from the intensity volume and the z position obtained from the differential phase volume are used to yield the entire particle fields. once a sequential pair of 3d volumes with particle fields is reconstructed these can be analysed using 3d cross-correlation analysis or a hybrid cross-correlation piv/ptv to reveal the 3c-3d fluid velocity field soria et al. (2014). acknowledgements this research was supported by the australian government through the australian research council’s discovery projects funding scheme. asif ahmed gratefully acknowledge the support through an australian government research training program (rtp) scholarship. references ahmed a, sun b, cadarso v, and soria j (2020) 3d localization of the tracer particles in digital inline holographic microscopy piv/ptv: do the bright regions in the intensity reconstruction volume really correspond to the tracer particles?. bulletin of the american physical society heifetz a, kong sc, sahakian av, taflove a, and backman v (2009) photonic nanojets. journal of computational and theoretical nanoscience 6:1979–1992 soria j, atkinson c, and buchmann n (2014) hybrid piv-particle tracking technique applied to high reynolds number turbulent boundary layer measurements. in 67th annual meeting of the aps division of fluid dynamics, san francisco, united states, nov. 23-25. sun b, ahmed a, atkinson c, and soria j (2020) a novel 4d digital holographic piv/ptv (4d-dhpiv/ptv) methodology using iterative predictive inverse reconstruction. measurement science and technology 31:104002 microsoft word ispiv_final abstract_miraekim_rev.docx volumetric lagrangian particle tracking measurements of jet impingement on convex cylinder mirae kim1, daniel schanz2, matteo novara2, andreas schröder2, eunseop yeom1, kyung chun kim1 1school of mechanical engineering, pusan national university, 46241 busan, south korea 2institute of aerodynamics and flow technology, german aerospace center (dlr), 37073 göttingen, germany impinging jets are widely used for heat and mass transfer because they are applicable to any type of body and can be easily implemented. they are also used in various industrial fields and design techniques. previous research investigated e.g. a jet impinging onto a flat surface. however, since most of the mechanical parts have curvature on their surface, it is necessary to study more detailed properties of the jet impinging on a curved surface using advanced measurements. therefore, in this study, three-dimensional flow structures of a round jet impinging on a convex cylinder surface were measured using volumetric lagrangian particle tracking (lpt). the experimental setup is shown in fig 1. the measurement model was a circular cylinder (d = 52 mm) and a round jet nozzle (d = 3 mm), which was inserted into a 16-faces glass water tank. oragasol polyamide particles with a mean diameter of 40 μm was used as seeding particles. four phantom v2640 high speed cameras were used to capture particle images, operated at 4 khz. for the volume illumination two arrays of high-power white leds were used and focused by two large 1,000 mm focal length lenses. finally, rectangular passe-partouts limited the common illuminated volume to about 80 × 160 × 50 mm3. impingement angles (α) of the jet were 0 and 45 degrees, the distance between the jet and the cylinder surface was fixed at 12 mm, and the reynolds number based on the jet diameter was 17,875. the measuring area consists of half of the lateral cylinder and the wake area below the cylinder. in order to improve experimental accessibility, the field of view was moved 10 mm in the x direction in the case of an impingement angle of 0° (see fig. 1). optical calibration of the imaging system was required to accurately triangulate the position of particles from all 2d images to 3d space. a two-plane calibration plate was placed in the cylinder position. geometrical calibration was refined using volume self-calibration [1] and calibration of the optical transfer function [2]. lagrangian particle tracking process was performed based on the variable time-step shake-the-box (vt-stb) algorithm (see [3, 4] or schanz et al. ispiv 2021), due to the high dynamic velocity range. the method showed distinct advantages in the reduction of ghost tracks and tracking accuracy over standard processing. using the flowfit-algorithm [5], the unstructured particle data containing position, velocity and acceleration is interpolated onto a structured grid of cubic b-splines with 0.7 mm spacing, while applying physical regularizations. the resulting continuous 3d function is sampled on a 3d cartesian grid with 0.42 mm step width. the lagrangian tracks and assimilated time-resolved 3d3c velocity and pressure fields confirmed that the curved wall jet spreads widely in spanwise direction after impingement, then merges to the jet centerline more downstream (fig. 2). three-dimensional entrainment occurs around the curved wall jet. an impinging jet flow with α=45° along the cylinder wall shows the coanda effect with a separation delay at a cylindrical angle of about 180°. however, for an impinging jet flow with α = 0°, flow separation occurs quickly and the flow takes the form of a concentric circle. the ensemble-averaged 3d flow fields near the cylinder wall are shown in fig. 3. along the streamwise wall jet flow, the streamwise vorticity was nearly zero because the attached curved jets no longer spread laterally, and were completely randomly generated even in the presence of a streamwise vortex structure in the instantaneous flow field. since the lateral momentum flux is relatively low compared to the streamwise momentum flux, the gap between the vortex pair structures when α = 45° is closer than that of α = 0°. the shape of the mean spanwise vorticity structure appeared in a semicircle at α = 0°, and a v-shape at α = 45°. the mean velocity distributions on the cylinder surface can be compared with the cooling area of the surface temperature field results in kim et al. [6]. white leds lens four high speed cameras α=45° α=0° cylinder jet fig. 1 left: experimental setup for volumetric lpt measurements, middle: submerged cylinder and jet nozzle, right: field of view schematic in side view (xy plane) with blue dashed line at α = 45° and green dashed line at α = 0° (b) α = 45°(a) α = 0° fig. 2 instantaneous lagrangian particle tracks and q structures (10,000 s-2) colored by v-velocity on convex cylinder (a) α = 0° (b) α = 45° ωxd/ujet: 2 0 -2 ωzd/ujet: 2 0 -2 1.2 0.6 0 u [m/s]: ωxd/ujet: 2 0 -2 ωzd/ujet: 2 0 -2 1.2 0.6 0 u [m/s]: fig. 3 ensemble-averaged streamwise and spanwise vortex structures and mean velocity distributions on cylinder surface references [1] wieneke, b. (2008) volume self-calibration for 3d particle image velocimetry. exp. fluids, 45(4), 549-556. [2] schanz, d., gesemann, s., schröder, a., wieneke, b., & novara, m. (2012) non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. meas. sci. technol., 24(2), 024009. [3] schanz, d., gesemann, s., & schröder, a. (2016) shake-the-box: lagrangian particle tracking at high particle image densities. exp. fluids, 57(5), 70. [4] schanz d., novara m. & schröder a. (2020) shake-the-box particle tracking with variable time-steps in flows with high velocity range (vt-stb). 3rd workshop on da & cfd processing for piv and lpt. [5] gesemann, s., huhn, f., schanz, d., & schröder, a. (2016, july) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th lxlaser, lisbon, portugal (pp. 4-7). [6] kim, m., kim, d., yeom, e. (2020) measurement of three-dimensional flow structure and transient heat transfer on curved surface impinged by round jet. int. j. heat mass transfer 161, 120279. acknowledgements this work was supported by the national research foundation of korea(nrf) grant funded by the korea government(msit) (no. 2021r1c1c2009287). this work was partly supported by the deutsche forschungsgemeinschaft (dfg) through grant no. schr 1165/5-1 as part of the priority programme on turbulent superstructures (dfg spp 1881, 2nd period). mytitle 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 hilbert transform revisited – proper orthogonal decomposition applied to analytical signals of flow fields jochen kriegseis1∗, matthias kinzel2, holger nobach3 1 institute of fluids mechanics (istm), karlsruhe institute of technology (kit), karlsruhe, germany 2 blacksky, spaceflight industries, seattle, wa, usa 3 max planck institute for dynamics and self-organization, göttingen, germany ∗ kriegseis@kit.edu abstract the modes delivered by proper orthogonal decomposition (pod) are uncorrelated as per definition; but interestingly, they are not necessarily independent in terms of spatio-temporal flow-pattern dynamics. for instance, periodic structures that travel as waves through a series of snapshots often consist of pairs of modes with harmonic functions shifted 90 degree in phase and/or a spatial offset by a quarter of the spatial wave length of the convective flow pattern. identification of such pairs, however, largely builds upon experience, visual inspection and/or the analysis of the reconstructed coefficients in cyclograms (lissajous figures). this effort becomes even more challenging if measurement noise or other spurious information contaminates the raw data under consideration. one possibility to automatically pair corresponding patterns with common pod algorithms is the immediate application of the pod method to complex data (see pfeffer et al., 1990). as outlined by horel (1984), the hilbert transform is a well-known and straight forward means to obtain the required extension of the original signal with an appropriate 90 degrees phase shift, which is independent of the fundamental frequencies. the complex extension of the original (real) signal xi and its (discrete) hilbert transform ht{xi} as the imaginary part xi + iht{xi} with the imaginary unit i is commonly known as the so-called analytical signal. when applied to a given data set as a preparation step to a subsequent snapshot pod analysis (sirovich, 1987), each property of the data at hand can be converted into a complex analytical signal in time. the complex extension based on the hilbert transform then applies along the snapshots direction for each point in space and for each component per spatial location individually. since the hilbert transform is the only modification of the original data which then undergoes the complex, but otherwise usual snapshot pod analysis, the proposed method will be abbreviated and referred to as hpod below. the results of the hpod are comprised of real eigenvalues and corresponding complex modes. note that the analytical signal obtained by the hilbert transform cannot increase the information content of the input data, i.e. the original data and the complex extended data have identical information. therefore, also the result of the modal decomposition by hpod contains equivalent information. however, the complex modes can combine the pairs of coupled modes to single complex modes. these complex modes, therefore, uniquely capture amplitude and phase of both spatial and temporal evolution of moving flow patterns (barnett, 1983), which can also uncover the phase drift for traveling wave structures, for instance. the major advantage, consequently, is a straight forward interpretation of the different modes, which moreover becomes largely independent of expertise and subjectivity. interestingly enough, the hpod approach remains as yet only rarely applied in fluid mechanics – despite these obvious advantages. the purpose of the present work, therefore, centers around a thorough elaboration of the hpod capabilities for an advanced analysis of flow-field information. in order to evaluate both advantages and limits of the hpod approach, three different tow-dimensional (2d) test cases are chosen, each of which is known to be dominated by periodic (oscillatory) convection of flow patterns. to demonstrate the independence of the analytical signal from the number of considered properties per spatial location, single-, twoand three component flow fields (1c,2c,3c) have been considered – random snap shots of all three test cases are shown in figure 1 for introductory purposes. to furthermore mimic temporally undersampled data, arbitrarily ordered snap shots have also been applied to the hilbert transform prior to the subsequent hpod application. mailto:kriegseis@kit.edu (a) burning candle 0 0.5 1 1.5 2 2.5 3 3.5 4 x/λ 0 0.2 0.4 0.6 0.8 y /λ (b) discharge-based stokes layer ω neg 0 pos o u t o f p la n e m o ti o n (c) side-channel flow figure 1: random snapshots of the measured flow fields under consideration: (a) 2d1c data: schlieren images in proximity of a flickering candle (data from laier, 2015), the white box indicates the range of interest (roi) for the present study; (b) 2d2c data: phase-resolved planar piv fields above an oscillatory operating plasma-actuator array (data from hehner et al., 2019); (c) 2d3c data: time-resolved stereo piv data in the side channel of a regenerative pump (data from mattern et al., 2017) . the comparison of hpod results with standard pod successfully demonstrates that the desired automatic identification of pairs of corresponding patterns is possible when applied to the analytical signal of the raw data, where two related pod modes are combined in a single complex hpod mode. the histories of reconstructed coefficients furthermore suggest that the analytical signal of the hilbert-transformed raw data keeps it’s helical character across intensity fluctuations, frequency sweep and spurious noise contributions of the respective dynamics. this insight holds for singleand multi-component data sets and does not suffer from low signal-to-noise ratios. furthermore, the artificially undersampled data sets lead to arbitrary imaginary patterns, yet preserve the salient modal patterns in the real part of the eigenvectors. this insight leads to the conclusion that an hpod application to undersampled data effectively only reduced to quasi-standard pod results, but still reveals meaningful information in the classical pod sense. as a final remark, the above insights and conclusions indicate that the hilbert-transform based conversion of raw data to an analytical signal is an advantageous additional robust and straight forward preprocessing step to advance beyond the classical pod method. the simplicity of this modification renders the hpod a promising decomposition option for periodical and/or fluctuating flow scenarios. references barnett tp (1983) interaction of the monsoon and pacific trade wind system at interannual time scales part i: the equatorial zone. monthly weather review 111:756–773 hehner mt, gatti d, and kriegseis j (2019) stokes-layer formation under absence of moving parts—a novel oscillatory plasma actuator design for turbulent drag reduction. physics of fluids 31:051701 horel jd (1984) complex principal component analysis: theory and examples. journal of climate and applied meteorology 23:1660–1673 laier m (2015) schlieren investigations into weak density gradients. bachelor’s project, institute of fluid mechanics, karlsruhe institute of technology mattern p, gabi m, and kriegseis j (2017) a plane-to-plane comparison of common averaged vs. pod patterns of time-resolved stereo-piv data within a pump. european journal of mechanics–b/fluids 61:321– 329 pfeffer rl, ahlquist j, kung r, chang y, and li g (1990) a study of baroclinic wave behavior over bottom topography using complex principal component analysis of experimental data. journal of the atmospheric sciences 47:67–81 sirovich l (1987) turbulence and the dynamics of coherent structures part i: coherent structures. quarterly of applied mathematics 45:561–571 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 1 eulerian time-marching in vortex-in-cell (vic) method: reconstruction of multiple time-steps from a single vorticity volume and time-resolved boundary condition y. j. jeon lavision gmbh, göttingen, germany yjeon@lavision.de abstract a data assimilation approach is proposed to enhance the dynamic range of the vortex-in-cell (vic) method by simulating futureand pastinstances. the vic method mainly considers a vorticity field from which velocity and acceleration fields are calculated through poisson equations, respectively bounded by prescribed conditions. in addition, a vorticity time derivative is also available by the vorticity transport equation. the proposed approach focuses on such already available data, i.e., the vorticity and its time derivative fields, for simulating additional instances and getting feedbacks from the corresponding measurement instances, e.g., particle image velocimetry (ptv). however, the self-simulated flow field can be depleted due to a lack of incoming information, which is out of the reconstruction domain at the source instance. to supply that kind of information and thus sustain the simulation, boundary conditions of the simulated instances are required and considered. as a result, the proposed approach can gather corrections from multiple ptv instances while optimizing a single vorticity volume and time-resolved boundary conditions. since the boundary grid points are much smaller in number than that of the whole volume, one can expect an increased dynamic range. a former work, vic# (jeon et al. 2018), which supplements additional constraints and coarse-grid approximation to vic+ (schneiders and scarano 2016), is selected as a 3d method to which the proposed 4d approach is applied. two explicit eulerian time-marching methods are tested as a simulation scheme: the forward euler and the runge-kutta methods. a numerical assessment is conducted using the synthetic ptv data, whose ground truth is known, and returns reconstruction qualities based on the velocity and the identified vortical structures. other practical features regarding convergence and computation complexity are also reported. to visually verify an improvement by the proposed approach, two kinds of time-resolved shake-the-box (stb) measurements, which were acquired in high-speed systems, are processed and discussed. 1 introduction three-dimensional particle trajectory velocimetry (ptv) (malik et al., 1993) can provide individual particle information with higher spatial resolution than correlation-based volume analysis (elsinga et al., 2006). shake-the-box (stb, schanz et al., 2016) has recently achieved accurate and ghostless reconstruction of lagrangian particle tracks under highly seeding conditions employing an iterative particle reconstruction (ipr, wieneke, 2012). however, because resulted data is randomly distributed, its conversion onto a regular grid is generally favorable to researchers for further analysis. to use binning to sample nearby particles at each grid point, e.g., the adaptive gaussian windowing technique (agw, agüí and jimenez, 1987), would be the simplest way but returns a spatially averaged result. such approaches have advanced to data assimilation, which considers flow physics. using a solenoidal to optimize flow field while enforcing mass conservation (schiavazzi et al., 2014; azijli and dwight, 2015) has shown that data assimilation can reduce measurement noise while keeping the spatial resolution. a new methodology, which solves an optimization problem based on the governing equations, i.e., navier-stokes and continuity, has been introduced by flowfit (gesemann et al., 2016) and also by vortex-in-cell-plus (vic+, schneiders and scarano, 2016). here, the optimization variable denotes amplitudes of each basis function from which physical flow variables are derived. as a basis function, flowfit and vic+ employ third-order b-splines and a gaussian-based radial basis function (rbf), respectively. for both methods, disparities between ptv input and the reconstruction constitute a principal cost function to be minimized. in addition, flowfit simultaneously minimizes the cost functions obtained from the governing equations. in contrast, because vic+ is based on the vortex method (christiansen, 1973), the continuities of velocity and acceleration are inherent. the time-derivative terms in vic+ are evaluated through the vorticity transport equation after invoking the navier-stokes equation. vic# (jeon et al., 2018) is based on vic+ and, at the same time, employs the cost functions from flowfit. besides, a coarse grid approximation is introduced to eliminate the necessity of an initial velocity field in vic+ and thus enables vic# to start from zeros and to generate initial conditions for finer grids autonomously. recently, both flowfit and vic+ are expanding their scope of considerations to temporal coherency between reconstructed instances. flowfit generates virtual trace particles from a physically valid reconstructed instance and advects them for 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 2 spatially enriching a subsequent instance (ehlers et al., 2020), and vic+ adopts time-segment assimilation to conduct vorticity time-marching (gonzález et al., 2019). both methods have shown that the added temporal coherency in the lagrangian frame improves reconstruction quality. the vortex method can derive spatially smooth enough flow variables, including a vorticity time derivative. simulations of vorticity fields in future and past instances under inviscid flow conditions are therefore feasible. here, the viscosity is only considered in pressure evaluation. schneiders et al. (2014) have exploited this feature for super-sampling double-pulse piv measurement using advected vortex particles. instead of such lagrangian vortex particles, the present study focuses on the flow variables themselves in eulerian fashion. the eulerian time-marching is relatively simple to produce simulated instances and thus requires less effort to retrieve feedback from them through the adjoint approach (gronskis et al., 2013). the boundary conditions in vic+ and vic#, which are essential to produce both velocity and acceleration fields, are literally outside of a measured particle cluster and have extrapolated nature. even though vic# corrects them employing the additional constraints based on flow physics, they have no potential to simulate themselves, and thus, both velocity and acceleration boundaries must be optimized in the simulated instances. vic# can be repeated on the simulated instances until it reaches both ends of the time domain. as a result, the present approach reconstructs multiple instances simultaneously while optimizing a single vorticity volume and time-resolved boundary conditions regarding velocity and acceleration. therefore, improved reconstruction quality can be expected as the number of reconstructed instances increases until it is overwhelmed by an accumulated numerical truncation, which is inevitable in the explicit time-marching. in this study, not only the forward euler method but also the runge-kutta method is adopted. both marching methods are verified in terms of reconstruction qualities concerning velocity and identified vortical structures. the computation cost regarding time and memory are reported. two time-resolved stb measurements, which were acquired under high-speed systems, are processed by the 3d method (vic#) and the proposed 4d approach, and their results are qualitatively compared. 2 method the present approach evenly simulates future and past instances and thus simultaneously reconstructs an odd number (𝐿) of instances by referring to the corresponding ptv instances. an optimization variable is made up of two parts: 3d, identical to the 3d approach (vic+ and vic#), and 4d, consisting of time-resolved boundary conditions regarding velocity and acceleration for the simulated instances. it can be expressed as: 𝛏4d(𝑡0, 𝐿) = {𝛏3d(𝑡0), 𝛏4d(𝑡0, 𝐿)} = {𝛏𝛚(𝑡0), {𝛏𝜕𝛀,𝐮(𝑡𝑖)}, {𝛏𝜕𝛀,𝜕𝐮/𝜕𝑡(𝑡𝑖)}} , where 𝑡𝑖 = − 𝐿 − 1 2 ∆𝑇 … 𝐿 − 1 2 ∆𝑇. (1) note that 𝛏3d = {𝛏𝛚 , 𝛏𝜕𝛀,𝐮 , 𝛏𝜕𝛀,𝜕𝐮/𝜕𝑡}, ∆𝑇 is the time interval between successive ptv instances, and the subscription, 𝜕𝛀, denotes that the variable is defined on the boundary. a vorticity field and boundaries of velocity and acceleration are evaluated by applying the gaussian radial basis function (rbf, 𝜙(𝑟) = exp(𝑟2/2.4 ℎ2)) to each element in eq. 1: 𝛚(𝐱) = ∑ 𝛏𝛚,𝑖𝜙(‖𝐱 − 𝐱𝑖‖) 𝛀 , (2a) 𝐮𝜕𝛀(𝐱) = ∑ 𝛏𝜕𝛀,𝐮𝜙(‖𝐱 − 𝐱𝑖‖) 𝜕𝛀 , (2b) 𝜕𝒖 𝜕𝑡 | 𝜕𝛀 (𝐱) = ∑ 𝛏 𝜕𝛀, 𝜕𝐮 𝜕𝑡 𝜙(‖𝐱 − 𝐱𝑖‖) 𝜕𝛀 . (2c) a velocity field and an acceleration field are then obtained by solving the following poisson equations with the prescribed boundary condition: ∇2𝐮 = −∇ × 𝛚 where 𝐮∂𝛀 = constant, (3) ∇2 ∂𝐮 ∂𝑡 = −∇ × ∂𝛚 ∂𝑡 where ∂𝐮 ∂𝑡 | ∂𝛀 = constant. (4) a vorticity time derivative is available from the vorticity transport equation under the inviscid assumption: ∂𝛚 ∂𝑡 = (𝛚 ∙ ∇)𝐮 − (𝐮 ∙ ∇)𝛚. (5) 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 3 a material acceleration and pressure field can be sequentially evaluated. the cost function is then evaluated from the disparities between the reconstruction and the ptv measurement (vic+) and the additional constraint (vic#). figure 1 shows a schematic of the processing chain of vic# for a single instance. figure 1: schematic of a single vic# procedure because vorticity fields at other time steps than 𝑡0 are not included in the optimization variable (eq. 1), they must be obtained explicitly from the reconstruction at 𝑡0, and thus eulerian time-marching is employed: 𝛚(𝑡0 + 𝑡) = 𝛚(𝑡0) + ∫ 𝜕𝛚 𝜕𝑡 (𝑡0 + 𝜏)d𝜏 𝑡 𝑡0 (6) its discrete implementation can be expressed as the forward eulerian method: 𝛚 (𝑡0 + ∆𝑇 𝑀 ) = 𝛚(𝑡0) + ∆𝑇 𝑀 ∂𝛚 ∂𝑡 (𝑡0), (7) where 𝑀 is the time marching frequency defined as 𝑀 = ∆𝑇/𝛥𝑡marching . when 𝑀 > 1 , reconstructions at fractional instances are required, and the corresponding boundary conditions are interpolated, linearly for acceleration and quadratic for velocity. figure 2 illustrates which flow variables are reconstructed in vic# and the proposed 4d approach, respectively. figure 2: comparison of 3d and 4d approaches when l = 5 and m = 2: squares indicate a volumetric flow variable where their outlines are boundaries. dashed lines indicate the interpolations at fractional instances. 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 4 the time marching is conducted forward and backward till the entire reconstructions are completed. at the fractional instances, because only ∂𝛚/ ∂𝑡 is required, only partial computations are required: approximately 6/13 based on the number of poisson equations to solve. a large value of 𝑀 is generally required to suppress an accumulated truncation error due to the explicit nature of the time-marching but also increases the computation time. since the majority of computation time is spent solving poisson equations, the following estimate can be made: (computation time)4d vic# (computation time)3d vic# ≅ 𝐿 + 6 13 (𝐿 − 1)(𝑀 − 1). (8) after the time marching is over, the cost functions at all the available ptv instances are collected. at each ptv instance (𝑡 = (𝐿 − 1)∆𝑇/2 … (𝐿 − 1)∆𝑇/2) , the adjoint procedure in vic# transforms the cost function into the adjoints on the optimization variable. the adjoint procedure is conducted in reverse order of the vic# processing chain illustrated in fig. 1. similarly, in the present 4d approach, the vorticity adjoint at the simulated instance (𝑡 ≠ 0), δ∗𝛚 (𝑡), is transformed into the adjoints at the previous reconstruction instance (𝑡 − ∆𝑇/𝑀): δ∗𝛚 (𝑡 − ∆𝑇 𝑀 ) = δ∗𝛚 (𝑡) (9a) δ∗ ∂𝛚 ∂𝑡 (𝑡 − ∆𝑇 𝑀 ) = ∆𝑇 𝑀 δ∗𝛚 (𝑡) (9b) the adjoint procedures, in vic# and eq. 9, are repeated till all the adjoints are gathered on δ∗𝛚(𝑡0). then, the optimization variables can be updated by using the limited-memory broyden-fletcher-goldfarb-shanno method (l-bfgs, liu and nocedal, 1989). in this study, a prescribed number of l-bfgs iterations is used. the fourth-order runge-kutta method (rk4) is a high order accurate numerical method among the explicit time-marching method. since the rk4 is a combination of multiple euler methods, it can be applied without much difficulty. here the rk4 requires the same computation resource that of the euler method when m = 4. figure 3 illustrates how the sequential computations between two instances are conducted by the euler method and the rk4 method, respectively. 𝛚(𝑡 + ∆𝑇) = 𝛚 (𝑡) + ∆𝑇 4 (𝑘1 + 𝑘2 + 𝑘3 + 𝑘4) 𝛚(𝑡 + ∆𝑇) = 𝛚 (𝑡) + ∆𝑇 6 (𝑘1 + 2𝑘2 + 2𝑘3 + 𝑘4) figure 3: schematics or the euler method when m = 4 (left) and the rk4 method (right) 3 numerical assessment the numerical assessment was conducted using a dataset preliminarily provided by leclaire et al. (2021) at the beginning of the data assimilation challenge campaign (sciacchitano et al., 2021). the dataset is based on les simulation and consists of synthetic ptv data and ground truth. note that this data is not identical to the dataset used in the challenge. two seeding densities, 0.03 and 0.16 particles per pixels (ppp), were provided. the final reconstruction grid scheme was selected as a dimension of 101 × 169 × 101. four grid schemes, i.e., 3 coarse grid schemes + 1 final grid scheme, were sequentially reconstructed during vic# and the proposed approach. in order to impose the wall information, artificial stationary particle tracks were added at each intersection of the wall and the gridlines, orthogonal to the wall. 200 and 300 iterations were conducted respectively for each seeding density case. ratios of averaged changes over the last 20 iterations of the ptv-based cost function (disparities between ptv input and the reconstruction) to the initial one at the final grid scheme, ∆𝐽ptv/𝐽ptv,level=0, were measured as smaller than the criterion 10-6 suggested by vic+ (table 1). 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 5 table 1: ratios of the final change of ptv-based cost functions methods ppp = 0.03 [ × 10-6] ppp = 0.16 [ × 10-6 ] 3d, l = 1 0.0309 0.0360 4d, l = 13, rk4 0.0108 0.0048 the computation was mainly conducted on a tesla v100 gpu card with 5120 cuda cores and 32 gb memory. figure 4 demonstrates the computation complexity in terms of measured computation time and occupied gpu-dedicated memory. the computation time estimated by eq. 8 shows a good agreement with the measured ones (fig. 4a). since the 3d and 4d methods solve the same poisson equations, the corresponding memory reservation is constant for all l (fig. 4b). the increasing memory occupations concerning l are almost linear, and thus, one can estimate a required memory for further computations. note that there would be room for more optimization. figure 4: computation resources for for ppp = 0.16 case. (a) computation time; dotted lines are estimates by eq. 8. (b) occupied memory on gpu; dashed lines denote linear trends. the performances of the 3d (vic#) method and the proposed 4d method were statistically evaluated by using the root-meansquare (rms) error of velocity and the reconstruction quality of vortical structure evaluated from cross-correlation of negative swirling strength, 𝜆2: √ ∑‖𝒖 − 𝒖𝐿𝐸𝑆‖ 𝑁grid points (10) ∑ 𝜆2 ∙ 𝜆2, 𝐿𝐸𝑆(𝜆2<0 ∧ 𝜆2, 𝐿𝐸𝑆<0) √∑ 𝜆2(𝜆2<0) ∙ ∑ 𝜆2, 𝐿𝐸𝑆(𝜆2, 𝐿𝐸𝑆<0) (11) such quantitative analysis is presented in figure 5. when m = 1, i.e., no fractional instance is reconstructed, the performance regresses compared to others due to the accumulated truncation error, especially for the dense seeding case (ppp = 0.16). however, in the lower seeding case (ppp = 0.03), adopting m = 1 still shows the improved statistics until l = 11. it implies that even though the simulated instances are truncated, considering more ptv realizations at other ptv instances is still beneficial under low seeding density conditions. the rk4 method and the euler method with m = 4 show similar performance curves, while rk4 is better at the higher l regime. the euler method with m = 8 was also tested, but its performance is slightly worse than rk4. from these results, one can assume that an optimal combination of l and m, which maximizes the reconstruction qualities, exist. the optimal l and m seem to be closely related to the seeding density and ∆𝑇, respectively. in addition, the effect of the spatial resolution of the grid scheme, i.e., the size of grid spacing, would be a significant factor. the corresponding investigations, however, may remain as further study. 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 6 figure 5: statistical performances for the ppp = 0.03 case (left) and the ppp = 0.16 case (right) figure 6 compares the reconstructed vortical structure for the ppp 0.03 case. the proposed 4d approach reconstructs more structures and connections between them comparing to that from the 3d method. note that a minimum recoverable length scale is larger than the grid spacing, h, due to the spatial basis function (rbf) and the nyquist criterion. it is also encouraging that the selection of small l also shows a visible improvement under the lower seeding density condition comparing to the 3d method. figure 6: vortical structures visualized by iso-surfaces of 𝜆2 = −30000 s−1 for the ppp = 0.03 case: contour indicates the wall-normal velocity component, 𝐮𝑧. statistics based on eqs. 11 and 12 are also provided. 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 7 4 experimental assessment two kinds of time-resolved stb measurement data, acquired from the high-speed measurement systems, were selected to verify the proposed approach by visually checking three-dimensional vortical structures: the circular jet in water, by courtesy of tu-delft (violato and scarano 2011) and the flow under rotating blade of an rc helicopter fixed on the ground, by courtesy of german aerospace center (schanz, schröder and huhn, dlr göttingen), which was measured as an experimental campaign during piv course 2018 in göttingen. the particle images were subjected to stb to reconstruct time-resolved particle tracks to which the data assimilation methods (3d and proposed 4d) are applied. scattered ptv vectors were sampled using a second-order polynomial trajectory. in order to exaggerate input noise, the sampling was conducted over only five ptv instances. table 2 summarizes the measurement conditions and the reconstruction data assimilation parameters for both measurements. table 2: summary of the measurement conditions and the reconstruction parameters water jet (by courtesy of tu-delft) rc-helicopter (by courtesy of dlr) measurement working fluid water air seeding particle polyamide particles helium-filled soap bubble (hfsb) illumination nd-ylf laser led acquisition frequency 1.3 khz 1.8 khz representative speed 0.5 m/s at the nozzle exit whose diameter is 10 mm (red = 5000) 12.5 m/s at the center of blades data assimilation stb sampling 2nd order polynomial over 5∆𝑇 2nd order polynomial over 5∆𝑇 number of tracks (ca.) 10,000 46,000 reconstruction volume 28 × 56 × 28 mm3 362 × 577 × 362 mm3 dimension of grid 61 × 121 × 61 (h = 0.47 mm) 85 × 135 × 85 (h = 4.3 mm) number of iterations 100 200 in the water jet experiment, a vortex ring is generated at the nozzle exit. as the vortex ring travels, its shape gets distorted and finally breaks into minor small structures. figure 7 compares two vortex rings, most stable and most distorted, reconstructed by the 3d method and the 4d approach using rk4 with different selections of l. as l increases, the stable one gets closer to a circular shape, and the most distorted one further restores a tortuous shape with a homogeneous thickness. figure 7: vortical structures in the water jet experiment visualized by iso-surfaces. the entire vortical structure (left) is from rk4 with l = 33. 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 8 moreover, how well the simulated instances represent physical phenomena is also a question. figure 8 compares five instances, which are reconstructed independently by the 3d method and simultaneously by the 4d approach, i.e., four instances other than 𝑡0 from the 4d approach are simulated ones. the simulated results show a good agreement in locations of vortical structures from the 3d method. how the vortex rings are transformed and moved around the jet core are well visualized by the 4d approach. the donut-like small vortex rings shown by the 3d method are caused by the relatively sparse vectors far from the jet core and are disappeared in the 4d approach. the upper half of the domain is filled with vortex fragments that might be from past vortex rings. the vortical fragments in this regime seem to be getting pressed by the incoming vortex ring faster than their bulk speed. the assumption explains why the vortical fragments are getting stronger and thus denser. 𝑡 = 𝑡0 − 16∆𝑇 𝑡 = 𝑡0 − 8∆𝑇 𝑡 = 𝑡0 𝑡 = 𝑡0 + 8∆𝑇 𝑡 = 𝑡0 + 16∆𝑇 3d (vic#) 4d-rk4 l = 33 (present) figure 8: temporal evolution of vortical structures. iso-surfaces share the same criteria as fig. 7; from independent reconstructions by the 3d method (top) and from a single 4d time block by the 4d approach (bottom) for the rc helicopter measurement, the 3d method and the 4d approach with rk4 for l = 33 were applied. in addition, the 3d method with an increased denoising factor of vic#, 𝑓dn = 5.0 (default = 1.0), was also tested, where 𝑓dn plays a role in strengthening the least-square optimization by the pressure poisson equation and thus suppresses spatial velocity fluctuations. the rotating blades generate strong down washing vortices at their tips whose moving direction is changed from vertical to horizontal due to the ground effect. figure 9 shows such curving movement and smaller secondary structures around. the blade tip vortex is twisted by the interaction with the secondary ones and sometimes transformed into the spiral vortex (fig. 9b). the velocity plane near the ground shows an impinging behavior (fig. 9c). in figs. 9b and 9c, even though the selection of increased 𝑓dn shows the smoothed flow structures as expected, the vortical structures cannot be further detailed. on the other hand, the proposed 4d approach can elaborate the vortical structures even further by supplying realizations from other ptv instances. figure 9c emphasis the near-wall vortical structures, color-coded by rotating direction. the large one is a slowly rotating cluster of small structures. the elongated structures in the x-axis with alternating color codes can be regarded as the streamwise vortices and are accelerated by rolling out by the down washing blade tip vortices. 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 9 3d (vic#) 3d (vic#, 𝑓dn = 5.0) 4d-rk4, l = 33 (present) figure 9: vortical structures under the rotating blades of the rc helicopter. iso-surfaces indicate 𝜆2 = −15000 s−1 and contours on planes denote the velocity magnitude, ‖𝐮‖. (a) overall view with boundary vector planes, (b) zoomed images of the spiral blade tip vortex, (c) vector planes and vortical structure near the ground while colors of iso-surface indicate a sign of 𝛚𝒙; red for positive and blue for negative. 5 conclusion a novel approach has been presented for reconstructing velocity fields on a regular grid from ptv measurement, based on the eulerian time-marching vorticity field, which significantly reduces the number of unknowns to be optimized. the timeresolved boundary conditions for velocity and acceleration allow the simulated vorticity field to yield other flow variables (velocity, acceleration, vorticity time derivative, and pressure) by the vortex method. both the forward euler method and the runge-kutta method are implemented as the time-marching scheme. the adjoint procedure for transforming the adjoints from the simulated instances to the source instance is proposed. the numerical analysis reports on the computational complexity with linear behaviors, and thus, it can be said that the optimization problem is well-developed and solved. significant improvement by the proposed approach is observed in both numerical and experimental assessments. the experimental assessment shows that the proposed approach works as expected so that vortical structures can be detailed further. therefore, one can conclude that the expected dynamic range improvement from the reduced number of unknowns is accomplished. the investigation on the optimal time-marching parameters such as the marching frequency (m) and the (a) (b) (c) 14th international symposium on particle image velocimetry – ispiv2021 august 1–5, 2021 10 number of reconstructing instances (l) may remain to be conducted by further studies. in addition, a superposition method should be introduced to obtain a complete time-resolved result set from multiple 4d results because it would significantly reduce computation time and efforts on large time-resolved data sets. acknowledgments this work has participated in the first data assimilation (da) challenge, conducted within the european union’s horizon 2020 project homer (holistic optical metrology for aero-elastic research). the author would like to thank the research groups (onera, tu-delft, and dlr göttingen) for sharing the data. references agüí j and jimenez j (1987) on the performance of particle tracking velocimetry. journal of fluid mechanics 185:447-468 azijli i and dwight rp (2015) solenoidal filtering of volumetric velocity measurements using gaussian process regression. experiments in fluids 56(11), 1-18 christiansen ip (1973) numerical simulation of hydrodynamics by the method of point vortices. journal of computational physics 13(3), 363-379 ehlers f, schröder a and gesemann s (2020) enforcing temporal consistency in physically constrained flow field reconstruction with flowfit by use of virtual tracer particles. measurement science and technology, 31(9), p.094013 elsinga ge, scarano f, wieneke b and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41(6), 933-947. gesemann s, huhn f, schanz d and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in proceedings 18th international symposium on applications of laser and imaging techniques to fluid mechanics gonzález g, sciacchitano a and scarano f (2019). dense volumetric velocity field reconstruction with time-segment assimilation. in proceedings 13th international symposium on particle image velocimetry – ispiv 2019 gronskis a, heitz d and mémin e (2013) inflow and initial conditions for direct numerical simulation based on adjoint data assimilation. journal of computational physics 242, 480–497 jeon yj, schneiders jfg, müller m, michaelis d and wieneke b (2018) 4d flow field reconstruction from particle tracks by vic+ with additional constraints and multigrid approximation. in proceedings 18th international symposium on flow visualization – isfv 2018 leclaire b, mary u, liazun c et al. (2021) first lagrangian particle tracking and data assimilation challenge: datasets description and evolution to an open online benchmark. in 14th international symposium on particle image velocimetry – ispiv 2021 liu dc and nocedal j (1989) on the limited memory method for large scale optimization. math program b 45, 503–528 malik na, dracos t and papantoniou da (1993) particle tracking velocimetry in three-dimensional flows. experiments in fluids 15(4), 279-294 schanz d, gesemann s and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57(5), 1-27 schiavazzi d, coletti f, iaccarino g and eaton jk (2014) a matching pursuit approach to solenoidal filtering of threedimensional velocity measurements. journal of computational physics 263, 206-221 schneiders jfg, dwight rp and scarano f (2014) time-supersampling of 3d-piv measurements with vortex-in-cell simulation. experiments in fluids 55:1692 schneiders jfg and scarano f (2016) dense velocity reconstruction from tomographic ptv with material derivatives. experiments in fluids 57(9) 1-22 sciacchitano a, leclaire b and schröder a (2021) main results of the first data assimilation challenge. in 14th international symposium on particle image velocimetry – ispiv 2021 violato d, scarano f (2011) three-dimensional evolution of flow structures in transitional circular and chevron jets. phys fluids 23:124104 wieneke b (2012). iterative reconstruction of volumetric particle distribution. measurement science and technology, 24(2), 024008 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 gridless determination of aerodynamic loads using lagrangian particle tracks christoph mertens∗, josé l. costa fernández, andrea sciacchitano, bas w. van oudheusden, jurij sodja delft university of technology, faculty of aerospace engineering, 2629hs delft, the netherlands ∗ c.mertens@tudelft.nl abstract the aerodynamic loads on a flexible wing in terms of the surface pressure distribution and the lift force along the span are determined experimentally based on non-intrusive lagrangian particle tracking (lpt) measurements. as the flexible wing deforms under the aerodynamic loads, its deformed shape is first reconstructed based on structural lpt measurements conducted together with the flow measurements in an integrated approach. based on the reconstructed wing shape, flow tracers data are collected along surface normals to evaluate the surface pressure, as well as along elliptic paths around the wing to determine the circulation. the lift force is calculated from the surface pressure by integrating the pressure difference along the chord, as well as from the circulation using the kutta-joukowski theorem. the circulation-based lift results are in very good agreement with reference measurements from a force balance, with differences in the total lift force on the wing of less than 5%. the lift estimation based on the extrapolated surface pressure is consistently lower than the circulation-based lift, by about 10%, due to the limited accuracy of the pressure extrapolation near the leading edge region, where a considerable fraction of the lift is generated. 1 introduction the experimental determination of the aerodynamic loads that act on flexible wings is relevant for aeroelastic research and development activities, in particular for providing reference data to validate numerical aeroelastic models. the situation of aerodynamic loads on highly flexible wings is particularly relevant because these wings can exhibit nonlinear structural behavior, which increases the complexity of the numerical aeroelastic model and as such the need for experimental validation data (dimitriadis (2017)). the installation of pressure sensors to measure the aerodynamic load on such highly flexible wings is difficult, or, depending on the respective design of the flexible wing skin, may even be impossible. it is therefore preferred to determine the aerodynamic loads non-intrusively, which can be achieved by measuring the flow field around the wing and then inferring the aerodynamic loads from these measurements by using the governing equations of the flow (van oudheusden (2013); rival and van oudheusden (2017)). lagrangian particle tracking (lpt) via the shake-the-box algorithm (schanz et al. (2016)) in combination with the use of helium-filled soap bubbles (hfsb) as flow tracers (scarano et al. (2015)) facilitates the performance of volumetric flow field measurements at a relatively large scale, which is required to obtain the aerodynamic loads in the relevant aeroelastic regimes. a further advantage of this technique is that it facilitates the simultaneous characterization of the structural response and the three-dimensional flow topology with an integrated approach, as described in mertens et al. (2021). however, a drawback of the lpt flow field measurements is its relatively poor spatial resolution, caused by the relatively large inter-particle distance, especially when large-scale measurements with hfsb are conducted. a method to mitigate this limitation is to perform a statistical analysis of the lpt data throughout the flow field by ensemble-averaging the track data in time on a cartesian grid (agüera et al. (2016)). a considerable disadvantage of this procedure for the application in a loads determination procedure on flexible wings is that the grid of the flow field does not automatically comply with the deformed shape of the wing, which impedes the loads determination. in this study, it is demonstrated how the particle track data from the lpt measurements of the flow field and the structure can be used to determine the aerodynamic loads on a flexible wing without requiring the additional step of ensemble averaging the lpt flow measurements on a regular grid. an important first step in this approach is the determination of the deformed shape of the wing under the aerodynamic load, which is performed based on the lpt measurements of structural markers. subsequently, two different approaches are considered to determine the aerodynamic load from the flow measurements. in the pressurebased approach, the measured shape of the wing is used to collect lpt data in the flow field along surface normals to find the pressure on the wing surface by extrapolation. in the circulation-based approach, the flow field lpt data is collected on elliptic contours around the wing to determine the lift force across the span. the loads are calculated using relations from potential flow theory, which only require measurements of the velocity, that are directly available from the individual lpt data points. results are compared to reference measurements of the overall lift force across the span from a force balance. 2 experimental procedures 2.1 wind tunnel setup the experiments were conducted in the open jet facility at delft university of technology, which is an open test section, closed return wind tunnel with an octagonal outlet of 2.85m×2.85m. the test object was a highly flexible wing that is similar to the aeroelastic benchmark model design that is described in avin et al. (2021), which can sustain very large deformations, with wingtip displacements of up to 50% of its span width. the wind tunnel was operated at a freestream velocity of u∞ = 18.3m/s, corresponding to a reynolds number of re = 122000 based on the wing chord. optical measurements of the flow and the position of the wing were conducted simultaneously with an integrated measurement approach. a sketch of the flexible wing and a photo of the measurement setup in the wind tunnel are shown in fig. 1. 30 38 .2 5 ø1.5 55 0 100 300 ø10 (a) 𝑈∞ x yz 1 2 3 4 (b) figure 1: experimental model and wind tunnel setup, (a) sketch with dimensions (in millimeter) of the flexible wing and structural markers grid, (b) photo of the experimental setup, 1: flexible wing, 2: highspeed cameras, 3: led illumination units, 4: stream of helium-filled soap bubbles the flexible wing model that is illustrated in fig. 1(a) has a chord length of c = 100mm and a span width of s = 550mm with a naca 0018 airfoil section. the wing structure is a 3d printed nylon 12 chassis, with a mounting base and a 300mm long tip rod, and an aluminum 7075 spar with a thickness of 1.5mm that is bonded to the chassis using loctite 495 glue. the wing skin is made out of black oralight polyester foil. structural measurements of the wing were performed by tracking reflective markers on the surface. for this purpose, white circular markers with a diameter of 1.5mm were painted on the wing surface using a laser-cut mask, markers were painted on the tip rod and at the spanwise locations of the ribs, which have a spacing of 38.25mm, with a chordwise spacing of the markers of 30mm. as visible in fig. 1(b), the wing was mounted vertically in the wind tunnel test section. it was mounted on a six-component force balance that was connected to a rotating table, which was used to set the geometric angle of attack α of the wing. in this study, two different angles are investigated, α1 = 5° and α2 = 10°, and force measurements acquired with the balance are used as a reference for the aerodynamic loads that are determined based on the optical lpt measurements. the optical measurement system that is shown in fig. 1(b) consists of three photron fastcam sa1.1 high-speed cameras with a sensor size of 1024× 1024 pixels and an image sampling rate of 5.4khz. the flow measurements were performed using helium-filled soap bubbles (hfsb) as tracer particles (scarano et al. (2015)). the hfsb were produced with a seeding generator that is placed in the settling chamber of the wind tunnel, upstream of the contraction of the wind tunnel nozzle. the seeding generator consists of 200 bubble-producing nozzles distributed over an area of 500mm×1000mm. the working principle of the bubble-producing nozzles is described in faleiros et al. (2019). the resulting hfsb seeding concentration was around 1cm−3. the hfsb flow tracers were illuminated with three lavision led-flashlight 300 modules, and the image acquisition and processing were performed with the lavision davis 10 software. 2.2 data acquisition and processing the data acquisition and processing to obtain the lpt measurements of the flow and the structure closely follows the procedure of the integrated measurement approach described in mertens et al. (2021). this procedure begins with the optical calibration of the system by performing a volume self-calibration (wieneke (2008)) and generating an optical transfer function (schanz et al. (2013)). afterward, the integrated flow and structural measurements are separated, as illustrated in fig. 2. optical measurements of the flow tracers and the structural markers are acquired by the cameras, as shown in fig. 2(a). to obtain the isolated information of only the flow or the structure, temporal filters are applied to the time series of the images; the application of a temporal high pass filter produces the isolated flow tracers information (sciacchitano and scarano (2014), see fig. 2(b)), and a temporal low-pass filter produces the isolated structural information (mitrotta et al., see fig. 2(c)). afterward, the lpt measurements of the structure and the flow are generated by applying the shake-the-box algorithm (schanz et al. (2016)) to the separate image data sets. (a) (b) (c) figure 2: image data processing procedure: (a) integrated optical measurement of flow and structure, (b) image data of the flow tracers, (c) image data of the structure the size of the measurement volume that was achieved with the optical measurement setup was around 27 liters (300mm× 300mm× 300mm), although part of this volume was obstructed by the presence of the wing, such that the lpt measurements were obtained within a volume of around 22 liters. for the aerodynamic loads determination, measurements from both sides of the wing and along the entire span are necessary. to obtain this data with the described measurement setup, the lpt measurements were performed in four separate acquisitions. first, two acquisitions were performed for the bottom half of the wingspan, where the angle of attack of the wing was set to +α and −α, respectively. the data acquired at −α (pressure side) was later mirrored in post-processing to the opposite side of the wing and merged with the data acquired at +α (suction side). thereby, the symmetry of the wing was exploited to simplify the lpt data acquisition, because, with this approach, it is not necessary to move and recalibrate the optical measurement setup. the same procedure is repeated for the top half of the wingspan. the resulting four separate acquisitions are merged by transforming the lpt data from the measurement coordinate system to the wind tunnel coordinate system with a rigid-body transformation. the translation and rotation matrices for this rigid-body transformation are determined based on reference lpt measurements of the structural markers on the wing, performed without wind tunnel operation before each manipulation of the measurement volume. the accuracy of the employed merging procedure can be assessed by comparing the flow velocity at corresponding positions with respect to the wing from different acquisitions. typical values of these differences were between 1% and 3% of the local velocity magnitude. since these values are of the same order of magnitude as when the merging of different flow measurement acquisitions is performed automatically based on position measurements with a robotic arm as in jux et al. (2018), these differences are considered acceptable and not further investigated. 3 wing shape reconstruction after the lpt measurements of the structural markers are transformed from the measurement coordinate system to the wind tunnel coordinate system, the marker position measurements are used to reconstruct the deformed shape of the wing. this is achieved by calculating the wing deflection as an average value of the marker positions for each spanwise section where the markers were painted (i.e., the ribs of the wing and the tip rod) and then fitting a polynomial through these measurements along the spanwise direction. following this procedure, the result of the polynomial curve fit is used as a reference spanwise axis to calculate the deformed wing shape. a fourth-order polynomial is used in this study to perform the curve fit, which satisfies the geometric boundary conditions of a wing that is clamped at the root, i.e. d(z = 0) = 0 and d′(z = 0) = 0, and is defined as d(z) = az4 +bz3 +cz2, (1) where the coefficients a, b, and c are determined with an optimization to provide the best fit to the experimental measurements in a least-squared sense. the individual marker measurements from 100 acquired images are averaged to reduce the effect of measurement noise and small-scale vibrations of the wing during the experiment. the results of the polynomial curve fit to the marker measurements for the two different values of α are shown in fig. 3. the standard deviation of the residual between the 15 measurement locations along the span and the curve fit is σ1 = 0.13mm for α1 and σ2 = 0.25mm for α2, corresponding to 0.28% and 0.29% of the respective wingtip displacement. note that the value of the spanwise position of the wingtip can exceed ztip/s = 1 because there are markers on the wingtip rod, which is not accounted for in the definition of the span length s. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 figure 3: displacement measurements along the span with polynomial curve fit to further characterize the deformed wing shape, knowledge about the torsional deformation is required as well. the torsional deformation can be expressed in terms of a twist angle ε of the wing around the reference axis. the twist angle ε of the wingtip can be estimated from the structural marker measurements on the tip rod. the experimentally determined twist angles were found to be ε1 = 0.26° for α1 and ε2 = 0.45° for α2. based on these small values of ε and to simplify the analysis, the twist has been neglected in the further analysis, assuming that the deformed wing shape can be reconstructed with sufficient accuracy directly from the polynomial curve fit of the deflection along the span. 4 loads determination methods 4.1 surface pressure determination in incompressible, inviscid, and irrotational steady flow, the local flow velocity and pressure in the entire field are related through bernoulli’s equation, yielding cp = p− p∞ 1 2 ρu2 ∞ = 1− v 2 u2 ∞ , (2) where p is the pressure, ρ is the fluid density, and v is the velocity magnitude. for attached flow around wings, the aforementioned conditions for the application of bernoulli’s equation are generally justifiable assumptions, except for the viscous flow inside the boundary layer. the presence of the boundary layer and, in view of random measurement errors, the prevalence of relatively strong velocity gradients near the surface obstruct a direct application of eq. 2 to the lpt measurements in the vicinity of the surface to determine the local surface pressure. it is therefore necessary to perform an extrapolation of the pressure obtained with eq. 2 from the flow field to the surface, as demonstrated in mertens et al. (2021). the lpt flow measurements provide discrete values for the pressure in the flow field by applying eq. 2 to each particle track. for the surface pressure extrapolation in this study, the lpt measurements within a given radius around a finite number of surface normals from the wing are used, instead of first interpolating them onto a regular grid. the surface normals are computed from the reconstructed wing shape by discretizing the wing shape with planar rectangular elements and then calculating the normal direction n and the tangential direction t from a sampling point at the center of each element. the coordinates of the lpt measurements are then transformed into the local coordinate system of the wing so that the data within a given normal and tangential distance around each surface normal can be used for the extrapolation of the surface pressure at the respective sampling point on the wing. the data collection procedure is illustrated schematically in fig. 4. figure 4: sketch of the lpt data collection procedure for a sampling point at x/c = 0.86. blue dots: lpt track data considered for the pressure extrapolation, red dots: lpt track data that is not considered in fig. 5, the lpt measurements along 100 surface normals with a length of nmax = 15mm (0.15c) are shown for a cross-section of the wing at α2 = 10° for the spanwise location z/s = 0.6. there are 50 normals on the suction (top) and pressure (bottom) side, respectively. the sampling points on the surface are distributed using a half-cosine spacing along the chord to concentrate the sampling points in the leading edge region of the airfoil where high pressure gradients are expected. the lpt data within a spanwise region that extends over 11mm (±0.01s) around the spanwise location z/s = 0.6 is considered. within this spanwise region, the lpt data with a maximum tangential distance of tmax = 2.5mm (0.025c) to the respective surface normal is collected and plotted along the normal in fig. 5 as a function of its respective wall distance n. figure 5: lpt-based pressure from bernoulli’s equation along surface normals at z/s = 0.6 for α2 = 10°. the labels (a-f) in the figure indicate the normals that are plotted in fig. 6 as visible in fig. 5, a considerable amount of random measurement noise and artifacts obstruct the application of eq. 2 in the direct vicinity of the surface. in particular, an unphysical increase in the pressure obtained with eq. 2 is observed close to the wing surface, most prominently near the trailing edge on the suction side. in this region, the presence of the boundary layer decelerates the flow near the wing surface, which according to eq. 2 implies an increase in pressure, whereas it is known from boundary layer theory that the pressure does not vary across the boundary layer (see schlichting and gersten (2017)). to determine the surface pressure from the pressure in the flow field as obtained from the lpt measurements with eq. 2 despite the presence of the boundary layer and the random measurement errors, an extrapolation of the surface pressure is performed by fitting a polynomial through the lpt data points in the wall-normal direction using a least-squares method. a second-order polynomial is used and data points with a wallnormal distance n up to nmax = 0.15c are considered for the fit. as for the illustration in fig. 4 and the measured data plotted in fig. 5, lpt data from a spanwise region of ±0.01s around the reference position, with a maximum tangential distance of ±tmax = 0.025c from the lpt data point to the respective surface normal in the cross-sectional plane is considered for the pressure extrapolation. the pressure extrapolation is illustrated in fig. 6 for the six example locations at z/s = 0.6 of which the locations are indicated in fig. 5. in general, the value of the polynomial at the wall is considered as the extrapolated surface pressure. the lpt data, the fitted polynomial, and the extrapolated surface pressure are indicated for x/c = 0.3 on the pressure side in fig. 6(a). the pressure extrapolation works as expected, despite the presence of a considerable amount of random error. the presence of random measurement errors is more critical when the error is not normally distributed, as near the stagnation point, which is illustrated in fig. 6(b), where all the outliers are associated with lower pressures. the effect of these outliers is diminished by using a robust least-squares polynomial fit with bisquare weights1, which is used at all chordwise locations. an extraordinarily challenging measurement region is the leading edge region on the suction side, which is the flow region in between the stagnation point and suction peak, where the spatial gradients of the flow velocity and the pressure are maximal. in this region, the measured pressure data near the wall exhibits a bifurcation behavior, as shown in figs. 6(c) and 6(d), which can be expected as a consequence of the non-zero value of tmax and the large pressure gradients in the wall-tangential direction in this region. as a result of the robust fitting approach, the polynomial fit follows the branch with the larger amount of measured data points in figs. 6(c) and 6(d). a different issue of the lpt-based pressure measurement estimation with bernoulli’s equation is the presence of the boundary layer where eq. 2 incorrectly implies an increase in pressure, in particular on the suction side. the effect of this issue on the curve fit is still negligible at x/c = 0.3 as shown in fig. 6(e), but clearly relevant further downstream, as shown in fig. 6(f). because the actual pressure does not vary across the boundary layer, the pressure outside of the boundary layer, where bernoulli’s equation is applicable, should be used for the extrapolation of the surface pressure, instead of the value of the polynomial 1https://mathworks.com/help/curvefit/least-squares-fitting.html https://mathworks.com/help/curvefit/least-squares-fitting.html fit at the wall. in figs. 6(e) and 6(f), it is shown that this value can be determined on the suction side by considering the minimum value of the polynomial fit in the wall-normal direction. this approach is used for all sampling points on the suction side of the wing downstream of x/c = 0.2, as these locations are most critically affected by the presence of the boundary layer. 0 0.05 0.1 0.15 -2 -1.5 -1 -0.5 0 0.5 1 (a) x/c = 0.30, pressure side 0 0.05 0.1 0.15 -1.5 -1 -0.5 0 0.5 1 (b) x/c = 0.028, pressure side 0 0.05 0.1 0.15 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 (c) x/c = 0.036, suction side 0 0.05 0.1 0.15 -2.5 -2 -1.5 -1 -0.5 0 0.5 (d) x/c = 0.065, suction side 0 0.05 0.1 0.15 -4 -3 -2 -1 0 1 (e) x/c = 0.30, suction side 0 0.05 0.1 0.15 -2 -1.5 -1 -0.5 0 0.5 1 1.5 (f) x/c = 0.80, suction side figure 6: surface pressure extrapolation at six different example locations at z/s = 0.6 for α2 = 10° 4.2 lift force determination for attached flow around wings at small angles of attack α, the lift force perpendicular to the inflow can be assumed as equivalent to the normal force on the wing, which acts perpendicular to the chord. for thin objects like airfoils, the sectional lift force can therefore be obtained by integrating the pressure difference between the suction and pressure sides along the chord, with the section lift in coefficient form given as c` = l′ 1 2 ρu2 ∞c = ∫ c 0 (cp,pressure−cp,suction)dx, (3) where l′ is the sectional lift force per unit span, and cp can be determined from the flow field as described before. if the determination of the pressure distribution itself is not of primary interest, the section lift l′ can alternatively be determined by using the kutta-joukowski theorem: l′ = ρu∞γ, (4) where γ is the circulation around the wing, which can be determined by performing a line integral of the flow velocity along a closed contour c around the wing: γ =− ∮ c ~u ·d~s. (5) although the kutta-joukowski theorem is derived based on the assumption of potential flow, previous studies have shown that it can be used to determine the lift accurately from experimental data for flows that exhibit moderate effects of viscosity, and when the circulation is calculated from velocity measurements outside of the region affected by these viscous effects (mertens et al. (2021); sharma and deshpande (2012); olasek and karczewski (2021)). in this study, the circulation is determined from the lpt measurements by defining an elliptic path around the wing section of interest and collecting the lpt data within a prescribed distance around this path, which is then integrated along the tangential direction to determine the circulation. because the lift force acts perpendicular to the freestream and the spanwise axis of the wing, the elliptic integration paths are defined in a local coordinate system of the respective wing section of interest, which is defined using the experimentally reconstructed wing shape. the ellipse has its origin at the mid-chord position of the wing section, the major axis is aligned with the chord and the minor axis is perpendicular to the chord in the cross-sectional plane. an example of the circulation determination procedure is visualized for α2 = 10° at z/s = 0.6 in fig. 7. -0.2 0 0.2 0.4 0.6 0.8 1 1.2 -0.4 -0.2 0 0.2 0.4 -1.5 -1 -0.5 0 0.5 1 1.5 (a) lpt data on an elliptic contour, colored by tangential velocity 0 0.2 0.4 0.6 0.8 1 -30 -20 -10 0 10 20 30 (b) tangential velocity along the elliptic contour figure 7: illustration of the circulation determination procedure at z/s = 0.6 for α2 = 10° in fig. 7(a), the lpt data along an elliptic contour around the wing at z/s = 0.6 is visualized. the elliptic contour has a major semi-axis length of a/c = 0.75 and a minor semi-axis length of b/c = 0.5. as for the pressure extrapolation, lpt data within a spanwise region that extends over 11mm (±0.01s) around the respective spanwise location is considered. the maximum distance in the cross-sectional plane of the lpt data point to the ellipse to be considered for the circulation determination is taken as 1mm (0.01c). the tangential velocity component ut of the lpt data at z/s = 0.6 along the elliptic contour is plotted in fig. 7(b). the origin of the contour is located upstream of the wing, aligned with the chordwise direction. the positive direction along the contour is counter-clockwise around the wing. to determine the circulation from this data, the tangential velocity of the individual lpt data points is filtered with a smoothing spline2. the smoothed data is then integrated along the length of the contour to obtain the circulation. while in the theoretical case of a potential flow the circulation would be independent of the contour as long as the object is fully enclosed by it, this assumption cannot be directly made for the present case that includes some effects of viscosity as well as due to the occurrence of measurement errors. therefore, the effect of the ellipse geometry parameters a and b on the circulation γ is analyzed as shown in fig. 8 for α1 and α2 at z/s = 0.6. (a) α1 = 5° (b) α2 = 10° figure 8: effect of the elliptic contour parameters on the circulation at z/s = 0.6 a relatively strong sensitivity of γ to b is observed when the elliptic contour is in the immediate vicinity of the wing, i.e. when the contour is located within the boundary layer. this effect is amplified for α2 = 10° as seen in fig. 8(b), where the boundary layer thickness on the suction side is increased due to a stronger adverse pressure gradient, when compared to α1 = 5° in fig. 8(a). further away from the wing, the circulation does not vary systematically with a or b, but it is subject to some level of variation, likely due to random measurement errors. to minimize the influence of these random errors, the circulation γ for a given spanwise location of the wing is determined in this study by averaging the value of γ from 100 different elliptic contours at that spanwise location, where the parameters of the ellipse are varied between 0.65≤ a/c≤ 1.1 and 0.25≤ b/c≤ 0.7. 5 results the results for the lpt-based pressure determination at four different spanwise locations for α1 and α2 are shown in fig. 9. as expected, the larger angle of attack α2 produces higher pressures on the bottom and lower pressures on the top side. within the range of z shown in fig. 9, no large variation of the pressure distributions with the spanwise position is observed. as an effect of the bifurcation in the data used for the pressure extrapolation near the leading edge that was discussed in the context of fig. 6, the pressure coefficient cp is positive on the suction side in the region from the leading edge until around x/c = 0.05 in all pressure distributions in fig. 9. 2https://mathworks.com/help/curvefit/smoothing-splines.html https://mathworks.com/help/curvefit/smoothing-splines.html 0 0.2 0.4 0.6 0.8 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 (a) z/s = 0.2 0 0.2 0.4 0.6 0.8 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 (b) z/s = 0.4 0 0.2 0.4 0.6 0.8 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 (c) z/s = 0.6 0 0.2 0.4 0.6 0.8 1 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 (d) z/s = 0.8 figure 9: lpt-based surface pressure distribution at four different spanwise locations the lift distributions obtained by integrating the pressure difference along the chord, as well as from the circulation-based method are compared in fig. 10. the lift distributions from both lpt-based methods show a plateau of the lift along most of the span and a drop towards the wing root and tip. this behavior is expected from aerodynamics theory due to the presence of the wing fixture at the root and the tip vortex. the pressure-based lift is consistently lower than the circulation-based lift, which is likely due to the reduction of the suction due to experimental errors near the leading edge, which were observed in fig. 9. furthermore, the pressure-based lift shows a larger level of random variation along the span compared to the circulationbased method, which is expected because the pressure-based method uses only lpt data measured in the vicinity of the wing, whereas, for the circulation-based method, several different integration paths were used and averaged. a quantitative assessment of the accuracy of the lpt-based loads determination is performed by integrating the lpt-based lift result from the pressureand circulation-based approaches along the span. these results are compared with the balance measurements in tab. 1. the differences of the circulation-based method to the force balance measurements are considerably smaller than for the pressure-based method, by around 10%. the difference to the force balance for both methods is increased for α2 compared to α1, but overall it remains below 5% for the circulation-based and below 15% for the pressure-based method. 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 (a) α1 = 5° 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 (b) α2 = 10° figure 10: comparison of the lift distribution across the span with different methods table 1: comparison of the lift force from the lpt-based methods with the force balance measurements α1 = 5° α2 = 10° method lift force difference lift force difference force balance 4.12 n 7.83 n pressure-based 3.74 n -9.3% 6.75 n -13.7% circulation-based 4.00 n -2.9% 7.48 n -4.5% 6 conclusion this study has demonstrated the non-intrusive flowfield-based determination of aerodynamic loads on a flexible wing with a gridless approach based on discrete lpt measurement data. contrary to most approaches in the published literature, the loads were not determined from ensemble-averaged data on a cartesian grid, but instead by first determining the deformed shape of the wing from lpt measurements of structural markers and then analyzing the discrete lpt flowfield data in a local coordinate system, which is given by the measured wing shape. the aerodynamic loads were evaluated for two different angles of attack, α1 = 5° and α2 = 10° and with two different methods, which are the pressure-based and the circulation-based approaches. for the pressure-based approach, flow measurements in the immediate vicinity of the wing are necessary. the lpt data in this region is associated with a considerable amount of random error, and it is furthermore more challenging to analyze due to the presence of the viscous boundary layer. these challenges were addressed in this study by performing an extrapolation of the surface pressure along surface normals. however, the lift estimation based on a chordwise integration of the pressure difference was up to 13.7% lower than the reference lift measured with the force balance, mostly due to the erroneous surface pressure evaluation in the leading edge region of the wing. in contrast, the circulation-based approach does not require measurements in the near vicinity of the wing, as such it suffers to a lesser extent from the measurement-related issues. when comparing the integral lift force along the span from this approach with force balance measurements, a very good agreement is observed, with differences in the lift force of less than 5%. therefore, the circulation-based approach is preferred for a more accurate and robust lift determination, if the pressure distribution itself is of no direct interest. a topic for future research is a performance assessment of the gridless approach by comparison to results obtained with an ensemble-averaging approach. additional topics include the improvement of the pressure extrapolation in the leading edge region and the application of the gridless approach to unsteady flows and flow situations in which the aerodynamic loads are more critically affected by viscous effects. acknowledgements the authors gratefully acknowledge the help of adrián grille guerra with the lagrangian particle tracking measurements during the wind tunnel experiments. this work has been carried out in the context of the homer (holistic optical metrology for aero-elastic research) project that has received funding from the european union’s horizon 2020 research and innovation programme under grant agreement no. 769237. references agüera n, cafiero g, astarita t, and discetti s (2016) ensemble 3d ptv for high resolution turbulent statistics. measurement science and technology 27 avin o, raveh de, drachinsky a, ben-shmuel y, and tur m (2021) an experimental benchmark of a very flexible wing. in aiaa scitech 2021 forum. american institute of aeronautics and astronautics dimitriadis g (2017) introduction to nonlinear aeroelasticity. john wiley & sons faleiros de, tuinstra m, sciacchitano a, and scarano f (2019) generation and control of helium-filled soap bubbles for piv. experiments in fluids 60 jux c, sciacchitano a, schneiders jfg, and scarano f (2018) robotic volumetric piv of a full-scale cyclist. experiments in fluids 59 mertens c, sciacchitano a, van oudheusden bw, and sodja j (2021) an integrated measurement approach for the determination of the aerodynamic loads and structural motion for unsteady airfoils. journal of fluids and structures 103 mitrotta fma, sciacchitano a, sodja j, de breuker r, and van oudheusden bw () experimental investigation of the fluid-structure interaction between a flexible plate and a periodic gust by means of robotic volumetric piv. in cj kähler, r hain, s scharnowski, and t fuchs, editors, 13th international symposium on particle image velocimetry. pages 645–656 olasek k and karczewski m (2021) velocity data-based determination of airfoil characteristics with circulation and fluid momentum change methods, including a control surface size independence test. experiments in fluids 62 rival de and van oudheusden bw (2017) load-estimation techniques for unsteady incompressible flows. experiments in fluids 58 scarano f, ghaemi s, caridi gca, bosbach j, dierksheide u, and sciacchitano a (2015) on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments. experiments in fluids 56 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57 schanz d, gesemann s, schröder a, wieneke b, and novara m (2013) non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. measurement science and technology 24 schlichting h and gersten k (2017) boundary-layer theory. springer. 9th edition sciacchitano a and scarano f (2014) elimination of piv light reflections via a temporal high pass filter. measurement science and technology 25 sharma sd and deshpande pj (2012) kutta–joukowsky theorem in viscous and unsteady flow. experiments in fluids 52:1581–1591 van oudheusden bw (2013) piv-based pressure measurement. measurement science and technology 24 wieneke b (2008) volume self-calibration for 3d particle image velocimetry. experiments in fluids 45:549– 556 introduction experimental procedures wind tunnel setup data acquisition and processing wing shape reconstruction loads determination methods surface pressure determination lift force determination results conclusion 14th international symposium on particle image velocimetry (ispiv 2021) august 1-4, 2021 — chicago, il usa development of echo-lpt for the study of particle-wall interactions in dense suspensions milad samie1*, mohammad reza najjari1, kai zhang1 and david e. rival1 1: department of mechanical and materials engineering, queen’s university, kingston, canada *corresponding author: m.samie@queensu.ca 1 introduction examining the behaviour of dense suspensions has proven to be difficult, both experimentally and numerically. using super water–absorbent polymer, piv measurement was successfully conducted in a hydrogel suspension with a volume fraction (vf) of φ =20% (see zhang and rival, 2018). however, due to the slightly refractive index mismatch, the image quality will degrade significantly as the particle loading of the hydrogel is increased. in order to achieve flow measurements in suspensions with high volume fractions, non-optical based techniques such as ultrasound imaging velocimetry (uiv) should be implemented. uiv has been developed for fluid dynamics applications and embraced by many researchers to study fluid flows (gurung and poelma, 2016; jeronimo et al., 2019). although, uiv provides useful information about the flow physics, it is unable to provide lagrangian quantities such as particle trajectories, which is a key parameter to study entrainment and particle-wall interactions. in this study, our goal is to investigate particle entrainment and particle-wall interactions in vortex rings created in dense suspensions using a lagrangian method based on ultrasound imaging techniques. we have provided the validation of our uiv and echo lagrangian particle tracking (elpt) results. the tracking results will be further post-processed by a pathline extension method (rosi and rival, 2018). the resulting pathlines describe the lifespan of each fluid parcel within the measurement domain and can be used to extract path-dependent quantities, including particle approach velocity, incidence angle, particle-wall collision rate, particle residence time, and depletion efficiency. 2 experimental setup and methods we have performed several uiv and elpt measurements using fundamental and harmonic imaging to measure vortex-ring flow fields. figure 1(a) shows the experimental setup for our vortex-ring generator. a confined vortex ring was generated by a piston driving the flow in a cylinder with an inner diameter of d0=38.2 mm. the piston is controlled by a linear traverse that moves at a constant speed of up=0.16–0.32 m/s over a stroke length of l=191 mm (l/d0=5). the generated vortex ring is confined within an acrylic tube with an inner diameter of d =76.2 mm and a length of 457 mm. to prepare the suspensions, various concentrations of sap beads (liquiblock 2g-110 from emerging technologies, inc.) were mixed with pure deionized water (diw). these sap beads have an absorption coefficient of 450 gwater/gsap when mixed with diw. three working fluids were tested in this study: the pure diw and suspensions with vfs of φ=20% and φ=40%. a vantage 128 ultrasound system (verasonics inc.) with an l14-5/38 linear ultrasound probe (128 elements with 0.3 mm pixel pitch) was used to acquire plane-wave radio frequency (rf) signals. in the plane-wave imaging technique, all of the transducer’s elements are activated together to form a planar acoustic wave. to increase the signal-to-noise ratio (snr) of plane-wave images, a series of tilted plane-waves with different angles is used to reconstruct a single frame (montaldo et al., 2009). in this study, we used a multi-planewaves (plane-wave compounding) approach with verasonics’ pixel-oriented reconstruction software to obtain high-quality b-mode images from rf data. echo-lagrangian particle tracking and particle image velocimetry: we have acquired images for both elpt and uiv. the particle density in elpt was lower to allow for accurate distinction of individual particles. acquired images were then processed using davis 8.4 (lavision) to obtain velocity maps. the 2d-ptv and piv time–series correlation with a final window size of 32 pixels with 50% overlap was used for elpt and 1 14th international symposium on particle image velocimetry (ispiv 2021) august 1-4, 2021 — chicago, il usa figure 1: (a) experimental setup of vortex-ring generator. (b) comparison of instantaneous velocity vectors and vorticity maps for φ = 40% suspension obtained via elpt and uiv. uiv, respectively. the spatial resolution in the final uiv results were 1.6 mm. the obtained uiv results were used as benchmark tests to validate the accuracy of elpt measurements. figure 1(b) shows the comparison of velocity and vorticity maps obtained with elpt and uiv. since the density of velocity vectors in elpt was not as high as uiv, we merged 3 phase-locked instantaneous results from 3 different runs to obtain the elpt vector field, which is then interpolated on a cartesian grid. this figure demonstrates the accuracy of our elpt results. further work will be done to extend the short pathlines obtained from elpt measurments, and to use the time history of each fluid parcel to elucidate the interactions between the suspended particles and the cylinder inner walls. references arati gurung and christian poelma. measurement of turbulence statistics in single-phase and two-phase flows using ultrasound imaging velocimetry. experiments in fluids, 57(11):171, 2016. issn 0723-4864. mark d jeronimo, mohammad reza najjari, kai zhang, and david e rival. extraction of particle residence time using echo-lagrangian particle tracking. in 13th international symposium on particle image velocimetry, munich, germany. url: https://athene-forschung. unibw. de/128884, 2019. gabriel montaldo, mickaël tanter, jérémy bercoff, nicolas benech, and mathias fink. coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography. ieee transactions on ultrasonics, ferroelectrics, and frequency control, 56(3):489–506, 2009. issn 0885-3010. giuseppe a rosi and david e rival. a lagrangian perspective towards studying entrainment. experiments in fluids, 59(1):19, 2018. issn 0723-4864. kai zhang and david e. rival. experimental study of turbulence decay in dense suspensions using indexmatched hydrogel particles. physics of fluids, 30(7), 2018. issn 10897666. doi: 10.1063/1.5031767. 2 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a representative driven system to interrogate passive dynamics of an airfoil in the wake of a cylinder morgan l. hooper1∗, beverley j. mckeon1 1 california institute of technology, graduate aerospace laboratories, pasadena, california u.s.a. ∗ mhooper@caltech.edu abstract passive motion of an airfoil in the wake of a circular cylinder is compared with driven motion of an airfoil in the same configuration, through simultaneous measurement of both the airfoil dynamics and the surrounding flow field. the passive mounting allows the airfoil to move in the transverse (heaving) direction in response to oncoming forcing, while introducing significant parasitic effects to the dynamics including friction. the driven motion of the airfoil reproduces important characteristics of the imperfect passive motion, validating idealized sinusoidal motion as a model for dynamics of the passive airfoil operating in a more realistic engineering context. particle image velocimetry (piv) of the driven case is then used to illuminate flow structures contributing to observed power and thrust production in both cases. 1 introduction in 2006, beal et al. found that a dead fish was able to produce enough thrust to overcome its own drag and ‘swim’ upstream through interactions with a von kármán vortex street shed by an upstream cylinder. it was then demonstrated that a compliantly mounted airfoil placed in a similar wake produced net thrust larger than its net drag, and passively extracted energy from the oncoming flow (beal et al. (2006)). thus, dynamics of a passive body reacting to patterns of oncoming vorticity offer insight for applications such as passive drag reduction, efficient vehicle navigation in unsteady flows, or small-scale energy harvesting (for example, see streitlien et al. (1996), lefebvre and jones (2019) or akaydin et al. (2010)). the behaviour of such systems is complex, combining aerodynamic interactions with oncoming vorticity, non-ideal fluid-structure interactions and added mass effects (for a detailed discussion of added mass, see for example corkery et al. (2019)). the current work extends the study by beal et al., combining time-resolved 2d2c particle image velocimetry (piv) with direct simultaneous measurement of the forces and motion of an airfoil interacting with the wake of a circular cylinder. the goal of the study is to relate the purely passive dynamics of an airfoil free to move in response to oncoming vorticity to the well-studied case of a driven airfoil in the same configuration, and to evaluate the role particular fluid-structure interactions play in enhancing its power extraction and thrust production potential. for this purpose, two sets of experiments are compared. one set considers a mechanically mounted airfoil that is allowed to move purely passively in response to oncoming vorticity, but whose dynamics are dominated by realistic parasitic effects such as friction. the other considers an airfoil driven through a prescribed trajectory that captures important features of the passive motion. piv with a sufficient field of view to interrogate flow structures in the wakes of both the cylinder and the airfoil is performed, while simultaneous motion and force data provide a complete time-resolved picture of fluid-airfoil interactions. we show that an airfoil undergoing purely passive motion induced by the flow, subject to effects of friction and other non-idealities, tends to operate in a regime where the transverse forcing aligns with the velocity while producing mean thrust larger than its mean drag (generating both power and thrust). through examination of flow structures associated with the motion of the driven airfoil, which exhibits similar performance to the passive case, we are able to identify flow structures which contribute to the observed dynamics. 2 background characterizing the dynamics of an airfoil in vortical flow is an active area of research, particularly for applications in vehicular navigation in an unsteady environment. for example, lefebvre and jones (2019) performed force and flow velocity measurements for a stationary airfoil placed downstream of a circular cylinder. for an airfoil at 3 diameters downstream and with the same chord as the cylinder diameter, they observed the formation of a leading edge vortex (lev) for static, geometric angles of attack ranging from 0-20o (lefebvre and jones (2019)). consequences of lev formation and shedding are discussed at length by eldredge and jones (2019). lefebvre and jones (2019) also demonstrated mean thrust production, even for a stationary airfoil, for most of the cases considered in the study when the geometric angle of attack remained moderate. to connect instantaneous dynamics with the passage of particular structures in the flow, hufstedler and mckeon (2019) collected time-resolved piv as well as force measurements of a stationary airfoil encountering an isolated vortical gust. such studies of stationary airfoils provide a basis to interpret results for more complex studies that allow for either actuated or passive airfoil motion. previous work on flapping or otherwise actuated foils in a uniform free stream has largely focused on optimization of pitching and heaving parameters (see for example xiao and zhu (2014)) with respect to either thrust production or power extraction. kinsey and dumas (2008) proposed that the behaviour of an airfoil undergoing forced harmonic oscillations in both heave and pitch (with a phase difference of 90o between them) in an oncoming free stream can operate either in a propulsive regime or in a power extraction regime based on the phase relationship between force and velocity. in addition, they showed that the formation of levs contributes to improved power extraction by maintaining the alignment between force and velocity over a larger portion of a cycle. if an airfoil is instead allowed to react passively in heave to a driven pitching motion, dynamic parameters of the mounting system also become important. su and breuer (2019) found that the optimal power output for such a semi-passive system was achieved when the driven pitching frequency matched the structural resonance of the mounting system, and the structural damping was tuned to achieve an induced heaving velocity that is in-phase with fluid forces. a foundational study combining both driven oscillatory motion and interactions with oncoming vorticity is that by gopalkrishnan et al. (1994). they found that a foil oscillating in both heave and pitch with the same frequency as vortex shedding was able to alter the structure of an oncoming cylinder wake (a drag-type wake) to produce a reverse von kármán wake (associated with thrust production) depending on the phase between the motion and oncoming vorticity. they were also able to show that the propulsive efficiency exhibits a strong peak at a phase associated with the emergence of the reverse von kármán wake and an overall reduction in combined wake vortex strength. this is reminiscent of the observation from (for example) kinsey and dumas (2008) that the switch from propulsion to energy extraction for an oscillating foil manifests as a switch from a thrust wake to a drag wake; however a key distinction between these studies is that for an airfoil interacting with oncoming vorticity, mean power extraction and thrust production may be occurring simultaneously. the present study quantitatively evaluates both the flow structures and forces acting on an airfoil in a similar configuration to that of gopalkrishnan et al. (1994), to begin disentangling thrust and power-producing interactions. 3 experimental setup the airfoil used for both the passive and representative driven experiments is a naca 0018 airfoil with a chord length of c = 10 cm. both sets of experiments took place in the noah free-surface water channel facility at the california institute of technology. in both cases, the foil was mounted vertically, secured above the tunnel to allow translation in the y-direction (transverse/heave), while its x-direction (streamwise) and z-direction (vertical/spanwise) motion was constrained. a circular cylinder with a diameter of d = 11.5 cm was mounted 3 cylinder diameters upstream from the quarter-chord location of the airfoil, creating a von kármán wake. the reynolds number based on cylinder diameter in both cases was approximately 40,000. the basic configuration for both the passive and driven cases is provided in figure 1. note that the position and size of the piv field of view is approximate, and varied slightly between the two sets of experiments. u∞ 3d d 4 d y(t) y x aoa c = 0.9d figure 1: sketch of water tunnel test section (top view) showing upstream circular cylinder, downstream airfoil. discussed axes of airfoil motion labelled at left. green regions indicate piv field(s) of view. u∞ c i r c u l a r c y l i n d e r a i r f o i l piv measurement plane angle sensor accelerometer (occluded) laser distance sensor force and torque sensor piv cameras side view cylinder mount figure 2: experiment schematic for the purely passive case. motion of airfoil and laser sheet extent are into and out of the page. not to scale. 3.1 passive airfoil configuration in the passive configuration, the airfoil was secured to a linear motion cart and allowed to move transversely in response to oncoming free stream vorticity. this mechanical mounting introduced significant friction, which opposed the nominally free motion of the airfoil. the airfoil was mounted to the cart through a rotary bearing on a shaft passing through its quarter-chord location; however, very little change in angle of attack was observed during any individual experimental run, so the airfoil is assumed to be stationary in pitch throughout this analysis (although for each passive run, the stationary pitch angle varied). the position of the cart was measured using a keyence lk-g502 laser distance sensor, and the signal was numerically differentiated using a savitzky-golay filter to obtain the cart velocity and acceleration as described by schafer (2011). this method was validated through comparison with the measured acceleration of the cart, obtained using an adxl 337 accelerometer. the angle of attack (aoa) of the airfoil was measured using a vishay 351 hall-effect (he) rotary encoder. finally, six-axis forces and torques acting on the airfoil were measured using an ati mini40 ip68 force/torque sensor. the laser distance sensor and force/torque sensor included appropriate signal conditioning through dedicated analog-to-digital conversion provided by the manufacturer. the acceleration and angle of attack signals were low-pass filtered prior to data acquisition to ensure compliance with the nyquist criterion, and eliminate high-frequency noise. data were sampled at 25 khz simultaneously for all sensors. an experimental schematic for the passive airfoil case is given in figure 2. 3.2 driven airfoil configuration for the driven experiments, the airfoil was mounted to the captive trajectory system (cts), a cyberphysical fluid dynamics (cpfd) system integrated with the noah water channel. the cts is able to precisely drive a test object through a prescribed trajectory in the three translational axes, as well as pitch. more details regarding cts performance were reported by shamai et al. (2020). forces and torques on the airfoil were measured using the same force sensor as in the passive experiments; however airfoil position, velocity and force data are available as digital output from the cts at a rate limited to 200 hz. the angle of attack of the airfoil was manually adjusted to 0o, and remained fixed at this value for each experiment. the airfoil was driven through a transverse sinusoidal trajectory with a known frequency and phase relative to the oncoming vortices, of the form y(t) = apsin(2π f t +ψ), (1) where y(t) is the transverse position as a function of time, and ap, f and ψ were fixed based on data from the passive case. to determine the appropriate frequency f , the transverse force and position from the passive experiments were analyzed. for vortex shedding at a reynolds number of 40,000, the value of the strouhal number, st = f d u∞ , (2) has been shown to remain fixed around a value of 0.2 (for example lefebvre and jones (2019), and references therein). this gives an expected dimensional shedding frequency of approximately 0.6 hz. to confirm that this frequency was dominant in the airfoil dynamics, measured transverse force and position for all passive experiments were windowed into temporal bins varying in length from approximately 5.5 s to 20.0 s (3.4t to 12.5t ), and linear de-trending was applied to the position signal. then, the frequency content of each bin was computed using an fft. in all cases, the windowed signals (with bins of any length) exhibited a strong primary peak in the region of 0.6 hz; however the position signal sometimes exhibited additional strong peaks at lower frequencies, perhaps due to long-term meander or dynamics induced by the mounting system. to remove this as a source of error in determining dominant oscillatory behaviour due to vortex shedding, only the transverse force signals were used to compute the oscillation frequency for the driven experiments. the peak locations in all transverse force signal bins were averaged resulting in the selection of 0.6226 hz, which gives a strouhal number of 0.22. to determine the appropriate phase offset between the measured force and the airfoil motion (a proxy for the phase between the vortex shedding and the airfoil motion), the difference in phase angle computed from the fft at the dominant forcing frequency in each bin between the force and motion was averaged. although this phase difference varied widely especially for shorter window lengths, the mean value was determined to be quite close to π/2. this value confirms a visual trend identified in the passive airfoil data, as well as enforcing the condition that the airfoil’s velocity is in-phase with the forcing. this is intuitively satisfying as it enforces that the rate of work done on the airfoil by the surrounding flow, p(t) = fy(t)ẏ(t) (3) is always positive. since there is no power input available for the airfoil to do mean work on the flow, this is a physically meaningful constraint; thus, for the driven sinusoidal motions discussed in the following sections, the phase ψ for the motion is set such that velocity and transverse force are (approximately) in-phase. finally, the appropriate amplitude for the driven sinusoidal motion was determined through analogy with the time-mean kinetic energy of the passive airfoil. considering a pure sinusoid, ē ∝ lim t→∞ 1 t ∫ t 0 [avsin(ωt)]2dt = a2 v 2 . (4) then, the mean kinetic energy of a signal that is not perfectly periodic can be matched to an equivalent value for a pure sinusoid. we consider: ē = a2 v 2 (5) av = √ 2ē = ωap (6) ap = √ 2ē ω (7) where av is the amplitude of the velocity, and ap is the amplitude of the position for a pure sinusoid. by calculating ē as the mean kinetic energy over all runs (ie, by summing square velocity at each recorded time step for all experimental runs for the passive case then dividing by total time steps), then applying equation 7, we can estimate the appropriate amplitude for our synthetic position signal as ap = 5.1 mm, or approximately 5% of the airfoil chord. in summary, for the driven case reported in this paper, the airfoil was driven through a prescribed sinusoidal trajectory given by the following equation (for position normalized by airfoil chord): y∗(t) = 0.05sin(2π(0.6226)t +ψ) (8) where ψ was fixed for each individual run to ensure that the velocity was in-phase with the force acting on the airfoil due to vortex shedding. 3.3 piv system for both the passive and driven cases discussed above, 2d2c piv was performed simultaneously with measurements of airfoil dynamics. piv images were captured at a rate of 800 hz using two phantom miro lab 320 cameras with a pixel resolution of 1920x1200 px. the two fields of view partially overlapped to form a single, continuous region of interest (see figure 1). both cameras were placed directly beneath the tunnel, perpendicular to the transparent tunnel bottom, and equipped with 35mm nikkor lenses. neutrally buoyant tracer particles are illuminated by a photonics dm20-527(nm) ylf laser in single-pulse mode, which was expanded through a cylindrical lens to form a sheet. the laser sheet entered the tunnel through a side wall parallel to the tunnel bottom. piv image acquisition and processing was completed using commercial software (lavision davis, version 10.1.2). raw images were first averaged to compute a background image, which was subtracted from each frame prior to processing. in addition, the outline and shadow created by the airfoil was masked out based on its measured position in each frame. prepared images are then processed sequentially to produce vector fields. a multi-pass correlation algorithm was used, where an initial pass using a 64x64 pixel square figure 3: airfoil phase-averaged position (left) and velocity (right) over one vortex shedding cycle. colours correspond to the following cases: dr; pa10; pa11; pa12. window was subsequently reduced to yield a final circular window size of 16x16 pixels, through three additional passes. each pass included a 50% overlap between windows, and outliers were removed between each pass based on a minimum correlation value threshold of 0.4, as well as median filtering. obtained vector fields were then post-processed using an additional median filter to remove outliers, as well as a 3x3 smoothing filter to reduce noise in the final fields. the resulting size of the field of view was 0.65 x 0.24 m (5.7 x 2.1 d) in the driven case, and 0.67 x 0.24 m (5.8 x 2.1 d) in the passive cases. 4 phase reference determination for passive and driven cases to define a global phase reference for both the driven and passive experiments, a proper orthogonal decomposition (pod) of the oncoming flow was computed. flow behind a circular cylinder exhibits von kármán vortex shedding, which has a relatively compact representation in a basis formed by its pod modes. this can be exploited to create a phase reference for vortex shedding based on direct observations of the flow field, as demonstrated by lefebvre and jones (2019) and van oudheusden et al. (2005). this is particularly useful for determining a quantitative phase reference in the passive case, where the motion and measured forcing is not perfectly periodic. it also allows for a more objective comparison between the driven and passive cases with respect to flow behaviour, which remains the same for both. thus, in the following sections the global phase of the cylinder-airfoil system is computed based on a proper orthogonal decomposition of the flow field upstream of the location of the airfoil (before flow around the airfoil disrupts the pattern of vortex shedding). first, the first two pod modes for this reduced flow field are calculated, and their projection coefficients at each piv time step are determined. then, the phase angle is calculated by considering (as in van oudheusden et al. (2005)) φ = atan ( a2 √ σ1 a1 √ σ2 ) , (9) where a1,a2 are the first and second pod mode coefficients, and σ1,σ2 are the associated singular values. 5 comparison between driven and passive airfoil dynamics using the global phase reference given by equation 9, position, velocity, lift, thrust and power data from the passive and driven cases are phase-averaged to reveal underlying trends associated with vortex shedding. the data are binned into 400 bins of equal width corresponding to 0.0157 radians or 0.0040 seconds, based on the estimated mean shedding period of t = 1.6062 s. figure 3 shows the phase-averaged position and velocity of the airfoil over one shedding cycle for both the driven case (case dr, the bolded line), and three different passive cases (cases pa10, pa11 and pa12), each with a different static angle of attack and mean tunnel position. as these factors affect airfoil performance, the passive cases were not phase-averaged together and instead are reported separately as thin lines in figure 3. a moving average was removed from the position signals for the passive case prior to phase averaging, to more clearly highlight the cyclic character of the airfoil motion and remove any mean position offset. in the driven case, phase averaging was only performed for periods when the velocity and measured forcing were in-phase to within 5% of t , to enforce this alignment for the phase-averaged data despite slight meander in fluid forcing frequency. the driven sinusoidal trajectory appears to capture the phase-averaged passive airfoil motion qualitatively well as evidenced by figure 3, although the passive cases exhibit some spread in the location of the velocity peaks. this is likely due to the variation in test conditions, as well as inherent cycle-to-cycle variability induced by non-ideal and nonlinear effects such as friction. frictional effects also induce the stick-slip motion observed in cases pa10-12, where the airfoil experiences brief periods of non-zero velocity surrounded by periods of inactivity rather than a smooth sinusoidal velocity variation as in case dr. in addition, phase averages for each passive case (pa10-12) are based on total time periods of 2.9t , corresponding to a single piv run each. by contrast, operating conditions were held constant in the driven experiments by design, allowing many individual runs to be averaged together in case dr. therefore higher variability in the phase-averaged results for the passive cases (pa10-12) is expected. figure 4 shows the phase-averaged thrust, lift and power coefficients for the driven and passive cases discussed above, where the coefficients are defined in the conventional manner as ct = t 1 2 ρu2 ∞sc cl = l 1 2 ρu2 ∞sc cp = p 1 2 ρu3 ∞sc , where s is the span of the airfoil submerged in the tunnel. the first panel shows the phase-averaged velocity reproduced from figure 3 for reference. again we see relatively good qualitative agreement between the behaviour in both the driven case and the passive cases. in all cases, we observe a roughly sinusoidal trend in cl induced by the passage of shed vorticity from the upstream cylinder; in addition we see that for all cases the phase-averaged velocity of the airfoil is roughly in-phase with this forcing (an enforced condition for case dr). although the passive cases seem to generally confer a maximum cl benefit (larger amplitude variation in cl), the phase-averaged power coefficient varies widely between passive runs. this figure 4: phase-averaged velocity (top left), thrust coefficient (top right), lift coefficient (bottom left) and power coefficient (bottom right) for passive and driven cases. dr; pa10; pa11; pa12. effect appears to be caused by longer periods of inactivity in some of the passive cases, caused by the action of friction opposing the startup of airfoil motion (evidenced by extended periods where ẏ = 0, especially for pa11 and pa12). however, when the airfoil does move, the power production in the passive case appears to exceed that of the driven case (at least in one recorded case, pa10). the action of friction in the transverse direction does not appear detrimental to thrust production: positive thrust production (in addition to positive power, or power extraction) is experienced at a similar magnitude in both the driven and passive cases. to investigate the flow features responsible for simultaneous power extraction and thrust production in these systems, phase-averaged velocity fields are discussed in the following section. based on the preceding discussion, we examine velocity fields for the driven case (dr) only, as the longer available time periods for averaging provide a clearer picture of the cyclic flow features of interest. the highly variable nature of the airfoil behaviour in the passive case presents a challenge in creation of a representative phase average velocity field in the region of the airfoil, and is therefore deferred for future exploration; however the similarity in the dynamics observed between the passive and driven cases above validates the use of the driven case as a model at least for the large-scale cyclic behaviour in the more complex passive case(s). 6 observed flow structures and influence on dynamics figures 5 and 6 provide phase-average snapshots of the flow field around the airfoil at three different vortex shedding phases, as indicated by the dashed lines in the left-hand panels. vortex shedding phase advances from top to bottom in the images on the right for each figure. in figure 5, the transverse (y-direction) velocity is provided. in figure 6, values of the γ2 criterion (a proxy for vorticity, as described by graftieaux et al. (2001)) for the same phase locations are provided. the top-right panel in each of figures 5 and 6 shows the flow at the moment corresponding to the first of two power production peaks observed in the cycle. we see that the airfoil is passing through its neutral position behind the cylinder, and experiencing its maximum upwards velocity. it is centered in a region of upwash generated by upstream vortex shedding, as shown in figure 5, and flow over the top of the airfoil is relatively well-ordered leading to a local maximum in the lift force. it is interesting to note that the peak in the thrust lags slightly behind the peaks in lift and power: this could indicate a stronger dependence of the thrust production on the location of the upstream vortices (global flow conditions), rather than the local conditions surrounding the airfoil itself. for example, in figure 6 in the top right panel we see that the airfoil is located downstream and above a counter-clockwise rotating vortex, but upstream and below a clockwise rotating vortex. both of these structures contribute to upstream forcing on the airfoil (though we emphasize that they do not create a region of reverse flow near the airfoil). the middle-right panel in each of figures 5 and 6 shows a moment midway between the peak and trough in the observed power production, and at the beginning of a trough in the thrust. we see strong evidence of the growth of an lev attached to the airfoil, especially in figure 6, as well as flow separation as indicated by the region of negative flow close to the airfoil’s surface in figure 5, despite its positive velocity. we see that the cl value at this moment remains high, with a sharper downwards slope at phases just beyond; as discussed by kinsey and dumas (2008), the growth of an lev may be helping to keep the lift high for the high-velocity portion of the cycle, resulting in augmented power production. by contrast, the oncoming counter-clockwise rotating vortex has encountered the airfoil, thereby losing some coherence: this could be contributing to the loss of thrust at this phase. the bottom-right panel in each of figures 5 and 6 shows a moment of minimum power production, which coincides with a maximum in airfoil position and therefore a zero-point in the velocity. since p = fy(t)ẏ(t), this velocity zero crossing is largely responsible for the dip in power output. at this moment, we see that the airfoil is perched between regions of upwash and downwash (engulfed in a counterclockwise-rotating vortex), and the flow over the airfoil’s surface is separated and highly disordered with regions of downwards flow especially evident over the trailing edge. in addition, the fast flow past the leading edge has been attenuated by the advancement of a region of downwash. these factors contribute to the small lift values experienced at this point in the cycle. interestingly, the thrust coefficient has passed its local minimum and has started to recover. this provides further evidence that thrust production behaviour may depend more strongly on global conditions, such as the advance of the new oncoming clockwise-rotating vortex upstream of the airfoil. -0.2 0 0.2 -0.2 0 0.2 -0.2 0 0.2 figure 5: snapshots of phase-averaged transverse velocity at indicated points in the vortex shedding cycle. left column reproduces data for case dr from figure 4: phase-averaged velocity (top), lift coefficient (middle) and power coefficient (bottom). left-hand figures also indicate the phase of each snapshot shown on right: top panel; middle panel; bottom panel. -0.5 0 0.5 -0.5 0 0.5 -0.5 0 0.5 figure 6: snapshots of phase-averaged γ2 criterion values at indicated points in the vortex shedding cycle. left column reproduces data for case dr from figures 3 and 4: phase-averaged position (top), thrust coefficient (middle) and power coefficient (bottom). left-hand figures also indicate the phase of each snapshot shown on right: top panel; middle panel; bottom panel. 7 conclusions experiments were performed to interrogate the behaviour of an airfoil in the wake of a circular cylinder, both when the airfoil was free to interact with oncoming vorticity, and when it was driven through an idealized sinusoidal trajectory. time-resolved piv coupled with measurements of airfoil dynamics allowed the creation of a phase-averaged picture of the airfoil behaviour in both cases, and it was shown that the idealized driven trajectory captures salient features of the more variable passive motion. thus, phase-averaged velocity and γ2 fields for the driven case were analyzed to determine dominant flow structures linked to the behaviour of the airfoil. simultaneous production of thrust and power are linked strongly to cyclic interactions with both regions of upwash and downwash as well as coherent vortices shed by the upstream cylinder. acknowledgements the support of the us army research office under grant number w911nf-17-1-0306, as well as that from the natural sciences and engineering research council of canada (nserc) is gratefully acknowledged. references akaydin hd, elvin n, and andreopoulos y (2010) wake of a cylinder: a paradigm for energy harvesting with piezoelectric materials. experiments in fluids 49:291–304 beal dn, hover fs, triantafyllou ms, liao jc, and lauder gv (2006) passive propulsion in vortex wakes. journal of fluid mechanics 549:385–402 corkery sj, babinsky h, and graham wr (2019) quantification of added-mass effects using particle image velocimetry data for a translating and rotating flat plate. journal of fluid mechanics 870:492–518 eldredge jd and jones ar (2019) leading-edge vortices: mechanics and modelling. annual review of fluid mechanics 51:75–104 gopalkrishnan r, triantafyllou ms, triantafyllou gs, and barrett d (1994) active vorticity control in a shear flow using a flapping foil. journal of fluid mechanics 274:1–21 graftieaux l, michard m, and grosjean n (2001) combining piv, pod, and vortex identification algorithms for the study of unsteady turbulent swirling flows. measurement science and technology 12:1422–1429 hufstedler eal and mckeon bj (2019) vortical gusts: experimental generation and interaction with wing. aiaa journal 57:921–931 kinsey t and dumas g (2008) parametric study of an oscillating airfoil in a power-extraction regime. aiaa journal 46:1318–1330 lefebvre jn and jones ar (2019) experimental investigation of airfoil performance in the wake of a circular cylinder. aiaa journal 57:2808–2818 schafer rw (2011) what is a savitzky-golay filter?. ieee signal processing magazine pages 111–117. date of publication: 15 june, 2011. shamai m, dawson stm, mezić i, and mckeon bj (2020) from unsteady to quasi-steady dynamics in the streamwise-oscillating cylinder wake. arxiv 2007.05635v1[physics.flu-dyn]. phys. rev. fluids, to appear. streitlien k, triantafyllou gs, and triantafyllou ms (1996) efficient foil propulsion through vortex control. aiaa journal 34:2315–2319 su y and breuer k (2019) resonant response and optimal energy harvesting of an elastically mounted pitching and heaving hydrofoil. physical review fluids 4:064701–1:18 van oudheusden bw, scarano f, van hinsberg np, and watt dw (2005) phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence. experiments in fluids 39:86–98 xiao q and zhu q (2014) a review on flow energy harvesters based on flapping foils. journal of fluids and structures 46:174–191 introduction background experimental setup passive airfoil configuration driven airfoil configuration piv system phase reference determination for passive and driven cases comparison between driven and passive airfoil dynamics observed flow structures and influence on dynamics conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 investigation of large scale motions in zero and adverse pressure gradient turbulent boundary layers using high-spatial-resolution piv d. jovic1,∗, m. shehzad1, b. sun1, y. ostovan2, c. cuvier2, j.m. foucaut2, c. willert3, c. atkinson1, j. soria1 1 laboratory for turbulence research in aerospace & combustion (ltrac), department of mechanical and aerospace engineering, monash university, clayton, 3800, victoria, australia 2 univ. lille, cnrs, onera, arts et metiers institute of technology, centrale lille, umr 9014 lmfl laboratoire de mécanique des fluides de lille kampé de fériet, lille, f-59000, france 3 institute of propulsion technology, german aerospace center (dlr), cologne, germany ∗ daniel.jovic@monash.edu abstract particle image velocimetry (piv) has been used to capture the high-spatial-resolution (hsr) two-component, two-dimensional (2c-2d) velocity fields of a zero-pressure-gradient (zpg) turbulent boundary layer (tbl) and of an adverse-pressure-gradient (apg) tbl. proper orthogonal decomposition (pod) is performed on the measured velocity fields to characterize the velocity fields as large or small scale motions (lsms or ssms), with further characterisation of the lsms into high and low momentum events. this paper reports the findings of the piv experiment and the subsequent analysis of the high reynolds number zpg and apg tbls. 1 introduction the investigation of lsms in tbl flows is essential in order to identify and characterize the dominant coherent structures in these flows. lsms are coherent patterns of alternating regions of high and low momentum, such as the velocity streaks of the buffer layer. proper orthogonal decomposition (pod) is performed on the velocity field to study the coherent structures in turbulent flow. this allows the investigation of distribution of turbulent kinetic energy (tke) as a function of scale in the tbl flows that are inhomogeneous in the streamwise direction liu et al. (2001). pod allows for lsms to be characterized as structures whose contribution to the domination spatial mode is above a threshold, with further characterization into high and low momentum events based on the temporal coefficient. 2 experimental methodology high-spatial resolution (hsr) 2c-2d single-exposed piv images were taken in the x−y plane of the turbulent boundary layers in the lmfl high-reynolds-number boundary layer wind tunnel at laboratoire de mécaniquedes fluides de lille (lmfl), lille, france. this facility has a 2m wide, 1m high and 20.6m long test section with the zpg, favourable-pressure-gradient (fpg) and apg sections, as shown in figure 1. zpg fpg apg fov fov 3.5m 2.2mue = 9m/ s x y -5 deg x = 6.8m s = 5.6m figure 1: schematic of the test section in the lml wind tunnel. figure adapted from cuvier et al. (2017). the fovs shown in figure 1 were illuminated using a dual-cavity bmi nd:yag laser with a wavelength of 532nm and an output energy of up to 200mj. this enabled an imperx bobcat b6640 29mp camera to image the seeding with a mean diameter of 1µm produced by a seeder using a water-glycol mixture. over 10,000 single-exposed image pairs were captured, which were subsequently analysed using an in-house multigrid/multipass cross-correlation piv algorithm written by soria (1996). due to the physical sensor array size of the camera, dewarping was used to correct for lens distortion, as done in sun et al. (2021). 3 results and discussion figure 2: mean streamwise velocity profile (u+) with high momentum lsms (u+ h ) and low momentum lsms (u+ l ). the results obtained from this experimental campaign are in good agreement with the euhit results from cuvier et al. (2017) which were collected in the same facility under identical operating conditions. the euhit results were captured with more cameras than the current experiment, which allowed measurement of a longer domain at significantly less spatial resolution. the analysis is performed using the snapshot pod method, and the results allow for the velocity fields used in the pod to be characterized as lsms that are high or low-momentum events, which aide in the investigation of the effect of lsms on the turbulent statistics. figure 2 shows that the results for the mean streamwise velocity profile of the zpg-tbl, which shows that the high momentum lsms have a higher mean streamwise velocity than the original ensemble and that the low momentum lsms have a lower mean streamwise velocity than the original ensemble. similar results were observed for the apg-tbl, which along with the effect of these events on the second-order turbulent statistics, will be presented. further details are available in shehzad et al. (2021). 4 acknowledgements the authors would like to acknowledge the support of the australian government on this research through an australian research council discovery grant. daniel jovic and bihai sun gratefully acknowledge the support through an australian government research training program (rtp) scholarship. callum atkinson was supported by an arc discovery early career researcher award (decra) fellowship. the authors also acknowledge the computational resources provided via a ncmas grant and an arc lief grant. references cuvier c, srinath s, stanislas m, foucaut jm, laval jp, kähler cj, hain r, scharnowski s, schröder a, geisler r, agocs j, röse a, willert c, klinner j, amili o, atkinson c, and soria j (2017) extensive characterisation of a high reynolds number decelerating boundary layer using advanced optical metrology. journal of turbulence 18:929–972 liu z, adrian rj, and hanratty tj (2001) large-scale modes of turbulent channel flow: transport and structure. journal of fluid mechanics 448:53–80 shehzad m, sun b, jovic d, ostovan y, cuvier c, foucaut jm, willert c, atkinson c, and soria j (2021) investigation of large scale motions in zero and adverse pressure gradient turbulent boundary layers using high-spatial-resolution particle image velocimetry. experimental thermal and fluid science soria j (1996) an investigation of the near wake of a circular cylinder using a video-based digital crosscorrelation particle image velocimetry technique. experimental thermal and fluid science 12:221–233 sun b, shehzad m, jovic d, cuvier c, willert c, ostovan y, foucaut jm, atkinson c, and soria j (2021) distortion correction of two-component-two-dimensional piv using a large imaging sensor with application to measurements of a turbulent boundary layer flow at reτ = 2386. experiments in fluids introduction experimental methodology results and discussion acknowledgements 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 piv and deformation measurements on the rotor blade of a rotating, scaled model wind turbine with flexible blades under tailored inflow conditions tom t. b. wester1∗, lars kröger1, apostolos langidis1, simon nietiedt2, robin rofallski2, martina goering2, thomas luhmann2, joachim peinke1, gerd gülker1 1 university of oldenburg, forwind institute of physics, 26129 oldenburg, germany 2 jade university of applied sciences, institute of applied photogrammetry and geoinformatics (iapg), 26121 oldenburg, germany ∗ tom.wester@uni-oldenburg.de abstract wind turbines face harsh inflow conditions when operating in the atmospheric boundary layer or in the wake of other wind turbines. the incoming velocity field can change within seconds due to the turbulent structures it contains, resulting in a rapid change of several degrees in the angle of attack for the rotating blade. aerodynamics are hence rapidly altered, leading to changes of the occurring forces on the rotor. such dynamic forces cause the blades to twist and bend, accelerating fatigue and reducing the lifetime of a turbine spinato et al. (2009). isolating these effects and analyzing them in more detail, however, presents a challenging problem. it is difficult to reproduce actual inflow conditions sufficiently well in both experiments and simulation. in addition, measurements on the blades of a rotating model wind turbine pose major challenge. in this study, this complex task is realized and a model wind turbine is investigated under three-dimensional tailored turbulent inflow. this experimental study combines the measurement of the occurring forces on the model wind turbine, detection of the blade deflections and turbine motions generated by the inflow, and the simultaneous measurement of the flow around the rotor blades using particle image velocimetry (piv). measurements are performed in a closed loop wind tunnel with an open test section at the university of oldenburg. the outlet of used wind tunnel has a size of 3m × 3m. the length of the open test section is 30m. a picture of the setup is shown in fig. 1(a). to generate realistic turbulent wind fields an active grid is used neuhaus et al. (2020). the grid is attached to the nozzle (purple square) and consists of 80 individual movable shafts each equipped with diamond shaped flaps to change the blockage locally. such grids can be used to reproduce very complex flow fields as often as desired kröger et al. (2021). to characterize the generated inflows a 2d itasca lda system with an focal length of 2.6m and sampling rates up to 2khz from tsi is used (orange square) during experiments. thus, a non-intrusive, but nevertheless simultaneous detection of the inflow is possible. for higher temporal resolution, additional independent hot-wire measurements at 20khz were performed at the same location. the mowito 1.8 model wind turbine berger et al. (2018) (yellow square) is exposed to the turbulent wind fields generated. the turbine with a rotor diameter of 1.8m is characterized by a blade design with high deformability. the deformability of the blades, which is based on the nrel 5mw turbine, enables an even more realistic investigation of the influence of turbulence on the blade motion. a multi-camera photogrammetry system is used to capture the three-dimensional blade motions across the entire rotor plane of the turbine. the system consists of four pco.dimax high-speed cameras (blue circles) and four high speed led panels for illumination, mounted upstream of the wind turbine. to guarantee synchrony all used measurement systems are synchronized to the 12 o’clock position of the turbine at each rotation. the synchronization of the systems was already optimized in previous studies nietiedt et al. (2019); kröger et al. (2020). the main focus of the presentation will be time-resolved stereoscopic piv measurements. the light sheet used during measurements is aligned parallel to the wind tunnel floor. the field of view is chosen at the 12 o’clock position of the turbine at different span positions along the blade. for measurements two phantom v1212 cameras are used with a sampling rate of 4khz and a measurement duration of 25s. they are mounted on a support structure above and below the turbine hub (red circles). an exemplary velocity field taken from the measurement at 70% span is shown in fig. 1(b). the figure shows the evolving ux velocity component of the flow around the blade in a top view. the tailored turbulent inflow is coming from the left-hand side (x-direction). the rotor blade passes the flow perpendicularly along the y-direction from top to bottom of the picture. the vector field nicely shows the influence of the rotor blade on the flow. the flow is accelerated by the blade in y-direction and thus follows the blade geometry. while the flow is accelerated at the leading edge of the blade, the flow at the trailing edge is reversed towards the inflow. in addition, the flow downstream of the rotor blade shows a clear velocity deficit due to the extracted energy relative to the flow upstream of the rotor plane. further influences of the tailored turbulent inflow on the aerodynamics and the resulting blade deflections will be discussed in more detail in the presentation during the conference. (a) experimental setup showing the active grid marked in purple, the mowito turbine marked in yellow, the 2d lda system marked in orange, the photogrammetry system marked in blue and the stereo piv system marked in red. (b) examplary velocity field taken from the piv measurement at 70% span position. the colors represent the normalized ux component of the flow field. the inflow comes from the left and the rotor blade moves from top to bottom through the field. the blade cross-section is drawn here in black. references berger f, kröger l, onnen d, petrović v, and kühn m (2018) scaled wind turbine setup in a turbulent wind tunnel. journal of physics: conference series 1104:012026 kröger l, hölling m, gülker g, and peinke j (2021) taming chaos with active grids–reproducibility in turbulent wind tunnel experiments. arxiv preprint arxiv:210104420 kröger l, wester t, langidis a, nietiedt s, göring m, luhmann t, peinke j, hölling m, and gülker g (2020) experimental study of fluid-structure interaction at a model wind turbine blade using optical measurement techniques. in journal of physics: conference series. volume 1618. page 032025. iop publishing neuhaus l, hölling m, bos wj, and peinke j (2020) generation of atmospheric turbulence with unprecedentedly large reynolds number in a wind tunnel. physical review letters 125:154503 nietiedt s, goering m, willemsen t, wester t, kröger l, guelker g, and luhmann t (2019) measurement of fluid-structure interaction of wind turbines in wind tunnel experiments: concept and first results.. international archives of the photogrammetry, remote sensing & spatial information sciences spinato f, tavner pj, van bussel g, and koutoulakos e (2009) reliability of wind turbine subassemblies. iet renewable power generation 3:387–401 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 trackaer: real-time event-based particle tracking alexander rusch1∗, thomas roesgen1 1 eth zurich, institute of fluid dynamics, zurich, switzerland ∗ arusch@ethz.ch 1 introduction & related work event-based cameras (lichtsteiner et al., 2008; posch et al., 2010; gallego et al., 2020) operate fundamentally different from frame-based cameras: each pixel of the sensor array reacts asynchronously to relative brightness changes creating a sequential stream of events in address-event representation (aer). each event is defined by a microsecond-accurate time stamp, the pixel position and a binary polarity indicating a relative increase or decrease of light intensity. thus, event-based cameras only sense changes in a scenery while effectively suppressing static, redundant information. this renders the camera technology promising also for flow diagnostics. in established approaches like piv or ptv vast amounts of data are generated, only for a large part of redundant information to be eliminated in data post-processing. in contrast, eventbased cameras effectively compress the data stream already at the source. to make full use of this potential, new data processing algorithms are needed since event-based cameras do not generate conventional framebased data. this work utilizes an event-based camera to identify and track flow tracers such as helium-filled soap bubbles (hfsbs) with real-time visual feedback in measurement volumes of the order of several cubic meters. the utility of event-based cameras for flow diagnostics has been demonstrated in a few studies already. drazen et al. (2011) used one of the first dynamic vision sensors (dvs) available for a proof-of-concept study showing that 2d particle tracking velocimetry is possible for pipe flows with solid particles as tracers. ni et al. (2012) performed particle tracking with event-based cameras in a microscopic environment. in order to distinguish microspheres from noise, they applied a circle hough transform. borer (2014) and borer et al. (2017) extended the idea of event-based particle tracking to a larger domain of interest and used multiple event-based cameras for volumetric ptv measurements. data sets were generated in a 3d calibrated setup of three dvs cameras and processed off-line. their tracking approach made use of a kalman filter for track prediction and relied on triangulating particle tracks after identifying them in each camera’s individual data stream. wang et al. (2020) used an event-based stereo camera setup for volumetric ptv measurements imposing an incompressibility constraint for regularization. their approach was evaluated using simulated data and with measurements in a centimeter-sized, water-filled cavity. 2 real-time algorithm there are two basic ways of processing the asynchronous event data stream: in one approach, events are accumulated in fixed time windows or fixed-size batches followed by processing steps using pseudo-frames reconstructed from the events. while this allows the application of well-established frame-based computer vision algorithms, it also implies a loss of the high temporal accuracy and low latency of event-based cameras. alternatively, events can be processed in a fully sequential manner, i.e., “event-by-event”, keeping the precise timing information and ordering of the events. no frames are reconstructed that could interface to classical computer vision algorithms for further processing. in this case, event-based algorithms are required that analyze the flow (motion) information contained in the asynchronous event stream. our work follows such a per-event approach, preserving the speed and scalability of the technology. the key to identifying and tracking a moving object from the event stream is to identify coherent spatio-temporal event activity. each incoming event may be added to a cluster, updating that cluster’s position and the list of contributing events. if no assignment can be made, the event information is registered to prepare a trigger for the future creation of a new cluster. stale events are pruned from existing clusters using an “age” criterion. this may happen in response to an occlusion in the scenery or when a moving object leaves the field of view. the algorithm self-supervises its performance and may selectively skip processing steps if necessary for real-time responsiveness. (a) trackaer event snapshot (16 ms time window). events are displayed indicating positive (white) and negative (black) polarity. tracked clusters are overlaid in red. (b) pseudo-streak integration from events over 10 s to visualize particle trajectories. only every fifth event is visualized and event polarity is not indicated. figure 1: visualization (field of view approx. 3.5 m × 2.0 m) of the flow caused by an indoor ventilation system. helium-filled soap bubbles are introduced at the bottom of the scene and convected. 3 results & conclusion for visualization only, pseudo-frames can be generated from the event stream and fused with the movement of the cluster trackers. no frames are used at any stage of the tracking algorithm. figure 1 shows results from a study of an indoor ventilation system. a room is partially seeded with hfsbs that move due to the flow induced by the ventilation system. events shown in the background are measurement noise. trackaer successfully ignores these spurious events and does not interpret them as tracer particles. more than 100 hfsbs are successfully tracked simultaneously and in real-time. our new real-time event-based detection and tracking algorithm, trackaer, provides immediate insight into flow fields during measurements. tracer particles are successfully detected and tracked in volumes of several cubic meters, whereas noise from the camera sensor and the scenery are effectively eliminated. ongoing research focuses on the actual flow field reconstruction as well as on the extension of the system to volumetric measurements. references borer d (2014) 4d flow visualization with dynamic vision sensors. ph.d. thesis. eth zurich borer d, delbruck t, and rösgen t (2017) three-dimensional particle tracking velocimetry using dynamic vision sensors. experiments in fluids 58:165 drazen d, lichtsteiner p, häfliger p, delbrück t, and jensen a (2011) toward real-time particle tracking using an event-based dynamic vision sensor. experiments in fluids 51:1465–1469 gallego g, delbruck t, orchard gm, bartolozzi c, taba b, censi a, leutenegger s, davison a, conradt j, daniilidis k, and scaramuzza d (2020) event-based vision: a survey. ieee transactions on pattern analysis and machine intelligence lichtsteiner p, posch c, and delbruck t (2008) a 128×128 120 db 15 µs latency asynchronous temporal contrast vision sensor. ieee journal of solid-state circuits 43:566–576 ni z, pacoret c, benosman r, ieng s, and régnier s (2012) asynchronous event-based high speed vision for microparticle tracking. journal of microscopy 245:236–244 posch c, matolin d, and wohlgenannt r (2010) a qvga 143 db dynamic range frame-free pwm image sensor with lossless pixel-level video compression and time-domain cds. ieee journal of solid-state circuits 46:259–275 wang y, idoughi r, and heidrich w (2020) stereo event-based particle tracking velocimetry for 3d fluid flow reconstruction. in european conference on computer vision. pages 36–53. springer introduction & related work real-time algorithm results & conclusion abstract a micro soap bubble generator for tracers for piv measurement was developed using a home stereolithography 3d printer. the nozzle has a coaxial triple pipe structure, and an orifice cap is attached to the nozzle head. the inner diameter of the central pipe is 0.7 mm, and the wall thickness of the central pipe is 0.7 mm. from the comparison of the smoke wire visualization result of the flow around the cylinder placed under the mainstream flow velocity of 3 m/s and the piv measurement result, it was confirmed that the generated micro soap bubbles have good followability to the flow. generated bubbles’ particle size was estimated to be φ0.2 mm at the minimum and φ6.3 mm at the maximum. the most common was φ0.9 mm ± 0.1 mm, accounting for more than 50% of the total. 1. introduction smoke particles are often used as tracers for piv measurement. however, if the light source's output is insufficient, the brightness of the particle image obtained by visualization will be inadequate due to inadequate light scattering from smoke particles. as a solution to this problem, a method to increase the image brightness by changing the scattered light intensity of the tracer particles without changing the light's output is conceivable. caridi (2018) reported that, using helium-filled soap bubbles (hfsb) as tracer particles, high reflection about 10,000 times more than smoke particles such as 2-ethylhexyl and dshe is obtained. as the intensity of light increases, it becomes possible to measure in a large-scale flow field as large as several meters. bosbach et al. (2009) performed piv measurement of the convection flow field inside the aircraft cabin using hfsb and obtained important knowledge about cabin ventilation. the particle size of smoke particles is about 1 µm; it can be considered that the followability to the airflow is satisfactory, on the other hand when a large particle such as hfsb is used as a tracer, the slip speed (difference between flow velocity and particle velocity used) increases and brings mis-followability (cao et al., 2014). for this reason, scarano et al. (2015) have developed an excellent hfsb generation system. they conducted a survey on the followability of systematic tracer particles for the flow around a cylinder to optimize it. performing tomographic piv measurement of the wake of a cylinder showed that hfsb with well-controlled particle size and buoyancy enables highly accurate turbulence measurement. flaleiros et al. (2019) used two types of bubble generators such as a pitot tube type and an orifice type, for comparison. by changing the supply amount of air, bfs (the bubble fluid solution), and helium gas, the bubble generation form and the effect on the soap bubble diameter were systematically investigated. they quantitatively clarified the flow condition of making the helium-filled microbubbles with neutral buoyancy. development of micro soap bubble generator for piv tracer using home stereolithography 3d printer shu shibata1, takumi yamazaki2 and hisashi matsuda3* 1 undergraduate student, hokkaido university of science (currently, mitsubishi materials techno co.), japan 2 undergraduate student, hokkaido university of science (currently, toshiba elevator and building systems corp.), japan 3 hokkaido university of science, department of mechanical engineering, sapporo, japan. *matsuda-h@hus.ac.jp in addition, barros et al. (2019) clarified the details of complex wake by 3d piv measurement for the flow around the sphere using micro air-bubbles of 10 to 30 μm as a tracer. the development of a generator capable of releasing a large amount of hfsb for wind tunnel experiments has also been reported by gibeau & ghaemi (2018). the bubble generator developed by scarano et al. has been commercialized (kanomax inc.); however, it is not easy to introduce from cost. if the micro soap bubble generator can be manufactured using a home 3d printer that has become widespread in recent years, the cost required for piv measurement can be significantly reduced. in this study, we attempted to manufacture a micro soap bubble generator nozzle using a home hot-melt 3d printer and a stereolithography 3d printer. the purpose is to realize a low-cost piv measurement system by developing a micro soap bubble generator. 2. development of nozzle for generating micro soap bubble 2.1 nozzle production using a hot-melt 3d printer as reported by bosback et al. (2006) and faleiros et al. (2019), the coaxial triple pipe structure is important for generating microbubbles. we understood that the key point is the mechanism that generates microbubbles in the inner double pipe part and separates the microbubbles one by one by sending air from the outermost pipe. in faleiros et al. (2019), both a pitot tube type and an orifice type nozzle were studied. it is difficult to accurately manufacture the pitot tube type nozzle with a home 3d printer. in addition, since it is impossible to check the manufacturing status even if the entire nozzle is integrated, we decided to adopt the bosback method (bosback et al. 2006), which combines an orifice cap with a coaxial triple pipe. following faleiros et al. (2019), we aimed to generate microbubbles with a diameter of 0.6 mm. for making the nozzle, we decided to use a hot-melt 3d printer (creality ender 3 pro, creality co.), which has become popular in recent years. a pla resin made by creality was used as the filament for the printer. cura 15.04 was used as the slicer software. the minimum stacking pitch of this printer is 0.1 mm. fig.1 shows the hot-melt 3d printer used, and table 1 shows the specifications of the printer. bosback et al. (2006) and faleiros et al. (2019) have reported schematic cross-sectional views of the microbubble generator. however detailed dimensions such as pipe wall thickness have not been clarified. therefore, as the first attempt, we decided to manufacture a coaxial triple pipe structure as shown in fig. 2. the design concept is to provide a central pipe for helium supply, stack a bfs pipe on the outside, and form an air pipe for separating the microbubbles on the outside. the helium supply is provided from the nozzle end, and the bfs and air supply are provided at the mid portion of the nozzle. first, we checked whether printing with the hot-melt 3d printer was possible for this coaxial triple pipe structure. a total of 12 nozzles were prototyped while changing the overall and detailed dimensions of the nozzle, and the bubble generation rate of each nozzle was tested. as the bubble fluid solution (bfs), a mixed solution of 30% water, 40% polyvinyl alcohol, and 30% cucute (kao corp.) was used. micro-compressors for fish raising were used to generate soap bubbles. aiming to generate micro soap bubbles with a diameter of 0.6 mm, we tried to reduce the diameter of the innermost central pipe as much as possible. we repeated trial production until the pipe with an inner diameter of 1 mm was formed without clogging. when we finally conducted a micro bubble generation test using the completed prototype nozzle, we could generate micro soap bubbles continuously for 16 seconds, albeit only once. fig.3 shows the state during operation. although the orifice cap was not attached, the validity of the triple coaxial structure was verified. however, it is difficult to reduce the thickness of the nozzle wall surface to less than 1 mm with the hotmelt 3d printer used in this study. in addition, it became clear that the reproducibility of production was low, and the yield was poor. fig.4 shows examples of failure. it turned out that there is a big problem in manufacturing accuracy in each case. fig.1 fused deposition modeling 3d printer table 1 specifications of the fused deposition modeling 3d printer fig. 2 nozzle for generating microbubbles for trial production fig. 3 state of micro soap bubbles generation by prototype nozzle fig. 4 examples of nozzle manufacturing failure using a hot-melt 3d printer print range [mm] 220×220×250 nozzle diameter [mm] 0.4 printing accuracy [mm] ±0.1 maximum printing speed [mm/s] 180 stacking pitch [mm] 0.1～0.4 supported filament [mm] 1.75 2.2 quality function deployment the micro soap bubbles were successfully generated, although it was only once, we decided to sort out the knowledge about nozzle design so far using qfd (quality function deployment). qfd is an effective tool for associating the quality required for the development target with technical characteristics. as orifice type coaxial triple pipe nozzle design variables, the central pipe diameter, the bfs pipe diameter, the air pipe diameter, the pipe length, the central pipe wall thickness, the bfs pipe wall thickness, the air pipe wall thickness, the nozzle cap diameter, and the nozzle cap thickness and the nozzle cap corner r were selected. as the requirements for a micro soap bubbles generator for these design variables, the required dimensional feasibility, pore depth processing accuracy, soap bubble feasibility, and wet edge area, were mentioned. the degree of influence on these requirements was evaluated from the findings obtained in the prototypes so far. as a result, four items, the central pipe diameter, and the bfs pipe diameter, the central pipe wall thickness, and the bfs pipe wall thickness, were extracted as important design variables. table 2 shows an excerpt of the qfd results. table 2 qfd results 2.3 nozzle production using a stereolithography 3d printer since it was found that the hot-melt 3d printer could not solve the problem of manufacturing accuracy, we decided to introduce a stereolithography 3d printer (nova3d bene4 mono) to improve the modeling accuracy of the design variables extracted by qfd. the minimum stacking pitch of this printer is 0.05 mm, and higher accuracy can be expected compared to the hot-melt type. the resin used was standard photopolymer resin (semi-transparent) manufactured by elegoo. the slicer software used was novamaker. fig.5 shows the appearance of bene4, and table 3 shows the specifications of bene4. depending on the placement direction of the model with respect to the platform, the finish accuracy of the modeled object will differ. since horizontal and diagonal placements are affected by gravity during molding, vertical placement was adopted. it was also found that the coaxial pipe size of the nozzle was increased by about 10% with respect to the design value. the influence of the platform position during molding was also investigated, and it was confirmed that the central part was suitable. we also investigated how thin a wall surface can be formed. it was confirmed that up to 0.2 mm of the partition wall can be modeled as a cylinder. we clarified the molding up to a pipe diameter of 0.6 mm to a depth of about 60 mm. the stacking pitch was set to 0.5 mm. the exposure time set to 3s. under the above processing conditions, we pursued the smallest possible hole diameter for the central pipe diameter while having high reproducibility. we searched for a wall thickness that enables stable molding of a central pipe with a length of 65 mm without cracking. as a result, a wall thickness of 0.7 mm was adopted. we also pursued the best shape by trial and error for the bfs pipe diameter and the bfs pipe wall thickness. after 60 prototypes, we succeeded in developing a nozzle that stably generates micro soap bubbles. the total length of the nozzle was 66 mm. the structure is such that the supply part of the central pipe is provided at the nozzle end, and the bfs liquid supply part and the blowout air supply part are provided on the side surface of the intermediate part of the nozzle. the production time with the 3d printer is about 3 hours. fig.6 shows the overall view of the completed final nozzle, and fig.7 shows the state when soap bubbles are generated (without the orifice cap). as for the orifice cap, since the coaxial triple pipe nozzle is not molded with the dimensions according to the design drawing, it is molded about 10% larger, so it was necessary to fine-tune the inner diameter while observing the quality of the nozzle. fig.8 shows a detailed cross-sectional view of the completed orifice cap and the completed nozzle. fig.5 stereolithography 3d printer table 3 specifications of the stereolithography 3d printer fig.6 complete nozzle fig. 6 completed nozzle fig.7 state during operation print range [mm] 130×70×150 printing accuracy [µm] 50×50 printing speed [mm/h] 10～30 stacking pitch [mm] 0.05 next, the suitable conditions for generating micro soap bubbles were adjusted under the condition that air was also supplied to the central pipe. the most stable conditions for generating microbubbles were 4.35 ml/min, 0.50 ml/min, and 0.45 ml/min, respectively, as the supply air, bfs, and helium alternative airflow rates. the flowmeters used for adjustment are pfm710 (smc corporation), lm05zzt-ar (horiba, ltd.), and mass flow meter model 3810dsii (koflock co., ltd.). the air compressor used was sk-11 sr-045 (fujiwara sangyo co., ltd.). fig.9 shows a configuration of the soap bubble generator developed. the total cost (including the cost of the stereolithography 3d printer) for constructing this system was about 1,400 dollars. fig. 8 detailed cross-sectional view of the complete orifice cap and nozzle fig.9 overview of the micro soap bubble generator generation system pc data logger nozzle flowmeter flowmeter flowmeter needle valve needle valve needle valve hand valve air compressor power supply : air piping : bfs piping : helium piping bfs tank 3. property test of the micro soap bubble generator following the research by scarano et al. (2018), the followability of the micro soap bubbles was evaluated for the flow around the cylinder. a cylinder (outer diameter 114 mm) was placed in a circulating wind tunnel (maximum wind speed: 25 m/s, ebara corporation) of an outlet of 400 mm x 400 mm. under the mainstream velocity of u=3m/s, the symmetry of the flow was checked using the smoke wire method. fig. 10 shows the experimental scene, and fig.11 shows the visualization result by the smoke wire method. liquid paraffin was used as the smoke material. next, using a high-speed camera of k7-usb (kato koken co., ltd.) and the analysis software of flow expert 2d2c-l (kato koken co., ltd.), ptv/piv measurements were carried out. in this measurement, the air was supplied to the central pipe instead of helium gas. for the experiment, adjustable focus blue laser (2.5w, chinanczone) for the light source, ccm5-p01/m (solab japan co., ltd.) for the optical mirror, lk1684l1-a (solab japan co., ltd.) for the cylindrical lens were used. fig.12 shows the trace lines of micro soap bubbles from ptv measurements, and fig.13 shows the same data piv-processed by the correlation method. from the piv measurement results, good symmetry was observed, as in the case obtained by the smoke wire method. it was confirmed that the micro soap bubbles generated from the developed nozzle had good followability. to find out what size soap bubbles were generated, we selected a total of 271 particles that could be clearly observed from 20 snapshots obtained during the measurement. the contours of the soap bubbles were photographed, and the actual diameter of the soap bubbles was estimated based on the angle of view and the number of pixels at the time of photography. an example of the snapshot image is shown in fig.14. a histogram of the measurement data is shown in fig.15. the minimum and maximum diameters of the micro soap bubbles generated by the newly developed nozzle were estimated to be about 0.2 mm and 6.3 mm, respectively. the most frequently generated particle diameter was 0.9 mm ± 0.1 mm, and the generation rate was about 50% of the total. although it was larger than our target of φ0.6 mm, we coould generate soap bubbles of φ1 mm or less stably. the equation of motion in the vertical direction of a particle is obtained as in eq. (1). here, m is the mass of the particle, up is the velocity of the particle, uf is the velocity of airflow, d is the diameter of the particle, ρp is the density of the particle, ρf is the density of air, and g is the acceleration of gravity (saito and nakajima, 2017). here, the mass m of the particles is obtained by multiplying the particle diameter by the film thickness in soap bubbles. the film thickness δt is assumed to be about 0.1 µm according to the literature (faleiros et al., 2019). the sedimentation velocity of the soap bubbles is calculated as (2). the most frequently occurring soap bubble with a diameter of 0.9 mm has a settling velocity of 0.029 m/s, and the settling distance, when measured at 1000 fps (0.001 s), is 0.03 mm. it can be judged that they had good followability. 𝑚 𝑑𝑢𝑝 𝑑𝑡 = 𝜋𝑑3 6 𝜌𝑝𝑔 − 𝜋𝑑3 6 𝜌𝑓𝑔 − 3𝜋𝜇𝑑 𝑢𝑝 − 𝑢𝑓 …… (1) 𝑢𝑡 = 𝑢𝑝 − 𝑢𝑓 = 𝛥𝑡𝜌𝑝 − 𝜌𝑓 𝑑 2𝑔 18𝜇 …… (2) fig.10 smoke wire visualization experiment fig.11 smoke wire visualization fig. 12 ptv analysis results fig. 13 piv analysis results スモークワイヤ法可視化結果 fig.14 snapshot of micro soap bubbles fig. 15 histgram of diameter of micro soap bubbles スモークワイヤ法可視化結果 4. wind tunnel test using micro soap bubbles as a tracer finally, piv measurement was attempted by applying the developed micro soap bubbles tracer to a wind tunnel experiment for a two-dimensional backstep (step height 20 mm) flow. fig. 16 shows the state during piv measurement. fig.17 shows the piv measurement results at the mainstream wind speed u = 5 m/s. the flow is from left to right in the figure. it was confirmed that the wind speed obtained from the piv measurement results was in good agreement with the wind speed measurement results by the hotwire anemometer. good measurement was confirmed even at mainstream speed u = 20 m/s. the piv measurement for the flow around the naca0015 (u=5m/s) blade of the chord length of 300 mm in an environment of -5 ° c was also carried out using the natural snow wind tunnel hokkaido university of science (matsuda et al., 2021). fig.18 shows the state of the wind tunnel experiment. vision research inc.'s phantom v1212 was used for the high-speed camera, and kato koken's 8w laser sheet was used for the laser light source. flow expert 2d2c-l (kato koken co., ltd.) was also used as the measurement software. in fig.19, the flow is from left to right. it was possible to observe large-scale separation from the leading edge of the blade, similar to the smoke visualization result. the bfs did not freeze even in a measurement environment of -5 ° c, and that the micro soap bubbles after generation also maintained good followability. it was found that the newly developed micro soap bubble generator is extremely effective for piv measurement under various conditions. fig.16 piv measurement of 2d backstep model fig.17 piv analysis result (u=5m/s) fig.18 natural snow wind tunnel facility of the hokkaido university science fig.19 piv analysis result (u=5m/s) スモークワイヤ法可視化結果 5. conclusion a micro soap bubble generator for tracers of piv measurement was developed using a home stereolithography 3d printer. the nozzle for generating micro soap bubbles has a coaxial triple pipe structure, and an orifice cap is attached to the nozzle head. the inner diameter of the central pipe of the nozzle for generating is 0.7 mm, and the wall thickness of the central pipe is 0.7 mm. a detailed crosssection of the entire nozzle was shown. it took about 3 hours to print one nozzle. from the comparison of the smoke wire visualization result of the flow around the cylinder and the piv measurement result, it was confirmed that the generated micro soap bubbles have good followability to the steady flow field. the particle size of the generated bubbles was estimated to be 0.2 mm at the minimum and 6.3 mm at the maximum. the most common occurrence was 0.9 mm ± 0.1 mm, which was about 50% or more of the total. applying the developed micro soap bubbles generator as a seeding device, a two-dimensional backstep flow and the flow around the blade were evaluated. it was found that the newly developed micro soap bubble generator is extremely effective for piv measurement under various conditions. this investigation was started as graduation research; we will proceed with the research toward the generation of micro soap bubbles that can cope with field piv measurement in the future. 6. acknowledgments this research started with the kind advice of prof. scarano (tu delft). for the particle size study, we were advised by associate professor tasaka of hokkaido university. wind tunnel experiments were helped by mr. toshiki takahashi and mr. tasuku tanaka (4th years student of the hokkaido university of science at that time). we would like to thank all the people involved for their kindness. references barros, d., duan, y., troolin, d., longmire, e.k. and lai, w. (2019), soap bubbles for volumetric velocity measurements in air flows, 13th ispiv 2019, munich, germany. bosbach, j., kühn, m. and wagner, c. (2009), largescale particle image velocimetry with helium filled soap bubbles. exp fluids 46:539-547, doi 10;1007/s00348-008-0579-0. cao x., liu j. and jiang n. (2014), particle image velocimetry measurement of indoor airflow field : a review of the technologies and applications, energy and buildings, doi:10.1016/j.enbuild.2013.11.012 caridi, g.c.a. (2018), development and application of helium-filled soap bubbles for large-scale piv experiments in aerodynamics. ph.d. thesis, doi.org/10.4233/uuid:effc65f6-34df-4eac-8ad93fdb22a294dc. fleiros, d.e., tuinstra, m., sciacchitano, a. and scarano, f. (2019), generation and control of helium-filled soap bubbles for piv, exp fluids 60:40, doi.org/10.1007/s00348-019-2687-4. gibeau, b. and ghaemi, s. (2018), a modular, 3d-printed helium-filled soap bubble generator for largescale volumetric flow measurements, exp fluids 59:178, doi.org/10.1007/s00348-018-2634-9. matsuda, h., chiba, t., yagami, m., tajima, y., watanabe, n., sato, h. and takeyama, m. (2021), control of snow falling flow around naca0015 blade using practical-use plasma electrode, asian conference of gas turbine 2021, quingdao, chaina, (scheduled to be presented) saito, y. and nakajima, r., (2017), visualization of inner flow inside air conditioning system with piv, calsonic kansei technical review vol.13 p22~26 (in japanese). scarano, f., ghaemi, s., cardi, g.c.a., bosback, j., dierksheide, u. and sciacchitano, a. (2015), on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments, exp fluids 56:42, doi 10.1007/s00348-015-1909-7. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 an experimental approach to analyze aerosol and splatter formation in a dental practice p. mirbod1∗, e. a. haffner1, m. bagheri1, j. e. higham2 1 university of illinois at chicago, department of mechanical and industrial engineering, 842 w. taylor street, chicago, il, 60607, usa 2 university of liverpool, school of environmental sciences, liverpool, uk ∗ pmirbod@uic.edu abstract the flow velocity, trajectories, and size distribution of droplets produced during a dental scaling procedure using a cavitron ultrasonic scalar (cus) has been investigated by optical flow tracking velocimetry and shadowgraphy measurements. the droplet sizes are found to vary from 5 -500 µm; these correspond to droplet nuclei that could carry viruses. the droplet velocities also vary between 0.7 m/s and 1.3 m/s. these observations confirm the critical role of aerosols in the transmission of disease during dental procedures, providing invaluable knowledge for developing protocols and procedures to ensure the safety of both dentists and patients especially during covid-19 pandemic. 1 introduction global emergence of novel covid-19 virus has required health care professionals to implement prescriptive adjustments. one of the high-risk areas of infection is dental offices since many of dental procedures produce aerosols because of high-speed dental instruments harrel and molinari (2004). this lead the researchers to design , e.g., aero-shields, barriers and high-powered suction equipment, to reduce the level of aerosol particle concentration and protect clinicians liu et al. (2019), and majidi and club (2020). to design the appropriate safety tools, it is crucial to understand how this virus, along with others, propagate throughout the atmosphere of the exam room. this plan is to perform experiments on the measurement of droplet sizes in the splatter created from a patient’s mouth by a cavitron ultrasonic scaler (cus) using optical flow tracking velocimetry (oftv) and shadowgraphy techniques. this study is the first of its kind to investigate droplet nuclei size and velocity distribution in detail using quantitative fluid mechanics methods with the implementation of dental instruments. the obtained data in this work can be employed to quantify the amount of virus transmitted to a poorly ventilated space in a dental clinic. in addition, they can be used to further model how airborne particles are transported into the human respiratory system. 2 materials and methods oftv (optical flow tracking velocimetry) is a commonly used method in fluid mechanics fullmer et al. (2020) that we used it to determine the velocity fields and lagrangian paths of droplets created by the cavitron select sps ultrasonic scaler (cus); using a 1 mm laser sheet created by a 527 nm nd-ylf (photonics industries, dm20-527) laser. we were able to illuminate a single plane inside the aerosol, providing us with a two-dimensional (2d) slice for analysis. using a high-speed camera (phantom) equipped with a nikon lens with a focal length of 60 mm, we were further captured the reflections from the water droplets. we considered two different planes, (p1 parallel, and p2 perpendicular to the tip of the cus), as shown in fig. 1(b,c). in each case, to ensure that the mean velocities were fully resolved, 3000 images were collected resolving more than 100 integral time scales. as in a dental practice, the tip of the slimline placed perpendicular to the front lower teeth pointing towards the gum line (fig. 1a) for all of the experiments where the cus connected to a standard water tap (i.e., 20 psi to 40 psi pressure). the measured flow rate defined as 29.5 ml/min. figure 1: (a) setup schematic for the optical flow tracking velocimetry (oftv) technique to detect the droplet velocity and lagrangian path. examples of the raw oftv images in the (b) p1 plane and (c) p2 plane recorded with a high-speed camera at 7.6 khz. (d) schematic of the experimental setup of backlight illumination for the shadowgraphy technique. (e) an example of backlight illumination at 0.08 s recorded using a high-speed camera at 7.6 khz and two halogen backlights. we also used shadowgraphy method which is a well-used technique in fluid mechanics to quantitatively visualize small droplets using simple optics settles (2001). to create these visualizations, we used a high magnification and back-light illumination (fig. 1d). the measurement plane is defined by the camera depth of focus in the focal plane. a navitar zoom lens (thorlabs, inc.) used attached to the high-speed phantom camera set to an exposure rate of 20 µs. this allowed us to zoom into a small region ( 100 µm thick) to accurately measure the size of the droplets on the order of 5 µm (see fig. 1e). from the raw images, we then used an in-house code to detect the particles and determine the size and location of each droplet. the code works by first binarizing the raw image based on an adaptive threshold, and an adaptive hough transform illingworth and kittler (1987), we then determined the circular regions, i.e., droplets, and defined the velocity of the droplets using oftv method. however, instead of using the eigenfeatures for droplet detection, we employed the centroids determined by the hough transform mirbod et al. (2021). to generalize the problem and to characterize the breakup of the fluid in more detail, we also examined some dimensionless parameters, for which we measured the characteristic length to be the cus tip diameter, d=635 µm. comparing these dimensionless values with those produced by coughing and sneezing bourouiba et al. (2014) reveals that some of the values reported in this study (e.g., reynolds number) are still lower compared to the turbulent flow produced by coughing/sneezing, while the stokes number due to the droplet formed by cus is much higher compared to coughing/sneezing cases meaning that most of the droplets settle down. however, our data shows that droplet size in the dental procedure are much smaller in size where precautions must be considered for the safety of those who are exposed to these droplets. more details can be found in mirbod et al. (2021) with the typographical errors in the table that are fixed herein. table 1: the experimental parameters for the different tests conducted at 20°c. the dimensionless parameters remained constant throughout all experiments 3 results fig. 2 shows the global velocity components (u, v, and magnitude) for the planes both parallel and perpendicular to the teeth, i.e., planes p1 and p2, respectively, obtained from oftv. figs. 2(a, d) demonstrate the maximum u velocity of 1.5 m/s that occurs near the tip of the cus close to the front teeth, while it is reduced far from the tip. the mean v velocity is the lowest at 0.2 m/s compared to the mean maximum velocity (2.5 m/s) of the magnitude velocity profile as can be seen in fig. 2(b,c,e,f). figure 2: the mean field of the (a) v (y-axis) velocity component, (b) u (x-axis) velocity component, and (c) velocity magnitude for the plane parallel to the cus tip, p1, and the (d) v (y-axis) velocity component, (e) u (x-axis) velocity component, and (f) velocity magnitude (y-axis) for the plane perpendicular to the cus tip, p2. the white arrows in the figures specify the velocity vectors. fig. 3(a,b), shows measured droplet sizes ranges from 5 µm to 500 µm with a maximum observed speed of 1.4 m/s. the experimentally obtained data are in agreement with the rosin-rammler equation rosin (1933) which is a well-known distribution function and a convenient representation of the droplet size distribution for liquid sprays. in particular, this fitting can be used as an initial condition in numerical simulations to further model how droplets are transmitted to the environment, including dental clinics/offices. figure 3: (a) histogram of the droplet size distribution, (b) the velocity distribution of the droplets, and (c) the rosin-rammler curve fitted for our obtained experimental droplet size data with a 29.5 ml/min flow rate. acknowledgements this work was funded by the university of illinois at chicago (uic) – college of dentistry (grant no. 200258-323152). references bourouiba l, dehandschoewercker e, and bush jw (2014) violent expiratory events: on coughing and sneezing. journal of fluid mechanics 745:537–563 fullmer wd, higham je, lamarche cq, issangya a, cocco r, and hrenya cm (2020) comparison of velocimetry methods for horizontal air jets in a semicircular fluidized bed of geldart group d particles. powder technology 359:323–330 harrel sk and molinari j (2004) aerosols and splatter in dentistry: a brief review of the literature and infection control implications. the journal of the american dental association 135:429–437 illingworth j and kittler j (1987) the adaptive hough transform. ieee transactions on pattern analysis and machine intelligence pages 690–698 liu mh, chen ct, chuang lc, lin wm, and wan gh (2019) removal efficiency of central vacuum system and protective masks to suspended particles from dental treatment. plos one 14:e0225644 majidi k and club hd (2020) dental clinic aerosol management with aero-shield mirbod p, haffner ea, bagheri m, and higham je (2021) aerosol formation due to a dental procedure: insights leading to the transmission of diseases to the environment. journal of the royal society interface 18:20200967 rosin p (1933) laws governing the fineness of powdered coal. journal of institute of fuel 7:29–36 settles gs (2001) schlieren and shadowgraph techniques: visualizing phenomena in transparent media. springer science & business media introduction materials and methods results 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 peregrine falcon wakes examined using volumetric piv chetan jagadeesh1, edward talboys1, daniel troolin2*, martin hyde2 1city, university of london, aeronautics and aerospace research centre, london, united kingdom 2tsi incorporated, fluid mechanics research instruments, st. paul, mn, usa *dtroolin@tsi.com abstract this study presents time-resolved volumetric measurements in the wake of a peregrine falcon model. the experiments were performed in a water flume with a freestream velocity of 10 cm/s and at an angle of 3.25°. the tsi volumetric piv system, using insight v3v-4g software, was used to capture the time-resolved volumetric flow field. the results compare well with previous stereo piv measurements; however, the present results also provide true 3-dimensional flow field information which helps decode the reason for the superior maneuverability. this is attributable to the vortex dominated flow field promoted by its morphology. 1 introduction the peregrine falcon (falco peregrinus) is well known to be the fastest avian species and aerodynamicists have been looking as to how these birds can achieve the speeds they have been observed to achieve in nature. when the bird is in its stoop, it increases speed by furling its wings up such that it is in its most aerodynamic form; named the teardrop configuration. once the falcon needs to control the stoop it opens its wings into the ‘m-shape’ where the bird has its most control. this is the configuration which is studied further herein. in a previous study (gowree et al., 2018) it was observed that the aerodynamics of the falcon is dominated by complicated vortical structures over the bird. in the present work we will be examining in more detail the vortices that are induced by the tip of the wings, named the ‘wing vortex’ and ‘primary feather vortex’. more recently selim et al., 2021 has built upon the results of gowree et al. by studying the stability of the falcon during the stoop phase. they report that when the falcon deploys the hand-wing, in the pull-out phase of the stoop, it creates extra vortex lift in a similar manner to combat aircraft. they also concluded that the falcon maximizes responsiveness by flying in a marginally longitudinally unstable mode where small changes in the hand-wings are used to help the bird stay in control giving them a competitive aerodynamic advantage over their prey. 2 experimental setup a tsi volumetric particle image velocimetry (vpiv) system was used to acquire velocity fields downstream of a peregrine falcon model in a water flume. the falcon model was manufactured using a polyjet 3d printer and possessed approximate dimensions of 0.3m by 0.17m. the water flume test section was 1.4m x 0.4m x 0.45m, and the falcon model was placed 0.4m from the inlet and along the centerline of the test section. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 the experimental setup can be seen in fig. 1. four phantom m310 cameras were arranged on a rail in a line configuration at angles from the normal of the side-wall of the flume of approximately -16°, 7°, 3°, and 12°, and labeled cameras 1, 2, 3, and 4, respectively. three of the cameras were fitted with 100mm lenses and camera 3 (one of the inner cameras) was fitted with a 105mm lens. the outer two cameras (1 and 4) were also fitted with scheimpflug mounts in order to correct for distortion effects associated with viewing the measurement volume through a refractive index change at a larger angle. fig. 1: experimental setup showing the position of the four cameras and the laser measurement volume downstream of the falcon model (flow is from right to left in this image). a litron ldy300 dual-head laser which produced approximately 20 mj/pulse was used to illuminate the measurement volume. a light arm was positioned at the exit of the laser in order to direct the laser light beneath the water channel. light volume optics including a -25mm cylindrical lens and an adjustable focal length spherical lens were used to direct the illumination cone of laser light up through the transparent bottom window of the channel illuminating the measurement volume of size 115×68×17.5mm. data was acquired at a freestream flow velocity of nominally 10 cm/s with the falcon model positioned at the centerline of the water channel at an angle of attack of 3.25° from the streamwise direction. the center of the measurement volume was located 80mm downstream of the wing-tip. data was taken at three separate positions along the span of the channel, offset by 10mm each. the result was three volumes that were overlapped with the neighboring volume by approximately 5mm. the position of the measurement volumes can be seen in fig. 2. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 fig. 2: schematic representation of the measurement volumes with respect to the falcon model. the images were captured at a frequency of 400 hz, or 2.5ms between images. the high capture rate allowed for tracking between frames separated by up to 6*dt, or 15ms. a benefit of this oversampling was that it allowed for a rolling ensemble of particle positions from 16 temporal realizations to be combined in order to achieve high spatial and temporal resolution measurements. insightv3v-4g software was used to coordinate the laser pulses and image capture timing as well as for performing the particle tracking and data analysis. for each experimental run, 2000 image pairs were acquired and processed. data vector processing was performed using dense particle identification and reconstruction (dpir), a technique detailed in boomsma and troolin, 2018. both ensemble and instantaneous velocity fields were calculated and examined. 3 results and discussion particle track positions consisting of 20 time-steps and colored by the streamwise velocity can be seen in fig. 3a. a region of blue stretching from the left side toward the right indicates the slower moving wake downstream of the wing-tip generating vorticity and vortex shedding that can be inferred from the alternating red/green coloring above the blue wake. figure 3b, shows the average streamwise velocity, with an isosurface of q-criterion. this isosurface indicates the position of the core of the vortex from the wing tip vortex. from the end plane, the wake deficit can be clearly seen from the model of the bird. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 (a) particle tracks for the wake downstream of the falcon model. flow is from left to right and into the page (x axis). (b) ensembled average of the three measurement zones. the contours show the streamwise velocity and the iso-surface shows the q-criterion at q = 3 sec-1. fig. 3: results of vpiv experiments the plot in fig. 4 is an instantaneous velocity field at position 2. this section is one where the vortex core was present. here, the slices represents streamwise velocity, and the red isosurfaces represent the q criterion a q = 3 sec-1. in this snapshot q shedding from the wing tip and propagating within the wake is clearly seen in the red isosurfaces that span from the left to the right as they convect downstream. fig. 4: instantaneous velocity field showing the streamwise velocity as well as an iso-surface of the q-criterion at a value of q = 3 sec-1. 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 fig. 5 shows a comparison between the averaged non-dimensional x vorticity from this study and the study carried out on the same falcon model, where the authors only used spiv. the differences in the two studies are that the flow medium was different, here was in a water tunnel and in gowree et al. was in a wind tunnel. as such the x-vorticity was non-dimensionalised with the respective freestream velocity and length scale (the length of the bird model). it can be seen that the magnitudes of the two contour levels are not quite the same as each other and is thought to be due to a slightly increased angle of incidence in the gowree study (α=5°). however, the general positioning and structure of the two vortices are the same. this gives confidence in the current experimental set-up, such that it could be used for future research using the vpiv to allude more details into the complex vortex driven flow of the peregrine falcon. it also gives confidence in the processing algorithms to accurately calculate and track the particles in a complex vortex driven flow field. fig 5: non-dimensional x-vorticity (ω* = ωxu/c) comparison of the current experiment (contour) and the spiv experiment (lines solid lines indicate positive vorticity and negative represents negative vorticity) carried out in gowree et al., 2018. 4 conclusion in the present work we have studied the complex fluid dynamics of the flow around the wing of a peregrine falcon in a stoop manoeuvre using the vpiv technique. the experiments were performed in a water flume with a freestream velocity of u = 10 cm/s and α = 3.25°. the results demonstrate that the complicated vortices being shed from the wing tip can be accurately captured using this set-up. comparisons made with previous spiv studies shows that the vpiv system and associated processing algorithms, can indeed accurately and quantitatively reconstruct the unsteady and coherent vortex structures shed arising from the wing tip. the complex vortex-driven flow field seems to play a key role in helping the peregrine falcon maintain an aerodynamic advantage over its prey. acknowledgments 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 we would like to thank prof. christoph bruecker of city, university of london, for allowing us to use the falcon model and water tunnel facility for this experiment. references gowree, jagadeesh, talboys, lagemann, & brücker (2018). vortices enable the complex aerobatics of peregrine falcons. communications biology, 1(1), 1-7. selim, gowree, lagemann, talboys, jagadeesh & brücker (2021). the peregrine falcon’s dive: on the pull-out maneuver and flight control through wing-morphing. aiaa journal, accepted awaiting proof. boomsma, troolin (2018) time-resolved particle image identification and reconstruction for volumetric 4d-ptv, 19th international symposium on the application of laser and imaging techniques to fluid mechanics, lisbon, portugal july 16-19, 2018. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a novel method to accurately align the laser sheet for planar and stereoscopic piv m. shehzad∗, s. lawrence, c. atkinson, j. soria laboratory for turbulence research in aerospace and combustion (ltrac), mechanical and aerospace engineering, monash university (clayton campus), melbourne 3800 vic, australia ∗ muhammad.shehzad@monash.edu abstract several techniques including two-dimensional (2d) and three-dimensional (3d) calibration are used for the calibration of two-component two-dimensional (2c-2d) particle image velocimetry (piv) and three-component two-dimensional (3c-2d) stereoscopic piv (spiv) systems. a major requirement of these techniques is to keep the calibration target exactly at the position of the laser sheet within the field of view (fov), which is very difficult to achieve (raffel et al., 2018). in 3c-2d spiv, several methods offer different correction schemes based on the disparity between the fov of two stereo cameras produced due to misalignment, to account for the misalignment error. these techniques adjust the calibration or the measured displacement field in different ways to reduce the error which may introduce an unintended error in the measurement position and/or velocity such as a bias in the measured three-component 3c displacements. this paper introduces a novel method to align the laser sheet with the calibration target so that the uncertainty in displacement measurements is minimal. ideally, it should be of the order of the uncertainty associated with piv measurement so that no ad hoc post-correction scheme is required. the key to this novel method is to position the laser sheet and align it in parallel to the calibration target. for this purpose, the calibration target is fixed in a frame that has the capability to check the parallelism of the laser sheet relative to the target. this is confirmed by shaping the frame in a hollow rectangular form which lets the light sheet pass through its one end which has a 1 mm wide slit and detects it on the opposite end using three collinear equally-distant photo-detectors (pd{1,2,3}) at yh = [+62,0,−62] [mm] where yh = 0 represents the location of the middle photo-detector. these pds, connected to a multi-channel oscilloscope, detect the intensity of laser light falling on them through 1 mm holes. the intensity measurement is indirect, in the form of a voltage (unit: millivolt, mv ). the rectangular frame which holds the calibration target in place is referred to as a calibration target mount and is the main component of the alignment setup. a schematic of the set-up is shown in figure 1(a) along with the calibration target and three photo-detectors. the ability to manoeuvre the laser sheet is achieved using at least one 90° laser mirror mount which is equipped with two adjusting screws to translate the reflected laser beam in the lateral and vertical directions before it is converted to a laser sheet. after the mirror, a rotation stage on which the sheet forming lens is fixed is used to rotate the laser sheet with an accuracy of 0.014°. the laser sheet is considered aligned with the target mount when maximum values of intensity are measured at all pds and the intensity values at pd1 (at yh = +62mm) and pd3 (at yh = −62mm) are very close to each other (within 2% of the maximum intensity measured at pd2). this position of the laser sheet is taken as a reference position, ψ0 where ψ is the angle of the laser sheet rotation with respect to the calibration target mount. rotating the laser sheet slightly about the expansion axis by increments of 0.1° with respect to the reference position while keeping the pivot point of the sheet rotation at the middle hole will decrease the intensity values measured at pd1 and pd3 while at pd2, the intensity would remain constant. if the rotation is greater than 0.92°, almost no intensity is expected to be detected at pd1 and pd3. this is evident in figure 1(b) which shows the intensity values at pd1, pd2 and pd3 relative to the maximum intensity at pd2 when ψ = ψo, for the sheet rotation from ψo to ψ = 0.9°. moving the laser sheet slightly along z axis will decrease the intensities of all pds while moving along a positive y axis will decrease intensities at pd2 and pd3 and increase at pd1. this sensitivity method assists in choosing the optimal laser sheet position relative to the calibration target and is therefore considered as the position of the light sheet where it is parallel to the calibration target. keeping the laser sheet fixed now and traversing the target mount by z = 8.5±0.01 mm using a micrometre translation stage will bring it to the middle of the laser sheet. an experiment has been performed to validate the application of the novel alignment method in 3c-2d spiv. a transparent box containing randomly dispersed micro-particles is illuminated by the aligned laser sheet and translated by several sets of the known true displacements tx ,ty and tz in x ,y and z axes. the ranges of the true displacements applied are: tx = [0.0,0.5] mm, ty = [0.0,0.38] mm, tx = [−0.5,0.5] mm. particle images are recorded at every set of translations using two stereo cameras (pco pixelfly). these cameras are mounted on the scheimpflug adapters and use micro-nikkor lenses of the focal length of 55 mm, with their optical axes at the nominal angles of +45° and −45° to z axis in the x −z plane. for the calibration, the images of the calibration target are recorded at ψo and z = [−0.5,0.0,0.5]± 0.01 mm. the soloff method (soloff et al., 1997) of 3d calibration is used to map the 3d object space to the 2d image plane. the particle images are then dewarped using the computed 3d mapping functions. the dewarped particle images are individually paired with the one at tx ,ty ,tz = [0,0,0]. multigrid/multipass 2c-2d digital piv cross-correlation analysis (soria, 1996) using an in-house software is performed on the image pairs of both cameras to compute the (u1,v1) and (u2,v2) displacement vectors with respect to x ,y,z = (0,0,0). the 3c displacement vector (u,v,w ) is computed from the 2c displacement vectors using the 3c reconstruction technique of willert (1997). the measured 3c displacements are then compared with the true displacements tx ,ty and tz to determine the residual error. a maximum uncertainty 7.6µm is found in the 3c-2d spiv measurements. this is below the accuracy of the translation stages (10µm) which were used to apply the true displacement. also, it is comparable to the uncertainty of the other methods used to correct the misalignment error e.g. the self-calibration method (wieneke, 2005). this shows that the new method provides a viable alternative to avoid or reduce the misalignment error without the risk of introducing bias into the results. light sheet calibration target mount calibration target photodetector −63 0 63 yh(mm) 0.0 0.2 0.4 0.6 0.8 1.0 r el at iv e in te ns ity increasing ψ ψo pd3 pd2 pd1 (a) (b) figure 1: (a) parametric view of the laser sheet alignment setup (b) intensity values at pd1, pd2 and pd3 relative to the maximum intensity at pd2 when ψ = ψo, for the gradual rotation of laser sheet with increments of 0.1°. the angle of rotation is increasing in the direction of the black arrow. acknowledgements the authors would like to acknowledge the support of the australian government for this research through an australian research council discovery grant. the authors also acknowledge the provision of the computational resources on massive through national computational merit allocation scheme (ncmas). muhammad shehzad also acknowledges the punjab educational endowment fund (peef), punjab, pakistan for funding his phd research. sean lawrence gratefully acknowledges the financial support of the maritime division of the defence science and technology group. c. atkinson was supported by the arc discovery early career researcher award (decra) fellowship. references raffel m, willert ce, scarano f, kähler cj, wereley st, and kompenhans j (2018) particle image velocimetry: a practical guide. springer soloff sm, adrian rj, and liu zc (1997) distortion compensation for generalized stereoscopic particle image velocimetry. measurement science and technology 8:1441 soria j (1996) an investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. experimental thermal and fluid science 12:221–233 wieneke b (2005) stereo-piv using self-calibration on particle images. experiments in fluids 39:267– 280 willert c (1997) stereoscopic digital particle image velocimetry for application in wind tunnel flows. measurement science and technology 8:1465 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 super-resolution piv using multi-frame displacement information zhenxing ouyang1, hua yang1∗, yunkang cao1, zhen yang1, zhouping yin1 1 state key laboratory of digital manufacturing equipment and technology, huazhong university of science and technology, wuhan, 430074, china ∗ huayang@hust.edu.cn abstract high-resolution (hr) fluid-flow velocity information is important to reliably analyze fluid measurements in particle image velocimetry (piv), such as the boundary layer and turbulent flow. efforts in piv to enhance the resolution of flow fields are mainly based on single-frame information, which follows the velocity field estimation and may influence the final reconstruction accuracy. in this study, we propose a novel super-resolution (sr) reconstruction technology from another perspective, which consists of two parts: a multi-frame imaging system and a bayesian-based multi-frame sr reconstruction algorithm. first, a splitbased imaging system is developed to obtain particle image pairs with fixed displacements. subsequently, we present a bayesian-based multi-frame sr (bmfsr) reconstruction algorithm to obtain an sr particle image. multi-frame particle images collected by the developed system are used as the input low-resolution images for the following novel sr reconstruction algorithm. synthetic and experimental particle images have been tested to verify the performance of the proposed technology, and the results are compared with the traditional and advanced reconstruction methods in piv. the results and comparisons show that the proposed technology successfully achieves good performance in obtaining finer particle images and a more accurate velocity field. 1 introduction high-resolution (hr) fluid-flow velocity information is important to reliably analyze fluid measurements in particle image velocimetry (piv), such as the boundary layer and turbulent flow. however, fluid-flow data are often sparse, have limited spatial resolution and are noisy in real life for various reasons, such as measuring device imperfections or instability in the observed scene, sensor resolution limitations in experiments or insufficient mesh size in computational fluid dynamics (cfd) simulations (gao et al., 2020). therefore, it is necessary to improve the flow field resolution to explore many different boundaries, small-scale structures, turbulence transitions and so on. in piv measurement, the hr flow field can be obtained by cfd methods, such as large eddy simulation (les) and direct numerical simulation (dns) (liu et al., 2020). nevertheless, simulations can only model the flow ideally and cannot fully analyze the real situation. consequently, it is essential and practically useful to reconstruct flow information from spatiotemporal low-resolution (lr) data. super-resolution (sr) reconstruction is a classic technique for improving the resolution of an imaging system. it can realize the resolution enhancement of a larger imaging system with hr data on a smaller domain (brunton et al., 2020). for decades, various sr reconstruction methods have been proposed, which can be divided into two types: traditional methods and deep learning (dl) methods. traditional sr reconstruction methods mainly utilize interpolation methods to improve the flow field resolution. keys (1981) employed bicubic interpolation based on the filter operation with low-pass characteristics to increase the resolution of digital images. takehara et al. (2000) proposed an sr reconstruction method based on a kalman filter and χ2-testing and verified its performance on two synthetic datasets. next, efforts (gunes and rist, 2007; alfonsi et al., 2013; he and liu, 2017) that applied proper orthogonal decomposition (pod) modes extracted from the dns dataset to obtain the corresponding coefficients and reconstruct the hr flow field were made. these traditional sr reconstruction methods are based on the least-squares approximation to estimate the weighting factors between the lr data and hr data, which limits spatial resolution improvement to some extent. in the last two decades, the application of sr reconstruction technology based on dl in fluid dynamics has attracted increasing attention. dl reconstruction is a data-driven technology that can provide an effective method for generating hr flow fields quickly without iteratively solving partial differential equations (pdes). fukami et al. (2019a,b) adopted the convolutional neural network (cnn) and hybrid downsampled skip-connection multiscale models to reconstruct two-dimensional attenuated isotropic turbulence. (deng et al., 2019) proposed a network-based generative adversarial network-based artificial intelligence framework to enhance the spatial resolution of complicated wake flow behind two side-by-side cylinders; however, (liu et al., 2020) proposed a multitime path cnn. to reduce the increase in the visual complexity to an lr input, which is caused by data-driven upsampling approaches, various efforts (raissi et al., 2019; gao et al., 2020; dwivedi et al., 2021) have been proposed. despite the advantages, the success of these dl models mainly relies on a large quantity of offline hr data as labels. all the models mentioned above, whether traditional or deep learning-based sr reconstruction methods, only utilize the spatial information on the lr fluid field based on single-frame data and reconstruct following the estimation of the velocity field. however, the information provided by only a two successive images is limited. moreover, the lr data that are used to generate the weighting parameters between the lr data and hr data are not obtained simultaneously, resulting in the pertinence of these lr data being low. furthermore, the lr data used in the methods mentioned before are generally not the image itself, which may influence reconstruction accuracy. thus, in this study, a novel sr reconstruction technology is presented from another perspective: sr particle image reconstruction using multi-frame displacement information. it is proposed based on the idea of simultaneously collecting two lr particle images with a fixed displacement and then generating the corresponding sr particle image with a novel sr reconstruction algorithm. as a result, this novel reconstruction technology consists of two parts: a multi-frame imaging system and a bayesian-based multi-frame sr (bmfsr) reconstruction algorithm. first, a split-based imaging system is developed to obtain pairs of particle images with fixed displacements. subsequently, an algorithm named bmfsr is proposed to obtain an sr particle image. multi-frame particle images collected by the developed system are used as the input lr images for the following novel sr reconstruction algorithm. in this way, more correlated particle images can be collected simultaneously, and more lr spatial information can be used. finally, we determine whether the novel technology can reconstruct better results. the rest of this paper is structured as follows: sect. 2 introduces the basic scheme of the novel sr technology, including the multi-frame imaging system and the bayesian-based multi-frame sr reconstruction algorithm. subsequently, experimental evaluations on synthetic images and real data are demonstrated in sect. 3. finally, conclusions are discussed in sect. 4. 2 the proposed super-resolution reconstruction technology the proposed super-resolution reconstruction technology is a novel sr particle image reconstruction method using multi-frame displacement information. this technology contains two main parts: a multi-frame imaging system to collect double lr particle images simultaneously with a fixed displacement and a bayesianbased multi-frame sr (bmfsr) reconstruction algorithm to generate the corresponding hr particle image. finally, the hr velocity field can be obtained with the corresponding two successive reconstructed hr particle images with an interval time. 2.1 multi-frame imaging system as mentioned above, traditional and deep learning sr reconstruction methods generate hr flow fields based on lr single-frame data. additionally, the lr data used are obtained from a series of two successive particle frames. different pairs of two successive frames are collected at different times, resulting in limited spatial correlation between them, which limits the spatial information and may influence the final reconstruction accuracy. hence, in this study, we design a multi-frame imaging system to collect two particle images simultaneously with a fixed displacement time to improve spatial relativity. the schematic and photographs of this system are shown in fig.1. as shown in fig.1 (a), this multi-frame imaging system consists of three parts: a spectral region, control unit and transmit unit. the particle image intensity is defined as i and the collecting time is t. to obtain the two relative particle images i1 t and i2 t at the same time t with a fixed displacement, in the spectral region, a splitter is designed to split the incident light into two identical parts collected by two high-rate sensors, sensor 1 and sensor 2, which are fixed with a preset constant displacement, and the displacement is generated with a contact translation stage (shown in fig.1 (c)). the particle image collection is controlled by the control unit, which mainly consists of three parts, namely, a field programmable gate array (fpga) controlling the exposure of the two sensors, double data rate ram (ddr) buffering the image data and a solid-state disk (ssd) storing all particle images collected within a certain time. after collection, particle images i1 t and i2 t are transmitted to a personal computer through the transmit unit to be estimated with the proposed bmfsr reconstruction algorithm. the outer and inner photographs of this multi-frame imaging system are shown in fig.1 (b) and (c), respectively. figure 1: schematic (a), outer photograph (b) and inner photograph (c) of the multi-frame imaging system. 2.2 bayesian-based multi-frame sr reconstruction algorithm current sr reconstruction methods in piv measurement are mainly based on a single frame, that is, one input and one output. the formulation of the single-frame-based sr reconstruction methods can be expressed as: argmin ψhr ∥∥ψlr −skψhr ∥∥2 +ηr(ψhr) (1) where ψlr denotes the lr flow data, such as the velocity field, and ψhr is the corresponding hr data to be reconstructed. s and k correspond to downsampling and filtering with a blur kernel, respectively. r is a function of the hr data ψhr to constrain the first term so that the solution is unique and the parameter η balances the first and second terms. with increasing input lr image numbers, the ideal hr flow data can be obtained from eq.1. however, lr particle images utilized in the single-frame-based methods are collected at different times, whether within one successive two-frame pair to estimate one lr velocity field or without, resulting in the spatial information of a single-frame particle image being limited, which may influence the final reconstruction accuracy. hence, based on the multi-frame imaging system, we also propose a bayesian-based multi-frame sr (bmfsr) reconstruction method, which involves two particle frames collected at the same time with a constant displacement into the reconstruction function and is modified from liu and sun (2014). this novel sr algorithm is proposed from another perspective: sr particle image reconstruction. let the image intensity be i, the first collecting time be t and the second be t +∆t, where ∆t is the interval time. then, taking time t as an example, the new reconstruction formulation is as follows: jt ∗ = argmin jt θ1 ∥∥skjt − i1 t ∥∥+η∥∇jt∥+θ2 ∥∥skfwjt − i2 t ∥∥ (2) where jt ∗ is the object function to be minimized and jt is the upsampling image to be reconstructed at time t. i1 t and i2 t are the lr particle images collected by sensor 1 and sensor 2 at time t. ∇jt is the gradient of hr image jt . fw is the warping matrix corresponding to the displacements w between j1 t and j2 t . η is a parameter that balances the influence of sparsity on the derivative filter to model the priors of hr image jt and is usually set to 0.02. θ1 and θ2 are parameters that control the noise and outlier when jt is warped to generate the adjacent frame. note that l1-norm penalization is adopted instead of l2-norm used in eq. 1, because that l1-norm can achieve better stability and convergence (seong et al., 2019). by solving eq. 2, the hr image ihr t can be obtained. in the same way, the correlated hr image ihr t+∆t will be obtained with eq.2 from the other two frames i1 t+∆t and i2 t+∆t . finally, the velocity field of the flow is estimated with an open source (vejrazka, 2021), which is a cross-correlation algorithm, named dcc in this paper. bicubic interpolation is used to obtain a full-size velocity field. with the bayesian-based multi-frame sr reconstruction algorithm, more spatial information at one time can be used to reconstruct the hr data, resulting in the reconstruction accuracy improvement. 2.3 minimization and parameter setting for the novel sr reconstruction algorithm, we can estimate the hr image by solving eq.2 when the current flow field w, blur kernel k and noise levels θ1 and θ2 are given. to simplify the estimation, we replace the l1-norm with a non-quadratic penalty function ϕ(s2) = √ s2 + τ2. the symbol τ is a prefixed small constant, which is usually set as τ = 0.01, to ensure that ϕ is strictly convex. this object function of eq. 2 can be solved by the iterated reweighted least squares (irls) method (liu et al., 2009), which iteratively solves the following linear system: [θ1kt st p1sk+η((jt) t x ps(jt)x+(jt) t y ps(jt)y)+θ2ft w kt st p2skfw]jt = θ1kt st p1i1 t +θ2ft w kt st p2i2 t (3) where (jt)x and (jt)y are the xand y-derivative matrices of the hr image jt . t is the transpose operator of the corresponding matrix; for example, st is the transpose of the downsampling s. to simplify the equations, we use the following notation: p1 = diag(ϕ′( ∥∥skjt − i1 t ∥∥2 )),ps = diag(ϕ′(∥∇jt∥2)),p2 = diag(ϕ′( ∥∥skfwjt − i2 t ∥∥2 )) (4) here, diag denotes the diagonal weight matrices. the irls iterates between solving eq. 3 and eq. 4 are based on the current estimation to obtain the final ideal hr particle image jt . the solution for solving eq.2 is based on the assumption that the flow field w, the blur kernel k and the noise levels θ1 and θ2 are given. the flow field w can be estimated with an optical flow drulea and nedevschi (2011). hence, the unknown parameters in the generative models include k, θ1 and θ2. we use bayesian maximum a posteriori estimation (map) to find the optimal solution: argmax i,w,{θ1,θ2} p(jt ,w,k,{θ1,θ2} ∣∣{i1 t , i 2 t }) (5) in addition, the sparsity on derivative filter responses is used to model the prior of hr image jt , flow field w, and the blur kernel k: p(jt)= 1 zjt (η) exp{−η∥∇jt∥}, p(w)= 1 zw(λ) exp{−λ(∥∇u∥+∥∇v∥}, p(k)= 1 zk(ξ) exp{−ξ∥∇k∥} (6) where zjt (η), zw(λ) and zk(ξ) are normalization constants only dependent on parameters η, λ and ξ, respectively. u and v are the horizontal and vertical components of the flow velocity w. then, similar to eq.2, when solving the noise levels θ1 and θ2, the hr image jt and the blur kernel k are given, and the bayesian map estimation for the noise parameters has the following closed-form solution: θi = α+nq −1 β+nī , ī = 1 n n ∑ q=1 ∥∥(ii t −skfwii)(q) ∥∥, i = 1,2 (7) where ī is the sufficient statistics, n is the pixels of the lr image and α and β are two constant parameters. for the blur kernel k, the solution is similar to the hr image jt ; the upsampling jt and downsampling matrix s are given. the minimization formulation is as follows: argmin k θ0 ∥∥sjtk− i1 t ∥∥+η∥∇k∥ (8) which is also optimized by irls and not discussed in detail here. with the iteration of the estimations of the noise controlling parameters θm 1 and θm 2 , optical flow field wm, intermediate upsampling image jm t and blur kernel km, where m is the current iteration number, the optimal hr particle image jt can be generated. we use 5 iterations to generate the hr particle image with η = 0.02 for the image derivative, λ = 1,000 for the optical flow field, ξ = 0.7 for the derivative of the blur kernel and α = 1 and β = 0.1 for noise. the upsampling scale is set to be 4. 3 experimental evaluations in this section, we illustrate the performance of the proposed sr reconstruction technology on synthetic and experimental images. first, we focus on the performance of the proposed bmfsr method and verify the advantage on a synthetic vortex flow in sect. 3.1. subsequently, in sect. 3.2, real experimental micropiv data are tested to demonstrate the practicality of the novel sr reconstruction technology combining the multi-frame imaging system and the bmfsr algorithm, which utilizes the multi-frame displacement information. hereafter, we follow a standard method to quantitatively evaluate the experimental results by computing the peak signal-to-noise ratio (psnr), the root mean square error (rmse) and the average angle error (aae) over n pixels of the image: psnr=10·log10 2552 1 n n ∑ n=1 |jt(n)−j(n)|2 , rmse= √ 1 n n ∑ n=1 |wes n −wtr n | 2, aae= 1 n n ∑ n=1 arccos( wes n ·wtr n |wes n |·|wtr n | ) (9) where j and jt are the ground truth and the reconstructed hr particle images, respectively. wtr and wes denote the ground truth and the estimated velocity fields. 3.1 test on synthetic vortex flow first, we investigate the performance of the proposed bmfsr method on a synthetic vortex flow. two pairs of hr particle images with 512 × 512 pixels are generated, whereby 7,864 particles with a mean diameter of 6 pixels and size variation of 0.3 pixels are randomly distributed. no out-of-plane motion or noise is considered, and the sheet thickness is set to 0.333. the displacement between these two pairs is set to 0.25 pixels and considered to be the background hr particle images of sensor 1 and sensor 2. in this experiment, a synthetic velocity field is a lamb-ossen vortex, similar to (carlier and wieneke, 2005). the exact solution of the navier-stokes equation is: u(r,θ) = γ0 2πr (1− e −r2 r0 2 ) (10) where γ0 is the initial circulation and r0 is the core radius. in this study, γ0 = 2000, r0 = 50 pixels. lr particle images are generated by downsampling the hr particle images above with a downsampling scale of 4. during dowmsampling, blur and noise are added to simulate the real scene. the hr particle images of the background reconstructed by the traditional bicubic interpolation and reconstructed by the proposed bmfsr are shown in fig.2. as shown, the image reconstructed by bmfsr is more approximate to the background particle image. in addition, we compare the reconstruction quality with the evaluation indices psnr, rmse and aae, and the results are shown in fig.3. compared to bicubic interpolation, the psnr of our proposed method bmfsr is the highest, whether for i1 t or i2 t . in table 2, bicubic-dcc denotes that the dcc results are set to be the background truth (ours-dcc is the same) because both bicubic interpolation and our method estimate the velocity with an open source dcc and it has its inherent estimation error. the bold denotes the best and the underlined denotes the second here. in table 2, it can be seen that the proposed method bmfsr performs better than the traditional bicubic interpolation method relative to whether the ground truth or the result of the basic dcc algorithm. we present the energy maps and velocity distributions of different methods in fig. 4. the comparison result suggests that the proposed bmfsr method outperforms the traditional bicubic interpolation method. in particular, at the bottom right, the bicubic result is worse, which may be caused by the blur and noise of the downsampling operator in generating lr particle images. however, the proposed bmfsr method can decrease the influence of blur and noise to some extent. it can be concluded that the proposed bmfsr reconstruction algorithm is well adapted to sr reconstruction and shows great advantages in particle image reconstruction and hr velocity estimation compared to the traditional bicubic interpolation method. then, the overall performance of the proposed super-resolution reconstruction technology is verified in a real experiment. (a) (b) (c) figure 2: hr particle images of (a) the ground truth; (b) the traditional bicubic method; (c) the proposed bmfsr method. figure 3: results of different methods on the reconstructed particle image psnrs and the estimated velocity errors. (a) (b) (c) (d) figure 4: energy maps and velocity distributions of different methods: (a) the ground truth; (b) result of dcc; (c) result of the traditional bicubic method; (d) result of the proposed bmfsr method. 3.2 test on experimental laminar boundary layer flow to illustrate the generalization of the proposed method in the real flow field, a micro-piv experiment was carried out to acquire the particle images of the laminar boundary layer with a constant inflow velocity, and the platform is shown in fig. 5(a). orange fluorescent particles with a diameter of 0.3 µm were dispersed in distilled water and stored in a syringe. then, an era ne-1000 injection pump drove the syringe at 79 µm/s. the flow field is in a microfluidic chip, whose cross-section is 30 µm wide × 28 µm deep. the whole flow field was illuminated using fluorescent light (nikon intensilight c-hgfi) with a wavelength of 532 nm, which was the same as the light passed by the filter in the multi-frame imaging system and imaged by a nikon eclipse ti-s inverted fluorescent microscope with a 60 × magnification lens. the field is captured using the multi-frame imaging system with an interest region of 1,296 × 408 pixels. the flow field that we set is a laminar flow field, which has minimum velocity at the edge of the pipe and maximum velocity in the center of the pipe. in the experiment, we compare the performance of the traditional bicubic interpolation reconstruction method and our proposed bmfsr method. note that the particle image that is used to generate the hr image of the bicubic interpolation method is only i1 t ; however, those of our proposed bmfsr are i1 t and i2 t . figure 5: (a): micro-piv platform; (b) hr image with bicubic interpolation; (c) hr image with our proposed method; (d) errors of different methods. lr hr_bicubic ours boundary layer structure: ours>hr_bicubic>lr none fine finer figure 6: top: the energy maps and velocity distributions of unsteady micro-piv flow. down: a close up in the region −20 ≤ y ≤−18 pixels and 38 ≤ x ≤ 51 pixels. low-resolution images are directly acquired by the two sensors mentioned above. the hr particle images reconstructed from the traditional bicubic interpolation and our proposed method are shown in fig.5(b) and (c), respectively. in comparison, the hr particle image reconstructed with our method is clearer because of the blur kernel estimation, and the result is consistent with the synthetic experiment above. the mainstream velocities measured are approximately 76.63 µm/s, 80.28 µm/s and 79.83 µm/s for ulr, uhr bi and uhr ba , respectively; that is, the errors with the theoretical velocity are 3.00%, 1.62% and 1.05%, as shown in fig.5(d). additionally, as shown in fig.5(d), the proposed method obtains the lowest rmse of the vertical component, which is 0.0832. to further verify the performance of our method, we compare the energy maps and velocity distributions of three different methods: lr ulr, hr with bicubic reconstruction uhr bi and ours uhr ba in fig.6-top. fig.6-down shows the close up of these three velocity distributions in the region −20 ≤ y ≤ −18 pixels and 38 ≤ x ≤ 51 pixels. the upsampling scale factor of reconstruction here is 4. the sampling rate in the horizontal direction of uhr bi and uhr ba is 4. we can observe that the distribution of uhr ba is finer at the boundary. therefore, it can be concluded that the proposed technology performs better in sr reconstruction. 4 conclusion in this paper, we propose a novel super-resolution (sr) reconstruction technology for particle image velocimetry from the perspective of sr particle image reconstruction using multi-frame displacement information. this technology consists of two parts: a multi-frame imaging system and a bayesian-based multiframe sr (bmfsr) reconstruction algorithm. first, two correlated particle images are collected by the multi-frame imaging system at the same time with a constant displacement. subsequently, these two images are utilized to generate an hr image with the proposed bmfsr method. this proposed sr reconstruction technology has been assessed by many experiments. first, a synthetic vortex flow is used as the benchmark to evaluate the performance of the proposed bmfsr algorithm. the results show that the proposed method can provide accurate reconstruction results. compared to the traditional bicubic interpolation method, it also shows a great advantage in terms of the quality of the reconstructed particle image or the estimated highresolution (hr) velocity. the overall performance of the proposed sr reconstruction technology is verified with an experimental laminar boundary layer flow. the results show that the l1 error for the mainstream velocity and the rmse of the vertical component of ours are both the lowest. in addition, the estimated flow structure of the laminar boundary layer of our proposed technology is also the finest. acknowledgements this work was supported by the national natural science foundation of china (grant no. 51875228) and the national key r&d program of china (grant no. 2020yfa0405700). references alfonsi g, lauria a, and primavera l (2013) proper orthogonal flow modes in the viscous-fluid wavediffraction case. journal of flow visualization and image processing 20:227–241 brunton sl, noack br, and koumoutsakos p (2020) machine learning for fluid mechanics. annual review of fluid mechanics 52:477–508 carlier j and wieneke b (2005) report 1 on production and diffusion of fluid mechanics images and data. fluid project deliverable 1.2. european project “fluid image analysis and description” (fluid). http://www.fluid.irisa.fr deng z, he c, liu y, and kim kc (2019) super-resolution reconstruction of turbulent velocity fields using a generative adversarial network-based artificial intelligence framework. physics of fluids 31:125111 drulea m and nedevschi s (2011) total variation regularization of local-global optical flow. in proceedings of the 14th international ieee conference on intelligent transportation systems, washington, dc, usa, october 5-7 dwivedi v, parashar n, and srinivasan b (2021) distributed learning machines for solving forward and inverse problems in partial differential equations. neurocomputing 420:299–316 fukami k, fukagata k, and taira k (2019a) super-resolution analysis with machine learning for lowresolution flow data. in 11th international symposium on turbulence and shear flow phenomena, southampton, united kingdom, july 30-august 2 fukami k, fukagata k, and taira k (2019b) super-resolution reconstruction of turbulent flows with machine learning. journal of fluid mechanics 870:106–120 gao h, sun l, and wang jx (2020) super-resolution and denoising of fluid flow using physics-informed convolutional neural networks without high-resolution labels. arxiv preprint page arxiv:2011.02364 gunes h and rist u (2007) spatial resolution enhancement/smoothing of stereo–particle-image-velocimetry data using proper-orthogonal-decomposition–based and kriging interpolation methods. physics of fluids 19:064101 he c and liu y (2017) proper orthogonal decomposition-based spatial refinement of tr-piv realizations using high-resolution non-tr-piv measurements. experiments in fluids 58:1–22 keys r (1981) cubic convolution interpolation for digital image processing. ieee transactions on acoustics, speech, and signal processing 29:1153–1160 liu b, tang j, huang h, and lu xy (2020) deep learning methods for super-resolution reconstruction of turbulent flows. physics of fluids 32:025105 liu c and sun d (2014) on bayesian adaptive video super resolution. ieee transactions on pattern analysis and machine intelligence 36:346–360 liu c et al. (2009) beyond pixels: exploring new representations and applications for motion analysis. ph.d. thesis. massachusetts institute of technology raissi m, perdikaris p, and karniadakis ge (2019) physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. journal of computational physics 378:686–707 seong jh, song ms, nunez d, manera a, and kim es (2019) velocity refinement of piv using global optical flow. experiments in fluids 60:1–13 takehara k, adrian r, etoh g, and christensen k (2000) a kalman tracker for super-resolution piv. experiments in fluids 29:s034–s041 vejrazka j (2021) pivsuite. https://www.mathworks.com/matlabcentral/fileexchange/45028-pivsuite 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 three-dimensional particle tracking velocimetry using a single time-of-flight camera s. e. morris1∗, a. d. goldman1, b. s. thurow1 1 auburn university, samuel ginn college of engineering, auburn, usa ∗ sem0116@auburn.edu abstract time of flight (tof) cameras are a type of range-imaging camera that provides three-dimensional scene information from a single camera. this paper assesses the ability of tof technology to be used for threedimensional particle tracking velocimetry (3d-ptv). using a commercially available tof camera various aspects of 3d-ptv are considered, including: minimum resolvable particle size, environmental factors (reflections and refractive index changes) and time resolution. although it is found that an off-the-shelf tof camera is not a viable alternative to traditional 3d-ptv measurement systems, basic 3d-ptv measurements are shown with large (6mm) particles in both air and water to demonstrate future potential use as this technology develops. a summary of necessary technological advances is also discussed. 1 introduction in this work, the ability of a single time-of-flight (tof) camera to perform three-dimensional particle tracking velocimetry (3d-ptv) measurements is explored. many flow fields are 3d and unsteady in nature, and require advanced diagnostic techniques for quantitative measurements. particle image velocimetry (piv) and particle tracking velocimetry (ptv) are two of the most common flow diagnostic tools (aguirre-pablo et al., 2017). piv returns an eularian perspective of the flow field, wherein velocity information does not rely on individual particle identification. the most recent major development in piv is that of tomographic piv, wherein the instantaneous three-component velocity field is measured from different angles to create the multi-dimensional perspectives necessary for 3d measurement and volumetric reconstructions (elsinga et al., 2006). in contrast, ptv yields lagrangian perspective of the flow field as individual particles are tracked through space (shnapp et al., 2019). a major drawback of modern 3d-piv/ptv techniques is that they can be cost-prohibitive for research laboratories. these techniques traditionally require significant laboratory space and the use of multiple research-level cameras, a synchronization unit, and a high-powered laser. furthermore, trained personnel and personal protective equipment are needed due to the risks of laser use. as a result, recent advances in 3d flow measurements have focused on moving towards single-camera systems for three-dimensional, three-component velocity field measurements. such single-camera systems for these measurements include plenoptic (light field) cameras, color-coded illumination, scanning laser sheets/ volumes and image splitters (for further details and examples see aguirre-pablo et al. (2019)). the use of range-imaging cameras such as lidar and tof technology as a flow diagnostic tool has been increasing, for example lidar-based piv has been shown to successfully analyze very large slow-moving solid objects like glaciers (telling et al., 2017), and tof cameras have been used in combination with traditional piv for data enhancement of seeded flows (augère et al., 2017). tof cameras have also been used to evaluate planar seeded flow, with independent camera and light sources (paciaroni et al., 2018). recently, single camera 3d-ptv has been achieved by romano et al. (2021) using a two-view splitter and rossi and marin (2020) by taking advantage of astigmatic aberrations. this work explores the use of a single off-the-shelf correlation tof camera as a flow diagnostic tool for 3d-ptv measurements. in addition to being a single-camera singular port system, this technique eliminates the need for separate volume illumination via a laser or other means. this paper will assess the ability of a tof camera to conduct simple 3d-ptv measurements, and evaluate the current state of technology of these cameras for this application. an overview of tof technology is discussed in §2, and experimental methods are presented in §3. the primary aspects of 3d-ptv that are assessed in this paper include: the flow field environment, the fluid medium, minimum resolvable particle size, particle type and (x,y,z, t) resolution; these are presented in §4. a further discussion of the state of tof technology is given in §5, and conclusions follow in §6. 2 time of flight camera technology tof cameras are a type of range-imaging camera that work by measuring the time it takes for light emitted by the camera to reflect off an object and return to the camera’s sensor (hansard et al., 2012). in doing so, the depth of objects in a scene are resolved. today, these cameras are commonly used in digital mapping (dowman, 2004), altimetry (hu et al., 2007), oceanography (churnside, 2013), construction (wang et al., 2015) and autonomous vehicles (wang et al., 2017). the tof camera light source is typically an infra-red led or laser diode, and can be either pulsed or continuous. in pulsed modulation, the time taken for the light to travel is directly measured. in continuous wave modulation (also known as indirect or correlation tof cameras), the phase-shift between the emitted light and reflected light is measured. these signals commonly take the form of sinusoidal or square wave signals. this phase-shift is proportional to the distance travelled, d: d = 1 2 c∆φ 2π f (1) where c is the speed of light, f is the modulation frequency and ∆φ is the phase difference. in correlation tof cameras, the depth (distance) of objects is determined by an image sensor (typically cmos) that measures these phase-shifts (he and chen, 2019; kadambi and raskar, 2017). as the modulation frequency is increased, the depth resolution and accuracy is also increased (kadambi and raskar, 2017). in contrast to a scanning mechanism (such as scanning lidar), each pixel in a tof image simultaneously measures the distance between the camera and the corresponding object seen by a given pixel (hansard et al., 2012). this information is stored as a depth map, wherein each (x,y) location is prescribed a depth (z). this is commonly output as 3d point cloud data. in comparison to traditional flow diagnostic cameras, tof cameras provide several advantages. as they are self-contained, they provide 3d field information via a singular port, lightweight unit. these cameras have in recent years become relatively inexpensive, and eliminate the need for volume illumination as their light source is in-built. in this paper, an off-the-shelf tof 3d camera is used to perform exploratory 3d-ptv experiments. the camera has a resolution of 0.3mp (640 × 480 px), and a field of view of 59◦ × 45◦ with a focal length of 6mm. the lens is in-built, and would require custom modifications to change. the camera has two working modes, near mode (1.5m depth working distance) and far mode (6m depth working distance). these have final working areas of 1.697m × 1.243m and 6.789m × 4.971m respectively. in this work, only the near mode will be considered. the precision of the camera decreases at further z depths: at z = 0.5m the precision is 0.69mm and at z = 1.5m the precision is 3.11mm (lucidvision, 2019). in this mode, the camera operates at a frame rate of 30fps. the exposure time can be chosen as 1000µs or 250µs. the camera uses a sony imx556 cmos sensor and four vertical cavity surface emitting laser (vcsel) diodes at 850nm with a modulation frequency of 100mhz and power of 2.2mw (continuous wave modulation). this sensor measures phase shifts by use of a current assisted photonic demodulator (capd) pixel structure. within each pixel’s photodiode, light is converted into electrons and the capd uses an alternating voltage to pull electrons to alternating detector junctions. the primary junction samples light at the same frequency it is transmitted and the secondary junction samples light 180◦ out of phase to calculate the phase shift (lucidvision, 2020). 3 experimental methods to evaluate the ability of an off-the-shelf tof camera to track particles for ptv measurements, a commercially available tof camera in near-mode (1.5m) with 250µs exposure is used. experiments were chosen to evaluate different aspects that contribute to the effectiveness and accuracy of 3d-ptv, such as scene reflections, different fluid mediums, the minimum resolvable particle size, particle types and (x,y,z, t) resolution. to measure the minimum resolvable particle size, an empty 5-sided glass tank is used as shown in figure 1 (a). in open-air experiments, the tof camera is pointed towards the empty side of the tank to eliminate any figure 1: (a) 5-sided glass tank used for open-air experiments, with a fishing line holding a single stationary bead. this set-up was further developed to include matte black felt lining on the inside of the tank (not shown). (b) example of plastic “seed beads” used in experiments. silver seed beads (not shown) also ranged in size from 1mm−6mm. (c) water tank setup with “trout bait” tracer particles. errors arising from refractive index changes. for the configuration shown in figure 1 (a), it was ascertained that having black card on the outside of the tank as shown was not sufficient to remove reflections of the vcsel diodes from the inner glass wall. as such, matte black felt material was placed inside the tank walls (not shown). this provided a number of benefits: the black felt removed any reflections from the walls, it provided a constant depth (z) background within the field of view, and it removed any aliasing arising from the camera measuring objects outside the region of interest (see §4.1). initially, different sized “seed beads” were held stationary, suspended via fishing line (see figure 1) in the camera’s field of view to determine the minimum resolvable particle size. seed beads are commonly used in jewelry making and can come in sizes as small as o(1mm). they are usually toroidal or cylindrical in shape, and have a hole through their center. two types of seed beads were used: plastic seed beads ranging in diameter from 2mm−6mm as shown in figure 1 (b), and silver beads of diameter 1mm–6mm (not shown). although it was determined that the camera could detect stationary particles as small as 2mm, for ptv experiments the seed bead size was kept as 6mm unless otherwise stated. to determine the ability of the camera to track multiple moving particles in (x,y,z, t), three seed beads were initially dropped in the middle of the camera’s field of view and tracked as they dropped and bounced in front of the camera due to gravity. although this showed the dynamic motion of the beads, due to the limited frame rate of the camera (30fps) it was determined necessary to slow the particles’ velocities to properly assess the camera’s ability to track the particles. in order to achieve this, a set of fishing lines both parallel and perpendicular to the camera were set such that a 6mm particle could slide along the line in predictable motions. the angle that the fishing line made with the horizontal (ground) controlled the velocity of the beads. ptv measurements were calculated in matlab, wherein a particle’s location in the point cloud was found via a peak search function in the measurement field of view. the velocity of the particle is calculated via a (two-point) forward time difference. following air experiments, the tank was filled with water with 6mm “trout bait eggs” used as tracer particles to determine the ability of the camera to track moving particles in water (see figure 1 (c). the trout bait have a slower settling velocity than seed beads, and so were able to stay briefly suspended in manually perturbed water. it must be noted that in practice this experiment would require a depth calibration, as refractive index changes occur when viewing through the glass wall and water, however as a proof-ofconcept experiment these calibrations were not performed. the back wall of the tank was lined with matte black felt to minimize reflections. in addition to solid particles, a set of experiments were performed to determine whether the camera could distinguish soap bubbles in the same manner as solid particles. a lavision helium-filled soap-bubble (hfsb) generator was used to generate 300µm neutrally buoyant particles, and a standard children’s bubble wand was used to generate bubbles on the order of 1cm–5cm. 4 results and discussion 4.1 environment as mentioned in §3, an idealized environment was necessary for reliable ptv experiments. as such, the background of the flow field of view needed to be controlled. the reasons for this are two-fold: to prevent aliasing, and to prevent reflections. aliasing occurs in tof cameras if the time taken for the emitted light to return to the sensor is longer than the period of the modulated light. this occurs when the distance to an object differs in phase by 360 degrees to the phase shift, and becomes indistinguishable (gokturk et al., 2004). the unambiguous distance, dunamb., (melexis, 2020) can be calculated by: dunamb. = c 2 f (2) for the camera operating in near-mode ( f = 100mhz), this is equal to 1.5m. by providing a constantdepth background within the unambiguous range, the camera will not report any aliasing of the background that may interfere with particle recognition or detection. in future tof ptv work, it is recommended that experimentalists provide a non-reflective, constant depth background for optimal measurements. with respect to preventing reflections, it is established that the colour, type of material and distance from camera can all influence the depth error recorded by a tof camera (he et al., 2017). shiny surfaces or objects with very high reflectivity can cause the pixel(s) to saturate, losing phase information and invalidating the depth calculation (lucidvision, 2019). as such, if the laser power of a tof camera is increased to detect smaller particles (raffel et al., 2018), care must be taken to ensure that the background or particles themselves do not over-saturate. similarly, dark or matte surfaces are good absorbers and hence poor reflectors of light: a black surface will absorb most of the photons, leading to a low depth accuracy of black surfaces (baek et al., 2020). as aforementioned, it was ascertained early that a glass-walled tank would reflect the four vcsel diodes back in the 3d depth map (and in fact over-saturate such that a depth could not be calculated). this is shown in figure 2 (a), wherein four black circles corresponding to the four vcsel diode reflections can be seen (indicated by the white circle). black matte felt material was added to the inner walls of the tank to remove these reflections; this is shown in figure 2 (b). figure 2: (a) open-air tank, showing the reflection of the four vcsel diodes (shown in white circle). the reflections are over-saturated and do not provide depth information. (b) open-air tank with matte black felt backing. no reflections are observed, and the backing provides a constant-depth background. colour indicates z depth, where green is closer to the camera and red is further away. 4.2 fluid medium and distortions tof technology works on the ability of the camera to emit a modulated light signal and receive it at its sensor. as light passes through different mediums, it will refract (snell’s law) due to the change in light speed. the implication of this in tof technology is decreased or changed location accuracy. this was observed experimentally by holding a piece of acrylic in front of the camera, and measuring the change in a stationary object’s distance. it is therefore recommended that depth calibrations be performed for tof 3d-ptv experiments that take place through glass or acrylic walls, or pass through water. 4.3 particle seeding it is well established that the particle seeding of a flow field is of importance when performing piv/ptv measurements. it is typically desirable that the particles be o(µm) or smaller and neutrally buoyant with the fluid. as such, it was necessary to ascertain the camera’s minimum resolvable particle size in air. initially, solid seed bead particles were held stationary in the matte black tank in front of the camera. for a set of silver seed beads, the camera’s minimum resolvable stationary particle size was found to be 2mm; when the particle was allowed to drop with gravity in front of the camera, the minimum resolvable size increased to 3mm. in near mode, this minimum resolvable particle size is comparable to the pixel size. as such, for particles smaller than a pixel, the signal returned to the pixel will be a combination of both the particle and any residual background light. it must also be noted here that the colour of the particle plays an important role in its detectability. as the tof camera operates using an infra-red camera, it has difficulty establishing the location of black or red particles (see §4.1). it is suggested that white or reflective (e.g. silver) particles are used for maximum detectability. an example of the depth map (3d point cloud) for a single solid particle is shown in figure 3 (a). a test of particle size was not performed in water, however figure 3 (b) shows the depth map for a collection of 6mm plastic particles (approximately 25 particles/gallon) in water. in addition to solid particles, the ability of the camera to detect soap bubbles was tested due to the increased popularity of using hfsb particles as fluid tracers. 300µm neutrally buoyant helium-filled soapbubbles generated by a lavision hfsb generator were recorded with the tof camera and were found to be figure 3: (a) single plastic particle detected in open-air experiment. (b) multiple “trout bait” particles detected in water. (c) hfsb particles detected in open-air, with no depth resolution. (d) soap bubble detected in open-air. vcsel laser diode reflections interfere with depth resolution. colour indicates z depth, where green is closer to the camera and red is further away. incapable of being resolved, even when the density of hfsb particles was decreased. figure 3 (c) shows the depth map of a set of hfsb particles. large circles indicate a soap bubble very close to the camera, and small circles further away. however, as can be seen, the camera is unable to determine any depth changes between them (all are the same depth colour). following this, large bubbles (1mm-5mm) were blown in front of the camera via a children’s bubble wand. in this case, a new problem arose: as can be seen in figure 3 (d), four distinct points can be seen on the bubble. these four distinct points represent a reflection from each of the four vcsel diodes. this reflection made the shape and distance of the bubble difficult to resolve; this could potentially be an issue in the future using hfsb bubbles, however may be mitigated due to their small size. currently, it is evident that the tof camera cannot resolve particle sizes required for traditional ptv measurements. as discussed in §2, the depth resolution and camera accuracy is increased as the modulation frequency of the light source is increased. in order to detect traditional ptv/piv particles, a tof camera will need a much higher modulation frequency (see §5 for further details on the ‘ghz gap’ (kadambi and raskar, 2017)). it is also noted that tof cameras act as a single line of sight camera. using a single line of sight camera introduces difficulty in 3d-ptv measurements, as any object behind another will not be present in the depth map. this is because each (x,y) location can only determine a single (z) depth. as such, there is a loss of information each time a particle passes behind another, limiting particle tracking in cases with crossover interactions. in future work, it is suggested that predictive algorithms in crossover interactions and a careful choice in particle seeding density be used. figure 4: (a) single particle travelling in open-air parallel to the camera face, shown in the (x,y) plane, and (b) in 3d. (c) single particle travelling in open-air perpendicular to the camera face, shown in the (y,z) plane and (d) in 3d. time steps are indicated from cool (blue) to warm (orange). 4.4 volumetric and time resolution in this section, the results of basic 2d and 3d motion experiments using the tof camera are reported. it must be noted that these are basic representations of ptv experiments using 6mm particles at 30fps, limited by the camera’s ability: for real flow experiments, improvements must be made in tof camera technology to allow for particle tracking of typical flow seeding particles (1-2 orders of magnitude smaller than used in the current experiments). furthermore, frame rate and exposure controls would be required to expand the camera’s capability to track both high and low reynolds number flows. 4.4.1 planar motion to evaluate the tof camera’s ability to track simple 2d motion, a series of 2d motion experiments were conducted in the matte black tank in air (camera viewing through the open face). the first test was the ability of the camera to track both in-plane (x,y) and out-of-plane (z) motions. to achieve this, a fishing line was set up firstly in the (x−y) plane (motion parallel to the camera face or in-plane), and a 6mm bead allowed to slide along it. as aforementioned, this ‘sliding’ technique was used to slow down the solid particle motion, as we were restricted to 30fps image acquisition. figure 4 (a) and (b) shows the superposition of multiple point cloud depth images, with the particles detected shown (increasing time is indicated as particles change colour from cool to warm). the camera is able to accurately track the motion of the bead in (x− y), with minimal (z) displacements. similarly, a fishing line was set up in the (y− z) plane (motion parallel to the camera face or out-of-plane). this is shown in figure 4 (c) and (d). the tof camera well captures the out-of plane (z) motion, with minimal (x) displacements. 4.4.2 3d motion following the success of the camera at tracking a single particle in air in a controlled environment, the camera was tested at tracking multiple particles in 3d. a simple experiment was initially conducted in air, dropping three beads and allowing them to bounce in front of the camera. the raw depth image (multiple time steps superimposed on each other) with particle identification is shown in figure 5 (a). time steps are indicated from cool (blue) to warm (orange). the 3d-ptv field is shown in (b). as can be seen, the lack of frame rate control becomes an issue in this case. due to the low time resolution, we are unable to resolve the bouncing motion sufficiently. as such, errant velocity vectors arise when a particle is known to be travelling downward, but the following time step particle has bounced above it. nonetheless, the camera is able to track the particle locations reasonably well. figure 5: (a) point cloud image of multiple time frames showing three beads dropping due to gravity in open air. (b) 3d-ptv field of the three particles. time goes from cool (blue) to warm (orange). as the frame rate of the camera limited the open-air experiments, 3d-ptv was also conducted in a water tank using 6mm “trout bait” particles. the water was randomly perturbed, and the motions tracked as the particles moved in 3d before settling. it must be noted that these experiments were not calibrated to account for refractive index changes, but were rather performed as a proof-of-concept. figure 6 (a) shows the superposition of multiple point cloud depth images, with the particles detected shown (increasing time is indicated as particles change colour from cool to warm). the 3d-ptv field is shown in figure 6 (b). the 3d-ptv field demonstrates the potential of a single tof camera to accurately track particle motion in 3d, however the limitations of particle size and camera frame rate must be improved before a ‘real’ flow can be accurately analysed with this technique. figure 6: (a) point cloud image of multiple particles being manually perturbed in water. (b) 3d-ptv field of the manually perturbed particles. time goes from cool (blue) to warm (red). 5 assessment of the state of technology the results of this study have shown that it is possible to perform multi-particle 3d-ptv using tof technology. at current standing however, the 3d-ptv fields obtained using a commercially available tof camera are severely limited. the following advancements are necessary for tof ptv to be a viable alternative to traditional ptv: 1. a primary limitation of correlation tof cameras for 3d-ptv is the depth resolution achievable with off-the-shelf cameras (the maximum precision of the current configuration is 0.69mm at z = 0.5m), and hence the minimum particle size capable of being detected. to improve depth resolution, higher modulation frequencies are required. however, the current state of image sensors are unable to detect these frequencies: this is referred to as the “ghz gap” in tof technology (kadambi & raskar 2017). one method suggested to improve the depth resolution of tof cameras without requiring ghz modulation frequencies is to incorporate heterodyning using a cascaded modulation scheme; a prototype demonstrates 3µm precision over a range of 2m (kadambi & raskar 2017). 2. the minimum detectable particle size is also related to the power output of the light source, as the particle image intensity (reflected light) is directly proportional to the scattered light power (raffel et al., 2018). increasing the light power may however also increase background reflections, and there may be a critical power limit to illuminate small particles with minimal background reflections. recently, qiu et al. (2019) have reported achieving high-efficiency 905nm pulsed lasers with a power as high as 150w for long-range lidar applications; this is orders of magnitude higher than the vcsel diodes (2.2mw) built-in to the tof camera used in these experiments. 3. as tof technology works on light line of sight, errors are introduced when there are refractive index changes or reflective/absorbing surfaces. in the case of refractive index changes, calibrations must be taken prior to experiments to account for these changes. in the case of reflective/absorbing surfaces, this limits the experimental configurations: light-coloured or reflective particles should be used for optimal detectability, and the flow field background should be matte black so as not to interfere with measurements and prevent aliasing. 4. as with other single camera flow diagnostic tools, a single line of sight camera will only provide a single perspective and so overlapping objects are not identifiable. this sets a limit on the particle seeding density, as the quality of ptv results will deteriorate with increased particle numbers (cierpka et al., 2013). pre-existing solutions that can be applied include adding additional cameras, or applying advanced time-resolved particle tracking algorithms. 5. the tof camera used in these experiments is limited by its fixed frame rate (30fps). for this method to be applicable to a wide range of reynolds number flows, the time resolution must be increased and adjustable. similarly, increased exposure control will be required at higher reynolds numbers to prevent particle streaking. 6 conclusions tof cameras have the potential to be used in the future as a single camera flow diagnostic tool for 3d-ptv measurements. however, given the current state of technology in common, off-the-shelf cameras, this is not yet a viable alternative for traditional 3d-ptv measurement systems. using a commercially available tof camera, tof technology was assessed in the context of 3d-ptv. the primary issues that are discussed that arose using this method include: particle size recognition, particle type recognition, refractive index changes, time resolution, and reflective/absorbing materials. despite these challenges, using multiple 6mm beads this paper shows basic 3d-ptv fields obtained from dropping particles (air) and from randomly disturbing the flow field (water) at 30fps. acknowledgements the authors would like to acknowledge the members of the advanced flow diagnostics laboratory and the applied fluid research group in the department of aerospace engineering at auburn university. references aguirre-pablo aa, alarfaj mk, li eq, hernández-sánchez jf, and thoroddsen st (2017) tomographic particle image velocimetry using smartphones and colored shadows. scientific reports 7 aguirre-pablo aa, aljedaani ab, xiong j, idoughi r, heidrich w, and thoroddsen st (2019) singlecamera 3d ptv using particle intensities and structured light. experiments in fluids 60 augère b, goular d, valla m, goular y, dolfi-bouteyre a, monnier j, gilliot a, and gallas q (2017) mise en œuvre d’un lidar doppler 1.5µm et de la spiv pour la caractérisation d’écoulements sur une plateforme d’appontage d’une maquette simplifiée de frégate en soufflerie. 23ème congrès français de mécanique 23 baek et, yang hj, kim sh, lee g, and jeong h (2020) distance error correction in time-of-flight cameras using asynchronous integration time. sensors (basel, switzerland) 20 churnside jh (2013) review of profiling oceanographic lidar. optical engineering 53 cierpka c, lütke b, and kähler cj (2013) higher order multi-frame particle tracking velocimetry. experiments in fluids 54:1–12 dowman i (2004) integration of lidar and ifsar for mapping. the. in international archives of the photogrammetry, remote sensing and spatial information sciences, vol. xxxv, part b2 elsinga ge, scarano f, wieneke b, and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 gokturk s, yalcin h, and bamji c (2004) a time-of-flight depth sensor system description, issues and solutions. in 2012 ieee computer society conference on computer vision and pattern recognition workshops. volume 4. page 35. ieee computer society, los alamitos, ca, usa hansard m, lee s, choi o, and horaud r (2012) time of flight cameras: principles, methods, and applications. springerbriefs in computer science. springer he y and chen s (2019) recent advances in 3d data acquisition and processing by time-of-flight camera. ieee access 7:12495–12510 he y, liang b, zou y, he j, and yang j (2017) depth errors analysis and correction for time-of-flight (tof) cameras. sensors 17:92 hu y, vaughan m, tepte c, weimer c, beherenfeld m, young s, winker d, hostetler c, hunt w, kuehn r, flittner d, cisewski m, gibson g, lin b, and macdonnell d (2007) elevation information in tail (eit) technique for lidar altimetry. optics express 15:14504–15 kadambi a and raskar r (2017) rethinking machine vision time of flight with ghz heterodyning. ieee access 5:26211–26223 lucidvision (2019) helios general technical reference. lucid vision labs lucidvision (2020) better time of flight: sony depthsense 3d sensor explained. lucid vision labs melexis (2020) time-of-flight (tof) basics. melexis inspired engineering paciaroni me, chen y, lynch kp, and guildenbecher dr (2018) backscatter particle image velocimetry via optical time-of-flight sectioning. opt lett 43:312–315 qiu y, xie y, wang w, liu w, kuang l, bai x, hu m, and ho j (2019) ultra-high-power and high-efficiency 905nm pulsed laser for lidar. in 2019 ieee 4th optoelectronics global conference (ogc). pages 32–35 raffel m, kähler c, willert c, wereley s, scarano f, and kompenhans j (2018) particle image velocimetry: a practical guide. springer. 3rd edition romano m, alberini f, liu l, simmons m, and stitt e (2021) lagrangian investigations of a stirred tank fluid flow using 3d-ptv. chemical engineering research and design 172:71–83 rossi m and marin a (2020) single-camera 3d ptv methods for evaporation-driven liquid flows in sessile droplets. pages 225–236 shnapp r, shapira e, peri d, bohbot-raviv y, fattal e, and liberzon a (2019) extended 3d-ptv for direct measurements of lagrangian statistics of canopy turbulence in a wind tunnel. scientific reports 9 telling jw, glennie c, fountain ag, and finnegan dc (2017) analyzing glacier surface motion using lidar data. remote sensing 9 wang h, wang b, liu b, meng x, and yang g (2017) pedestrian recognition and tracking using 3d lidar for autonomous vehicle. robotics and autonomous systems 88:71–78 wang j, sun w, shou w, wang x, wu c, chong hy, liu y, and sun c (2015) integrating bim and lidar for real-time construction quality control. journal of intelligent and robotic systems 79:417–432 introduction time of flight camera technology experimental methods results and discussion environment fluid medium and distortions particle seeding volumetric and time resolution planar motion 3d motion assessment of the state of technology conclusions microsoft word ispiv2021_paper_schroeder_etal_184.docx 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa large-scale 3d flow investigations around a cyclically breathing thermal manikin in a 12 m³ room using hfsb and stb a. schröder1*, d. schanz1, j. bosbach1, m. novara1, r. geisler1, j. agocs1, a. kohl2 1: german aerospace center (dlr), inst. of aerodynamics and flow technology, dept. experimental methods, göttingen, germany 2: german aerospace center (dlr), inst. of aerodynamics and flow technology, dept. ground vehicles, göttingen, germany *andreas.schroeder@dlr.de abstract exhalation of small aerosol droplets and their transport, dispersion and (local) accumulation in closed rooms have been identified as the main pathway for indirect or airborne respiratory virus transmission from person to person, e.g. for sars-cov 2 or measles (morawska and cao 2020). understanding airborne transport mechanisms of viruses via small bio-aerosol particles inside closed populated rooms is an important key factor for optimizing various mitigation strategies (morawska et al. 2020), which can play an important role for damping the infection dynamics of any future and the ongoing present pandemic scenario, which unfortunately, is still threatening due to the spreading of several sars-cov2 variants of concern, e.g. delta (kupferschmidt and wadman 2021). therefore, a large-scale 3d lagrangian particle tracking experiment using up to 3 million long lived and nearly neutrally buoyant helium-filled soap bubbles (hfsb) with a mean diameter of ~ 370 µm as passive tracers in a 12 m³ generic test room has been performed, which allows to fully resolve the lagrangian transport properties and flow field inside the whole room around a cyclically breathing thermal manikin (lange et al. 2012) with and without mouth-nose-masks and shields applied. six high-resolution cmos streaming cameras, a large array of powerful pulsed leds have been used and the shake-the-box (stb) (schanz et al. 2016) lagrangian particle tracking algorithm has been applied in this experimental study of internal flows in order to gain insight into the complex transient and turbulent aerosol particle transport and dispersion processes around seated breathing persons. introduction an enhanced understanding of the transient, turbulent and partly laminar dynamics of lagrangian transport processes of aerosol particles around cyclically breathing persons with and without protective masks or shields in closed rooms at full temporal and spatial resolution is desired for estimating the risk for infecting other persons in the same room during a specific time span and for implementing proper technical mitigation strategies against the spreading of respiratory viruses, especially sars-cov-2. speaking, singing and coughing generate a large number of variously sized aerosols (johnson et al. 2011, fenneley 2020) and an animal study with airborne influenza virus using ferrets indicates effective transmission of viruses in aerosols larger than 1.5 µm (zhou et al. 2018). the virus load or the number of viral particles in droplets and aerosols is determined by the location of their generation in the infected human airways and by the size of the carrier droplet or aerosol. sars-cov-2 is only about 0.08 to 0.12 µm in diameter but is carried through the air in particles of respiratory fluid, which differ in size between 0.2µm and 100µm. while the larger aerosol droplets follow ballistic pathways towards the floor within less than a second, it can be shown for droplets smaller than ~20 µm that the liquid phase evaporates during the time span between exhalation and settling under typical indoor conditions and the remaining aerosol particle diameter can shrink down to less than 5 µm thus becoming an almost passive tracer within the typical mixed convective flow regimes. recent studies demonstrated that highly infectious covid-19 patients exhale up to a million of sars-cov-2 rna copies per hour into the air (ma et al. 2020) while the critical number of inhaled viruses with contact to human airway cells (zuo et al. 2020) is around a few hundred to one thousand for a 50 % risk of getting infected (lelieveld et al. 2020), which also depends on the present virus variant. infectious sars-cov-2 virions can be found as well in aerosol particles with a diameter down to 0.25 0.5 µm (liu et al. 2020). aerosol particles < 5 µm can follow the internal airflow for several minutes and 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa even up to hours depending on the present buoyancy or pressure forcing in the flow while the settling time for aerosol particles < 2µm in air is even in the order of hours for quiescent air and a height of 2 m. more recently, a study clarified the reasons for seemingly contradictory results from various, partly clinical studies on the effectiveness of masks against transmission of airborne viruses (cheng et al. 2021). they concluded that masks are a very effective measure for preventing respiratory virus infections in closed rooms especially when the concentration of virus laden aerosols in the room is limited and/or the residence time of persons inside such rooms is relatively short, while ffp2/3 masks are showing a significant protection gain in comparison to surgical masks or even simpler mouth-nose-masks. infections despite wearing surgical masks in clinical studies happened almost always in closed rooms with heavy virus loads and/or via accumulation of inhaled virions over longer time-spans. other studies based on epidemiological data showed as well a clear effectiveness of masks against infections with sarscov-2 in daily usage scenarios (mitze et al. 2021). while masks are without doubts most effective against airborne virus transmission, as they retain droplets and aerosols directly at the place of exhalation and inhalation, (mobile) air cleaning technologies come next in a row of mitigative measures and should be seriously considered as an additional infection risk reduction device (curtius et al. 2020, kähler et al. 2020). they do not rely on human behavior and can help reducing infection risks in occupied places, in addition to wearing protective masks or where it is not possible or problematic to wear masks, that is, in nurseries, classrooms, offices, restaurants and other places. based on the gained knowledge from recent worldwide research activities on airborne transmission of sars-cov-2 viruses between humans in closed rooms with and without wearing masks or other mitigation measures it is still of specific high interest to understand in detail the lagrangian transport processes and pathways of small aerosol particles exhaled by a human source including their dispersion and accumulation characteristics. over longer time spans a local and global accumulation of virus laden aerosols can occur in confined rooms while the sars-cov-2 virus has been proven to be stable in airborne particles with a half-life time of more than one hour (van doremalen et al. 2020). therefore, it is possible that sharing the same room with an infectious person even under ventilated or limited virus load conditions can lead to inhaling a critical number of viruses over several minutes or even hours accumulatively. consequently, the governing unsteady and large-scale fluid dynamics inside a whole room is still of major interest: depending on the location of the spreading source, on the specific constellation of the room geometry, furniture positions, persons and their dynamics and on employing active or passive ventilation inside such confined rooms the resulting dynamic spatial distribution of aerosol particles changes significantly. therefore, volumetric flow measurements with sufficient temporal resolution are needed to enhance the understanding of the related aerosol particle transport mechanisms. the measurement technique has to be capable of capturing all relevant scales starting from the impulsive and jet-like individual cycles of in– and exhalation over medium scale turbulent transport and diffusion processes in wakes and plumes up to the largest (and slowest) flow-scale circulations in the full room. existing probe-based measurement methods using detection of gaseous tracers emitted at a potential source position need to rely on statistics at some individual measurement positions while the pathways from the source to the measurement points is kept unknown. the lagrangian aerosol particle transport inside a populated room is mainly governed by temperature gradientsor buoyancy driven flows (body heat plume, heating systems, electric devices, open windows, stratification etc.), pressure gradient driven flows (open doors and/or windows on opposite sides, active ventilation systems etc.) and by transient and mainly turbulent flows caused by the individual cyclically breathing, speaking, singing etc. events and active movements of persons. as a result, a complex multi-scale and partly turbulent flow situation develops. in order to optimize mitigation concepts for airborne transmission of viruses all mentioned flow properties need to be understood in detail. as a first step the flow in a generic and idealizedroom with a seated and cyclically breathing thermal manikin has been investigated in the present study: therefore, a large-scale 3d lagrangian particle tracking (lpt) experiment enabling the instantaneous tracking of up to ~3 million submillimeter helium-filled-soap-bubbles (hfsbs) representing the small aerosol particles as passive tracers in a 12 m³ generic test room has been performed at dlr göttingen in the framework of the project aeromask, which allows to fully resolve the flow field in the complete room around the manikin. 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa set-up and procedure six high-resolution cmos streaming cameras, a large array of powerful pulsed leds, four hfsb generator nozzles and the shake-the-box (schanz et al. 2016) lpt algorithm have been combined in this large-scale volumetric experimental study (see fig. 1, 2 and 3). based on the reconstructed dense hfsb trajectories covering the complete room volume the related lagrangian particle transport and dispersion processes are captured over the whole time series of ~52 sec for each test case. furthermore, many insights into the complex transient and turbulent flow features around the breathing manikin have been discovered after application of the flowfit data assimilation scheme (gesemann et al. 2016). the manikin’s surface has been heated homogenously to ~36° c by ~80 w electric power through equidistantly placed heating wires winded around the manikins’ body. the manikin has got tailored black clothes and “hair” in order to create a realistic setting and reduce the light reflections from the pulsed led array. the black clothing led to a specific surface temperature distribution (see infrared camera images in figure 3 (middle)). in our studies various breathing and coughing scenarios driven by a programmable artificial lung, basically a software controlled motorized piston connected with a hose to the mouth of the 3d printed dummy head (for details see kohl 2020) have been investigated. breathing with and without protective measures creates different fluid dynamical interactions with the thermal plume induced by the heated manikin. for each inand exhaling cycle, measurements were conducted with and with-out an applied mask, a face-shield or a plane acrylic glass shield placed approx. 60 cm in front of the dummy’s face (see fig. 4). all potentially light reflective surfaces and backgrounds have been covered by black curtain or self-adhesive foil (see. fig 1 (left)). figure 1: experimental set-up at 12 m³ glass room with seated manikin, led-array and imaging system with six highresolution cmos cameras (left) and calibration target on honeycomb material aligned with laser levels (right) the camera system consisted of 4 x 50 mpx (lavision imager mx 50m) and 2 x 25 mpx (avt bonito pro x-2620) global shutter cmos cameras equipped with scheimpflug mounts from lavision and nikon lenses with a focal length of f = 50 mm at aperture number of f# = 16, each connected by four coaxpress cables to frame grabbers of two acquisition pcs. one pc was connected to the four imager mx 50m cameras and used the davis10 acquisition software, which as well controled a ptu (programmable timing unit) from lavision for synchronization of led pulses and camera image acquisitions. the other pc was connected to the two avt cameras and used a self-adapted acquisition software based on the provided avt software development kit. the camera system allowed almost full views through the whole volume by each of the 50 mpx cameras and two overlapping part-volume views by the two 25 mpx cameras, the latter placed in the center of the aligned camera set-up (see fig. 1 (left)). only small shadow regions behind the manikin and its legs could not be captured volumetrically. the cameras have been 3d calibrated by using the images of a large planar dot marker target (2.5 m x 1.25 m) (see fig 1 (right)) at two planes separated in depth by 1.0 m for gaining 3d -2d point correspondences for all camera views. in a second step, a volume self calibration (vsc) procedure (wieneke 2008) based on particle images of a sparse distribution of hfsbs inside the room and a subsequent optical transfer function (otf) determination of each camera and sub-volume (schanz et al. 2012) have been performed. the use of wide angle lenses, as well as a slight waviness of the thin plexiglass wall leds 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa induced small decalibrations in the of up to 0.3 px that were not correctable by the used second order camera model. a two-dimensional b-spline corrector field was calibrated for each camera using the averaged differences between the reprojected and the detected real peaks (see schanz et al. 2019). using this corrector field the camera errors could be corrected well below 0.1 px. before each measurement sequence several millions of long-lived and nearly neutrally buoyant helium-filled-soap-bubbles (hfsb) (bosbach et al. 2009) with ~370 µm mean diameter and ~1.5 mm/sec settling velocity have been homogenously introduced into the room using four flush mounted generator nozzles in the back wall of the room, connected to a lavision hfsb generator (see fig 2 (left)). the geometry of the hfsb nozzle and shadow-graphic images of the bubble generation can be found in fig. 2 (middle). in order to increase the half-life time of the bubbles to approx. 3.75 min we developed an in-house bubble fluid solution. this half-life time corresponds to a time-constant tau of the fitted exponential function or a mean life-time of approx. 5.5 min (see j. bosbach et al. contribution to this ispiv’21). figure 2: helium-filled soap bubble (hfsb) generator from lavision (left), geometry (bosbach et al. 2009) with shadow graphic images of hfsb nozzle (middle) and cyclically breathing thermal manikin with surrounding illuminated hfsbs (right) after stopping the hfsb seeding device a waiting time of 2 minutes was always allowed to let the initially disturbed flow to settle down to the internal flow situation basically forced by the breathing cycles and the heated manikin before starting the image acquisition using a davis10.x software package. a ptu from lavision was used for synchronization of the large-scale illumination of the whole room, which was realized by a planar arrangement of various pulsed and collimated led arrays (9 x hardsoft ilm-501 (see stasicki et al 2019), 6 x led-flashlight 300 by lavision and 8 x panels with less dense arranged leds (in total 1509 leds)) and a back-reflection via a large mirror made of self-adhesive foil from 3m fixed on a 2 x 2 m² flat wooden plate on the opposite side of the test room. the pulsed light from the array of leds had a pulse length of 4 ms each which corresponds to a duty cycle of ~1: 9.6 avoiding smearing effects of the hfsb imaging. the dlr implementation of the shake-the-box (stb) method (schanz et al., 2016) using an advanced iterative particle reconstruction (ipr) code for the “shaking” step and internal loops (jahn et al. 2021; wieneke 2013) and the variable time-step stb procedure (vt-stb) (see schanz et al. contribution to this ispiv’21) has been applied for the evaluation of the gained time-series of particle images captured by the camera system at between 26 and 28 hz over time spans of ~52 seconds for each test case. the duration of the time series was limited by the available ram capacity of the davis10 acquisition pc to approximately 1380 timesteps. the lagrangian particle trajectories resulting from the stb evaluation allow following between 1.5 and 3 million individual hfsbs in time and space inside the complete volume of the 12 m³ room with a mean position accuracy of ~60 µm. subsequently, the dlr own data assimilation method flowfit (gesemann et al., 2016) has been applied to the dense particle trajectory data which provides the related full time-resolved 3d velocity gradientand pressure fields. 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa figure 3: system of led arrays used for pulsed illumination (left); thermographic image of the heated manikin (middle); breathing apparatus (mechanical lung) (right). figure 4: masks and shields applied for cyclically breathing thermal manikin: surgical mask (left), transparent face shield (middle) and acrylic glass plate 0.6 m in front of manikin face (right) the eulerian representation of the flow fields enables additional insights into the turbulent mixture by the advection of vortical flow structures in the room which are mainly induced by shear flow events generated by the cyclic breathing and the thermal plume above the heated manikin (see fig. 5 (middle and right)). while during the heavy breathing case, which is sinusoidal breathing at 0.33 hz with 1.1 liters of volume per breathing cycle, the high momentum jetlike fluid which is cyclically exhaled by our thermal manikin’s mouth reaches even the opposite wall at ~1.75 m distance within a few seconds, the same breathing situation with surgical mask applied results in a massive reduction of the horizontal transport of fluid and related aerosol particles. for the situation with mask applied in fig.5 (bottomleft) the induced pressure loss of the mask enables the hfsbs around the manikin’s head to move only slightly as a result ofthe exhaled air. by a small leakage flow of the mask on both sides of the nose the air is partly pushed towards the ceiling (positive y-values) which is also typical for not perfect fitting masks at real humans and well known by people wearing glasses. the exhaled air volume in that case stays in close vicinity of the head and manikin’s body and the related hfsbs are transported upwards and get mixed-up with the surrounding air by the vortices of the turbulent thermal plume (see fig. 5 (middle)) (see for comparison huhn et al. 2017). approaching the ceiling the hfsbs trajectories are bended towards a horizontal direction and are transported further in a concentrically way while creating a circular pattern of vortices in the turbulent shear and boundary layer (see fig. 5 (bottom-left) similar to a low reynolds number impinging jet (huhn et al. 2018) which leads to further mixing of the exhaled air with the 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa surrounding air. while during the heavy breathing case without a mask applied the exhaled air and corresponding aerosol particles reaches the opposite wall (or a hypothetical other person sitting face-to-face in ~1.7 m distance) within a few seconds the pathway of the exhaled air with mask applied gets strongly decelerated at the mask and first travels with the thermal plume towards the ceiling, gets further slowed down and then concentrically distributed along the ceilings surface. after many seconds up to a minute the mixed air with a therefore massively lowered local concentration of exhaled aerosol particles reaches the side walls and starts to descend into the room while creating large low-speed and almost laminar recirculation rollers (see fig. 5 (bottom-left)). in the case without mask applied high concentrations of horizontally exhaled aerosol particles would directly hit another person’s head, which could inhale a critical viral load within a few minutes while on the other hand the mask is not only filtering out many aerosol droplets (depending on the quality of the mask and its tight fitting in the face by ~40 to 90 %) also, those which bypasses the mask would be mixed up in the room and would travel a long way before reaching another person. any ventilation system would further reduce the viral load in the room and other persons wearing masks would additionally profit from their filter capacities. of course, wearing masks in a not well-ventilated room would as well cause a critical accumulation of virus laden aerosol particles within several minutes or a few hours depending on the size of the room and the quality of the mask. but the possible residence time for a person in such a scenario before getting infected would be significantly extended. the void regions related to the heavy breathing cycles in fig 5 (top-left) signify the fact that the used mechanical lung volume could not be seeded by hfsb and that very fast hfsbs could not be tracked reliably due the low temporal resolution < 28 hz of the imaging frequency: displacements of more than 40 pixels in between time-steps have been detected in the exhaled air jet and subsequent strong acceleration events during entrainment of those tracks into vortices in the exhaled air-jet’s shear layer poses a main tracking challenge in the present stb evaluation. however, an adaptive tracking system is under development that might account at least partly for this lack of temporal sampling for this small fraction (~0.5 %) of bubbles with respect to the overall reconstructed hfsb tracks. figure 5: tracked hfsbs in central 0.24 m slice of the volume, cut from the full extent of 3.0 m (left); related vortical structures in the full 12 m³ volume based on flowfit data assimilation, sideview (middle), top view (right). isosurfaces of q-values at 6 1/s² colour coded by vertical velocity. 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa a quite positive effect in terms of aerosol transport pathway deflections and mixing can be described as well for applying an acrylic glass plate with a size of 80 x 80 cm placed almost vertically at ~60 cm distance in front of the mouth of the manikin (see fig. 6), which is a typical safety measure in small shops, restaurants or at cashier desks in supermarkets. here, the cyclic exhale-jets of the heavy breathing case impinge on the surface of the vertical glass plate which creates a large ring-like vortex structure with temporally increasing diameter. when this vortex ring is passing over the plates edges the rotational fluid entrains air from the room opposite to the plate towards the manikin which in turn creates a larger recirculation structure on the side of the manikin. therefore, the exhaled air (and corresponding aerosol particles) gets trapped on the manikins (humans) side of the plate, and it is then mainly further transported by the thermal plume towards the ceiling and distributed in concentrically, partly turbulent pathways along its surface, very similar as for the case with mask applied (see fig 5). please keep in mind, that for the case with wearing a faceshield (see fig. 7) as well as for the vertical plate there are no filter mechanisms acting at the exhaled aerosol particles (beside impingement of large droplets at the face shields surface). therefore, the overall viral load in the room would still increase unbraked, but for both applied shield methods a fast and direct horizontal transport of aerosol particles with a possible high local concentration towards a hypothetical next person inside the room can be avoided. any residence of persons over longer time spans would become critical after shorter time-spans compared to the case with masks applied. in order to find a proper measure to indicate critical time spans of personal residences inside populated rooms together with one-spreader one would need information about the whole specific transport and mixing processes, which for our generic test case will be a future postprocessing step on our lagrangian tracks using information from literature e.g. lelieveld et al. 2020. nevertheless, even when assuming isotropic turbulent diffusion with certain time scales, knowing the number of virions exhaled per minute by a spreader and the critical number of inhaled virions for starting an infection at another person allows quite accurately to determine the risk of an infection with an online available calculator (see https://aerosol.ds.mpg.de/en/). further coughing and breathing cases have been studied with and without masks and shields applied and the results will be presented in an upcoming journal paper. as mentioned, in a further postprocessing step the full 3d lagrangian transport processes of potentially infectious exhaled aerosol particles inside the room shall be mimicked and reconstructed with high temporal resolution by using a cyclically increasing subfraction of the hfsbs originating from the exhaled flow volumes. those will be followed individually during the whole measurement time representing potentially virus laden small bioaerosols. it will allow us to visualize the respective transient and turbulent dispersion process representing an infectious person starting to spread aerosols at the starting point of our measurements. based on simplifying assumptions further dispersion processes can be studied by extending the time span of one measurement case (~52 seconds or ~12 to 17 breathing cycles) by appending the same volumetric and time-resolved lpt data after the end of a time series temporally and choosing the next closely neighbouring particle in space at the end of each track for extending the statistics towards a few minutes, while newly entering aerosol particles during this time span can be represented by another distinct subfraction of hfsb originating from the exhaled flow volumes. the gained lagrangian and eulerian data from the present study and further postprocessing will be used in a followup project supported by the german research foundation (dfg). here the lagrangian and eulerian data is used as input and validation data for the development of numerical methods enabling flow simulations and inertial as well as passive aerosol particle dispersions predictions. the developed codes shall be applicable with relatively low computational costs to flow scenarios in more complicated and realistic constellations with additonal dynamics and/or ventilation devices in larger rooms. 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa figure 6: tracked hfsbs for a heavy breathing case with acrylic glass plate (shown in red) installed 60 cm in front of the manikins’ face. shown are 24 cm deep volume slices each from side view (top-left) and top view (top-right) and corresponding full volume flowfit results with iso-surfaces of q-values at 6 1/s²color coded by the vertical velocity (bottom) figure 7: tracked hfsbs for the heavy breathing case with face shield placed in front of the manikin’s face. shown are 24 cm deep volumes slices of hfsb color coded by vertical velocity (left) and lagrangian tracks over ~50 timesteps color coded by x -component of acceleration (right) each from sideview 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa conclusions in the present research work an unprecedented large-scale volumetric lagrangian particle tracking (lpt) experiment with up to 3 million instantaneously reconstructed trajectories of submillimeter hfsbs has been performed providing time-resolved velocity and acceleration measurements along all particles’ trajectories around a seated and cyclically breathing thermal manikin inside a confined rectangular volume of 12 m³ over a time span of ~52 sec for each case. assuming nearly neutral buoyancy of small aerosol particles and droplets (d < 5 µm) typically exhaled by humans, the nearly neutrally buoyant long-lived hfsbs with ~ 370 µm mean diameter can be considered as their replacements as they act as passive tracers in the present described experimental set-up which is aiming at mimicking a flow situation with a seated person. full lagrangian transport processes from various cyclically human breathing and coughing scenarios inside the room with and without masks and shields applied have been captured in 3d with temporal resolution by the dlr in-house shake-the-box (stb) evaluation scheme. only a small selection of the investigated cases could be shown in the present paper. furthermore, the application of the navier-stokes regularized data assimilation scheme flowfit delivered the complete eulerian flow field based on the scattered lpt data including the time-resolved 3d velocity gradient tensorand pressure fields at high spatial resolution. this allows studying the transient and turbulent flow features governing the transport and mixing processes of the small aerosol particles for this generic flow situation in detail. the jet-like cyclically heavy breathing events in case the manikin is not wearing a mask or face shield are the most powerful horizontal transport events in our investigation. on the other hand, the thermal plume of the heated manikin governs the turbulent transport and mixing mechanism in the scenario when protective masks or shields are applied or the breathing is soft. here, the mean direction of the transport of exhaled aerosol particles is going towards the ceiling, because the decelerated aerosol particles first remain near the body after exhalation. the deceleration and deflection of the exhaled aerosol particles by the investigated mitigation devices is quite advantageous, because the fast horizontal transport of locally highly concentrated aerosol particles and its direct impact at the position of another person is avoided. nevertheless, over longer time spans an accumulation of aerosol particles occurs in confined rooms without proper ventilation or filtering devices which limits the critical residence time for several persons. therefore, wearing masks with a high filtration capability of aerosol particles down to diameters ~300 nm (ffp2/3) is highly recommended. additional shields should be applied in order to separate the flow regimes around individual persons at least for short to intermediate time spans. unfortunately, the majority of the human population on earth will not be vaccinated during this year and new mutants of sars-cov-2 with higher infection rates and/or escape properties are and will be underway. therefore, the correct application of protective measures (masks and shields) and the detailed understanding of aerosol transport processes in closed rooms are still necessary preconditions for damping the infection risks and chains by optimizing proper technical devices and their application locations (e.g. air purifiers or displacement ventilation systems in buildings, public transport vehicles and air cabins). finally, the gained knowledge shall give recommendations for human behavior and awareness of critical situations. the complete present lagrangian and eulerian flow field data will be used as input for the development of numerical methods allowing to optimizing ventilation systems in closed rooms or transport vehicles with respect to avoiding airborne infection pathways. acknowledgements support with hardand software for illumination and image acquisition by lavision gmbh is gratefully acknowledged. this work was supported by the dfg through grant schr 1165/5-2 in the priority programme on turbulent superstructures (spp 1881) and the dlr project aeromask. thanks for support of a breathing medical dummy head by oth regensburg (prof. krenkel). thanks for technical support at dlr by c. fuchs, t. herrmann and t. kleindienst. 14th international symposium on particle image velocimetry • august 1-4, 2021 • virtual, chicago, il usa references bosbach, j., kühn, m., wagner, c. (2009): “large scale particle image velocimetry with helium filled soap bubbles”. exp fluids 46:539–547. https://doi.org/10.1007/s00348-008-0579-0 cheng, y., n. ma, c. witt, s. rapp, p.s. wild, m.o. andreae, u. pöschl, h. su (2021): “face masks effectively limit the probability of sars-cov-2 transmission”. science, 372:6549, pp. 1439-1443, doi: 10.1126/science.abg6296 http://science.sciencemag.org/content/early/2021/05/19/science.abg6296 curtius, j., granzin, m., schrod, j. (2020): “testing mobile air purifiers in a school classroom: reducing the airborne transmission risk for sars-cov-2”. aerosol science and technology, 55:5, https://doi.org/10.1080/02786826.2021.1877257 van doremalen, n.; bushmaker, t.; morris, d.h.; holbrook, m.g.; gamble, a.; williamson, b.n.; tamin, a.; harcourt, j.l.; thornburg, n.j.; gerber, s.i.; et al. (2020): “aerosol and surface stability of sars-cov-2 as compared with sars-cov-1”. n. engl. j. med. 2020, 382, 1564–1567 fennelly, k. p. (2020): "particle sizes of infectious aerosols: implications for infection control." the lancet respiratory medicine gesemann, s., huhn, f., schanz, d., and schröder, a. (2016): “from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties”. 18th lisbon int symp, july 3-7, 2016, portugal huhn, f., schanz, d., manovski, p., gesemann, s., schröder, a. (2018): “time-resolved large-scale volumetric pressure fields of an impinging jet from dense lagrangian particle tracking”. exp fluids 59:81, doi 10.1007/s00348-017-2390-2 huhn, f., schanz, d., gesemann, s., dierksheide, u., van de meerendonk, r., schröder, a. (2017): “large-scale volumetric flow measurement in a pure thermal plume by dense tracking of helium-filled soap bubbles”. exp. fluids 58:116, doi: 10.1007/s00348-017-2390-2 jahn, t., schanz, d., and schröder, a. (2021): „advanced iterative particle reconstruction for lagrangian particle tracking”. submitted for publication at experiments in fluids johnson, g.r., et al. (2011): “modality of human expired aerosol size distributions”. journal of aerosol science, 2011. 42(12): p. 839-851 kähler, c.j., fuchs, t., hain, r. (2020): „können mobile raumluftreiniger eine indirekte sars-cov-2 infektionsgefahr durch aerosole wirksam reduzieren?“ doi: 10.13140/rg.2.2.27503.46243 kohl, a. (2020): „entwicklung eines systems zur experimentellen simulation der atmung von passagieren“. masterarbeit, tu ilmenau, https://elib.dlr.de/136986/ lange, p., westhoff, a., schmeling, d., and dehne, t. (2018): “low-cost thermal manikin a competitive instrument to simulate thermal loads and to determine thermal passenger comfort”. in: 12th international manikin and modelling meeting, 29.-31. aug. 2018, st. gallen, schweiz kupferschmidt, k., and wadman, m. (2021): „delta variant triggers new phase in the pandemic”. science, 372:6549, pp. 13751376, doi: 10.1126/science.372.6549.1375 liu, j.; ning, z.; chen, y.; guo, m.; liu, y.; kumar gali, n.; sun, l.; duan, y.; cai, j.; westerdahl, d.; et al. (2020): “aerodynamic analysis of sars-cov-2 in two wuhan hospitals”. nature 2020, 582, 557–560. lelieveld, j., helleis, f., borrmann, s., cheng, y., drewnick, f., haug, g., klimach, t., sciare j., su, h., and pöschl, u. (2020): “model calculations of aerosol transmission and infection risk of covid-19 in indoor environments”. int. j. environ. res. public health 2020, 17(21), 8114; https://doi.org/10.3390/ijerph17218114 mitze, t., kosfeld, r., rode, j., and wälde, k. (2021): “face masks considerably reduce covid-19 cases in germany“, proc natl acad sci usa 117:51,doi: 10.1073/pnas.2015954117 morawska, l., cao, j., 2020: “airborne transmission of sars-cov-2: the world should face the reality”. environ. int. 105730 morawska, l., tang, j.w., et al. (2020): "how can airborne transmission of covid-19 indoors be minimised?" environ int 142: 105832. schanz, d., gesemann, s., schröder, a., wieneke, b. and novara, m. (2013): “non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction”. meas. sci. tech. 24:024009 schanz, d., gesemann, s., and schröder, a. (2016): “shake-the-box: lagrangian particle tracking at high particle image densities”. exp fluids 57:70, 2016, doi 10.1007/s00348-016-2157-1 schanz d, schröder a, novara m, geisler r, agocs j, eich f, bross m, and kähler cj (2019) large-scale volumetric characterization of a turbulent boundary layer flow. in proceedings of the 13th international symposium on particle image velocimetry. 182. pages 251–265. universität der bundeswehr münchen: atheneforschung stasicki b, schröder a, boden f, and ludwikowski k (2017): “high-power led light sources for optical measurement systems operated in continuous and overdriven pulsed modes”. in optical measurement systems for industrial inspection x. volume 10329. page 103292j. international society for optics and photonics van doremalen, n., bushmaker, t., morris, d.h., holbrook, m.g., gamble, a., williamson, b.n., et al. (2020): “aerosol and surface stability of sars-cov-2 as compared with sars-cov-1”. n. engl. j. med wieneke b (2008): “volume self-calibration for 3d particle image velocimetry”. exp. fluids 45:549–556 wieneke b (2013): “iterative reconstruction of volumetric particle distribution”. meas. sci. tech. 24:024008 zuo, y.y., uspal, w.e., wei, t. (2020): “airborne transmission of covid-19: aerosol dispersion, lung deposition, and virusreceptor interactions”. acs nano 2020 14 (12), 16502-16524 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 three-dimensional temperature and velocity measurements in fluids using thermographic phosphor tracer particles m. stelter1∗, f. j.w.a. martins1,2, f. beyrau1, b. fond1 1 institut für strömungstechnik und thermodynamik, otto-von-guericke-universität magdeburg, germany 2 current address: institut für verbrennung und gasdynamik, universität duisburg-essen, germany ∗ moritz.stelter@ovgu.de many flows of technical and scientific interest are intrinsically three-dimensional. extracting slices using planar measurement techniques allows only a limited view into the flow physics and can introduce ambiguities while investigating the extent of 3d regions. nowadays, thanks to tremendous progress in the field of volumetric velocimetry, full 3d-3c velocity information can be gathered using tomographic piv or ptv hence eliminating many of these ambiguities (discetti and coletti, 2018; westerweel et al., 2013). however, for scalar quantities like temperature, 3d measurements remain challenging. previous approaches for coupled 3d thermometry and velocimetry combined astigmatism ptv with encapsulated europium chelates particles (massing et al., 2018) or tomographic piv with thermochromic liquid crystals particles (schiepel et al., 2021). here we present a new technique based on solid thermographic phosphor tracer particles, which have been extensively used for planar fluid temperature and velocity measurements (abram et al., 2018) and are applicable in a wide range of temperatures. the particles are seeded into a gas flow where their 3d positions are retrieved by triangulation from multiple views and their temperatures are derived from two-colour luminescence ratio imaging. in the following, the experimental setup and key processing steps are described before a demonstration of the concept in a turbulent heated jet is shown. the measurement system is illustrated in fig. 1a. two lasers are employed as light sources, a double-pulse green laser (532 nm) for particle position and velocity measurements using mie scattered light and a singlepulse uv laser (266 nm, synchronized with the first green laser pulse) to excite the phosphor luminescence. the laser beams are superimposed and shaped to illuminate a 5 mm diameter probe volume. a gas jet with co-flow emanating from the square tube below the laser beams is seeded with phosphor particles. to reconstruct 3d particle locations and velocities, particle images are acquired using four cameras (p1–p4) in double-frame single-exposure configuration. to maintain a large depth of field and to minimise reconstruction errors, these cameras’ lenses are equipped with scheimpflug adapters and stopped down to f/16. the emitted luminescence is captured simultaneously by two separate cameras (t1 and t2) with fully opened apertures to maximize signal levels. as a result, not all particles are imaged in focus (fig. 1b). cameras t1 and t2 are equipped with specific spectral filters so that the ratio of luminescence intensities between both cameras’ images is a monotonic function of temperature (fig. 1c). as described in the next paragraph, each sextet of particle images is used for extraction of particle position, velocity and temperature information. figure 1: experimental setup (a) with schematic of particle image formation in ptv and luminescence cameras (b) and normalized zno emission spectra from 293k to 488k in 15k intervals showing its temperature induced shift (c). normalised transmission profiles of the spectral filters are added in red and blue. first, all six camera views are calibrated by translating a 2d dot-target through the measurement volume. then, the 3d reconstruction of particle positions in both 532 nm-illuminated frames is performed by an inhouse particle triangulation code using the images of cameras p1 to p4. the reconstructed positions from the first frame are then projected onto the images of cameras t1 and t2. particles are paired with these positions based on the closest particle image centre. the luminescence signal for each particle is spatially integrated within the images of cameras t1 and t2 using a 2d-gaussian fit-based mask. a ratio is calculated from these intensities and is converted to temperature using calibration data, resulting in a discrete 3d temperature field. particle velocity is assessed based on the displacement of paired particles between both reconstructed fields. a first displacement guess is gained by a 3d ensemble cross-correlation and then pairing is achieved by the closest particles. as proof of concept, a demonstration experiment was performed using a 4 mm jet heated to a nozzle exit temperature of 383 k at a bulk velocity of 28 m/s surrounded by a low-velocity co-flow at room temperature. both flows were seeded with zno particles (volume equivalent diameter 600 nm). 3d data of particle temperature and velocity accumulated over 366 single-shot measurements are plotted in fig. 2. as expected, hot particles are grouped within a cylindrical region corresponding to the jet flow showing an axisymmetric temperature distribution. data from a cylindrical 2 mm diameter sub-volume centred in the jet flow region and considered isothermal were used to establish the particle-to-particle temperature precision, which was 18 k for a mean temperature of 369 k. highest particle velocities are also detected at the jet centre and their values decrease with radial distance. the present results demonstrate the ability of our new technique to measure 3d temperature and velocity fields. future work will concentrate on improving the measurement density and decreasing the random temperature uncertainty by using more advanced 3d reconstruction algorithms and different thermographic phosphor materials. figure 2: reconstructed particle positions as dots with colour encoded temperature in 3d (a) and top view (c) accompanied by the particle velocity field in 3d (b) and top view (d). inner (4 mm) and outer (6 mm) diameter of the jet nozzle are indicated in grey. funding from the german research foundation dfg (project number 427979038) is gratefully acknowledged. references abram c, fond b, and beyrau f (2018) temperature measurement techniques for gas and liquid flows using thermographic phosphor tracer particles. progress in energy and combustion science 64:93–156 discetti s and coletti f (2018) volumetric velocimetry for fluid flows. meas sci technol 29:042001 massing j, kähler c, and cierpka c (2018) a volumetric temperature and velocity measurement technique for microfluidics based on luminescence lifetime imaging. experiments in fluids 59:1–13 schiepel d, schmeling d, and wagner c (2021) simultaneous tomographic particle image velocimetry and thermometry of turbulent rayleigh–bénard convection. meas sci technol 32:095201 westerweel j, elsinga g, and adrian r (2013) particle image velocimetry for complex and turbulent flows. annual review of fluid mechanics 45:409–436 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 error propagation dynamics of velocimetry-based pressure field calculations (2): on the error profile matthew faiella1, corwin grant jeon macmillan1, jared p. whitehead2∗ and zhao pan1† 1 university of waterloo, department of mechanical and mechatronics engineering, on n2l 3g1, canada 2 brigham young university, mathematics department, provo, ut 84602, usa ∗ whitehead@mathematics.byu.edu † zhao.pan@uwaterloo.ca abstract this work investigates the propagation of error in a velocimetry-based pressure field reconstruction (vpressure) problem to determine and explain the effects of error profile of the data on the error propagation. the results discussed are an extension to those found in pan et al. (2016). we first show how to determine the upper bound of the error in the pressure field, and that this worst scenario for error in the data field is unique and depends on the characteristics of the domain. we then show that the error propagation for a v-pressure problem is analogous to elastic deformation in, for example, a euler-bernoulli beam or kirchhoff-love plate for oneand two-dimensional problems, respectively. finally, we discuss the difference in error propagation near dirichlet and neumann boundary conditions, and explain the behavior using green’s function and the solid mechanics analogy. the methods discussed in this paper will benefit the community in two ways: i) to give experimentalists intuitive and quantitative insights to design tests that minimize error propagation for a v-pressure problem, and ii) to create tests with significant error propagation for the benchmarking of v-pressure solvers or algorithms. this paper is intended as a summary of recent research conducted by the authors, whereas the full work has been recently published (faiella et al., 2021). 1 introduction using particle image velocimetry (piv) to reconstruct the pressure field in a fluid flow has many promising applications (for example, see zhang and porfiri (2019); zhang et al. (2020); deem et al. (2020); pereira et al. (2020)). while uncertainty quantification for velocity fields obtained from piv experiments has been studied in depth (wieneke, 2017; raffel et al., 2018; sciacchitano, 2019), less research has been conducted into assessing uncertainty in the calculated pressure field. de kat and van oudheusden (2012) provides the first analysis on the error associated with sampling frequency (spatial and temporal) in the context of v-pressure problems. it was commented that the central finite difference based pressure poisson solver acts as a low-pass filter, effectively eliminating the highfrequency errors (and signals) in the pressure calculation. the ratio of the grid spacing of the numerical method to the temporal or spatial wave length of the experimental data impacts the frequency response of the pressure poisson solver. specifically, high frequency data (or noise) is filtered resulting in the loss of high-frequency physics (or low-pass filtering effect). similarly, low frequency errors (and signals) are more likely to propagate through the pressure calculation. however, the results are constrained to a ‘local’ analysis of a specific numerical scheme. the effect of the ‘global’ setup of the flow domain, including size, shape of the domain and configuration of boundary conditions on the frequency response was not covered. pan et al. (2016) analytically discussed how the error in the data field propagates to the calculated pressure field. the upper bounds of the error in the calculated pressure field are derived for different setups. it showed that the error propagation dynamics of a v-pressure problem can be significantly affected by the ‘global’ setup of the domain, especially the configuration of the boundary conditions. under the general analytical framework, this work indicated that the error propagation is also influenced by the error profile in the data field. however, this paper did not identify a worst case error profile in the data field that leads to the maximum overall error in the calculated pressure field. moreover, how the error in the data field with different profiles affects the error propagation was not discussed. in the present work, we show a systematic method for finding the worst case error profile in the data field which causes the most error in the pressure field to be reached. the procedure for finding this worst case (or most dangerous) error in the data field demonstrates how the profile of the error in the data (e.g., spatial frequency and location of error peaks in the domain) combined with the fundamental configuration of the domain (i.e. size, dimension, shape, and boundary condition configuration of the domain) affects the error propagation. 2 worst case error and the effect of fundamental domain configuration the error propagation from the data field (ε f ) to the calculated pressure field (εp) for a v-pressure problem can be modelled via a poisson’s equation with respect to error (pan et al., 2016): ε f = ∇ 2 εp. (1) the power of the error, averaged over the space of the domain, can be measured by the l2 norm; for example, the error level of the calculated pressure field is ||εp||l2(ω) = √∫ ε2 pdω |ω| , (2) where ω is the domain of the flow field, and |ω| is the length, area or volume of the domain, for a 1d, 2d, or 3d problem, respectively. to quantitatively assess error propagation from the data field to the pressure field, the ratio between the error levels pressure field (can be considered as an output) and data field (considered as an input) can be used. thus, to find the worst case error for a given domain, we seek the function ε f to satisfy: ar∗ = max ε f ar = max ε f ||εp||l2(ω) ||ε f ||l2(ω) , (3) subject to (1) with the appropriate bcs on the domain. ar is the ratio of the error level in the calculated pressure field to the error level in the data (i.e. ar = ||εp||l2(ω) ||ε f ||l2(ω) ). we will refer to ar as the error amplification ratio, and refer to the ε f function which satisfies (3) as the worst error, denoted ε∗f . the worst error ε∗f can be thought of as the most dangerous error in the data field that corrupts the pressure field reconstruction most. we will only be considering cases where ε f is non-zero in order to avoid division by zero, and to reflect the reality that all experimental data will have some error. as an example, we will consider the optimization problem shown in (3) with pure dirichlet boundary conditions (note that neumann or mixed boundaries can be treated similarly). applying the calculus of variations (gelfand and fomin, 1991), we can find that the calculated pressure field will satisfy the eulerlagrange equations: ∇ 4 εp =− 1 λ εp, (4) with εp = 0 and ∇2εp = 0 on ∂ω, subject to |ω|‖∇2εp‖2 l2(ω) = 1, when accurate dirichlet boundary conditions are applied. equation (4) also appears as the characteristic equation of vibrations of elastic bodies (timoshenko et al., 1937), which will be discussed further in §3. as long as the operator remains self-adjoint, as is the case for the example shown, then there will be a countable number of solutions to the system, each solution corresponding to a natural frequency βn = 4 √ −λ−1 n , where λn > 0,n = 1,2,3... are the eigenvalues. to obtain ε∗f , the smallest of these eigenvalues −λ −1 1 is used. the corresponding eigenfunction will be the worst error function which yields the highest possible error amplification ratio. fundamental configurations of the flow domain, such as the size and shape of the domain, the dimension of the domain, and the type and configuration of boundary conditions will affect the eigenvalue (see also pan et al. (2016)), and consequently the error propagation. table 1: type of boundary conditions (bcs) of the original pressure poisson equation, the corresponding bcs of the eigenvalue problem of the worst error and the induced natural boundaries. g, g, h, and h are functions on the boundary ∂ω, and n̂ is the unit outward pointing normal on ∂ω. type of bcs bcs of pressure poisson equation essential bcs of eigenvalue problem natural bcs of eigenvalue problem dirichlet p = g εp = g ∇2εp = 0 neumann ∇p · n̂ = h ∇εp · n̂ = h ∇ ( ∇2εp ) · n̂ = 0 the fourth order eigenvalue problem resulting from the fourth order variational problem can be complex and require long calculations even for simple 1d cases. while this calculation may be unfamiliar to fluid mechanics researchers, it has been studied extensively in solid mechanics (e.g., timoshenko et al. (1937)), taking the form of the euler-bernoulli beam problem in 1d, and kirchoff-love plate problem in 2d. tables of solutions for standard boundary conditions and simple domains can be found in several solid mechanics textbooks (e.g. harris and piersol (2002)), and would be easy to look up for researchers using table 1. in a 1d system with two dirichlet bcs, for example, the solution to the eigenvalue problem (4) is as follows (see faiella et al. (2021) for a more detailed derivation): ε f n =± √ 2sin (nπ l x ) , n = 1,2,3, . . . (5) which will yield corresponding error in the calculated pressure field: εpn =± √ 2 l2 n2π2 sin (nπ l x ) , n = 1,2,3, . . . (6) substituting (5) and (6) into (3), the error amplification ratio is ar = β −2 n = l2 π2n2 , n = 1,2,3, . . . (7) noting the presence of the n2 term in the denominator of (7), the worst error occurs for the first eigenvalue (n = 1 and ar∗ = l2/π2). thus, the error amplification ratio is larger for lower values of n, which corresponds to lower fundamental frequencies in the data error, while ar→ 0 as n→ ∞. the poisson equation acts as a low-pass filter for the data error, allowing lower frequency error to propagate while eliminating the high frequency errors. also, the l2 term in the numerator of (7) shows that the error amplification ratio is increased as the length scale of the domain increases. in general, such a trend also holds for other boundary condition configurations. for example, for a 1d system equipped with one dirichlet bc and one neumann bc at each end, the error amplification ratio is ar = 4l2 π2(2n−1)2 ,n = 1,2,3, . . . (8) and also possesses low-pass filter characteristics. this low-pass filtering behaviour is a fundamental property of the poisson equation, and thus will be presented regardless of numerical solving scheme chosen. we wish to emphasize that the frequency response shown in this paper is different than the results obtained when ‘local’ analysis is used. for example, in de kat and van oudheusden (2012), the amplitude response of a signal or error passing through a poisson solver is given by: tps(h,λx) = |p| | f | = |εp| |ε f | = 1+ cos ( π 2h λx ) 2 sinc ( 2h λx ) , (9) where tps is the transfer function of the poisson solver, h is the grid spacing, and λx is the spatial wavelength of the input signal (or error) to the numerical poisson solver. in (9), as h/λx→ 0, tps(h,λx)→ 1. this implies that if the mesh is sufficiently fine, the error propagating through a poisson solver is expected to be unfiltered. this expectation holds only when analysing a local region in a domain and is up to the local choice of numerical scheme and grid spacing. the analysis in the current work (e.g., (7) and (8) for 1d) is a ‘global’ result that holds for all numerical pressure poisson solvers, and complements the aforementioned ‘local’ analysis. invoking λx ∼ 1/n, ar(λx) = cλ2 x , where c is a constant which is dependant on the fundamental features of the domain. 3 analogy to bulking elastic bodies interestingly, a parallel can be drawn between the deformation of elastic bodies and the propagation of error in v-pressure experiments. we next use euler-bernoulli beam theory, as a 1d example, to demonstrate the intuitive analogy and evaluate the magnitude of the error propagation in v-pressure. consider a homogeneous beam of length l which undergoes transverse vibrations. the normalized deflection profile of the beam is governed by the differential equation: d4y dx4 = d2y dt2 , (10) where y (x, t) is the beam deflection in the direction that is perpendicular to the x coordinate, and t is time. by separation of variables (y (x, t) = x(x)t (t)), where t (t) is a function of t and x(x) is a function of the spatial x coordinate and hence describes the modes of the vibrating beam, the corresponding eigenvalue problem of (10) is: d4x dx4 = γx , (11) where γ is the eigenvalue, and k = 4 √ γ (timoshenko et al., 1937) is the spatial frequencies of the buckled beam. different eigenvalues (γn = ω−2 n , n = 1,2,3, ...) correspond to different natural frequencies (ωn) of the vibrating beam and the eigenfunctions (xn) describe the modes of the beam deflections. larger eigenvalues correspond to beam modes with higher spatial frequencies. we also recall the normalized governing equations of a bending beam: dx dx = θ, (12) d2x dx2 =−m, (13) d3x dx3 =−q, (14) d4x dx4 =−w, (15) where θ is the slope, m is the bending moment, q is the shear force in the beam, and w is the transverse load on the beam, respectively. one may notice that (11), which is from euler-bernoulli beam theory, is the 1d equivalent of (4), which arises in the error propagation problem of pressure-velocimetry calculations. in addition, (13) describes the relationship between the second order derivative of the beam deflection and bending moment; and it takes the form of the poisson’s equation about error propagation, i.e., (1) in one dimension. we now observe the analogy between the euler-bernoulli problem and the dynamics of v-pressure error propagation, from (13) and (1): the buckling of a beam (x) as a result of an applied bending moment (m) is equivalent to the profile of the error in the pressure field (εp) as a result of the error in the data (ε f ) for the v-pressure error propagation problem. solving (11) requires four boundary conditions. for example, if both ends of the beam are simply supported (also called hinged in some textbooks, see figure 1(a) for illustration), the displacement at the ends are constrained by the kinematic boundary conditions (also called essential boundary conditions): x(0) = x(l) = 0, (16) and natural boundary conditions indicating that no bending moments are exerted at the ends (see harris and piersol (2002) and (13)): x ′′(0) = x ′′(l) = 0. (17) (a) (b)(b) (a) (b)(b) figure 1: bent euler-bernoulli beam with different supporting mechanisms: (a) simply supported at both ends (associated with dirichlet-dirichlet bcs for v-pressure problem) and (b) simply supported at the left end and supported by a slide at the right end (associated with dirichlet-neumann bcs). we can see that the boundary conditions (16) mimic the essential boundary conditions of the eigenvalue problem (4) that arise from homogeneous boundary conditions, εp(0) = εp(l) = 0. similarly, the boundary conditions (17) mimic the corresponding natural boundary conditions that arise from the calculus of variations ε′′p(0) = ε′′p(l) = 0. the analogy between beam deflection and v-pressure error propagation is shown more clearly in table 2. this table shows the physical interpretation of different variables/equations in the beam problem, as well as their equivalent variables/equations in v-pressure error propagation. the table also draws the parallel between a homogeneous neumann boundary in the pressure poisson equation and a slide-support in elastic dynamics (illustrated in figure 1(b)). the analogy of the buckling of elastic bodies will be further reinforced in the following section (§4) in the context of v-pressure error propagation. 4 impact of the location of the error the dynamics of error propagation to the pressure field from the data field is a function that depends on both the domain’s fundamental features and the location of the error. to demonstrate this, we can use a sharp peak error function that is constrained to have a finite error power. for example, the following rectangular peak can be used for 1d analysis: ε f = δπ(x− x0) = { ξ, |x− x0| ≤ π 2 0, |x− x0|> π 2 , (18) where δπ(x−x0) is a rectangular pulse function with a small pulse width π centered at x = x0. the resulting εp and the corresponding error amplification ratio (ar) for each x0 ∈ (0,l) then can be evaluated by solving (1). ar = ar(x0) is thus a quantification of how sensitive the pressure solver is to the error at a given location x0. 0 0.2 0.4 0.6 0.8 1 -0.08 -0.06 -0.04 -0.02 0 (a) (b) 0 0.5 1 1.5 2 0 0.05 0.1 0.15 0.2 0.25 (a) (b) figure 2: error amplification ratio (ar) and error profile in the pressure field εp when concentrated error (ε f = δ0.01l(x−x0) is introduced at different locations (x0)). (a) ar corresponding to the location of concentrated error (x0) for domains with different sizes and configurations of boundary condition. (b) profiles of εp over a domain with size l = 1, when concentrated error ε f = δπ(x−x0) is introduced at x0 = 2/3,1/2,1/3. the solid curves indicate the results on the domain with dirichlet-dirichlet bcs, and the dashed curves indicate the results on the domain with dirichlet-neumann bcs, respectively. figure 2(a) demonstrates a case study of the error amplification ratio ar(x0) caused by error concentrated at different places in a 1d domain with different sizes (l= 1 or 2) and configurations of boundary conditions. table 2: analogy between the beam vibration problem and the error propagation problem raised by the velocimetry-based pressure reconstruction. the concentrated error source is constructed using (18) with width π = 0.01l and height ξ = 10. the solid curves, which represent domains with pure dirichlet boundaries, have the highest value of ar at the center of the domain, which is the location which is farthest from any dirichlet boundary, while ar vanishes as the dirichlet boundaries are approached. the dashed curves, which represent domains with dirichlet-neumann conditions, have the highest value of ar at the neumann boundaries, and also have ar(x0) approach 0 at the dirichlet boundaries. this implies that the data near a dirichlet boundary is less sensitive to error, while data far from dirichlet boundaries or close to a neumann boundary is sensitive to error in the data. figure 2(b) shows the reconstructed pressure field, εp, for a concentrated error located at x0 = 1/3,1/2, and 2/3 for pure dirichlet (solid lines) and mixed (dashed lines) boundary conditions. the error for the pure dirichlet case reaches its highest peak for x0 = 1/2, when the concentrated error is furthest from the dirichlet boundaries. for the mixed boundary conditions, the error reaches its highest value for x0 = 2/3, which is when the concentrated error is closest to the neumann boundary. the error for the pure dirichlet case is much lower than the equivalent error for mixed boundary conditions. figure 2(b) can be thought of in terms of the buckling beam example, where x0 is the location of an applied moment on the beam, and εp is the beam deflection profile. the pure dirichlet condition would be equivalent to the beam shown in figure 1(a), while the mixed condition would be equivalent to figure 1(b). the beam shown in figure 1(a) would deflect the most when the moment was applied to its center, just as the error is maximized for the pure dirichlet condition with error at x0 = 1/2. the beam in figure 1(b) would deflect the most for an error next to the free support, just as the mixed boundary condition has the greatest error for x0 = 2/3. finally, the beam in figure 1(b) would deflect much more than the beam in figure 1(a) for an equivalent moment, since its free end allows more movement and provides less support than the two “fixed” supports. this effect of dirichlet and neumann boundaries on error propagation is also present in 2 dimensions. the error sensitivity can again be examined using a pulse function of the form: ε f = δπ(xxx− xxx000) = { 2√ ππ , |xxx− xxx000| ≤ π 2 0, |xxx− xxx000|> π 2 , (19) where xxx000 = (x0,y0) is the coordinate of the center of the concentrated error. (a) (b) log10(ar) (a) (b) (c)log10(ar) log10(ar) figure 3: error amplification ratio ar(x0,y0) responding to concentrated error located at xxx000 = (x0,y0) for domains with (a) pure dirichlet boundaries and (b) & (c) mixed boundaries, respectively. dirichlet boundaries are marked by green solid lines in (a) & (b), and the green dot in (c). neumann boundaries are marked by orange dashed lines. figure 3 shows the error sensitivity map on a 1×1 domain for three distinct bc configurations, where ar(x0,y0) is a function of the location of the concentrated error source as illustrated. the concentrated error source is constructed using (19) with a width of π = 0.02/ √ |ω|. we again show that error near a dirichlet boundary is less sensitive in terms of error propagation, while the error near a neumann boundary and/or far away from a dirichlet boundary is more dangerous. in figure 3(a), ar is lowest around the edges of the domain where dirichlet boundaries are present, while ar is largest in the center of the domain, far from the dirichlet boundaries. in figure 3(b), ar is again low near the dirichlet boundaries, but increases along the neumann edges. ar is highest at the center of the neumann boundary where proximity to a neumann boundary is maximized while proximity to a dirichlet boundary is minimized. finally, in figure 3(c), ar is high everywhere in the domain except for the region near xxx000 = (0,0), where ar is tamed by the presence of a dirichlet boundary. we now finalize the analogy between the deformation of elastic plates and the v-pressure error propagation. the behavior of error near boundary conditions can be thought of intuitively using the analogy to a bending beam in 1d or plate in 2d. an accurate dirichlet boundary on the v-pressure domain is analogous to a simply supported edge on a plate which constrains the deflection to be vanishing at the boundary. we recall that loads applied next to a simply supported edge cannot deflect the plate much due to the relatively ‘firm’ support nearby. however, as we move away from this firm support, the plate becomes easier to bend. in contrast, an accurate neumann boundary on the v-pressure domain is analogous to a sliding support which allows any amount of deflection but constrains the local slope to be zero. a moment applied near this boundary will deform a large segment of the plate; due to the constraint on the slope of the plate at this boundary, the sliding mechanism will ‘pull’ on other sections of the plate and bring them along with the loaded section. long neumann boundaries are more ‘dangerous’ than short ones, as this effect is carried out over a longer distance. these observations about the effect of the distance from an error source to boundaries with different bcs can also be explained using green’s function for the poisson equation. consider, in 2d, a concentrated error source in the data field taking the form of the dirac delta function, ε f = −δ(xxx000), located at xxx000 = (x0,y0). the error in the pressure field caused by this concentrated error source is the fundamental solution of the poisson equation given by the green’s function. when the distance from the error to a nearby boundary is much shorter than the distance to any other other boundaries, the local error near the source (and the nearby boundary) can be approximated by the green’s function on a half plane by the method of images. for example, the green’s function on a half plane with a homogeneous dirichlet boundary at x = 0 is εp = g(xxx,xxx000) = 1 2π ln [ 〈(x,y),(x0,y0)〉 〈(x,y),(−x0,y0)〉 ] , (20) where 〈(x,y),(x0,y0)〉= √ (x− x0)2 +(y− y0)2 is the distance from xxx to xxx000 (tikhonov and samarskii, 2013). as the location of the error approaches the boundary (x0→ 0), g(xxx,xxx000)→ 0 and thus, εp vanishes quickly towards the dirichlet boundary. for an error source close to a neumann boundary, the corresponding green’s function on the halfplane is εp = g(xxx,xxx000) = 1 2π ln [〈(x,y),(x0,y0)〉〈(x,y),(−x0,y0)〉] . (21) as the location of the concentrated error source approaches the neumann boundary (x0→ 0), g(xxx,xxx000)→∞ and εp blows up at the neumann boundary. this irregular behavior is unique to the green’s function analysis and is not physical, as ε f cannot be a strictly dirac delta function in reality. despite this singularity, the mathematical intuition that arises from this analysis shows how the location of the error in the data coupled with the bcs configuration affects the error propagation. (a) (b) log10(ar) figure 4: error amplification ratio ar(xxx000) corresponding to concentrated error located at xxx000 = (x0,y0) for domains featuring an airfoil of chord length lc. neumann bcs are applied on the surface of the airfoil. the domains feature (a) dirichlet bcs on the outer boundaries and (b) mixed bcs on the outer boundaries. dirichlet boundaries are marked by green solid lines and neumann boundaries are marked by orange dashed lines, respectively. we further demonstrate the dependence of ar(xxx000) to the placement of error (xxx000) using a more complex domain. figure 4 shows error sensitivity maps for a 3×2 domain with an airfoil, nondimensionalized by the airfoil chord length, for different bc configurations. ar(x0,y0) is the error amplification ratio as a function of the location of concentrated error as illustrated. figure 4(a) shows that concentrated error near a dirichlet bc is tamed by the boundary, as seen by the low value of amplification ratio ar around the edges of the domain. concentrated errors far from dirichlet boundaries and/or close to a neumann boundary show more propagation, and thus a higher value of ar occurs near the center of its domain. in figure 4(b), we see that error amplification is highest in the middle of ‘long’ neumann boundaries such as the left and right edges of the domain as well as the suction and pressure surface of the airfoil. the leading edge of the airfoil can be considered a ‘short’ neumann boundary due to its high curvature, and thus shows less propagation than these long neumann boundaries. figure 5 shows the reconstructed pressure field for a concentrated error located at different coordinates. in figure 5(a)-(c), the outer boundaries are dirichlet, while the airfoil boundaries are neumann. figure 5(a) shows the effect of concentrated error near a dirichlet boundary; error rapidly dissipates as the dirichlet boundary is approached, and does not significantly propagate and contaminate the whole pressure field. in contrast, figure 5(b) shows a concentrated error near a long neumann boundary, where the error is amplified due to its proximity to a neumann boundary and the center of the domain and contaminates a large area of the domain. figure 5(c) also shows a concentrated error near a neumann boundary, however the pressure figure 5: error in the reconstructed pressure field (εp) caused by concentrated error in the data field located at different locations (ε f = δ(x0,y0)). the type of bcs of the domain are indicated by green solid lines for dirichlet boundaries, and dashed orange lines for neumann boundaries. the locations of the error (x0,y0) are marked by the green arrow heads. the legend in each subplot indicates the error amplification ratio (ar = ||εp||l2(ω)/||ε f ||l2(ω)) corresponding to the the ε f at each location. field is less contaminated than figure 5(b). this is due to the high curvature of the boundary at this point, which is considered a ”short” neumann boundary and thus the error spreads less. in figure 5(d)-(f), the outer boundaries are mixed boundary conditions, while the airfoil remains as a neumann boundary. the error shown in figure 5(d) is now beside a neumann boundary instead of the dirichlet boundary in figure 5(a). as a result, the error propagates much more and the ar is greater. in figures 5(e) and (f), we see that the concentrated error propagates more than the error in figure 5(b) and (c). this is because the taming dirichlet boundaries are lost and replaced with amplifying neumann boundaries, so error propagates much more freely. 5 conclusion in the current work, we present a systematic method for finding the worst case error profile in the data field which causes the most error in the pressure field. this is corresponding to the upper bound of the error in the calculated pressure field discussed in pan et al. (2016). the worst case error profile in the data field can be found by solving an eigenvalue problem derived from an euler-lagrange equation maximizing the the error propagation. the procedure for finding the worst error in the data field shows how the profile of the error in the data (e.g., spatial frequency and location of error peaks in the domain) coupling with the fundamental features of the domain (i.e. size, dimension, type of bcs) affects the error propagation. we show that the euler-lagrange equations used to find the worst error function lead to the same eigenvalue problem from the buckling of an euler-bernoulli beam in 1d and a kirchoff-love plate in 2d. the data field error can be thought of as a bending moment applied to an elastic body, with the resulting pressure field being equivalent to the deformation of the elastic body. thus, being familiar with the theories of elastic beams and plates (timoshenko et al., 1937) can be useful in understanding error propagation in v-pressure problems in a more intuitive way. we point out that error propagation is significantly affected by the location of the error and the error proximity to dirichlet and/or neumann boundaries. this behavior can be explained by finding green’s function for the poisson equation using the method of images. this result can also be explained intuitively using the solid mechanics analogy. all results in this work represent fundamental properties of the poisson equation, which hold regardless of experimental setup and choice of numerical solver. the results and analogy-based method can help experimentalists studying fluid mechanics to design better tests which avoid error profiles similar to the worst case, and limit the error in sensitive locations, thus improving overall accuracy and robustness of the test. in addition, the results can be used to create worst case scenarios and challenging test cases to benchmark v-pressure solvers or algorithms. finally, we emphasize that the present work studies how error in the data field propagates to the reconstructed pressure field. how to interpret error in the data field (ε f ) from the error in the velocity field (εuuu) can be challenging. the error propagation analysis from velocity to data (εuuu → ε f ) involves the temporal and spatial resolution of velocimetry and specific numerical schemes that evaluate gradients, and thus is out of the scope of the current analytical research. we will leave this topic for future studies, however, some relevant results can be found in, for example, mcclure and yarusevych (2019) and pan et al. (2018). references de kat r and van oudheusden b (2012) instantaneous planar pressure determination from piv in turbulent flow. experiments in fluids 52:1089–1106 deem ea, cattafesta iii ln, hemati ms, zhang h, rowley c, and mittal r (2020) adaptive separation control of a laminar boundary layer using online dynamic mode decomposition. journal of fluid mechanics 903:a21 faiella m, macmillan cgj, whitehead jp, and pan z (2021) error propagation dynamics of velocimetrybased pressure field calculations (2): on the error profile. measurement science and technology 32:084005 gelfand im and fomin sv (1991) calculus of variations. dover harris cm and piersol ag (2002) harris’ shock and vibration handbook. volume 5. mcgraw-hill new york mcclure j and yarusevych s (2019) generalized framework for piv-based pressure gradient error field determination and correction. measurement science and technology 30:084005 pan z, whitehead j, thomson s, and truscott t (2016) error propagation dynamics of piv-based pressure field calculations: how well does the pressure poisson solver perform inherently?. measurement science and technology 27:084012 pan z, whitehead jp, richards g, truscott tt, and smith bl (2018) error propagation dynamics of pivbased pressure field calculation (3): what is the minimum resolvable pressure in a reconstructed field?. arxiv preprint arxiv:180703958 pereira ltl, ragni d, avallone f, and scarano f (2020) pressure fluctuations from large-scale piv over a serrated trailing edge. experiments in fluids 61:1–17 raffel m, willert ce, scarano f, kähler cj, wereley st, and kompenhans j (2018) particle image velocimetry: a practical guide. springer sciacchitano a (2019) uncertainty quantification in particle image velocimetry. measurement science and technology 30:092001 tikhonov an and samarskii aa (2013) equations of mathematical physics. courier corporation timoshenko s et al. (1937) vibration problems in engineering. technical report wieneke b (2017) piv uncertainty quantification and beyond. ph.d. thesis. delft university of technology zhang j, brindise mc, rothenberger s, schnell s, markl m, saloner d, rayz vl, and vlachos pp (2020) 4d flow mri pressure estimation using velocity measurement-error-based weighted least-squares. ieee transactions on medical imaging 39:1668–1680 zhang p and porfiri m (2019) a combined digital image correlation/particle image velocimetry study of water-backed impact. composite structures 224:111010 introduction worst case error and the effect of fundamental domain configuration analogy to bulking elastic bodies impact of the location of the error conclusion 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 lagrangian particle tracking: a link between localisation error and fraction of missed particles p. cornic1∗, f. champagnat1, b. leclaire2 1 onera – the french aerospace lab, f-91761 palaiseau, france 2 onera the french aerospace lab, f-92190 meudon, france ∗ philippe.cornic@onera.fr abstract this paper aims at analysing the behaviour of particle localisation error in 3d lagrangian particle tracking (lpt) techniques, with a particular emphasis on general properties, independent of a specific algorithm. based on the hypothesis that in lpt algorithms, errors on the image formation models are solely due to random noise, we show/prove the existence of a best achievable root mean square error (rmse) on particle localisation, that, for a setup at a given seeding density, depends only on the noise level. we provide a procedure to estimate this lower bound, and show that it can only be reached if there are no missed detections; further on, we establish a link between localisation error and fraction of missed particles. we illustrate the consistency of this model on the results of the recent first challenge on lpt (see ispiv21 papers by leclaire et al. and sciacchitano et al.) 1 introduction lagrangian particle tracking (lpt) is gradually becoming the new standard for high seeding density 3d velocity measurements, both for time-resolved series (see e.g. schanz et al. (2016)) and double-frame data (then also referred to as 3d ptv, see e.g. fuchs et al. (2016), yang et al. (2019), lasinger et al. (2019), cornic et al. (2020)). whereas 3d piv, relying on cross-correlation, induces important spatial averaging, and thus smoothing of corresponding turbulent scales, residual error on lpt vectors is much smaller, of the order of a fraction of the particle image size. to cope with high seeding densities, where algorithmic performance is usually observed to drop, 3d ptv algorithms are often faced with a dilemma in the choice of the operating point, between retrieving as many vectors as possible – at the risk of getting ghost vectors a.k.a. false positive (fp), and emphasising reliability i.e. obtaining as few fp as possible – at the cost of a large number of missed true vectors a.k.a. false negative (fn). recent literature shows that no clear consensus yet exists, the two possible choices being made depending on the algorithms. our purpose is twofold. the first one is to show that there is a best achievable root mean square error (rmse) on particle localisation, depending, for a given flow and camera setup, essentially on the image noise and the seeding density. we provide a way to estimate it. the second one is to show that the choice consisting in reducing as much as possible the number of ghosts, leading potentially to less true vectors retrieved, might have some unexpected consequences on the particles localisation error, and consequently on the rmse on the velocity vectors. more precisely, we find that a low velocity rmse is achievable only provided that very few vectors are missed; a coupling which, to the best of our knowledge, has not yet been documented in the literature. while we demonstrate this result in the framework of the recently introduced df-tptv algorithm (cornic et al., 2020), performance metrics obtained match with results of the most advanced methods at the 1st challenge on lpt (sciacchitano et al., 2020), (leclaire et al., 2021) thus confirming its global scope. the paper is organised as follows. section 2 briefly describes the synthetic data generation, intended to reflect as much as possible the one of the 1st challenge on lpt (leclaire et al., 2020). section 3 briefly states the common principles of tomographic lpt algorithms and introduces the best achievable root mean square error on particle localisation (bar). it highlights the requirement of a suitable preconditioning technique to perform gradient-based optimisation to refine all particle position and intensity. section 4 presents the rmse on particle localisation model depending for a given setup and seeding density on only (a) (b) figure 1: (a): cameras setup. (b): crop 256×256 of a synthetic image (ppp=0.12). two parameters and deals with the consistency of the model predictions with the results of the 1st challenge on lpt. 2 synthetic data generation the ground truth of 1st lpt challenge data is strictly dedicated to the evaluation of the lpt challenge and forthcoming submissions to the benchmark site (leclaire et al., 2021). it is not available for other purposes, including this work. the starting point of this work being to get a better understanding of the lpt challenge results, we built a dedicated synthetic two-pulse dataset that mimics as much as possible the images available to the participants. we have used the particles trajectories of the publicly available dataset of the 1st challenge on data assimilation https://w3.onera.fr/first lpt and da challenge/. the physical situation of this case is a wall-bounded turbulent cylinder wake flow (resolved by les), with a momentum thickness reynolds number of the boundary layer of around 4,500. we used the same optical setup four virtual cameras are set along an arc of circle as shown figure 1(a) and image settings as for the lpt case of the challenge, as disclosed during the presentation of the challenge results during the 3rd cfd for piv workshop (leclaire et al., 2020). in particular in terms of particles’ polydispersity with uniform intensity distribution in [500,1700], diffraction limited particle image, photon noise (20 counts mean and 8 counts standard deviation), and shot noise. we named this dataset hmdb standing for home made data base. 3 determination of best achievable root mean square error on particle localisation most state-of-the-art lpt algorithm based on tomographic principles share the same organisation principle as sketched figure 2. an image-based detection task is performed that yields a rough localisation that is refined through an optimisation process. recorded images are subtracted with predicted images to form the residue images the process loops on. this loop may include in addition a prediction from previous time steps. 3.1 particle accurate localisation many different tomo lpt algorithms, schanz et al. (2016), yang et al. (2019) and cornic et al. (2020) resort to minimising the discrepancy between recorded images and predicted images given by a particle imaging model depicted in figure 3(a). this is also the case for ipr wieneke (2013). this boils down to minimising a criterion which is a function of 3d coordinates xp and intensities ep of each particle p. we note: x,e = {xp,ep; p = 1 · · ·p} the set of all the particle 3d coordinates and intensities, p is the number https://w3.onera.fr/first_lpt_and_da_challenge/ figure 2: schematic of tomo lpt algorithms. a rough detection followed by an optimisation step looping on residue images. (a) (b) figure 3: (a): imaging model. (b): true location and estimated location due to the noise. of particles. the criterion writes: c (x,e) = ∑ c ∑ x ∥∥∥∥∥ic(x)−∑ p ephc(x−fc(xp)) ∥∥∥∥∥ 2 , (1) where fc is the projection function for camera c, hc denotes the point spread function and x is a pixel coordinate. we assume that fc and hc have been calibrated with enough accuracy so that they can be considered as perfectly known. 3.2 best achievable root mean square error on particles localisation on synthetic experiments, the recorded images ic are computed from x? p and e? p, the true location and intensity of particle p corrupted with additive noise n: ic(x) = ∑ p e? phc(x−fc(x? p))+n(x) (2) let x̂, ê denote the minimizer of c . due to the noise, the value of the criterion at true locations and intensities, c (x?,e?) is not zero and furthermore (x?,e?) is not a minimizer of c . due to noise, x̂ drifts away from x? leading to discrepancies between x̂ and x?. for low noise level, the perturbation ∆x(n) is a linear function of the noise realisation n (fessler, 1996). a similar result holds for ê . the best achievable root mean square error on particle localisation (bar) is the expected value of the norm ‖∆x(n)‖ for the distribution n of n. it writes: bar = en [ ‖∆x(n)‖√ p ] . (3) here it is important to note that the bar is defined as a “true” rmse. it writes : √ 1 p ∑ p p=1 ∥∥∥x̂p−x? p ∥∥∥2 and differs from a mean positional error: 1 p ∑ p p=1 √∥∥∥x̂p−x? p ∥∥∥2 , whose value is lower. estimating the bar would require to generate many images with different noise realisations ni according to the law of n and then average the obtained ||∆x(ni)||. as typical residual image noise (i.e. once possible light reflections have been removed by background subtraction) is uncorrelated in space, and as our synthetic experiments involve thousands of particles already at low seeding density, estimating the bar can be achieved on the basis of a single snapshot, which will lead enough particle position realisations to enable convergence of the expected value: en [ ‖∆x(n)‖√ p ] ≈ ‖∆x(n = nic)‖√ p , (4) where n = nic stands for the noise realisation of the recorded image. 3.3 optimisation computing ∆x boils down to finding the minimizer of c close to (x?,e?). a straightforward way to do so is to use an optimisation algorithm suitable for non linear high dimension problems – here four times the number of particles because we also must account for the particles intensity – starting from the first guess (x?,e?). with tens of thousand of particles, computing the hessian matrix of c or its inverse is impractical and newton’s methods are definitely out of reach. even quasi-newton method like bfgs algorithm with a computational complexity of o(16p2) turns out to be impractical and one has to turn to l-bfgs with complexity o(4p) or improved gradient descent like eg. conjugate gradient (cg). but straightforward application of latter techniques fail in practice due ill conditioned criterion c . 3.4 preconditioning c suffers from a conditioning problem that originates in the fact that positional gradients are several order of magnitude greater than intensity gradients. when using l-bfgs or cg, it results in intensity values that virtually do not change through the iterations and impede the accuracy of localisation. this can be illustrated on a toy example with only one particle and no noise. the first guess has a localisation error on the 3 axes of [0.74, -0.45,1] voxel (vx), whose size is equal to the backprojection of a pixel ie. a voxel to pixel ratio v/p equal to 1, and an intensity error of 10%. initial residue images (ic− iguess) are shown figure 4(a). negative values, appearing dark blue, show how much shifted the guessed particle is. it may be seen figure 4(b) that bfgs which determines the descent direction by preconditioning the gradient with curvature information is not prone to the conditioning problem and correctly estimates the intensity. this is not the case for l-bfgs: the intensity stay still through the iterations and leads to a localisation error 2.5 times higher as shown figure 4(b). a good conditioning is when the criterion has more or less the same curvature in all the directions, ie. when its hessian is close to the identity matrix (up to a scale factor). let’s note θ the vector of particles positions and intensities. preconditioning amounts to applying a change of variable θ′ = mθ such that the condition number of c̃ (θ′) = c (m−1θ′) is better than that of c (θ). it can easily be shown that: ∇2c̃ (θ′) = m−t∇2c (m−1θ′)m−1. using the cholesky decomposition: ∇2c (m−1θ′) = llt and setting m = lt yields: ∇2c̃ (θ′) = i (nocedal and wright, 2006). green curve in figure 4(a) shows that using this preconditioning for θ equal to the first guess, the optimisation through l-bfgs reaches the same performances as bfgs with a good estimation of intensity. but this approach is impractical with tens of thousands of particles since we cannot neither compute/store ∇2c (θ) nor its cholesky decomposition. we have implemented a solution that considers an approximate block diagonal hessian, this amounts to apply the same change of variable m, as in the single particle case, to the p particles. in practice, we compute a “mean particle hessian” m by averaging the hessian over a hundred of randomly chosen particles in the first guess. 3.5 bar for the home made data base figure 5(a) presents the bar (black solid line) as a function of the ppp (particle per pixel, tightly related to seeding density) for the dataset described section 2. we have verified that the bar value does not depend (a) (b) figure 4: toy example. (a): initial residue images. it may be seem how much shifted the guessed particle is. (b): localisation (up) and intensity (bottom) error as a functions of optimisation iterations. the voxel (vx) size is equal to the backprojection of a pixel. blue: bfgs, orange: l-bfgs without preconditioning, green: l-bfgs with preconditioning. on the noise realisation. it is also of practical interest to know if the bar can be reached initialising the optimisation process from an other first guess than x?,e? mimicking the rough localisation step sketched on figure 2. the solid curves present the final rmse resulting from an optimisation using the above described preconditioning technique from various first guess with initial rmse, named ε, respectively equal to 0.5, 0.75 and 1 voxel. in this experiment, the various initial rmse are obtained by initialising the particles on the closest node of a voxel grid as shown in the schematic figure 5(b). the greater the grid step, the greater ε. the initial intensities are set by solving in a least squares sense the tomographic system (cornic et al., 2015) with the particles being on the nodes of the grid. the dashed coloured curves show the final rmse without using preconditioning. it may be seen that the greater the ppp and ε, the farther the result is from the bar. conversely, using pre-conditioning with the same first guesses (see solid coloured curves), it may be seen that the final rmse virtually does not depend on the first guess. whatever a reasonable rough initialisation, the bar can virtually be reached for all ppp provided the preconditioning technique is used. 4 model for predicting an algorithm’s rmse on particle position based on its detection performances df-tptv (cornic et al., 2020) is a recently introduced two frame lpt algorithm relying on tomographic and sparsity principles. it may be seen in the left hand side figure 6(a) that its performances in terms of rmse get farther from the bar as the ppp grows. this algorithm was originally designed to yield as few ghosts as possible. indeed, the precision figure 6(b) which measures the fraction of true particles among detected ones is almost 1 up to ppp equal 0.08. it indicates that ghosts are not involved in the rmse soaring. the choice of having few ghosts has for this algorithm the consequence of missing particles as shown by the dropping recall (fraction of retrieved particles) as the ppp grows. this suggests that rmse and recall might be anti-correlated. a qualitative explanation could be as sketched figure 7(a) and 7(b). when the ppp is low, the particles do not significantly overlap. a missed particle (ie. not detected) do not perturb the optimisation of the detected one (red) whose image through the point spread function can be matched in a least square sense with the recorded one (green) as shown figure 7(a). this is no longer the case when the ppp gets higher and particles overlap. the missed particle interferes with the optimisation that results in a compromise solution as displayed on figure 7(b). accurate location is no longer possible through optimisation. when the particles overlap a missed particle results from the optimisation point of view in a much stronger “noise” than background noise. (a) (b) figure 5: (a): black: bar as a function of the ppp for the home made dataset (uniform intensity distribution in [500,1700], 20 counts mean and 8 counts standard deviation photon noise); coloured curves: rmse resulting from various first guess (see text) and optimisation technique. (b): the particles are displaced on the grid node for initialisation. 4.1 modelling the false negative effect on rmse false negative (fn) are the missed particles whose percentage is given by 1− recall. an interesting question to deal with is whether the rmse of df-tptv and more generally of any lpt algorithm relying on tomographic principles can be approximated by simply optimising c from a first guess with the same amount of adequately selected fn. figure 8(a) shows that optimising with the same amount of randomly selected fn from a first guess with ε = 1 results, except for low ppp, in overestimating the rmse. it is not surprising because, at least for algorithm relying on tomographic principles, there are particles that are more liable than others to be missed. one then might think that a random selection is not appropriate. indeed, with missed particles being chosen among the least bright, one can see that we get a quite good match between model prediction and df-tptv results as shown figure 8(b). this result is remarkable because it establishes a link between the root mean square error on particle localisation and the percentage of missed particles. 4.2 rmse on particle localisation model section 3.5 has shown that without missed particles, ε the rmse of the first guess, if reasonable, has almost no influence on the final rmse. but this no longer holds in presence of missed particles. for ppp ranging from 0.005 to 0.12, figure 9 shows the rmse as a function of fn percentage, missed particles being chosen among the least bright. to get this bunch of curves, we optimised criterion c from initial first guesses with a given rate of fn among the least bright and various initial rmse. the box plot spans ε = 0 to ε = 1 voxel. the coloured solid curves are for ε = 0.5. given a certain amount of fn, the foot of the box plot is the best one can do in terms of rmse. it may be seen that for the lowest ppp in blue, with no significant overlap, fn rate and ε have virtually no influence on the rmse. it is consistent with the quantitative explanation given section 4. the greater the ppp, the greater the influence of the fn rate and ε. the later being visible on the extent of the box plot. the bar can be retrieved from the foot of the box plot for a fn percentage equal zero. 4.3 consistency with 1st lpt challenge results this rmse on particle localisation error model is very simple. it involves, for a given ppp, only 2 parameters. originally built to study the performances of df-tptv, the question of its scope naturally arises. (a) (b) figure 6: (a): df-tptv rmse and bar as a function of the ppp. (b): df-tptv precision and recall as a function of the ppp. (a) (b) figure 7: green particles are the recorded one, the detected (red) particle’s location has to be optimised. (a): the particles do not overlap. (b): overlapping particles, the optimisation results in a compromise solution. to answer this question we asked the participants’ and organisers’ permission to compare the results of the 1st lpt challenge (sciacchitano et al., 2020) with the model predictions. it should be stressed that even if they share the same principles, the algorithms of each team are different and we do not know exactly how they work. it should also be highlighted, as already mentioned, that the lpt challenge’s ground truth is not available for the bar and rmse model. five teams competed in the two pulse lpt challenge, namely: dlr, lavision, irae, ethz and onera. the rmse prediction given their detection performances is reported for all the teams except ethz, for which the model is not directly applicable. dlr and lavision teams submitted results for all the proposed ppp (ie. up to 0.16) while irae and onera stopped at ppp=0.08. figures 10(a), 10(b), 10(c), 10(d) show for the four teams, their rmse, evaluated with the ground truth of the 1st lpt challenge, the bar and the model prediction as a box plot given their detection performances yielded using the hmdb. please note that the y-scale are not the same and depend on the team’s performance. the model predicts quite well the dlr’s performance that is very close to the bar, betraying detections without missed particles. the model’s predictions are not too far from lavision results, and suggest, if we trust the model, that given their detection performances, slightly better rmse performance is achievable. in the same manner, irae’s performance is also captured reasonably well by the model that suggests achieved rmse could also be slightly better. as far as onera is concerned, we used an iterative version of dftptv to compete in the challenge, named i-df-tptv v0. the model predicts far better rmse performance than the achieved one, given the detection performances, suggesting there was something wrong with the optimisation step of our algorithm, that did not make use of preconditioning. furthermore, the understanding of the key role of fn lead to significant changes in the algorithm structure, now v1. figure 11 compares (a) (b) figure 8: df-tptv performance in terms of rmse (blue) (a): rmse predicted by optimisation with the same amount of randomly selected fn. (b): rmse predicted by optimisation with the same amount of fn being chosen among the least bright. v0 and v1 performances. note that v0 is evaluated on the challenge data while v1 is evaluated on the home made data base. but in the latter, evaluation and model prediction does not use the same set of particles. it may be seen that v1 performance is now consistent with the model prediction, and much closer to the bar than it used to be for v0. 5 conclusions we have highlighted that for a given synthetic setup there is a best achievable root mean square error on particle localisation (bar) that depends on image noise and ppp. we have shown that the bar can virtually be reached starting from a reasonable rough first guess provided there are no missing particles (fn) and that a suitable optimisation algorithm using an appropriate preconditioning technique is used. we have brought up that missing particles, in view of the optimisation involved in the accurate localisation steps, results – at ppp larger than 0.025 – in a much stronger noise than background image noise. for a given ppp, we proposed a model that relies on only 2 parameters: the rate of missed particles among the least bright and the first guess rmse on particle localisation. one might have noticed that ghosts do not take part in the model. contrary to fn they are not easy to simulate since intensity balance is also required. but we have indications that the model holds even with a large amount of ghosts associated with fn. of course, this model is too simple to be perfect, but it matches quite well with 1st lpt challenge results, at least for 3 teams. although we have demonstrated this model in a two frame context we think that to a large extend it might apply to multi pulses process. finally, it is well known that synthetic images are a pale reflection of experiments images, but the model suggests that if an accurate localisation is of critical importance, one should set a ppp such that the used lpt algorithm misses as few particles as possible. acknowledgements the authors wish to thank the organisers and participant teams of the 1st lpt challenge for agreeing on the use of their results. we hope this work will be useful to improve the performances of their methods. references cornic p, champagnat f, cheminet a, leclaire b, and le besnerais g (2015) fast and efficient particle reconstruction on a 3d grid using sparsity. experiments in fluids 56:62 cornic p, leclaire b, champagnat f, le besnerais g, cheminet a, illoul c, and losfeld g (2020) doubleframe tomographic ptv at high seeding densities. experiments in fluids 61:1–24 figure 9: rmse on particle localisation as a function of the fn percentage (missed particles being among the least bright) and initial rmse ε of the first guess. a box plot spans ε = 0 to ε = 1 voxel. uniform intensity distribution in [500,1700], 20 counts mean and 8 counts standard deviation photon noise. fessler ja (1996) mean and variance of implicitly defined biased estimators (such as penalized maximum likelihood): applications to tomography. ieee transactions on image processing 5:493–506 fuchs t, hain r, and kähler cj (2016) double-frame 3d-ptv using a tomographic predictor. experiments in fluids 57:174 lasinger k, vogel c, pock t, and schindler k (2019) 3d fluid flow estimation with integrated particle reconstruction. international journal of computer vision pages 1–16 leclaire b, mary i, liauzun c, péron s, sciacchitano a, schröder a, cornic p, and champagnat f (2021) first lagrangian particle tracking and data assimilation challenge: datasets description and planned evolution to an open online benchmark. in 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5 leclaire b, mary i, liauzun c, péron s, sciacchitano a, and schröder a (2020) lpt and da challenge: datasets generation.. in in 3rd workshop on data assimilation and cfd processing for piv and lagrangian particle tracking. online meeting nocedal j and wright s (2006) numerical optimization. springer science & business media schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. exp fluids pages 57–70 sciacchitano a, leclaire b, and schröder a (2020) main results of the lpt challenge. in 3rd workshop on data assimilation and cfd processing for piv and lagrangian particle tracking. online meeting wieneke b (2013) iterative reconstruction of volumetric particle distribution. measurement science and technology 24:024008 yang y, heitz d, and mémin e (2019) lagrangian particle image velocimetry. in 13th international symposium on particle image velocimetry, ispiv 2019. munich, germany (a) (b) (c) (d) figure 10: bar, rmse on particle localisation and model prediction (bar plot) in voxel units. bar and model prediction are computed using hmdb. rmse are from the 1st challenge results (a): dlr (b): lavision. (c): inrae (d): onera. note the y-scale are not the same. figure 11: bar, i-df-tptv v0 and v1 rmse as a function of the ppp. model’s prediction for i-df-tptv v1. introduction synthetic data generation determination of best achievable root mean square error on particle localisation particle accurate localisation best achievable root mean square error on particles localisation optimisation preconditioning bar for the home made data base model for predicting an algorithm's rmse on particle position based on its detection performances modelling the false negative effect on rmse rmse on particle localisation model consistency with 1st lpt challenge results conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 robust approach to monitoring lagrangian transport in very large volumes f. kaiser∗, a. haramis, j. galler, d. e. rival department of mechanical and materials engineering, queen’s university, kingston, ontario, canada ∗ f.kaiser@queensu.ca abstract state-of-the-art flow measurements utilize four or more high-speed cameras to perform highly-accurate lagrangian particle tracking (lpt) in small to medium-sized measurement volumes (schanz et al., 2016). hou et al. (2021) suggested a novel approach to allow measurements in significantly larger measurement volumes (o(10m3)) while reducing the experimental effort. a single camera is used to track centimeter-sized soap bubbles in three dimensions by not only evaluating the bubble-center location but also the bubbleimage size. possible applications of the suggested approach include but are not limited to measurements in industrial wind tunnels (hou et al., 2021), full-scale measurements in the atmospheric boundary layer (rosi et al., 2014; toloui et al., 2014), and the characterization of airflow in indoor spaces, such as offices or classrooms (kähler et al., 2020). in the context of the recent pandemic, the latter application could help to reduce infection risk by designing appropriate air circulation. hereby, frequent air exchange is recommended, while direct airflow from individual to individual should be avoided (who, 2020). the present study strives to optimize and simplify the experimental set-up as well as to characterize the accuracy of the novel single-camera approach. figure 1(a) shows the set-up used to characterize the novel approach. figure 1: (a) sketch of the experimental set-up; (b) bubble images recorded at t1 and t4 with varying bubbleimage size (db); (c) linear optics producing the bubble images of size db dependent on bubble size (db) and position (o); and (d) bubble-image size (db) in pixels as a function of object distance o with a f = 35mm lens and a pixel size of 10µm. dashed lines visualize the planes shown in (a). the flow over an open-jet wind-tunnel nozzle (cross section 0.13m× 0.13m) was captured in a 1m × 1m × 1.2m measurement volume via two cameras: (i) a main camera that was mounted above the wind tunnel; and (ii) a secondary camera that was used for validation purposes. large soap bubbles (db ≈ 30mm) are illuminated by a light source placed perpendicular to both cameras. dependent on the distance of the bubble to the camera o(t) the bubble-image size db(t) varies in time; see figure 1(b). assuming o ≫ i (image distance i, see figure 1c) the lens equation leads to i ≈ f , which in turn simplifies the magnification equation to o ≈ db f db . (1) using equation 1, the object distance o and thus the three-dimensional position of a bubble can be determined with a single camera if db is known. figure 1(d) presents the interplay of db, o and db for two different bubble sizes. to simplify future experiments, a custom bubble generator has been developed to produce uniformly-sized bubbles (db ≈ 30mm). note that an error of db propagates linearly to the estimated object distance (see equation (1)) and that therefore a high degree of bubble-size uniformity is required. the bubble generator is designed such that it can be placed in a uniform flow and produce bubbles without an additional air supply. the uniformity of the generated bubbles was evaluated by placing the bubble generator on the open-jet wind tunnel and db could be measured via shadowgraphy. the resulting probability distribution is presented in figure 2(a). for the present bubble-generator design 97% of all measured bubbles were within ±5% of the mean diameter. figure 2: (a) bubble-size probability distribution of the novel bubble generator (sample size: 180 bubbles). the inset shows an exemplary bubble image generated via shadowgraphy. (b) raw image of bubbles and their glare points. (c) exemplary tracks of selected bubbles. two glare points per bubble result in pairs of similar tracks. an additional unknown for the present single-camera approach are the errors made while determining the bubble-image size db. in the present set-up the light source is placed perpendicular to the camera(s). as such the bubble image consists of two glare points with a glare-point spacing dg = √ 2/2db; see figure 2(b). classical piv and ptv utilize gaussian peak fitting to approximate particle position at 0.1px accuracy. however, as the bubble glare points have a non-gaussian brightness distribution, larger errors are expected. to quantify these errors that are introduced by falsely estimating db, a starting vortex generated by the openjet wind tunnel is captured via two cameras (figure 2c). by recording the same bubble from two different perspectives (black and purple cameras in figure 1a), the bubble positions can be determined in two ways: (i) by using two perspectives and photogrammetry; and (b) equation (1). the results of both approaches are compared and provide an estimate of the accuracy of the single-camera approach first suggested in hou et al. (2021). references hou j, kaiser f, sciacchitano a, and rival de (2021) a novel single-camera approach to large-scale, threedimensional particle tracking based on glare-point spacing. experiments in fluids 62:100 kähler cj, fuchs t, mutsch b, and hain r (2020) school education during the sars-cov-2 pandemic-which concept is safe, feasible and environmentally sound?. medrxiv rosi ga, sherry m, kinzel m, and rival de (2014) characterizing the lower log region of the atmospheric surface layer via large-scale particle tracking velocimetry. exp fluids 55:1736 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:70 toloui m, riley s, hong j, howard k, chamorro lp, guala m, and tucker j (2014) measurement of atmospheric boundary layer based on super-large-scale particle image velocimetry using natural snowfall. exp fluids 55:1737 who (2020) q&a: ventilation and air conditioning in public spaces and buildings and covid-19 available at: www.who.int . last accessed: 01/13/2021 mytitle 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 dptv-based analysis of the flow-structure/wall-shear interplay in open wet clutches robin leister1∗, jochen kriegseis1 1 institute of fluids mechanics (istm), karlsruhe institute of technology (kit), germany ∗ robin.leister@kit.edu extended abstract the trend to lower energy consumption in the automotive industry still offers potential in various fields of application. one powerful saving strategy is described by the idling behavior of wet clutches, where the speed difference between drive and output, and the cooling oil in combination with a sub-millimeter spacing leads to significant amounts of wall shear stress (wss) and accordingly drag torque. minimization of this adverse effect has been found to be possible by means of grooved clutch-disk geometries, which have been demonstrated to correlate with the drag torque (see e.g. neupert et al., 2018). the main interplay between torque and fluid flow in open wet clutches has been analyzed by leister et al. (2020) in a dimensionless way. today, a detailed investigation of a clutch flow, however, is missing for a larger variety of groove patterns and the cause-effect relations remain yet to be fully understood. especially, the clear identification of the so-called foot print of a particular groove geometry in the flow field and corresponding wss – thus drag-torque predictions – still requires further research efforts. to advance beyond the level of drag-torque measurements (at most) in combination with qualitative flow visualization, the method of defocusing particle tracking velocimetry (dptv) in combination with an in-situ calibration approach (fuchs et al., 2016) has been successfully adapted to open wet clutches by leister et al. (2021). the chosen experimental setup and dptv working principle are sketched in figure 1. particularly, the achieved spatial resolution of 12 µm provides reasonably well resolved 3d3c flow information in the rotor-stator gap and, moreover, inside the grooves under investigation. in continuation of the earlier study by leister et al. (2021), which focuses on the fluid mechanic insights, the present study now additionally explicitly addresses the capabilities and limitations of the used dptv r2 r1 µ, ρ ω h (a) test rig with relevant parameters h w h (b) camera setup (left) and open clutch test rig with groove parameters (right) lens focus layer glass plate grooved disk (c) sketch of the dptv working principle in the rotor-stator gap figure 1: detailed sketches of (a) the test rig, (b) the set-up and typical groove geometries, (c) the measurement principle. mailto:robin.leister@kit.edu (a) defocused diameter distribution and corresponding intensity of one particle averaged in circumferential direction. the data is acquired with a back-illuminated 10 µm pinhole, which mimics a particle. (b) cavity roller in the rotor-fixed frame of reference. contours of radial velocity ur are superimposed by γ1-isolines (–) and vectors of uϕ −ωrm and uz. (•) indicates the γ1 vortex-center location. figure 2: example results for a radial groove of width w = 1.35 mm and height h = 0.97 mm approach as well as the conducted post-processing steps and the resulting changes upon their variation. since for this scale of application, where the magnification is relatively moderate, compared to microscopic scenarios, the use of a normal piv set-up, instead of a microscope, offers a large variety of possibilities and adjustment options. both used detection methods are evaluated according their suitability and robustness for this scenario of application. the acquisition related interplay between magnification and defocusing sensibility, where the trade off between aperture and object distance must be considered, is analyzed both theoretically and explicitly for this scenario and recommendations regarding further choice of equipment are given. figure 2(a) shows the diameter of the defocused image and the corresponding intensity. the particle image ranges from a gaussian shape at z∗ = 0 to a defocused ring with low intensity 2 mm apart the focus layer. to complement the study, 3d3c velocity information from the measurements are discussed according to both their respective measurement accuracy and corresponding insights for a deeper fluid mechanic understanding of the flow. figure 2(b) shows all three velocity components for a radial groove, where a cavity roller manipulates the wall-shear stress in the vicinity of the groove. the γ1-criterion indicates the vortex-center location, which coincidences with the maximum outflow velocity ur. the derived insights are foreseen to provide a valuable contribution to the drag-torque predictions and accordingly design optimization strategies for future clutch optimization efforts. references fuchs t, hain r, and kähler c (2016) in situ calibrated defocusing ptv for wall-bounded measurement volumes. measurement science and technology 27:084005 leister r, fuchs t, mattern p, and kriegseis j (2021) flow-structure identification in a radially grooved open wet clutch by means of defocusing particle tracking velocimetry. experiments in fluids 62:29 leister r, najafi af, gatti d, kriegseis j, and frohnapfel b (2020) non-dimensional characteristics of open wet clutches for advanced drag torque and aeration predictions. tribology international 152:106442 neupert t, benke e, and bartel d (2018) parameter study on the influence of a radial groove design on the drag torque of wet clutch discs in comparison with analytical models. tribology international 119:809 – 821 page 1 of 10 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 piv measurements of entrainment process of directly injected media in internal combustion engines elsayed abdelhameed1, takahide aoyagi1, daisuke tsuru1, hiroshi tashima1* 1 interdisciplinary graduate school of engineering sciences, kyushu university, japan *corresponding author: hiroshi tashima, interdisciplinary graduate school of engineering sciences, kyushu university 6-1 kasuga-koen, kasuga, fukuoka, japan tel.: +81-92-583-7592 email: tasima@ence.kyushu-u.ac.jp abstract piv measurements have been successfully applied to various flow fields relating internal combustion engines such as in-cylinder air motion, air flow in an intake port, and even a discharging passage of an ignition plug. measurements of induced air motion around diesel sprays can be said to be a significant example of the piv applications because the air motion is reflected in an unsteady complicated flow structure. instead of the apparent entrainment exaggerated by spray droplet dispersing, substantial air entrainment through momentum exchange between liquid and gas was finally obtained by combining piv and spray profile observation. piv measurements of this kind were extensionally applied to other direct fluid injection by the authors. the second object was a high-pressure gas jet directly injected under gas pressure as high as 30 mpa. it was found the gas jet has strong air entrainment through momentum exchange in a single gaseous phase between fuel gas and ambient air. the third directly injected medium in internal combustion engines should be torch flame ejected from nozzle holes of a pre-combustion chamber (pcc) to a main combustion chamber (mcc) of a so-called df (dual-fuel) engine. in this study, mixture entrainment process of torch flames is discussed on the piv results for the first time. however, chamber configurations of a real df engine are hard to simulate since it requires several auxiliary pcc devices such as an ignition plug, a sub gas injector, and so on. all of them should be actuated synchronously with an engine crank angle. in the case of a constant volume vessel (cvv), the synchronization is not necessary, but the mixture control in the pcc becomes problematic because of the lack of compression and expansion strokes that assures pcc gas exchange. for overcoming the situation, rupture of a membrane was introduced in this study. the membrane turns the upper part of the pcc into an air pressure reservoir and low-pressure air jets eject from the nozzle holes after a solenoid-driven needle pierces the membrane for rupturing. the differential pressure between the upper chamber and the lower one was chosen as a main parameter of the experiment. since the measurements and analysis of the entrainment of the low-pressure air jets are yet to finalize, the outlook of the cvv, the piv specifications, and prime results of the air entrainment page 2 of 10 are attached herewith. after all, the piv measurements revealed essential difference among air entrainment processes of the above three directly injected media in internal combustion engines. 1 introduction because of the high restrictions regulations to the emissions, the researchers payed intensive attention to investigate the combustion process aiming to enhance the fuel combustion process and reduce emissions zhao et al. (2020). the in-cylinder combustion process is highly dependent on the fuel-air mixture as air entrainment phenomena thiripuvanam et al. (2017). not only burning diesel fuel, but large internal combustion engines that burn natural gas have also appeared in marine engines as well healy et al., (2008); lion et al. (2020). therefore, studying the air entrainment for different fuel types can increase the combustion process knowledge. piv technique has been used previously by many researchers. xia et al. xia et al. (2019) have studied in details the atomization of diesel spray in marine diesel scale concluding that the liquid phase of the spray is smooth and stable compared showing shorter penetration. increasing the ambient pressure leads to decrease in tip velocity. zhang et al. zhang et al. (2019) used three different techniques to study the spray penetration and cone angles in marine diesel scale. the results showed that the higher the ambient temperature the lower the liquid penetration. the cone angle is highly affected by the ambient temperature and ambient density. piv (particle image velocimetry) is a general term for flow velocity measurement methods that identify the flow velocity based on the processing of particle images zegers et al. (2012). in this research work, unconventional piv technique has been proposed to estimate the air entrainment in case of gas jet compared to ordinary piv. the jet body brightness eliminates detecting the particles velocity in the detached area around the spray/jet body leading to difficulties in calculating the air entrainment into the spray or jet. using fluorescence piv included suspending tracer particles into the ambient to indicate velocity vector around the methane jet. moreover, the process of introducing the air into the high-pressure methane jet was visualized and measured from the flow field measurement of the air flow by piv (particle image velocimetry) using a high repetition pulse laser. light oil jis#2 was injected into a visualization container with less disturbance, and the outer diameter of the spray and the flow field of the surrounding fluid was obtained. the outer shape of the spray is dark by the fluorescence piv, making it difficult to distinguish it from the background. midian blur and gaussian blur were applied both before and after binarization on the image processing program to distinguish the spray that had been removed, and the tracer particles were erased to obtain the outer shape of the spray. on the other hand, the mixture entrainment process of torch flames has been discussed using the piv technique. 2 experimental equipment and test procedures chamber configurations of a real df engine are hard to simulate since it requires several auxiliary pcc devices such as an ignition plug, a sub gas injector, and so on. all of them should be actuated synchronously with an engine crank angle. in the case of a constant volume vessel (cvv), the synchronization is not necessary, but the mixture control in the pcc becomes problematic because of the lack of compression and expansion strokes that assures pcc gas exchange. for overcoming the situation, rupture of a membrane was introduced in this study. the membrane page 3 of 10 turns the upper part of the pcc into an air pressure reservoir and low-pressure air jets eject from the nozzle holes after a solenoid-driven needle pierces the membrane for rupturing. the differential pressure between the upper chamber and the lower one was chosen as a main parameter of the experiment. a high-speed camera model sa-z monochrome (photoron) was used for the piv measurement with specifications shown in table 1. table 1 high-speed camera specifications high-speed camera high-speed camera frame rate 20,000 fps resolution 1,024 ×1,024 pixels exposure time 23.39 μs lenses micro nikkor 105 mm, f2.8 +2.0-power teleconverter table 2 high frequency light source details nd:yag pulse laser ldp-100mqg (lee laser) wavelength 532 nm frequency 20 khz (δt = 50 μs) pulse energy 2.0 mj/pulse pulse width 4.0 μs timing controller lc880 (labsmith) the cvc has been charged with tracer particles and the suspension of the particles was insured by the aid of air pressurizing. figure 1 illustrates the layout of the optical system which has been incorporated in the piv technique. figure 1 fluorescence piv optical system page 4 of 10 3 results and discussion in this section, the results from fluorescence piv measurements for induced air motion around diesel sprays, a high-pressure gas jet directly injected under gas pressure as high as 30 mpa and a directly injected medium in internal combustion engines as a torch flame ejected from nozzle holes of a pre-combustion chamber (pcc) to a main combustion chamber (mcc) of a so-called df (dual-fuel) engine will be explained. fluorescence piv measurement principle in this study unconventional technique called fluorescence piv has been employed aiming to avoid the light scattering phenomena in the conventional piv technique as can be seen clearly from the comparison illustrated in figure 3. using tracer particles can enable precise and clear air entrainment calculations. to remove scattered light from the boundary surface, figure 2 shows scf560 filter which has been attached to the camera lens to eliminate the laser light with 532 nm wavelength allowing the light discarded from the fluorescent with 590 nm wavelength. figure 2 frequency characteristics of sharp cut filter transmittance versus wavelength page 5 of 10 figure 3 comparison between the method in this study and the conventional method (left is conventional method while right is fluorescence piv method) table 3 shows the experimental conditions in this study while table 4 lists the details of the tracer particles used in this study. table 3 experimental conditions fuel light oil jis#2 nozzle diameter 0.125 mm nozzles number 6 and 8 injection pressure 60 and 70 mpa injection time 500 μs ambient gas nitrogen ambient pressure 1.56 mpa ambient temperature 296 k table 4 tracer particles specifications type godd ball, b-5c company name suzukiyushi industrial corporation material hollow ball sio2 average diameter 2-2.5 μs bulk density 180-450 kg/m3 using the spray surface area calculations, total air entrainment at two different injection pressures 60 and 70 mpa. the entrainment in case of high injection pressure seems to be accumulated after 1 ms asoi while it shows more stable values in case of 60 mpa. figure 4 air entrainment rate at 60 mpa and 70 mpa injection pressures piv measurements for gas jet table 5 piv analysis specifications page 6 of 10 software koncert ii (seika corporation) algorithm recursive direct cross-correlation method inspection window size 16*16 pixels (2.55mm*2.55mm) overlap 50 % 3.2.1. test condition in the recent study, methane gas was examined under different conditions of pressure and temperature. a 0.4-hole injector was used in the case of methane gas with rating injection pressure (20, 30 and 40) mpa at 293 k. figure 5 shows the results of piv analysis for spray. the jet grows with a similar shape with a capturing section that has an exclusion flow that spreads radially at the tip of the jet and an entrainment section that has a flow that continues from the root and faces the inside of the jet. in addition, the flow field around the jet was found to have a size about 1.0 to 2.0 [m/s] stronger than that of spraying. figure 6 shows the distribution of the atmosphere introduction velocity at the spray boundary in the injection axis direction. as can be seen from the piv results, vortices are generated actively in the jet, and an intensive air entrainment has been noticed. figure 5 flow field around methane jet at 36.3 mpa ambient density page 7 of 10 figure 6 distribution of accompanying flow flowing into the spray ρa = 36.3 [kg / m3] figure 7 shows the time change of the mass atmosphere introduction rate and the total introduced mass under the conditions shown in the above figure. as can be seen from the figure below, it was observed that the total mass of the ambient atmosphere introduced increased as the injection pressure increased in both cases of spraying and jetting. figure 7 air entrainment for methane jet under different injection pressures page 8 of 10 air entrainment rate and total air entrainment versus time at 36.3 mpa ambient density regarding the jet, only the introduction from the entrainment section is considered, but the ratio of both spray and jet is explained to be about the same, and this measurement is valid. in addition, it seems that one of the reasons for the strong introduction of jets from the entrainment section is the entrainment of a large atmosphere due to the large-scale vortex structure as shown in figure 8. figure 8 distribution of the accompanying flow flowing into the spray and the moment of introduction of the atmosphere by the vortex seen in the jet pinj=40[mpa], 𝜌𝑎=36.3[kg/m3] piv measurements for torch flame 3.3.1. test condition in this study, the air has been examined in the pre-chamber of the torch flame. neglecting the amount of fuel into the pre-chamber since the fuel is lean, the air has been considered to be examined in this case. moreover, using the air can ensure a high level of torch flame stability. figure 9 illustrates the piv measurements and spry contour for a spray in prechamber. it worth to be mention that in this case using direct shot to get the contour of the spray was not applicable due to the difficulties of density difference. instead, the contour data has been extracted from velocity vector analysis. from the figure, it can be noticed that strong eddies occur leading to increase the air entrainment rate while no entrainment has been noticed in the capturing section due to strong pushing out. the contour of the air spray seems to be same as the ordinary shape of the diesel spray. figure 9 piv measurements for spray in torch flame at 2msasoi figure 10 shows the total air entrainment for air jet in the prechamber at different injection pressures 2, 3 and 4 mpa. it is clearly seen that the higher the injection pressure the higher the total air entrainment. this attribution could be due to the higher movements of the spray body which in turn generates more eddies allowing more air to be grasped into the main spray body. page 9 of 10 figure 10 total air entrainment in the torch flame 4 conclusion in this research work, florescence piv measurements have been considered to study the entrainment process for the first time. due to the difficulties of simulating the real df engine, the piv measurements have been considered as a tool for detecting the air entrainment process. the following results have been gotten: the scattered light of the spray was suppressed by the fluorescence piv, and the velocity field around the spray could be analyzed accurately. the air entrainment rate is directly proportional to the injection pressure. the high-pressure gas jet undergoes an atmosphere introduction process similar to ordinary liquid spraying, but it is observed that the atmosphere introduction in the entrainment section is active with a flow velocity. 5 references healy d, curran hj, simmie jm, kalitan dm, zinner cm, barrett ab, petersen el, bourque g (2008) methane/ethane/propane mixture oxidation at high pressures and at high, intermediate and low temperatures. combust flame 155: 441–448. lion s, vlaskos i, taccani r (2020) a review of emissions reduction technologies for low and medium speed marine diesel engines and their potential for waste heat recovery. energy convers manag 207: 112553. thiripuvanam t, tashima h, tsuru d (2017) air entrainment and combustion process of highpressure gas jet in gas direct injection engines. in 9th international conference on modeling and diagnostics for advanved engine systems, comodia, okayama, japan, july 25-28 xia j, huang z, xu l, ju d, lu x (2019) experimental study on spray and atomization characteristics under subcritical, transcritical and supercritical conditions of marine diesel engine. energy convers manag 195: 958–971. zegers rpc, luijten ccm, dam nj, de goey lph (2012) preand post-injection flow characterization in a heavy-duty diesel engine using high-speed piv. exp fluids 53: 731– page 10 of 10 746. zhang w, li x, huang l, feng m (2019) experimental study on spray and evaporation characteristics of diesel-fueled marine engine conditions based on optical diagnostic technology. fuel 246: 454–465. zhao j, liu w, liu y (2020) experimental investigation on the microscopic characteristics of underexpanded transient hydrogen jets. int j hydrogen energy 45: 16865–16873. 14th international symposium on particle image velocimetry – ispiv 2021 chicago, usa, august 1-4, 2021 particle position prediction based on lagrangian coherency for flow over a cylinder in 4d-ptv ali rahimi khojasteh1∗, dominique heitz1, yin yang1, lionel fiabane1 1 inrae, opaale, f-35044, rennes, france ∗ correspondent author: ali.rahimi-khojasteh@inrae.fr abstract recent developments in time-resolved particle tracking velocimetry (4d-ptv) consistently improved tracking accuracy and robustness. we propose a novel technique named ”lagrangian coherent predictor” to estimate particle positions within the 4d-ptv algorithm. we add spatial and temporal coherency information of neighbour particles to predict a single trajectory using lagrangian coherent structures (lcs). we found that even a weak signal from coherent neighbour motions improves particle prediction accuracy in complex flow regions. we applied finite time lyapunov exponent (ftle) to quantify local boundaries (i.e. ridges) of coherent motions. synthetic analysis of the wake behind a smooth cylinder at reynolds number equal to 3900 showed enhanced estimation compared with the recent predictor functions employed in 4d-ptv. results of the experimental study of the same flow configuration are reported. we compared predicted positions with the optimised final positions of shake the box (stb). it was found that the lagrangian coherent predictor succeeded in estimating particle positions with minimum deviation to the optimised positions. 1 introduction this paper discusses a novel approach in time-resolved particle tracking velocimetry (4d-ptv) to predict particle positions over space and time based on lagrangian coherent structures (lcs). in the classic 4dptv algorithm, predicted particle positions are given to the optimisation process for further corrections. the optimisation can deal with slight deviations between the predicted position and the true position. however, the optimisation fails to find the true position if the deviation is large enough to have multi-candidates for a single particle at tn+1. this shows the importance of having an appropriate prediction in dense and complex motions. the proposed idea is initiated by arguing that predictions in ptv techniques focus on a single particle individually, while this single particle is not acting alone [1]. we propose this approach to locally differentiate coherent and non-coherent motions of neighbour particles around a single particle position to improve prediction accuracy, as shown in figure 1. on the other hand, the information of coherent particles should be shared with each neighbour particle to predict their behaviour accurately and avoid misprediction. the present study was designed as a complementary function for 4d-ptv algorithms such as stb [2] and klpt [3]. briefly, it is assumed that particle positions are known for n time steps (four to five). afterwards, a mathematical prediction function is implemented to estimate particle positions for time-step n+1 followed by ”shaking” and position refinement. it should be noted that the ”shaking” process tries to look for a candidate true position very close to the predicted position. if misprediction happens, no matter how many times we perform ”shaking”, the true position is not achievable. this implies the importance of producing accurate predictions. this paper seeks to investigate the possibilities of improvements in motion estimation by adding meaningful physics into the prediction function. a simple prediction approach is a polynomial function, suggested by schanz et al. [4], resulting in reasonable predictions and 3d particle position reconstruction in simple flows [4, 5, 6]. however, significant off prediction occurs in case of flow associated with complexities such as high turbulence level, high reynolds number, and mixing flows [7]. in such conditions, even by increasing the order of the polynomial predictor functions from 3 to 10 [7], off prediction stays remained. the solution for this challenge is implementing optimal temporal filtering such as the wiener filter, which has been first examined in 4d-ptv experiments by schröder et al. [5]. since then, this concept became consistent in the stb studies due to its high robustness and accurate motion estimations [8, 7]. as figure 1: particle prediction scenario from tn to tn+1: a), known particle positions from history starting from tn−4 up to tn (particle size is increasing gradually to show time-step differences); b), the trajectory (golden line) obtained from filtered curve fitting of known particle positions; c), prediction based on extrapolating of the fitted trajectory (red dash line) from tn to tn+1; d), modified prediction (grey dash line) using velocity and acceleration information of coherent particles in neighbourhood of the target particle at tn. mentioned, the wiener filter showed robust behaviour in prediction with complex flows but still suffers in high motion gradients. this implies the fact that the prediction function suffers from a lack of information to find true positions. worth mentioning that these prediction-based techniques rely on one particle individually, excluding it from surroundings. all the information we know from an individual particle is its history. even if we implement filtering and smoothing schemes such as stb using wiener filter [8], our information is limited by the history of the target particle, ignoring that every particle is spatially and temporally coherent with a specific group of other particles following the same behaviour. this motivated us to take into account a group of coherent motions for predicting a single particle. we propose to locally determine information of coherent and non-coherent particles during the trajectory procedure by using the finite-time lyapunov exponent (ftle). more details of coherent motion detection are discussed in section 2. after that, we address the prediction function with the minimisation approach in section 3. in the following sections 4 and 5, we study and evaluate our proposed technique using synthetic and experimental case studies of the wake over and behind a smooth cylinder at reynolds number equal to 3900. 2 coherent and non-coherent neighbours every single particle is spatially and temporally coherent with a specific cluster of other particles following the same behaviour [1]. figure 2 shows a schematic of coherent and non-coherent groups of neighbour particles in different colours evolving by time (t1 − t5). a particle can spatially meet a group of other particles in which there is no coherency link between them. there are many available concepts to identify lagrangian coherent structures (lcs) from looking for separatrix lines or surfaces which divide structures into different coherent regions [9]. we introduced such a concept for the track initialisation in 4d-ptv studies, named lagrangian coherent track initialisation (lcti), in synthetic flow configurations of the recent lpt challenge [10] and for a real jet impingement experiment [1]. lcti showed that ftle is locally applicable for surrounding sparse trajectories to determine coherent neighbours. to this end, we defined a local eulerian frame around each particle, while all neighbourhood particles inside this area must be classified as coherent or non-coherent with the target particle. this frame is fixed during a series of time-steps that can provide an eulerian view of the neighbourhood behaviour. velocity values of the target particle are used to quantify the eulerian frame size in each direction. if 2d / 3d velocity values are equal in each direction, then the shape would be a circle / sphere around the target particle; however, more directional gradients would adjust the shape (see figure 1.d). all particles inside the eulerian frame in the same phase or with phase delay are considered neighbourhoods. by tracking each figure 2: schematic of particle trajectories in 2d pair vortices starting from t1 to t5: t1), the target particle with coherent neighbour particles located in a clockwise vortex (golden cluster), non-coherent particles belong to different clusters; t2), the target particle trajectory (golden line) approaching to particles in the red cluster; t3), the target particle separation with non-coherent particles in the red cluster and approaching to particles in the grey cluster; t4), separation of non-coherent particles in the grey cluster with the target particle; t1−t5), full trajectory view of the target particle alongside with coherent particles in golden cluster. lagrangian particle in the flow over a finite time (see figure 2), we can compute the ftle value based on neighbour trajectories as, σ t t0 = 1 |t | √ λmax (∆) = 1 |t | log( δx(t) δx(t0) ) (1) where σt t0 is named the scalar ftle value showing the amount of stretching over the interval time t = t − t0, and δx is the displacement of neighbour particles. λmax is the maximum eigenvalue of the right cauchy-green deformation tensor [11] obtained from the displacement map. a lower ftle value means a neighbouring particle is coherent and acts in the same behaviour with the target particle spatially over a specific temporal scale. as a result of this classification, the mean values, including velocity and acceleration of the coherent neighbour particles, can be superimposed (weighted averaged) on the target particle (see figure 1). this physics-based information is added to the resulting prediction function. the prediction function of this study is a 3rd order polynomial predictor that must satisfy particle history and additional coherent dynamics. details of the prediction function is addressed in section 3. 3 prediction function polynomial function is the most simple predictor that can be used in the time resolved particle tracking techniques. the polynomial coefficients must be determined optimally by minimising mean square error such that the corresponding polynomial curve with order of n best fits the given positions. this can be formalised as, n ∑ j=n−m n+1 ∑ i=1 ai.t i−1 j = yn−m,n, (2) where ai is unknown coefficients of the predictor function. yn−m,n is known positions of the last finite frames (in this study m = 4). therefore, the least square cost function is, j = 1 n n ∑ i=n−m (xi− yi) 2 , (3) figure 3: lagrangian particle trajectories obtained from transport of synthetic particles through dns eulerian fields. the coherent prediction function adds information obtained from temporal / local spatial lagrangian coherent particles to come up with additional constraints in the polynomial cost function (equation 3). in the worst-case scenario where there is no coherent neighbour information, the prediction function is just a simple polynomial function without additional constraints. each particle carries sets of information, including position, first and higher-order derivative values. assuming positions of at least three time steps m are known. in this function, we impose first and second-order derivatives of each coherent particle into the prediction function as below, n+1 ∑ i=2 ai,n+1.(i−1)∗ t i−2 n = ÿ lcs n n+1 ∑ i=3 ai,n+1.(i−1)∗ (i−2)∗ t i−3 n = ÿ lcs n . (4) therefore, each particle will end up with the weighted averaged of local coherent velocity and coherent acceleration values (ẏlcs , ÿlcs). in the present study, we take four time step histories of particles to minimise the cost function and then predict the next step. the first and second derivatives of all coherent particles are weighted averaged based on their ftle level and distance to the target particle. two weighted averaged values, velocity and acceleration, of each target particle can be obtained for the estimation. therefore, the modified cost function (i.e. coherent predictor) can be written as, j = 1 n n ∑ i=1 (xi− yi) 2 +(ẋn− ẏn) 2 +(ẍn− ÿn) 2. (5) velocity constraint controls the direction of the prediction function, while in the case of having high acceleration gradients, a second-order constraint is required to control the acceleration of the prediction. the solution for the cost function in equation 5 is not only smooth on the history of the target particle but also satisfies local coherent first and second-order derivatives. we compared the performance of the coherent predictor with three other prediction functions, as listed in table 1. dns predictor was defined as a reference using the euler equation to transport particle positions by the ground truth dns velocity. predicted particle positions are followed by shaking or other optimisation techniques. therefore, all particles are either tracked or untracked except for the inlet and outlet trajectories. in every time-step, untracked particles are like additive noises and might gradually cause to collapse of the whole trajectory process. due to this, untracked particles must be fed by other complementary treatments. to this end, new information can be extracted if any groups of tracked particles are found to be located in the neighbourhood of untracked particles with a time step phase delay (i.e. tn+1). this phase delay means that new tracked particles at time-step tn+1 are method fit parameters cost function prediction a) dns predictor xn+1 = ẋdns · tn+1 b) polynomial predictor ∑ n j=n−` ∑ n+1 i=1 ai, j · t i−1 j = yn−`,n j = 1 n ∑ n i=n−m (xi− yi) 2 yn+1 = ∑ n+1 i=1 ai,n+1 · t i−1 n+1 c) wiener filter ∑ ` i=1 wi.un = yn j = (xn−ut n w)2 yn+1 = ∑ `+1 i=2 wi.un d) coherent predictor ∑ n j=n−` ∑ n+1 i=1 ai, j.t i−1 j = yn−`,n j = 1 n ∑ n i=1 (xi− yi) 2 +(ẋn− ẏn) 2 +(ẍn− ÿn) 2 yn+1 = ∑ n+1 i=1 ai,n+1 · t i−1 n+1 ∑ n+1 i=2 ai,n+1.(i−1)∗ t i−2 n = ẏ lcs n ∑ n+1 i=3 ai,n+1.(i−1)∗ (i−2)∗ t i−3 n = ÿ lcs n table 1: prediction function formulation locally coherent with one specific untracked particle at time-step tn. another technique to reduce the number of untracked particles is to use backward prediction, which is well established in classic schemes such as nearest neighbour trajectory. similarly, we implemented the backward predictor to search for additional information from the coherent particles to estimate in reverse pace followed by backward shaking. on the one hand, surrounding information of an untracked particle can provide the least information to predict in backward pace. in addition, this treatment can also connect spilt tracklets for reconstructing longer particle trajectories. this process is iterative, meaning that every forward step is embedded with a series of backward estimations from the current time-step up to the first step. in the present study, we evaluated and compared the performance of coherent predictor only in forward prediction. figure 4: normal pdf of particle position error in x direction of four predictor functions. 4 synthetic evaluation to evaluate our novel particle position prediction scheme, we used a dns simulation of the wake behind a smooth cylinder at reynolds number equal to 3900 computed by an open-access code named incompact3d [12]. particle trajectories around the cylinder are shown in figure 3. particles are transported by every 10 dns time step using the fourth order runge kutta temporal and trilinear spatial schemes. the synthetic dataset is available to the public for interested readers [13, 14]. in the synthetic case, particle trajectories are smooth and predictable when the synthetic temporal scale is with the same order of the dns time step due to the small travelling distance between two time steps (less than the kolmogorov timescale). however, the travelling distance is comparably large for a real ptv experiment. to mimic the real experiment, we created figure 5: position estimation error averaged in z direction: a), dns predictor; b), polynomial predictor; c), wiener filter; d), coherent predictor. around 150,000 ground truth trajectories associated with noise for every 20 dns time step. by increasing the temporal scale, less particle position temporal information is available, and then the prediction would be more challenging. therefore, even a weak signal of coherent motion would lead to a better prediction. we compared position prediction of four schemes with the ground truth particle trajectories (see table 1). first, we predicted particle positions based on known ground truth dns velocity with a linear euler transport function. in such a scenario, we can estimate the minimum uncertainty level that can be achieved in this sparse temporal scale. both wiener filter and polynomial predictors are also selected to be compared with the lcs based predictor (i.e. coherent predictor). figure 4 shows normal pdf of the predicted position error in x direction of four schemes. position error in x direction shows that deviations for coherent predictor stay virtually below 0.05 ε/d, where d is the cylinder diameter. on the contrary, a significant number of particles are mispredicted in both polynomial and wiener filter techniques. similar significant improvements of using coherent predictor are observed in y and z directions. figure 5 shows the projected distribution of the position error on xy plane for each predictor function. interestingly, the prediction error is highly correlated with the flow behaviour. although the dns predictor (see figure 5.a) uses known ground truth velocity information, the travelling distance is large enough to introduce the prediction errors, particularly inside the wake region. as shown in figure 5.b, third order polynomial has the worst prediction error, which can be up to 0.2 ε/d around the cylinder leading edge and inside the wake region. the polynomial prediction error distribution is fully shaped by the flow motion meaning that any gradients inside the flow create huge estimation error. overall and local performance of the wiener filter is better than the polynomial predictor. wiener filter succeeded to reduce the prediction error in most of the peak regions (see figure 5.b.c). error distribution reveals that coherent predictor has the best performance locally and globally compared to wiener and polynomial predictors. worth mentioning that a small prediction error reduces the probability of picking a wrong particle from the surroundings in the optimisation process of 4d-ptv. 5 experimental evaluation an experimental study of the cylinder wake flow at reynolds number equal to 3900 (same value as the synthetic data) was performed. we designed an experimental setup with four cameras as shown in figure 6.c. four cmos speedsense dantec cameras with a resolution of 1280×800 pixels and the maximum frequency of 3 khz are empowered. cameras are equipped with nikon 105 mm lenses. the first two cameras are positioned in backward light scattering, while the second two cameras received maximum intensity signal in forward scattering. the calibration error was lower than 0.06 pixel and reduced to 0.04 after the a) b) c) 100 200 300 400 500 600 700 800 900 1000 100 200 300 400 500 600 700 800 900 1000 2 3 4 5 5.5 v el o ci ty (m / s) figure 6: the cylinder wake flow at reynolds 3900 with four cameras: a), snapshot of the 4d-ptv experiment; b), side view of particle trajectories superimposed by vorticity iso-surfaces; c), schematic of the experimental setup. volume self calibration. the volume of interest was 200 mm× 150 mm× 46 mm starting from roughly 4d downstream of the cylinder, knowing that the vortex formation zone ends at 4d. the aperture was set at 11 to achieve 46 mm depth of focus. we used an led system to illuminate this large volume. the seeding particles were helium filled soap bubbles (hfsb) [15] resulting desired intensity signal with appropriate particle size. however, bubbles are limited by three main factors in the wind tunnel experiments, including generation rate, lifetime, and image glare points. we placed 50 bubble generator nozzles with airfoil-shaped structures inside the wind tunnel chamber. the nozzles were far upstream of the measurement section to ensure a sufficient number of bubbles are created, and the main flow field is not disturbed by the existence of nozzles. the bubble lifetime is very short (less than 2−3 minutes) inside the wind tunnel, mainly because they explode by passing through honeycomb layers. to overcome this issue, we injected bubbles inside the chamber for up to 5 minutes when the wind tunnel is off before starting the acquisition. we found that particles larger than three pixels create two glare points on two sides of the bubble. this requires more -5 -2.5 0 2.5 5 position error (pixels) 0 0.2 0.4 0.6 0.8 1 n or m al p d f coherent predictor polynomial predictor wiener -lter figure 7: experiment normal pdf results of particle position error in x direction of three predictors. each predictor is compared with final optimised positions of stb davis. image treatments before running the 4d-ptv algorithm to avoid false particle reconstruction. however, the intensity of two glare points can diffuse and merge if the particle size is around two pixels. therefore, we adjusted the camera magnification to reach two particle pixel sizes on average to surpass the glare point issue. one snapshot of the experiment is shown in figure 6.a. trajectory results of the current experiment with superimposed vorticity iso-surfaces are shown in figure 6.b. to quantify the results of different schemes, we compared predictions with optimised positions obtained from stb davis. as a result of the experiment, stb managed to successfully build nearly 12000 particles as shown in figure 5.b. noisy particle reconstruction of four time steps was used as an input of the prediction functions. we compared three techniques, polynomial, wiener filter, and coherent predictors, with final optimised positions. the deviation of position estimated of each technique is shown in figure 7. the distribution shows that the coherent predictor has more accurate estimations within 1 pixel deviation from the optimised positions. position estimations of wiener filter and coherent predictors stay below 2.5 pixels deviation for nearly all particles. on the contrary, the polynomial predictor has maximum deviation with stb davis. 6 conclusion we proposed a robust technique to predict particle positions based on their local temporal and spatial coherent motions. lcs can classify and divide the coherent neighbour motions. we imposed first and secondorder derivatives of the neighbour coherent motions into the predictor function in addition to the particle history. to assess the proposed method named coherent predictor, we performed the synthetic analysis of the wake behind a smooth cylinder at reynolds number equal to 3900. we compared three predictor functions. polynomial predictor showed maximum deviation with the ground truth data. whereas coherent predictor provided the most accurate position estimation. we found that the flow regions highly impact the estimation error. inside the wake region, particularly the vortex formation zone and the two sideward shear layers, cause more challenges in prediction. these mentioned regions are featured by high acceleration and 3d directional motions. we also performed the 4d-ptv experiment of the wake flow behind a cylinder at the same reynolds number. it was found that the coherent predictor is reliable to estimate particle positions very close to the optimised positions. references [1] ali rahimi khojasteh, yin yang, dominique heitz, and sylvain laizet. lagrangian coherent track initialisation (lcti). in arxiv, volume 9, 2021. [2] daniel schanz, sebastian gesemann, and andreas schröder. shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids, 57:1–27, 5 2016. [3] yin yang and dominique heitz. kernelized lagrangian particle tracking. 4 2021. [4] daniel schanz, andreas schröder, sebastian gesemann, dirk michaelis, and bernhard wieneke. ’shake the box’: a highly efficient and accurate tomographic particle tracking velocimetry (tomoptv) method using prediction of particle positions. in 10th international symposium on particle image velocimetry, 2013. [5] andreas schröder, daniel schanz, dirk michaelis, christian cierpka, sven scharnowski, and christian j. kähler. advances of piv and 4d-ptv ”shake-the-box” for turbulent flow analysis -the flow over periodic hills. flow, turbulence and combustion, 95(2-3):193–209, 2015. [6] daniel schanz, andreas schröder, and sebastian gesemann. ’shake the box’ a 4d ptv algorithm: accurate and ghostless reconstruction of lagrangian tracks in densely seeded flows. 17th international symposium on applications of laser techniques to fluid mechanics, pages 7–10, 2014. [7] shiyong tan, ashwanth salibindla, ashik ullah, and mohammad masuk. an open-source shakethe-box method and its performance evaluation. in 13th international symposium on particle image velocimetry, volume i, 2019. [8] andreas schröder, daniel schanz, reinhard geisler, sebastian gesemann, and christian willert. nearwall turbulence characterization using 4d-ptv shake-the-box. in 11th international symposium on particle image velocimetry, 2015. [9] george haller. lagrangian coherent structures. annual review of fluid mechanics, 47:137–162, 2015. [10] ali rahimi khojasteh, dominique heitz, yin yang, and sylvain laizet. lagrangian coherent track initialisation. in 3rd workshop and 1st challenge on data assimilation & cfd processing for piv and lagrangian particle tracking, 2020. [11] shawn c. shadden, francois lekien, and jerrold e. marsden. definition and properties of lagrangian coherent structures from finite-time lyapunov exponents in two-dimensional aperiodic flows. physica d: nonlinear phenomena, 212(3-4):271–304, 12 2005. [12] sylvain laizet and ning li. incompact3d: a powerful tool to tackle turbulence problems with up to o(105) computational cores. international journal for numerical methods in fluids, 67:1735–1757, 12 2011. [13] ali rahimi khojasteh, sylvain laizet, dominique heitz, and yin yang. lagrangian and eulerian dataset of flow over a circular cylinder at reynolds number 3900, 2021. [14] ali rahimi khojasteh, sylvain laizet, dominique heitz, and yin yang. lagrangian and eulerian dataset of the wake over a smooth cylinder at a reynolds number equal to 3900. data in brief, 2021. [15] fulvio scarano, sina ghaemi, giuseppe carlo alp caridi, johannes bosbach, uwe dierksheide, and andrea sciacchitano. on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments. experiments in fluids, 56:1–12, 2 2015. introduction coherent and non-coherent neighbours prediction function synthetic evaluation experimental evaluation conclusion microsoft word ispiv-2021-abstract-v7.docx 14th international symposium on particle image velocimetry – ispiv 2021 august 1-5, 2021 | chicago, il usa numerical uncertainty in density estimation for background oriented schlieren jiacheng zhang1§, lalit k. rajendran2§, sally p. m. bane2, pavlos p. vlachos1* 1 purdue university, school of mechanical engineering, west lafayette, usa. 2 purdue university, school of aeronautics and astronautics, west lafayette, usa. *pvlachos@purdue.edu abstract background oriented schlieren (bos) is an image-based density measurement technique. bos estimates the density gradient from the apparent distortion of a target pattern viewed through a medium with varying density using cross-correlation, tracking, or optical flow algorithms. the density gradient can then be numerically integrated to yield a spatially resolved estimate of the density [1]. a method was recently proposed to estimate the a-posteriori instantaneous and spatially resolved density uncertainty for bos [2] and showed good agreement between the propagated uncertainties and the random error. however, the density uncertainty quantification method could not account for the systematic uncertainty in the density field due to the discretization errors introduced during the numerical integration, which could be much larger than the displacement random errors [2]. in this work, we propose a method to estimate the numerical uncertainty introduced by the density integration in bos measurements, using a richardson extrapolation framework. a procedure is also introduced to combine this systematic uncertainty with the random uncertainty from the previous work to provide an instantaneous, spatially-resolved total uncertainty on the density estimates. the method will be tested with synthetic fields and synthetic bos images. with the richardson extrapolation [3], the discretization error of a numerical estimation can be estimated based on the residual between two sets of results with different grid levels as: 𝜖!̅ = − "!#""! $##% , (1) where 𝜖!̅ is the estimated numerical error of the result obtained on a grid with spacing ℎ, 𝑓! and 𝑓$! are the results obtained on the grids with spacing ℎ and 𝑟ℎ, respectively, with 𝑟 being the downsampling factor (usually 𝑟 = 2), and 𝑝 is the order of accuracy of the discretization scheme. in this study, 𝑝 is 2 since the second-order central differencing scheme was used for carrying the numerical integration. the estimated error is then employed as the numerical uncertainty (𝑈 = |𝜖!|). with the random uncertainty obtained using the previous method [2] as the standard deviation of the random error distribution, and the numerical uncertainty interpreted as the standard deviation of the bias error distribution, the standard total uncertainty can be expressed as 𝑈&'&()* = 𝑈+,(-* + 𝑈$(./'0* , (2) thereby providing a framework for combining the random uncertainty estimates to estimate the overall uncertainty in the density integration. the proposed uncertainty estimation method was tested using a synthetic sinusoidal scalar field as: 𝑓(𝑋, 𝑌) = 𝑠𝑖𝑛 6*1 2 𝑋7 𝑠𝑖𝑛 *1 2 𝑌, (3) where 𝑓 represents the scalar field, and 𝜆 represents the wavelength. a zero-mean gaussian distributed noise was added to the scalar field with prescribed noise levels. one thousand (1000) realizations of the corrupted field were generated, and for each realization, the integration was performed with the noisy gradient fields to estimate the error. the results are shown in figure 1 for two noise levels: 1% and 10% of the peak value of the scalar field. it is seen in both levels that the spatial variation of the total uncertainty matches that of the total error, and the rms of the total uncertainty coincides with the rms of the error distribution. this validates the framework used to combine the bias and random uncertainty estimates. § these authors contributed equally to this work. the numerical uncertainty estimation was also applied to the synthetic bos images rendered using a raytracing based image generation methodology [4]. a sinusoidal density field was chosen for the error analysis as described by equation (4): 𝜌(𝑋, 𝑌) = 𝜌3 + 𝛥𝜌3 𝑐𝑜𝑠 6 *1 2 𝑋7 𝑐𝑜𝑠 6*1 2 𝑌7, (4) where 𝜌3 is the ambient density, δ𝜌3 is the peak density difference and 𝜆 is the wavelength. a 2d slice of the density field is shown in figure 2(a). the rendered images were processed using prana with a standard crosscorrelation procedure for two passes in an iterative window deformation framework. a sample instantaneous displacement field are shown in figure 2(b). the displacement fields were used to calculate the depth averaged density gradient field ∇𝜌, which were then spatially integrated using the poisson solver to obtain the projected density field. the error of the density field was determined as the deviation from the original density field used to render the synthetic images, and the numerical uncertainty was estimated using the richardson extrapolation method. the results of the density error and uncertainty are compared in figure 2(c) and (d). the numerical uncertainty of the density integration was lower than the total density error, because the density error was also due to the discrepancy between the ray tracing displacements and the theoretical displacements because of the linear approximation of the non-linear ray trajectory through density gradients [4]. efforts are ongoing to apply the proposed method to experimental bos data. references [1] m. raffel, “background-oriented schlieren (bos) techniques,” exp. fluids, vol. 56, no. 3, pp. 1–17, 2015. [2] l. k. rajendran, j. zhang, s. bhattacharya, s. p. m. bane, and p. p. vlachos, “uncertainty quantification in density estimation from background-oriented schlieren measurements,” meas. sci. technol., vol. 31, no. 5, 2020. [3] p. j. roache and p. m. knupp, “completed richardson extrapolation,” commun. numer. methods eng., vol. 9, no. 5, pp. 365–374, 1993. [4] l. k. rajendran, s. p. m. bane, and p. p. vlachos, “piv/bos synthetic image generation in variable density environments for error analysis and experiment design,” meas. sci. technol., vol. 30, no. 8, 2019. figure 1 error and uncertainty statistics for the sinusoidal field for two noise levels. (a) and (b) represent the spatial variation of the statistics and probability density functions respectively for a 1% noise level, with (c) and (d) representing the results for the 10% noise level. figure 2 results of the analysis with synthetic bos images. (a) 2d slice of the density field used to render the synthetic bos images, (b) image displacements from cross-correlation analysis, (c) error in the density field, and (d) numerical uncertainty ispiv2021_template_paper.pdf 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a novel laboratory pushing the limits for optics-based basic turbulence investigations s. l. ribergaard1, y. zhang1, h. abitan1, j. s. nielsen1, n. s. jensen1, c. m. velte1∗, 1 turbulence research laboratory, technical university of denmark, department of mechanical engineering, kgs. lyngby, denmark ∗ cmve@dtu.dk abstract developments in theoretical investigations and experimental techniques are reaching a level of maturity for which it is finally becoming possible to answer some of the most pressing questions in turbulence. the prevailing classical theories all have their strengths and drawbacks based on their respective principal assumptions. to better understand the implications of these assumptions, we have developed a theoryintensive experimental strategy. for these purposes, a laboratory has been established at the department of mechanical engineering, technical university of denmark. the objective being to provide the data necessary to test the (bounds of) validity of the existing theories; most prominently the classical richardsonkolmogorov-batchelor paradigm, but also other generally adopted views such as rapid distortion theory and equilibrium similarity. the measurements will be analyzed within a novel theoretical framework that enables not only quantification of the degree to which the small and intermediate scale turbulence behaves according to the existing theories (and their central assumptions), but also unveiling the underlying processes that create the respective state of turbulent flow. the present work will describe the current state of the developments of building up the laboratory. 1 introduction 1.1 rationale for proposed experiments our current general understanding of turbulence is not based exclusively on the equations that govern fluid flow. central to the classical understanding is a set of assumptions ultimately based on an analogy between the fluid and the flow. similar to molecules in a thermodynamic equilibrium in relation to a macroscopic thermodynamic state, no matter what the dynamics are at the large scales, the small and intermediate scales of turbulence are assumed to be effectively decoupled from the energy containing large scales, leading to a (universal) statistical local (small and intermediate scale) equilibrium as long as the reynolds number is sufficiently high, see figure 1(a). however, it is important to remember that these very fundamental assumptions are not anchored in the equations that govern fluid flow. in a very simple thought experiment, as presented earlier in velte and buchhave (2021), one can imagine the process of two large co-rotating scales in close vicinity to each other. as they rotate, smaller structures will be able to form in between and energy will be directly transferred between these large and small structures. thus, even dynamic variations in time will be able to transfer directly between these widely different sizes of structures. this thought experiment thus illustrates an intuitive example of non-local interactions. if non-local interactions can occur, then dynamics from the large scales can be transferred directly to the small scales, and the second assumption of local equilibrium is also potentially violated. so for the theory to remain valid, if this picture holds true, all scales are required to be in equilibrium. this is valid, at least in an averaged sense, in some flows – like the round turbulent jet. carefully designed and conducted experiments that are based on theoretical considerations is an important step in increasing our understanding. that is why we at the turbulence research laboratory at the technical university of denmark aim to provide this solid empirical foundation to properly test local equilibrium. the measurements will be analyzed in light of the governing equations using a theoretical (a) local interactions leading to local equilibrium. (b) thought experiment: non-local interactions and non-equilibrium. figure 1: (left) the principal assumptions of the richardson-kolmogorov paradigm. (right) thought experiment illustrating the possibility for non-local interactions. framework carefully developed over the past years. in the current work, the objective is to describe the experimental aspects of this effort. previously, we have developed formalism that shows that time must be included in the analysis as an independent variable, buchhave and velte (2019), which has previously been neglected, c.f. batchelor (1953). the developments are, however, limited to the description of the frequency content in a (measurement) point for statistically stationary turbulence. to be able to properly describe the underlying processes of energy exchange between wavenumber and frequency components, a four-dimensional full-field description is required. analyzing the dynamic statistics of the turbulent kinetic energy, i.e. second order moments, requires extensive amounts of data to obtain the required statistical convergence (as compared, e.g., to first order moments such as the mean velocity). at present, direct numerical simulations are unable to provide such extensive statistics, not least considering the amount of parameter variations that will be necessary to answer the underlying questions. fortunately, with recent developments in laser technology, leds, high-speed cameras and big data handling as well as particle tracking processing software, existing technology has developed to a level of maturity where these experiments are in fact feasible. and although it may still not be possible to measure the smallest relevant (dissipative) scales and the energetic and inertial scales simultaneously in the same experimental test rig, it is indeed possible to conduct two separate experiments and scale the jet in a manner that matches dimensionless numbers, such as the reynolds number, between the experiments. in order to test the range of validity of the universal equilibrium assumption and the assumed locality of the scale interactions, our group at the dtu turbulence research laboratory are in the process of establishing a state of the art laboratory tailored for these investigations. the facilities are located at, and are a part of, the department of mechanical engineering at the technical university of denmark and funded by the european research council (starting grant 803419) and the poul due jensen (grundfos) foundation. two separate experiments have thus been designed; a high-resolution [hr] and a full-field [ff] experiment to test, respectively, the hypothesis of local equilibrium (as assumed by kolmogorov) and the locality of scale interactions (the richardson cascade). in this manner, we will be able to test directly whether these two very fundamental assumptions are invalidated and if local interactions indeed lead to universal equilibrium – independently of the dynamics at the large scales. the experiments are thus designed to target the akilles heel of the main assumptions that the richardson-kolmogorov-batchelor paradigm is based upon. 1.2 the round turbulent jet – the optimal test bed common means to create non-equilibrium flows comprise spatially accelerated flow such as contractions, flows close to separation and fractal grids. in our current investigations, the aim is to create a temporal acceleration of a flow that is very close to equilibrium when stationary – the round turbulent jet. this flow is ideal to test departures from equilibrium caused by non-steadiness since it can create, isolate and quantify deviations from local equilibrium by accelerating the flow in time. the main advantages include: • the jet is close to equilibrium, because the flow achieves an approximate balance between production and dissipation of the dissipation, i.e., dε ≈ pε. so the stationary jet is expected to follow the equilibrium kolmogorov theory predictions. • the round jet was the very first flow for which the theory of kolmogorov was supported by displaying a −5/3 range in the power spectrum gibson (1962). • unlike almost all evolving flows (in time or space), the far-field jet evolves at constant re =u0δ1/2/ν, since the jet half-width δ1/2 ∼ x and the axial velocity u0 ∼ 1/x, where x is the axial distance from the jet exit. hence, any turbulent scale (e.g. the kolmogorov scale) is always proportional to any of the other scales (e.g. the taylor microscale or the integral scale). this includes the two-point equations (c.f. ewing et al. (2007); buchhave et al. (2021); hodzic and velte (2021)). • the smallest scales of interest can be made sufficiently large and slow to make direct measurements of the full velocity gradient tensor possible, and thereby also the dissipation ε. • it develops an inertial subrange even at relatively low reynolds numbers. • it can be easily accessed optically. • in the unsteady jet, the reynolds number can be readily changed by adjusting the jet exit velocity, without changing the initial conditions, thereby effectively isolating the reynolds number effects (for the same upstream profile and flow geometry). • this is also one of few flows that evolve sufficiently rapidly to be practical for these investigation purposes on laboratory scale. • it is a canonical flow that is well understood today from extensive measurements and theory developments and basically adheres to any scaling unless altered. no other flow has all these necessary properties altogether. the plane wake, the only other flow that also evolves at constant reynolds number, evolves quite slowly and is therefore often unpractical with the attainable spatial measurement (or computational) domains and without a very large and long wind tunnel. collecting data for various degrees of acceleration is thus expected to result in various degrees of nonequilibrium. since the stationary jet is (very close to) equilibrium, we expect to be able to calibrate the degree of non-equilibrium to the degree of temporal acceleration. this will result in a high-quality calibrated database that can be used to map out the missing gap between the two extremes; the kolmogorov theory and rapid distortion theory. 1.3 theory framework significant effort has been put into developing a framework that allows us to understand and analyze turbulence on a more general level, including for turbulence in flows that change with time. this includes spectral analysis and decomposition of turbulence, similarity analysis, the workings of the nonlinearities in the navier-stokes equation and better understanding the turbulent kinetic energy and dissipation transport equations and their processes. 2 flow generation facilities 2.1 test-cells – confinement in order to confine and shield the two experiments from external disturbances, each experiment resides in one of two confined test cells, separated by a control room, see figure 2. the test cells protect the free shear flows from external disturbances and provides an environment in which one can carefully control conditions of the flow as well as measurement technical aspects such as e.g. temperature, seeding density and seeding distribution between the jet and the ambient. the test cells are inwardly painted with matt black paint to reduce unwanted reflections. in hussein et al. (1994), it was established that the round turbulent jet is sensitive to generate back flow in limited confinements due to momentum conservation. to experimentally approximate a free jet, one must thus design the confinement relative to the jet exit diameter and the jet width at the downstream position at which one wishes to carry out the measurements. if this is not taken into consideration, one may risk the added consequence that the jet can be accelerated (squeezed) out of its near global equilibrium by the finite confinement. the cells have thus been generously dimensioned to reduce back-flow to approximate free jets to as high a degree as practically possible, following the guidelines in hussein et al. (1994). the cells have an inner height of 4.930m, a depth of 4.010m and a length (in the streamwise direction) of 4.600m (full-field) and 6.970m (high-resolution), respectively. test cells are thus designed such that the cross sectional area at the downstream position where we would like to measure, for each respective experiment, adheres to the following requirements: • hr: at 30 jet exit diameters downstream of the jet exit, the momentum loss is less than 95% • ff: at 38 jet exit diameters downstream of the jet exit, the momentum loss is less than 1% each test cell is equipped with four phantom v2640 cameras (288 gb) to be used for particle tracking velocimetry (ptv) and particle image velocimetry (piv) measurements. a q-switched water cooled 40w blizz laser (innolas photonic gmbh) with max repetition rates of 400khz, m2 < 1.4 tem00 at 532nm will serve as the light source in the high-resolution experiment, while the light source for the full-field experiment is yet to be confirmed. at present, commercially available leds are being employed (lavision led-flashlight 300 white). however, we are currently developing our own in-house high power led sources in several configurations for illumination of large volumes as well as exploring several additional options. in addition, we have established a ventilation system (similar to a wind tunnel) for recirculating the air in each respective test cell and provide air from the respective test cell with the appropriate seeding density to avoid conditional seeding. the jet generator is co-axial, allowing further variations of the inlet conditions. to create temporal variations, a jet modulation mechanism has been designed and constructed. both experiments have been prepared for full automatic control including monitoring signals of temperature variations, pressure ambient and across the jet contraction, jet modulation phase position and several other important parameters. the big data handling poses significant challenges, in that each measurement will require up to 288 gb of storage per camera, including handling bottlenecks for data transfer speeds. we have managed to reduce these bottlenecks so that the most time consuming aspect is the actual processing of the measurement images. all of these aspects will be described in further detail in the following. figure 2: illustration of the test cells constituting the flow confinement. the hr experiment is conducted in the left cell and the ff experiment in the right cell. between the two test cells, a control room is located. 2.2 high-resolution experiment a drawing of the complete experimental setup can be found in figure 3(a). to measure the dissipation (and even the dissipation of the dissipation), a round jet is designed large enough to produce optically and temporally resolvable scales (kη ≈ 4, where k is the wavenumber and η the kolmogorov microscale) within the reynolds numbers range defined (re ≈ 2.000− 75.000). using particle tracking techniques, the full velocity gradient tensor will be measured instantaneously. ptv algorithms have today reached a level of maturity where even spatial velocity gradients can be measured accurately. the ‘shake the box’ algorithm is particularly well suited for this, c.f. schanz et al. (2016). the practical limitations such as the resolution requirements in combination with the required size of the jet (and consequently the jet confinement), ultimately results in a magnification close to ∼ 1 : 1. light (a) complete hr setup (b) camera setup (preliminary) figure 3: (left) drawing showing the complete hr setup. (right) picture of a preliminary version of the camera setup used for dissipation measurements. budget considerations are important in these experiments, but proper imaging is still proven to be possible. another challenge with the high magnification arises in terms of the resulting large scheimpflug angles required. since such scheimpflug-adaptors are not commercially available (and are not designed to carry the heavy optics), we have developed a solution tailored for this purpose with seven degrees of freedom which is described in a companion paper, see ribergaard et al. (2021). see also figure 3(b) for a picture of a preliminary version of the camera setup. the scheimpflug adaptor is furthermore able to establish scheimpflug focusing along one or two axes, that provides more general possibilities for combining positioning and alignment compared to commonly available or traditional scheimpflug mounts. to be able to accurately trace the flow at the resolved temporal and spatial scales, ∼ 1μm seeding particles consisting of atomized oil drops will be used. preliminary light budget estimates as well as direct tests have confirmed that the particles can be properly imaged at the required scales with the existing equipment. extensive experience of the team with using these seeding tracers indicates that no significant problems with loss of seeding particles is expected within the recirculation system and hence the seeding of the jet and ambient can be considered homogeneous to a good approximation. 2.3 full-field experiment experimentally testing the degree of locality of the interactions between wavenumber components requires measurements that to some degree cover the global dynamics of the flow. this includes all three spatial dimensions and time, as omitted dimensions will be aliased onto the measured ones and thus not produce a complete and true representation of the actual flow. in the past decade, developments in volumetric ptv techniques facilitated particle tracking in relatively large volumes (above 103 cm3) compared to what was previously possible. this was demonstrated by using 300μm diameter helium filled soap bubbles and the ‘shake the box’ algorithm (schanz et al. (2016)) at khz repetition rates, c.f. barros et al. (2021). although the helium-filled soap bubbles are sufficiently large to be measured across such large domains, the commercially available ∼ 15μm air-filled tracer soap bubbles of tsi exhibit critical properties motivating us to instead employ these in our experimental investigations. some of the necessary properties of these smaller bubble traces include; a high degree of durability to keep the seeding density of the jet flow close to that of the ambient flow of the jet (including passing through contractions, screens, pumps etc.), an ability to accurately trace the flow at the scales resolved in the measurements and a high attainable seeding density so the bubbles can be uniformly and sufficiently densely dispersed in the test cell and recirculation system. furthermore, our measurements require millimeter accuracy of the ptv measurement in large volumes, which favors using 15μm soap bubbles in the current experiments. since mie-scattering is proportional to the quadratic power of the particle diameter, it is found that the required pulse energy for such large volumes is about 400 times larger than that required for the 300μm bubbles (zhang et al. (2021); abitan et al. (2021)). this corresponds to lasers with pulse energy and average power that are not available commercially and their development would be prohibitively expensive. (a) drawing of the complete ff setup (preliminary) (b) picture of the complete ff setup (preliminary) figure 4: (left) drawing showing the complete ff setup. (right) picture of the current preliminary version of the camera, led and jet setup used for global jet measurements in four-dimensions. as a consequence, between the two bubble seeding types there exists a gap in previously attained measurement volume sizes for high-speed imaging due to restrictions in light budget, see barros et al. (2021). the current measurements exist within this gap (zhang et al. (2021)). to be able to extend the field of view using the ∼ 15μm air-filled soap bubbles, several techniques have be tested and the most promising one(s) will be further developed and refined – all balanced in relation to the resolved turbulent spatial and temporal scales as described in the companion papers zhang et al. (2021) and abitan et al. (2021). the techniques for large volume ptv illumination explored comprise: • laser light sheet scanning using an acousto-optic modulator for fast velocity light sheet scanning in combination with an off-axis parabolic mirror yielding a volumetric and parallel beam scanning, see abitan et al. (2021). • multi reflections between two opposing parallel mirrors to maximize the usage of the available light, see abitan et al. (2021). • commercially available leds (lavision led-flashlight 300 white). • in-house development leds tailored for the ff experiment (under development). at present, we are using the commercial leds, see figures 4(a) and 4(b). but the most targeted effort to address this challenge constitutes developing our own in-house high power led sources in several configurations for illumination of large volumes that are seeded with 15μm soap bubbles. we develop robust electronic drivers that are suitable for driving high power leds (such as those offered by luminous). we address the heat management so that the leds will be easy to use in experiments and we investigate optics to collimate the high power leds in the most efficient manner. further, we are still exploring the first two options for risk mitigation. 2.4 jet flow generator & jet modulation the axisymmetric jet flow generator, see figure 4(a), is of a co-axial type where each nozzle can be run independently with either a chosen constant jet exit velocity or with a modulation as a zero net mass flux (a) co-axial jet nozzle (b) jet modulation mechanism figure 5: (left) co-axial jet nozzle for the ff experiment. (right) current version of jet modulation mechanism. jet. it has been designed with a constant area ratio between the inner and the outer nozzle based on a series of rans-simulations. the inner nozzle follows a 5th order polynomial contraction to create a top-hat profile in accordance with the nozzle type commonly used by the group, daehan (2001). the outer nozzle consequently has a much steeper slope. the rans simulations indicate that no separation occurs as the walls continually contract, which has been confirmed in the final jet design. the inner and outer jets can be connected to a constant volume flow or a zero net mass flux velocity modulation, respectively. the modulation mechanism, see figure 4(b), is designed to create a zero net mass flux modulation that can be coupled to either the outer or the inner jet, respectively. a cylindrical cam mechanism connected to a rocker arm drives a piston moving within a cylinder to displace the air. the rocker arm has an adjustable fulcrum, allowing variable amplifications of the linear motion produced by the cam. the design further allows the generation of a general type of periodic motion by using a cam tailored to the modulation characteristics desired. since the modulation mechanism will be subjected to heavy dynamic loads, the reciprocal moving parts have been carefully designed and dimensioned to limit the weight while retaining the strength of the construction. the modulation mechanism can be scaled to fit either of the two experimental setups. the modulation mechanism has been designed so that it, to as large a degree as possible, creates a flow that accelerates faster than the estimated eddy turnover time. however, since all theoretical considerations are in one way or another limited to equilibrium turbulence, the actual required accelerations will have to be tested and confirmed in the experiments. 2.5 air recirculation the air recirculation operates with two parallel wind tunnel recirculation circuits, each lining emanating into one of the two respective test cells, see figure 6. the two test cells have a similar design, except for the seeding and general dimensioning according to each respective volume flow. the inner and outer jets are furthermore connected to independent air recirculation systems, consisting of blowers, valves, filters, flow meters and pressure sensors. the difference between the two circuits is that the inner jet circulation has three valves to be able to alternate between injecting a steady flow of air into the inner jet directly or to replace the air circulation with the output of the jet modulation mechanism. each ventilation circuit has a flow rate capacity of 1663m3/h, corresponding to a reynolds number of 100.000 for each test cell, respectively. if both ventilation circuits are used simultaneously, e.g. for filtering out the bubble from the test cell, it is estimated to take approximately five minutes to exchange or filter out the air in the test cell. the air recirculation is controlled by the central automatic control system, which communicates with a lavision acquisition system, as well as other components, to realize automatic recording and storage. figure 6: schematic of the air recirculation system of both test cells, spanning between the ground level and the laboratory basement. 2.6 control system during active experiments, for security reasons and to not disturb the ongoing experiments, no one is allowed to reside inside the test cells. hence, operation and monitoring must take place from outside of the test cells. the two test cells therefore share a common control system that consists of a management layer, a control layer and a device layer, see figure 7. the management layer primarily provides the experiment execution plan management service, data storage and data access service. one can use the experiment execution plan management service to program the execution of the experimental plan, and use the data access service to read the data resulting from the experiment. the operator can operate the facility and monitor the status of the experiment execution process according to the experimental plan. the facility will thus be running automatically and can be supervised by a web interface, which provides real-time process data and an emergency stop functionality. three different emergency functionalities are provided with different purposes: (1) a quick stop for device fault, (2) a quick fresh air and bubble filtering response in case of unexpected door opening and (3) cut-off of all power in case the fire alarm is activated. once the experimental execution plan has been defined, the operator can start the experiment execution and check the status of all devices. the local control panel and bus connection to the central controller can be accessed through touch screen. the piv/ptv acquisition is based on a system from lavision. a quality criterion for the flow and ambient conditions of the experiment can be defined, including ambient pressure and temperature, test cell pressure and temperature, air recirculation pressure and flow rate, particle density and velocity etc.. after running steadily for a fixed amount of time, e.g. an hour, the cameras and light source(s) will receive a command to begin the recording. for experiments requiring time averaging or phase averaging, the flow generation will typically continue after recording. therefore the piv/ptv acquisition system will continue to record after storing the images in the server, as the controller keeps the running status stable. this procedure makes data acquisition of extensive statistics, in particular for non-steady turbulent flow, more practical and manageable. a database will be automatically generated for each experimental execution. this will contain the real-time process data (pressure, temperature, flow rate, velocity etc.) and the piv/ptv recordings. all the data are tagged by an acquisition number, time and recording name, so it is convenient to navigate in the history of recordings and related process data. the web service of the control system will provide an online monitoring service for all computers and mobile devices with user name and password. once the experimental measurement plan has been initiated, the experiments will run automatically. figure 7: the control system consists of a management layer (bottom), a control layer (middle) and a device layer (top). 2.7 big data handling in these experiments, significant amounts of data will be produced. the data has to be handled, processed and analyzed and all at very high speeds. the setup consists of a total of eight high-speed cameras, each producing up to 288 gb of video data per recording, which can take as little as 5 seconds. our infrastructure must be able to offload this data within a reasonable time-frame to a storage such that consecutive measurements can be done with minimal wait time. to store the data, a high-performance huawei 2.5 pb network attached storage server has been acquired, connected to the two acquisition pcs via two redundant 40 gbe fiber connections. each acquisition pc has four 10 gbe connections to the cameras and is responsible for generating the files from the data streams that the cameras deliver. the data handling structure is illustrated in figure 8. when the data is stored, dedicated processing pcs will access the video files and produce the velocity field data that is then ready for our analysis. the processing will be the bottleneck limiting the data we can put through our pipeline. the final number of processing pcs needed is currently unknown. figure 8: big data handling structure. 3 conclusions a novel laboratory for fundamental turbulence research is in the process of being established at the department of mechanical engineering at the technical university of denmark as a part of the dtu turbulence research laboratory. the objective is to test the range of validity of classical theories, including the richardson-kolmogorov-batchelor paradigm of turbulence as well as other views such as rapid distortion theory and equilibrium similarity. the experiments are designed to push the limits for the underlying assumptions, not least the principal assumption of local interactions in wavenumber space, assumed to result in universal equilibrium in the intermediate and small scales. the degree of equilibrium will be quantified for varying reynolds numbers and accelerations by direct measurements of the full dissipation rate tensor. this will also provide valuable information about the true nature (e.g. intermittency) of the dissipation. similarly, a matching, but smaller, jet will be used to reveal which processes lead to the resulting dissipation measured in the first experimental setup. do local interactions lead to the final value of dissipation? or are other kinds of processes responsible for the spectral energy flux than the classical richardson cascade? the experimental test cells will be fully operational in 2021. acknowledgements this project has received funding from the european research council (erc) under the european unions horizon 2020 research and innovation program (grant agreement no 803419). financial support from the poul due jensen foundation (grundfos foundation) for this research is gratefully acknowledged. the department of mechanical engineering at the technical university of denmark is also acknowledged for their generous additional support in establishing the laboratory. professor william k. george is acknowledged for many helpful discussions. asbjørn dyre jespersen and malthe lundsgaard are acknowledged for their contribution in developing the jet modulation mechanisms. references abitan h, zhang y, ribergaard sl, and velte cm (2021) development of optical techniques for large volume ptv measurements. in 14th international symposium on particle image velocimetry ispiv21, (virtual) chicago, illinois, usa, august 1-4 barros dc, duan y, troolin dr, and longmire ek (2021) air-filled soap bubbles for volumetric velocity measurements. experiments in fluids 36:933–947 batchelor gk (1953) homogeneous turbulence (2nd ed.). cambridge university press buchhave p and velte cm (2019) dynamic triad interactions and evolving turbulence spectra. under review, arxiv:190604756 [physicsflu-dyn] buchhave p, zhu c, and velte c (2021) similarity scaling of a free, round jet in air. in r örlü, a talamelli, j peinke, and m oberlack, editors, progress in turbulence ix. springer proceedings in physics. springer. iti conference in turbulence ; conference date: 25-02-2021 through 26-02-2021 daehan j (2001) an investigation of the reynolds-number dependence of the axisymmetric jet mixing layer using a 138 hot-wire probe and the pod. phd dissertation, state university of new york ewing d, frohnapfel b, george w, pedersen j, and westerweel j (2007) two-point similarity in the round jet. journal of fluid mechanics 577:309–330 gibson mm (1962) spectra of turbulence at high reynolds number. nature 195:1281–1283 hodzic a and velte c (2021) two-point similarity in the round jet revisited. journal of fluid mechanics hussein hj, capp sp, and george wk (1994) velocity measurements in a high-reynolds-number, momentum-conserving, axisymmetric, turbulent jet. journal of fluid mechanics 258:31–75 ribergaard sl, olesen pj, jensen ns, nielsen js, and velte cm (2021) mounting and support for pseudo biaxial scheimpflug focusing for unity-magnification, high-speed particle velocimetry. in 14th international symposium on particle image velocimetry ispiv21, (virtual) chicago, illinois, usa, august 1-4 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids velte c and buchhave p (2021) dynamic triad interactions and non-equilibrium turbulence. in r örlü, a talamelli, j peinke, and m oberlack, editors, progress in turbulence ix. springer proceedings in physics. springer. iti conference in turbulence ; conference date: 25-02-2021 through 26-02-2021 zhang y, abitan h, ribergaard sl, and velte cm (2021) a novel volumetric velocity measurement method for small seeding tracers in large volumes. in 14th international symposium on particle image velocimetry ispiv21, (virtual) chicago, illinois, usa, august 1-4 14th international symposium on particle image velocimetry – ispiv 2021 chicago, usa, august 1-4, 2021 adjustable interogation window for 2d piv estimation based on local lagrangian coherency ali rahimi khojasteh1∗, dominique heitz1, yin yang1 1 inrae, opaale, f-35044, rennes, france ∗ correspondent author: ali.rahimi-khojasteh@inrae.fr abstract we present a novel approach to adjust shapes of the interrogation windows (iw) in particle image velocimetry (piv) measurements as a function of temporal and spatial local coherent motions. lagrangian coherent structures (lcs) has been widely utilized to determine local flow boundaries. we propose using finite-time lyapunov exponent (ftle) to quantify lcs separatrix boundaries (i.e. ridges) and adjust the interrogation window. we integrated the proposed method with a local optical flow piv algorithm. the evaluation was performed using synthetic particle images of 2d homogeneous isotropic turbulence obtained from direct numerical simulation (dns). the results showed significant improvements in regions with complex flow behaviours, particularly shear, vortex and hyperbolic motions. we studied improvements of the velocity estimation in a real experiment of the wake flow behind a cylinder at reynolds number equal to 3900. it was found that optical flow featured by coherency based interrogation window (coherent optical flow) reveals detailed vector field estimations in regions with complex behaviours inside the wake flow. 1 introduction in particle image velocimetry (piv) algorithms, both correlation-based and local optical flow techniques rely on the interrogation windows. the importance of interrogation window has been studied widely for obtaining effective methods of adapting the window size and shape, which directly impacts the spatial accuracy of velocity estimation [1, 2, 3]. since the flow behaviour inside the interrogation window has clusters of small and large scale coherent motions, piv techniques involve window size reduction to avoid those non-coherent areas and increase the maximum achievable spatial resolution. generally, the interrogation window size is gradually reduced based on empirical precalculations and tunings, while this empirical approach can be adjusted by temporal and local spatial information. this means flow behaviour in different times and spaces would result in different interrogation window shapes, which is the main objective of this paper. to demonstrate the performance of the proposed method, we integrated the adjustable interrogation window with the local optical flow piv algorithm. in the local optical flow approach, all pixels inside the window are considered for calculating a single-pixel velocity at the centre of the window. however, to estimate more accurate motions, it is crucial to ignore areas that are non-coherent with the centre pixel. this study seeks to adjust the interrogation window shape in motion estimation by calculating locally coherent and non-coherent areas. we propose performing lagrangian coherent structures (lcs) by looking for the local separatrix ridges that divide the flow field into clusters of coherent regions [4]. the idea of applying lcs in particle image velocimetry (piv) / particle tracking velocimetry (ptv) algorithms was demonstrated by khojasteh et al. [5]. to this end, all neighbour pixels inside the interrogation window must be classified as coherent or non-coherent with the centre pixel. similar interrogation window adjustment can be implemented in cross correlation-based piv techniques. 2 local optical flow classic optical flow works under the intensity consistency assumption of the acquired images that is inspired by horn and schunck [6] formulation. it can be also written in terms of the optical flow constraint equation (ofce) as following, target pixel coherent pixels non-coherent pixels coherent vector field non-coherent vector field attracting lcs repelling lcs figure 1: schematic of window adjusting based on lagrangian coherency to calculate velocity for a centre pixel (dark grey pixel), attracting and repelling separatrix lines, grey pixels are coherent with the centre pixel and coherent pixels d f dt = +υ.∇ f , (1) where v is the desired velocity of one time step and f is the image intensity. the operator ∆ denotes gradient over 2d area. on the other hand, we try to minimise the energy function with intensity consistency assumption. however, real piv images are featured with temporal changes of intensity between consecutive images due to illumination and trigger setup. so this assumption can be violated in piv applications. schuster et al. [7] improved the intensity inconsistency problem by introducing stochastic optical flow formulation. in the stochastic approach, the eulerian flow velocity field is decomposed into a large-scale smooth component and a small-scale turbulent component. in the present study, we use the same stochastic approach implemented into the lucas-kanade optical flow estimator [7]. in theory, optical flow provides one velocity vector for each pixel of two consecutive images based on spatial and temporal variations of the image intensities. while cross correlation based piv techniques result in coarse resolution estimation. therefore, optical flow piv techniques might provide more details of the flow behaviour in turbulent flows. 3 coherent interrogation window lagrangian coherent structures (lcs) divide the local flow field into regions of coherent motions [4]. lcs is also known as the skeleton of flow that can be utilised as a deterministic criterion to shape the interrogation window. we computed the lcs separatrix ridges using finite-time lyapunov exponent (ftle) by employing modified versions of two open-access codes named lcs kit [8] and lcs tool [9]. ftle is a scalar value that measures the amount of spatial stretching over a finite time. in this study, the spatial region is determined by the interrogation window to compute the ftle value locally. khojasteh et al. [10] showed that using ftle in the local spatial regions over sparse neighbour particles can reveal signs of local ridges that can be employed in the velocimetry algorithms. ftle analysis provides spatial and temporal flow field behaviour. we propose to adjust the interrogation window based on separatrix ridges, resulting in different window shapes in space and time. the window shape will not change if the area is entirely coherent. on the other hand, the shape of the interrogation window does not change if all pixels are coherent with the target pixel. the major problem happens when the interrogation window consists of multi-scale dynamics. figure 1 is a classic example of hyperbolic flow when two or more vortices interact with each other in 2d turbulent flows. forward and backward ftle calculations determine two attracting and repelling lines, where flow optical flow 1 128 256 1 128 256 p ix el 0 0.12 r m s er ro r coherent optical flow 1 128 256 1 128 256 coherent optical flow 1 128 256 pixel 1 128 256 0 9 a n gu la r er ro r optical flow 1 128 256 pixel 1 128 256 p ix el optical flow 1 128 256 1 128 256 p ix el 0 0.05 v or ti ci ty er ro r coherent optical flow 1 128 256 1 128 256 figure 2: angular error comparison between local optical flow with and without coherent adjustable window in three scenarios locally selected from 2d homogeneous isotropic turbulence: a), vortex flow; b), shear flow; c), hyperbolic flow. only high values of angular error are shown. figure 3: angular error comparison between local optical flow with and without coherent adjustable window in three scenarios locally selected from 2d isotropic homogeneous turbulence: a), vortex flow; b), shear flow; c), hyperbolic flow. only high values of angular error are shown. particles do not cross these lines. flow motions in between these boundaries have coherent motions. depending on the centre location, coherent flow motions (in the blue vector field) and regions (in yellow pixels) are on one side of these lines (see figure 1). any pixel inside the coherent region is considered for the spatial and temporal gradient of intensity computation. we need to have prior knowledge about the velocity field to compute the ftle map. the minimisation process in the optical flow is an iterative approach. we found that it is unnecessary to compute the whole iterative process with additional lcs computations since it is costly in time. therefore, we introduce the lcs computation in the last three iterations of the minimisation process. in this way, we provide near to the final solution vector field for the first lagrangian separatrices computation. 4 results and evaluation 4.1 synthetic evaluation we performed synthetic analyses to examine the performance of the proposed technique. the synthetic piv images were generated from direct numerical simulation (dns) of a 2d homogeneous isotropic turbulent flow. the boundary condition of each side of the domain was set at periodic. the dns resolution was 256×256 mesh cells. we created the synthetic particle trajectories using linear euler transport function in time and linear velocity interpolation in space. more details of the dns simulation can be found in [11]. we assessed improvements of using coherent interrogation window in velocity estimation results of local optical flow technique. as a result, three terms, including rms (representing the magnitude of velocity estimation), vorticity, and angular errors, were defined to quantify the local and overall performances of the proposed technique. in an overall view, as shown in figure 2, we gained around 5% global increase in accuracy of velocity estimation compared with the classic local optical flow. however, it should be noted that the main objective here was to increase the resolution and accuracy around separation and non-coherent areas. without using adjustable windows, cross-correlation and optical flow techniques would result in up to 50% false estimation at those separation and non-coherent areas. in detail view, figure 3 shows improvements in three specific flow behaviours, vortex, shear and hyperbolic flows selected locally from 2d synthetic data. these three regions are intentionally picked to illustrate differences in detailed motions. we found that local optical flow with square iw suffers from inaccurate angular estimation compared with the dns reference in the core vortex regions when the interrogation scale is larger than the vortex scale. disagreement hits over 7 degrees of angular vector field misestimation, with over 50% angular error. figure 3 shows significant 1 500 1000 pixel 1 500 1000 p ix el -2.5 -1.5 -0.5 0 0.5 1.5 2.5 v el o ci ty er ro r (p ix el / d t) figure 4: angular error comparison between local optical flow with and without coherent adjustable window in three scenarios locally selected from 2d isotropic homogeneous turbulence: a), vortex flow; b), shear flow; c) hyperbolic flow. only high values of angular error are shown. local improvements in such a region if an adjustment is performed. similar motion refinements were also observed when high shear or hyperbolic behaviour occurs. we found that coherent optical flow has better velocity estimation in complex local regions. these local improvements impact the overall assessment of the technique in a global view as well. 4.2 experiment case study we performed a 2d2c piv experiment of the wake behind a cylinder in the wind tunnel to study the capability of the proposed technique on real experiment images. the reynolds number corresponding to the cylinder with 12 mm diameter was set at 3900. an scmos camera with 2560×2160 pixels was employed to acquire images in 49.2 hz frequency. the measurement plane was illuminated using a 200 mj laser (evergreen from quantel). the disparity of the velocity estimation between optical flow with and without adjustable interrogation window of the current experiment is shown in figure 4. as mentioned in section 3, the window shape stays unchanged if the flow motion is coherent inside the interrogation window. this means that disparity should be almost zero in the majority of freestream regions. in agreement with the synthetic analysis, coherent adjustable window only refined velocity estimations of complex motions such as shear, wake, and mixing regions (see figure 4). we, therefore, compared our proposed technique with the cross-correlation results obtained from davis software (10.1.2 version). a snapshot of the instantaneous vorticity and vector fields are shown in figure 5 that is illustrating the existence of complex mixing and vortex generations downstream of the cylinder. the vorticity field shows signs of strong shears in two sidewards of the wake immediately downstream of the cylinder (x/d< 4). these regions are featured by high velocity and acceleration gradients. we compared the cross-correlation results with coherent optical flow, knowing that the synthetic analysis showed significant misestimation in such regions (see figure 5.a). a 2d sliding average filter was used for both techniques for the image pretreatment. the cross-correlation final spatial resolution was 16 pixels with multi-pass vector calculations starting from 64×64 down to 16×16 and 75% overlap. as mentioned in section 2, the resolved resolution of coherent optical flow is the same as the camera resolution. therefore, the comparison was performed between high resolution coherent optical flow and coarse resolution cross-correlation results. the vector field estimations of coherent optical flow and cross-correlation piv techniques captured shear 1 1280 2560 pixel 1 1080 2160 p ix el -0.75 -0.5 -0.2 0 0.2 0.5 0.75 #103 v or ti ci ty (1 /s ) coherent optical flow davisa b c a c b figure 5: instantaneous snapshot of vorticity and vector fields obtained from the piv experiment at a reynolds number equal to 3900: a), local view of the vector field estimation comparison between coherent optical flow and davis cross correlation in high shear region; b), comparison of vector estimation inside the wake region; c), comparison of vortex estimation. with high gradient vector change. in contrast, coherent optical flow estimated detailed vector change in normal to shear direction with smooth change of vectors representing more physics of the flow behaviour. figure 5.b shows complex vortex and mixing inside the wake region. we found that the centre of the vortex is not aligned in two techniques. there is roughly 3 pixels shift between two estimations. coherent optical flow maintained smooth rotation with a stretch in diagonal directions. moreover, the vector field is decreasing gradually toward the vortex centre. however, the cross-correlation technique only captured the large scale motion with a weak signature of stretching in the diagonal direction. the third local comparison is in the formation region with a strong vortex (see figure 5.c). similarly, we observed disagreement in the vortex centre estimation between the two techniques while the large scale motions are almost equal. the upper right corner of the vortex is nearby of the large velocity motions (see figure 5.c). by contrast, the vortex centre is located inside the wake, with drastically lower velocity values. such a gradient associated with the flow rotation creates a complex local region for piv estimation. comparison of two techniques shows that using a coherent adjustable interrogation window resolves more details of the flow field than the classic cross-correlation techniques. 5 conclusion a novel approach to adjust the piv interrogation windows based on local spatial and temporal coherent motions is proposed. we quantify the coherent and non-content regions using lagrangian coherent structures (lcs) as skeletons of flow. the synthetic analysis showed that coherent optical flow locally improves the velocity estimation accuracy up to 50%. the main advantage of the proposed technique was the improvement in angular estimation in regions with high velocity and acceleration gradients. we also demonstrated our coherent optical flow performance in a real piv experiment of the wake behind a cylinder at reynolds number equal to 3900. the experiment case study revealed well-resolved velocity estimations in complex motions such as high shear, wake, and mixing regions. references [1] raf theunissen, fulvio scarano, and michel l. riethmuller. spatially adaptive piv interrogation based on data ensemble. experiments in fluids, 48(5):875–887, 5 2010. [2] bernhard wieneke and karsten pfeiffer. adaptive piv with variable interrogation window size and shape. in 15th international symposium on applications of laser techniques to fluid mechanics, lisbon, 2010. [3] raf theunissen, fulvio scarano, and michel l. riethmuller. an adaptive sampling and windowing interrogation method in piv. in measurement science and technology, volume 18, pages 275–287. institute of physics publishing, 1 2007. [4] george haller. lagrangian coherent structures. annual review of fluid mechanics, 47:137–162, 2015. [5] ali rahimi khojasteh, yin yang, dominique heitz, and sylvain laizet. lagrangian coherent track initialisation (lcti). in arxiv, volume 9, 2021. [6] berthold k.p. horn and brian g. schunck. determining optical flow. artificial intelligence, 17(13):185–203, 1981. [7] romain schuster, dominique heitz, and etienne mémin. motion estimation under location uncertainty, application to large-scale characterization of a mixing layer. in 19th international symposium on the application of laser and imaging techniques to fluid mechanics, pages 16–19, 2018. [8] shawn c. shadden, john o. dabiri, and jerrold e. marsden. lagrangian analysis of fluid transport in empirical vortex ring flows. physics of fluids, 18(4):1–11, 2006. [9] kristjan onu, florian huhn, and haller haller. lcs tool: a computational platform for lagrangian coherent structures. journal of computational science, 7:26–36, 2015. [10] ali rahimi khojasteh, dominique heitz, yin yang, and sylvain laizet. lagrangian coherent track initialisation. in 3rd workshop and 1st challenge on data assimilation & cfd processing for piv and lagrangian particle tracking, 2020. [11] dominique heitz, etienne mémin, and christoph schnörr. variational fluid flow measurements from image sequences: synopsis and perspectives. experiments in fluids, (3):48, 2010. introduction local optical flow coherent interrogation window results and evaluation synthetic evaluation experiment case study conclusion 14th international symposium on particle image velocimetry – ispiv 2021 chicago, usa, august 1-4, 2021 pressure from data-driven-estimated velocity fields using snapshot piv and fast probes marco raiola1∗, junwei chen1, stefano discetti1 1 universidad carlos iii de madrid, aerospace engineering research group, madrid, spain ∗ mraiola@ing.uc3m.es abstract this work explores the use of data-driven techniques to retrieve time-resolved information from snapshot piv by exploiting the information from synchronized high-repetition rate sensors measuring flow quantities in few points, and to compute from it the instantaneous pressure field leveraging the navier-stokes momentum equation of the flow. this work focus on a technique rooted in the extended proper orthogonal decomposition, which already proven good performances in estimating time-resolved velocity fields from a finite number of probes synchronized with field measurements. the performances of the technique and its robustness to noise are tested on 2 synthetic dataset, a laminar one and a turbulent one, and compared to the most commonly applied technique to retrieve time-resolved information from snapshot piv which exploits taylor’s hypothesis. 1 introduction the availability of three-dimensional three-components (3d-3c) velocity fields, with time-resolution (thus 4d-3c) has open the path in the last decade to the measurements of pressure fields (van oudheusden, 2013; van gent et al., 2017). this is normally achieved enforcing the validity of the momentum equation: ∇p =−ρ du dt +µ∇ 2u = f(u) (1) where µ is the fluid dynamic viscosity, du/dt is the lagrangian acceleration, and ∇ is the gradient operator. when the full 3d velocity and acceleration (either eulerian or lagrangian) is available, the above equation, or equivalent formulations derived from it, enables the estimation of 3d instantaneous pressure fields. such information can be exploited, for instance, for the study of unsteady pressure forces on surfaces or to locate noise source. this approach is possible for low-speed flows, for which hardware for time-resolved measurement is available, thus allowing to directly measure du/dt. for medium/high reynolds number measurements, where time-resolution is often not available, the pressure can be obtained only under strong assumptions, such as selection of the magnitude of the convection velocity (van der kindere et al., 2019) or non-dissipative advection of vortices (schneiders et al., 2018). a promising approach to obtain time-resolution from standard low-repetition-rate equipment is the combination of piv with fast point probes located strategically in the flow field. statistical evidence of correlation between probe and field measurements can be enforced to train the probes to estimate flow fields. one popular solution is based on extended proper orthogonal decomposition (epod, borée 2003), which relates the most relevant features observed on synchronized measurements of flow fields and probe data via modal analysis. the method was implemented and successfully applied in the past years (tinney et al., 2008; hosseini et al., 2015), with particular success in flows with dominant frequencies which allow a compact representation with only few relevant modes. discetti et al. (2018) proposed an implementation including a robust filtering, which enabled the application to spectrally-rich turbulent flows and demonstrated its feasibility in an unprecedented high-reynolds-number pipe-flow experiment in the ciclope facility (discetti et al., 2019). in this work we combine simultaneous non-time-resolved field measurements and time-resolved pointwise measurements to achieve the time resolution needed to obtain pressure fields from the integration of the momentum equation. the field estimation is carried out using epod and the virtual probes method (hosseini et al., 2015; discetti et al., 2018). the method consists in enforcing the correlation between field and probe data by including for each snapshots the data recorded by the probe within a time segment (i.e. not only at the same instant the snapshot was recorded). for convective flows, this is equivalent to have an additional set of virtual probes, thus making available more information to establish the correlation between field and probe data. whether the reconstructed fields are of sufficient quality to be used for pressure estimation from eq. 1, it is still an unexplored field. the method is tested using a dns-database of the wake of three cylinders in a configuration referred as fluidic pinball (deng et al., 2020) and a dns-database of a turbulent channel flow from the johns hopkins turbulence database (jhtdb, li et al., 2008). 2 epod-based estimation of time-resolved velocity fields pod (proper orthogonal decomposition) is an unsupervised learning data-driven method to obtain modal decomposition of datasets. this method splits the velocity field data into the weighted sum of modes (both temporal and spatial) orthogonal to each other and arranged by decreasing energy content. assume that nt snapshots of the fluctuating velocity field are arranged into a matrix u, where each row (with length np) contains the velocity components in all the nodes of the domain. the matrix u (of size nt × np, where typically nt ≤ np) can be decomposed by the economy-size singular value decomposition (svd), i.e. u = ψσφ t (2) in the decomposition of eq. 2, the columns of the nt×nt orthogonal matrix ψ contains the temporal modes ψi, the columns of the nt × np orthogonal matrix φt contains the spatial modes φi , σ is a square diagonal matrix containing the singular values σi arranged in a decreasing order. the same decomposition can be applied on the probe snapshot matrix upr containing velocity data from s high-frequency probes synchronized with velocity field measurements. in order to increase the quantity of probe data available for each snapshot, the virtual probe approach (sicot et al., 2012; hosseini et al., 2015) is employed: for each physical probe, a time-resolved sequence of q probe samples is extracted after the velocity field sampling time and considered as additional probes under the taylor’s hypothesis. this results in a matrix upr with nt rows (as the velocity field snapshots) and ntt = s× q columns which can be decomposed as upr = ψprσprφ t pr (3) for the problem under investigation, the extended pod modes φe corresponding to the field measurements can be estimated as ψ t pru = σeφ t e = φ t prψσφ t = ξσφ t (4) where the subscript e refers to extended pod modes and the matrix ξ = ψt prψ is a matrix containing the information about the temporal correlation between field and probe modes. knowing the pod spatial modes (φ and φpr) and singular values (σ and σpr) of the velocity field and of the probe snapshot matrix, as well as the temporal correlations matrix ξ, it is possible to estimate the velocity field uest at an off-sample instant from a probe data snapshot use sampled at that instant: uest = useφprς −1 pr ξσφ t = ψestσφ t (5) as shown by eq. 5, the estimation of the velocity field depends on all the probe modes through the matrix ξ, accounting also for mode interaction. while this approach removes the need for multiple-time delays (used for instance in multi-time delay linear stochastic estimation), it also might result in a contamination of the estimation from spurious correlations between flow field and probe modes. to this purpose, discetti et al. (2018) proposed to filter out low-correlation entries from the matrix ξ leveraging on the consideration that uncorrelated random modes might still produce a non-null random entry in ξ with a standard deviation equal to n−0.5 t . the entries ξi j in the matrix ξ are therefore truncated following the 3-sigma rule ξi j = 0, when − 3 √ nt ≤ ξi j ≤ 3 √ nt , i, j = 1,2, ...,n (6) (a) (b) (c) figure 1: (a) pressure from dns, (b) pressure estimated using iterative method, (c) error of pressure estimation. which, on the hypothesis that the spurious-correlation entries follow a normal distribution, guarantees that 99.7% of them are removed. while this approach is extremely robust to noise, it might also cut out a small portion of the actual correlation between probes and flow fields. this approach will be referred to as ξ-filtered approach in the reminder of the paper. the need of filtering the estimation is especially relevant for pressure reconstruction, since spurious correlation might produce unacceptable levels of noise on the estimated fields, which are later amplified by the time derivative. other alternatives for the filtering are based on the time-filtering of the estimated temporal mode ψest .in the present work a 6th order low-pass butterworth filter with cutoff frequency of 0.05 times of data sample rate is applied to the coefficient of every mode. this approach will be referred to as ψ-filtered approach in the reminder of the paper. 3 pressure integration algorithm from velocity field data since the time-resolved fields to compute the lagrangian acceleration are obtained through a process of estimation from point probes, it is possible that noise is amplified in the process. for this reason, a technique with high robustness to noise is implemented for integration of the pressure gradient. the pressure is estimated by integrating eq. 1 using a finite-differences version of the modified richardson iteration method (richardson, 1910). for each point xm in the domain, the iteration uses the value in the surrounding points xn to refresh it, enforcing the pressure gradient ∇p = f(u) from the momentum equation pi+1(xm) = 1 n n ∑ n=1 (pi(xn)+ f(u)|x′n · (xm−xn)) =pi(xm)+ 1 n n ∑ n=1 (f(u)|x′n · (xm−xn)− pi(xm)− pi(xn) |xm−xn| (|xm−xn|)) =pi(xm)+ 1 n n ∑ n=1 (f(u)|x′n−∇pi|x′n) · (xm−xn) (7) where n is the number of neighbouring points (for a cartesian grid, 4 in 2d, 6 in 3d), the gradients are calculated in the middle point x′n = (xm +xn)/2 to reduce truncation error, and i is the index of iteration. a relaxation parameter ω < 1/n is introduced into eq. 7, which becomes pi+1(xm) = pi(xm)+ω n ∑ n=1 (f(u)|x′n−∇pi|x′n) · (xm−xn) (8) points outside the domain are excluded from the computation in eq. 8 when xm is near the boundary, thus reducing n. the iteration is initialized with p0 = 0, updates globally, and interrupts when the difference between the pressure in two loops is below a threshold ε, i.e. when ‖pi+1− pi‖2 < ε, where ‖ · ‖2 is the (a) (n) 35 30 25 20 15 10 5 0 100 80 60 40 20 0 n / i [% ] i= 1 n t 2 2 i / i [% ] n t i= 1 2 2 i= 1 n (b) | field mode number (j) p ro b e m o d e n u m b er ( i) 0 100 200 300 400 100 200 300 400 0 0.02 0.04 0.06 0.08 0.1 |ξij| figure 2: (a) kinetic energy (blue) and cumulative kinetic energy (red) contained in the first 24 pod modes of flow field; (b) absolute value of ξ for the fluidic pinball test case. l2 distance over all the points of the domain and the threshold ε = 10−5 is determined accordingly to the maximum accuracy of pressure that can be attained depending on velocity field data precision. iterative methods have been used in pressure estimation before by tronchin et al. (2015). in their algorithm, the pressure value in xm is updated using the first row of eq. 7, i.e. only using of the pressure in the surrounding points and the gradient, without including the value of pressure in xm. this causes it harder to converge when the noise or error in the pressure gradient is significant. besides, the global update in this paper makes the iteration result not rely to typical integration direction. the performances of the iterative integration method described above are shown for a single snapshot of the fluidic pinball dns database in fig. 1. the dataset will be described in the following section. the estimation error is very low in most of the domain except for the top-right and bottom-right corner, where the dns grid is more sparse and the truncation error is not negligible when the data are interpolated from the dns grid to the cartesian grid. 4 validation 4.1 fluidic pinball the method is applied to synthetic data to assess the performance of the epod-based estimation of both velocity and pressure fields. the first synthetic dataset has been extracted from a 2d-dns of the wake of a fluidic pinball (deng et al., 2020). the simulation features three cylinders with radius r = 0.5 standing in the domain, whose centres form an equilateral triangle with side length equal to 3r. one cylinder is located upstream while the other two are abreast, downstream with respect to the first one, see fig. 1. the two-dimensional dns is performed at re = 130 (referred as chaotic regime, deng et al., 2020). the region selected to test the epod-based estimation is placed in the wake of the obstacles, ranging from x = 1 to x = 7 and from y = −3 to y = 3. the velocity data are interpolated on a cartesian grid with distance between two adjacent points of 0.08 in order to simulate the results of a piv experiment. five point probes measuring the 2 inplane components of velocity, each recording 60 samples-per-frame at a sample rate of 1/0.08, are placed at the downstream edge of the region (x = 7), with a spacing of 1 in the y direction. the training dataset is composed of 4685 velocity field snapshots as well as of the synchronized virtual probe data, forming the matrices u and upr, respectively, as reported in §2. the snapshots are selected to have a temporal spacing of 0.88. fig. 2a reports the energy distribution of the pod modes (λi = σ2 i ) with blue line, as well as the accumulated energy distribution with red line, after normalization with the total energy. the first few pod modes contain most of energy, over 95% of the total energy are in the first 12 modes. fig. 2b shows the absolute value of the upper-left portion of unfiltered matrix ξ, which is representative of the correlation between the ith temporal mode of probes and the jth temporal mode of flow field, where the i and j is the number of row and column in ξ. the matrix ξ shows a clear diagonal dominance for at least the first 100 modes, which indicates an almost biunivocal correspondence between probe and field modes. as the number of mode is increased this dominance disappears and each probe mode tends to correspond to a larger number of field modes. the performances of the ψ-filtered epod estimation are reported in fig. 3 for a single snapshot not included in the training dataset, both in terms of flow field (fig. 3a-b) and in terms of pressure (fig. 3c). the dns data are reported for comparison (fig. 3a-c) as well as the error of the estimation with respect to the dns (fig. 3f-h). the error mainly affects the streamwise velocity component in the wake region (from x = 2 to x = 4), producing an error pattern which suggests the misplacement of flow structures in the y-direction. the crosswise velocity component shows lower levels of error, still localized in the same region. the localization of the reconstruction error might be an effect of the presence of intense small-scale flow features, strongly subjected to stretching and deformation. additionally, this region stands farther from the probes. these two aspects contribute in the reduced capability of the probes to sense accurately the fluctuations in this region. despite the presence of the error on the velocity field, the pressure reconstruction is affected by considerably lower levels of estimation error, suggesting that the integration is smoothing down the error in the spatial derivatives. a more precise assessment of the estimation error has been carried out using the rms of the error with respect to the dns over 1500 estimated snapshots not included in the epod training dataset and which constitutes the testing dataset. the assessment includes also the estimation through the taylor’s hypothesis (th), which is, to date, the most common option to estimate time-derivatives from snapshot piv (van der kindere et al., 2019). taylor’s hypothesis relies on the assumption that the flow field fluctuations are advected with a velocity corresponding to the ensemble-averaged flow field ū, i.e. ∂u′/∂t =−(ū ·∇)u′. this enables the estimation of the time derivative of velocity, and thus of the pressure, for a measured snapshot. additionally, the th can be used to propagate the measured frame in time, obtaining an estimated time-resolved sequence of velocity fields. the simplest way to fulfill it is by means of a unidirectional euler propagation, which is u(t0 +dt) = u(t0)+ ∂u ∂t ∣∣∣∣ t0 dt = u(t0)− (ū ·∇)u′(t0)dt (9) in the present case, the time-resolved sequence has been estimated with th using a 4th order runge-kutta method. fig. 4 shows the rms estimation error for the unfiltered epod estimation (fig. 4a-c), the ξ-filtered epod estimation (fig. 4d-f), the ψ-filtered epod (fig. 4g-i) and the estimation using the taylor’s hypothesis (th). fig. 4 reports the error on the streamwise component of velocity on the left column (fig. 4a,d,g), the error on the time-derivative on the streamwise component of velocity in the central column (fig. 4b,e,h,j) and the error on pressure in the right column (fig. 4c,f,i,k). for the th, the estimation has been carried out in the least error conditions, i.e. assuming that the exact velocity field was available at the selected snapshot, thus using the th only to estimate the time derivative. despite the velocity estimation from the non-filtered epod (fig. 4a) has reasonable levels of error, the pressure estimation (fig. 4c) is affected by a large estimation error. the error on the pressure is mainly produced by the time derivative of the velocity (fig. 4b), due to the amplification of the small estimation errors in the pod time coefficients by the time differentiation. similar levels of error are present in the pressure estimation from the th (fig. 4k), also in this case produced by large errors in the time derivative (fig. 4j). the ξ-filtered epod, instead, produces slightly worse results in terms of estimated velocity fields (fig. 4d), but shows much lower errors on the time derivative (fig. 4e) and, thus, on the pressure estimation (fig. 4f). the results of the ψ-filtered epod shows, at least for the present dataset, the lowest levels of error both in term of velocity field estimation (fig. 4g) and of its time derivative (fig. 4h), which lead to very low errors in the pressure estimation (fig. 4i). it is worth to remark that the epod estimation, differently from the th, provides by default a set of timeresolved velocity fields, thus can be employed to estimate the history of velocity and pressure fluctuations, which can be employed in time-dependent studies. taylor’s hypothesis, by contrast, is generally employed to estimate the time-derivative in a measured flow field snapshot, even if it can be used to propagate the velocity field as explained above. to clarify how the propagation of th will accumulate noise, the rms error of the estimated pressure in the whole domain is plotted in fig. 5a over 60 frames (which corresponds to 1 convection time for the main flow) from the beginning of propagation. the results are compared both to the th-based pressure estimation without propagation, i.e. assuming that the exact velocity field is known at each frame, and to the epod estimation. the ψ-filtered epod estimation is the most accurate method to reconstruct time-resolved flow and pressure field series, keeping the least error all the time. the error of th without propagation has higher levels of error that the epod, but is keeping stable around a fixed value through time. the error of th with propagation is similar for the first 10 frames and starts to grow u v p 0 0.5 1 1.5 -0.5 0 0.5 -0.8 -0.6 -0.4 -0.2 0 0.2 d n s (a) (b) (c) ψ -fi lt. e po d (d) (e) (f) udns−uepod vdns− vepod pdns− pepod -0.2 -0.1 0 0.1 0.2 -0.2 -0.1 0 0.1 0.2 -0.2 -0.1 0 0.1 0.2 ψ -fi lt. e po d er ro r (g) (h) (i) figure 3: estimated and exact velocity and pressure fields for a single snapshot: (a) streamwise velocity from dns; (b) crosswise velocity from dns; (c) pressure from dns; (d) streamwise velocity from epod; (e) crosswise velocity from epod; (f) pressure from epod; (g) epod estimation error on streamwise velocity; (h) epod estimation error on crosswise velocity; (i) epod estimation error on pressure. u du/dt p 0 0.05 0.1 0.15 0.2 0.25 0 0.05 0.1 0.15 0.2 0.25 0 0.02 0.04 0.06 0.08 0.1 e po d (a) (b) (c) ξ -fi lt. e po d (d) (e) (f) ψ -fi lt. e po d (g) (h) (i) t h (j) (k) figure 4: rms error map of velocity and pressure fields estimation using the epod without filter, the ξ-filtered epod, the ψ-filtered epod and the taylor’s hypothesis. the first column shows error on the streamwise velocity, the second column shows the one on the time derivative of streamwise velocity, and the last column shows the error on pressure. (a) 0 1 2 3 4 5 t t 0 10 -2 10 -1 10 0 -filt. epod -filt. epod epod th from u(t) th from u(t 0 ) (b) 0 1 2 3 4 noise [%] 10 -2 10 -1 10 0 -filt. epod -filt. epod epod th from u(t) th from u(t 0 ) figure 5: (a) rms error of estimated pressure over the whole domain as propagates in time after the measured frame. (b) rms error of estimated pressure over the whole domain and for 10 snapshots propagation for different levels of noise in training data. ψ-filtered epod (blue circles), ξ-filtered epod (purple leftward triangles), un-filtered epod (green rightward triangles), non-propagated th (red upward triangles) and time-propagated th (yellow downward triangles). quickly after that point. in fig. 5b, the rms error of estimated pressure in the whole domain and for the first 10 snapshots after the measured one is reported for different levels of noise in the training data and probe measurement in testing data using the same methods as in fig. 5a. gaussian noise with zero mean value and standard error up to 4% of the freestream velocity is used. it shows that the ψ-filtered epod estimation has significant less error in the pressure estimation than th (whether propagation is used or not) for all the noise levels tested. by contrast, the propagated th error explodes as soon as the noise level is higher than 0.5% of the freestream velocity. 4.2 channel flow the epod estimation is validated using a second synthetic dataset extracted from the dns of a channel flow contained the in johns hopkins turbulence databases (li et al., 2008; yu et al., 2012). the dns is solved in a domain of size 8π x 2 x 3π, using 2048 x 512 x 1536 nodes, at friction-velocity-based reynolds number reτ≈ 1000, and the time interval in storage is 0.065. the epod estimation is evaluated in a training dataset composed by sub-domain of size 1 x 1 with a time interval of 2/3 of the turnover time, thus being non-time-resolved. additionally, the dataset includes 10 probes measuring the 2 in-plane components of velocity placed along the downstream boundary (x = 1) of the sub-domain spaced of 0.1 in the y direction and recording 152 samples for each snapshot with a time-spacing of 0.065, which corresponds to one subdomain turnover time. to collect enough independent snapshots, the sub-domains are extracted from different positions exploiting statistical homogeneity, similarly as to what reported in (discetti et al., 2018). the rms error map of pressure using the ξ-filtered epod estimation and the taylor’s hypothesis (both with and without propagation) are shown in fig. 6. the epod for this case is trained over 6400 snapshots. the testing dataset, instead, is composed by 240 time-resolved frames. unlike the fluidic pinball case, the un-propagated taylor’s hypothesis (fig.6b) performs better than the epod estimation (fig.6a), especially in the near wall region (0.7 < y < 1) and in the upstream boundary of the domain (0 < x < 0.1). this higher error might be explained by several reasons. firstly, the channel flow reported here is characterized by a moderate reynolds number, thus being completely turbulent and having a much larger wealth of turbulent scales (generally recovered by a larger wealth of pod modes), lowering the correlation between field and probe modes. secondly, larger turbulence introduces stronger three-dimensionality in the flow, thus further reducing the correlation level. thirdly, the channel is characterized by much lower convection velocity in the near-wall region. this means that in the temporal span recorded by the fast probes (roughly one turnover time, i.e. the time required by a fluid particle to span the entire sub-domain when convected at the centerline velocity) is not long enough to sense all the fluid structures passing. finally, the near-wall region is characterized by a stronger deformation of the small-scale fluid structures as well as by their interaction with (a) (b) (c) figure 6: rms error map of velocity and pressure fields estimation using (a) ξ-filtered epod estimation, (b) the un-propagated taylor’s hypothesis, (c) time-propagated taylor’s hypothesis. larger structures, meaning that the correlation between the field modes and probe modes is lower. despite this, the epod estimation offers reasonably good results in terms of pressure (fig.6a). additionally, epod estimation offers an inherently advantage with respect to the th in that it provides time-series for tracking the fluctuations of pressure and velocity in time. while this can be achieved also by the th by propagating in time the velocity fields, the results of such estimation contains much higher levels of noise (fig.6c). fig. 7a compares the epod estimation and the taylor’s hypothesis in recovering time-series out of an initial snapshot in terms of rms pressure estimation error over the sub-domain. as already commented, in the channel flow, the th-based estimation with no time-propagation of the flow field is superior to the epod approach. however, when the th is used also to propagate the velocity field from a single snapshot, the error increases quickly with time. on the other hand, the epod approach mantains stable levels of error through all the time sequence, producing better results than the th after 20 steps. fig. 7b reports the rms error of the pressure in the whole sub-domain and over the first 10 snapshot of propagation with different levels of noise on the velocity field data. the non-propagated th proves to be the most robust one to noise. epod, independently for the filtering method, has rather constant error independently from the noise level (the unfiltered epod has only slightly increasing noise). the th with propagation, instead, has an error which increases with the noise, even if the propagation is limited to 10 frames, proving to provide the least robust pressure time-series estimation. 5 summary a novel approach to estimate instantaneous pressure fields using snapshot piv (i.e. without time resolution) has been presented. the method is based on using synchronized field measurements from piv and point measurements using high-repetition rate probes (such as hot-wires or pressure transducers, among others). the field are then estimated at the same time resolution of the probes using extended pod, and the pressure gradient is extracted from the navier-stokes equations and integrated in space. the method has demonstrated to be sufficiently accurate to perform this task, and superior to taylor’s hypothesis if the pod reconstruction is sufficiently compact, and provided that some filtering is applied to reduce time fluctuations. the proposed approach has also the advantage of having error independent on the time when piv snapshots have been adquired, and indeed it only needs probe measurements once the training data have been captured. this opens the path to reconstruct pressure fields not only corresponding to the instants when piv fields have been captured, but also in-between snapshots, or in general in instants when piv is not available (for example, for a separate probe data sequence capture outside of the training dataset). acknowledgements this project has received funding from the european research council (erc) under the european union’s horizon 2020 research and innovation programme (grant agreement no 949085). this document reflects only the author’s view (a) 0 1 2 3 4 5 t t 0 10 -2 10 -1 -filt. epod -filt. epod epod th from u(t) th from u(t 0 ) (b) 0 1 2 3 4 noise [%] 10 -2 10 -1 -filt. epod -filt. epod epod th from u(t) th from u(t 0 ) figure 7: (a) rms error of estimated pressure over the whole domain as propagates in time after the measured frame. (b) rms error of estimated pressure over the whole domain and for 10 snapshots propagation for different levels of noise in training data. ψ-filtered epod (blue circles), ξ-filtered epod (purple leftward triangles), un-filtered epod (green rightward triangles), non-propagated th (red upward triangles) and time-propagated th (yellow downward triangles). and the agency and the commission are not responsible for any use that may be made of the information it contains. references borée j (2003) extended proper orthogonal decomposition: a tool to analyse correlated events in turbulent flows. experiments in fluids 35:188–192 deng n, noack br, morzyński m, and pastur lr (2020) low-order model for successive bifurcations of the fluidic pinball. journal of fluid mechanics 884 discetti s, bellani g, örlü r, serpieri j, vila cs, raiola m, zheng x, mascotelli l, talamelli a, and ianiro a (2019) characterization of very-large-scale motions in high-re pipe flows. experimental thermal and fluid science 104:1–8 discetti s, raiola m, and ianiro a (2018) estimation of time-resolved turbulent fields through correlation of non-time-resolved field measurements and time-resolved point measurements. experimental thermal and fluid science 93:119–130 hosseini z, martinuzzi rj, and noack br (2015) sensor-based estimation of the velocity in the wake of a low-aspect-ratio pyramid. experiments in fluids 56:13 li y, perlman e, wan m, yang y, meneveau c, burns r, chen s, szalay a, and eyink g (2008) a public turbulence database cluster and applications to study lagrangian evolution of velocity increments in turbulence. journal of turbulence 9:n31 richardson lf (1910) the approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam. philosophical transactions of the royal society a 210:307 schneiders jf, avallone f, pröbsting s, ragni d, and scarano f (2018) pressure spectra from single-snapshot tomographic piv. experiments in fluids 59:57 sicot c, perrin r, tran t, and borée j (2012) wall pressure and conditional flow structures downstream of a reattaching flow region. international journal of heat and fluid flow 35:119–129 tinney c, ukeiley l, and glauser mn (2008) low-dimensional characteristics of a transonic jet. part 2. estimate and far-field prediction. journal of fluid mechanics 615:53–92 tronchin t, david l, and farcy a (2015) loads and pressure evaluation of the flow around a flapping wing from instantaneous 3d velocity measurements. experiments in fluids 56 van der kindere j, laskari a, ganapathisubramani b, and de kat r (2019) pressure from 2d snapshot piv. experiments in fluids 60:32 van gent p, michaelis d, van oudheusden b, weiss pé, de kat r, laskari a, jeon yj, david l, schanz d, huhn f et al. (2017) comparative assessment of pressure field reconstructions from particle image velocimetry measurements and lagrangian particle tracking. experiments in fluids 58:33 van oudheusden b (2013) piv-based pressure measurement. measurement science and technology 24:032001 yu h, kanov k, perlman e, graham j, frederix e, burns r, szalay a, eyink g, and meneveau c (2012) studying lagrangian dynamics of turbulence using on-demand fluid particle tracking in a public turbulence database. journal of turbulence 13:n12 introduction epod-based estimation of time-resolved velocity fields pressure integration algorithm from velocity field data validation fluidic pinball channel flow summary abstract submission template on the unsteady dynamics of synthetic leaves: laboratory experiments using synchronized piv and dic lai wing1, dan troolin1, shyuan cheng,2 jiao sun, 2 and leonardo p. chamorro2 1 tsi incorporated, usa. 2 department of mechanical science and engineering, university of illinois, 61801, usa. abstract the unsteady 3d dynamics of various synthetic leaves and the induced turbulence are systematically studied experimentally for representative cauchy numbers in a wind tunnel under nearly uniform incoming flows. synchronized digital image correlation (dic) and high-frame-rate particle image velocimetry (piv) are employed to track the structure dynamics simultaneously and the surrounding flow field to uncover the fluid-solid interaction. a high-resolution six-axis load cell is also used to quantify the synthetic leaves' induced force and torque under various flows. the shapes of synthetic leaves inspected are representative of selected environments (e.g., calm to windy weather; tropical to temperate climate). the cauchy number is set to resemble those observed in natural conditions. this presentation will discuss insights from synchronized piv-dic techniques on the synthetic leaves' distinct behavior and wake flow response. particular emphasis is placed on characterizing flow instability and the leave shape's role in the motions and force. for this purpose, we inspected the instantaneous force and torque as well as their structure. we will also discuss the relationship between leave shapes with force and torque fluctuations linking them with the leaf motion obtained from dic measurements. in particular, the results show that selected leaf shapes experience significantly larger and distinct force and torque fluctuations and larger pitch magnitude, as shown in fig. 5. a shared monotonically decreasing trend of the nondimensional frequency (strouhal number, st = fl/u) is evidenced for standard environmental conditions. figure 1. basic geometry of the synthetic leaf shapes. figure 2. photographies of the general setup illustrating a type-5 leaf geometry. figure 3. example of an instantaneous velocity field in the near wake of a synthetic leaf. figure 4. left: tangential force fluctuation for various incoming velocities for all leaf shapes. right: non-dimensional tangential force-frequency. figure 5. left: illustration of the leaf 2 mean deformation from dic. right: pitch angle time series of leaf 2, 3 and 8 at 𝑈𝑈 = 4 m/s and 8 m/s. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 spatially and temporally resolved measurements of turbulent rayleigh-bénard convection by lagrangian particle tracking of long-lived helium-filled soap bubbles j. bosbach*, d. schanz, p. godbersen, a. schröder department of experimental methods, institute of aerodynamics and flow technology, german aerospace center (dlr), göttingen, germany * johannes.bosbach@dlr.de abstract we present spatially and temporally resolved velocity and acceleration measurements of turbulent rayleighbénard convection spanning the whole volume (~ 1 m³) of a cylindrical sample with aspect ratio one. with the "shake-the-box" (stb) lagrangian particle tracking (lpt) algorithm, we were able to instantaneously track up to 560,000 particles, corresponding to mean inter-particle distances down to 6 8 kolmogorov lengths. we used the data assimilation scheme ‘flowfit’, which involves continuity and navier-stokesconstraints, to map the scattered velocity and acceleration data on cubic grids, herewith recovering the smallest flow scales. lagrangian and eulerian visualizations reveal the dynamics of the large-scale circulation and its interplay with small scale structures, such as thermal plumes and turbulent background fluctuations. as a result, the complex time-dependent behavior of the lsc comprising azimuthal rotations, torsional oscillation and sloshing can be extracted from the data. further, we found more seldom dynamic events, such as spontaneous reorientations of the lsc in the data from long-term measurements. 1 introduction rayleigh-bénard convection (rbc), where a fluid is heated from below and cooled from above under welldefined conditions, is the most generic type of thermal convection and a configuration suited ideally to study the fundamentals of buoyancy driven flows (bodenschatz et al. 2000; chillà and schumacher 2012). it is characterized by three dimensionless parameters, which are the aspect ratio , the prandtl number pr and the rayleigh number ra. herewith, the aspect ratio is defined by  = d/l, d being the diameter and l the height of the fluid sample while the prandtl number pr = is a fluid property and given by the ratio of kinematic viscosity and thermal diffusivity . the actual driving of the flow due to the applied temperature gradient is quantified by the rayleigh number, which is a dimensionless measure for the ratio of buoyancy and dissipative forces and given by ra = gl³t/(),  and g being the isobaric thermal expansion coefficient and the acceleration of gravity, respectively. in many fluids of practical relevance, even for moderate temperature gradients, ra is already above a critical value such that the convective flow between the plates is turbulent. a prominent feature of the turbulent rb system is the presence of a large-scale circulation (lsc). it develops from self-organization of the thermal plumes, that erupt from the top and bottom thermal boundary layers. in cylindrical fluid samples of aspect ratios close to one with a high degree of symmetry, the lsc reveals complex shortand long-term dynamics involving rotations, cessations and restarts (brown and ahlers 2006a), torsional oscillations (funfschilling et al. 2008; zhou et al. 2009) and sloshing modes (zhou et al. 2009). even the earths coriolis force was found to influence the long-term motion of the lsc (brown and ahlers 2006b). although the dynamics of the lsc in turbulent rbc has gained much attention in the past, direct volumetric measurements of the lsc are still rare. while tomographic piv (paolillo et al. 2018; schiepel et al. 2018) or lpt (liot et al. 2017; schiepel et al. 2018) measurements have been reported recently, measurements at full spatial and temporal resolution covering the whole sample were still lacking. the same holds for direct measurements of the velocity fields of the lsc and its lagrangian transport properties. to bridge this gap, we performed the experiments and analyses described in the following. 2 experimental set-up 2.1 rbc apparatus we developed a dedicated convection experiment, which allowed generating classical turbulent rbc and at the same time application of time-resolved lpt in the whole fluid volume (figure 1). the convection cell has an aspect ratio of  = 1 and a height of l = 1.1 m. by using air at atmospheric pressure as working fluid (pr ~ 0.7), rayleigh numbers up to ra ~ 109 could be reached with moderate temperature differences. figure 1: convection cell (left) and optical set-up with six scientific cmos cameras and array of pulsed leds for time-resolved lpt with long-lived hfsb (right) (photographic work by j. agocs) thermal control of the experiment is enabled by an electrically heated aluminum plate with a thickness of 15 mm and a water-perfused cooling plate, which allows for illumination of the sample from the top. for the sake of a high particle image quality, the sidewall consisted of two bended sheets of acrylic glass with a thickness of 2 mm only. the heating plate and the rear part of the sidewall were covered with a self-adhesive, matte black foil to reduce optical reflections and stray light from the light source to a minimum. for the temperature measurements, a dedicated temperature logger based on an array of integrated ics with constant current source, 24-bit adc and i2c interface was built for this purpose and operated in combination with 1/3 din b pt1000 resistance temperature detectors (rtds), connected in four-wire mode. the sensors were placed at three positions in the heating plate, at the inand outflow of the cooling plate and at two positions in the air surrounding the cell. 2.2 long-lived helium-filled soap bubbles due to the large dimensions of the experiment, tracer particles suitable for air as working fluid with high scattering efficiency are required. for this purpose, sub millimeter helium filled soap bubbles have been established as the tracer of choice for mixed convective flows (bosbach et al. 2009; kühn et al. 2009, 2012) and recently for low speed wind tunnel (gibeau et al. 2020; schanz et al. 2019; scarano et al. 2015) and even free field tests (spoelstra et al. 2019). however, their application to rbc was impeded by the limited lifetime before. hence, specifically for investigation of large-scale thermal convection, we developed a bubble film solution (bfs), which provides a much longer bubble lifetime as compared to commercial fluids and thus allows for measurement runs as long as 30 minutes. herewith, the main constraint was given by the necessity that we wanted the nozzle design to remain unchanged, which limited the amount and candidates of polymers, which could be used in the bfs. the final solution is composed besides water and additives of minor impact by a mixture of several surfactants and polymers. herewith, the challenge was to provide as stable as possible operation while maintaining the required shell thickness for neutral buoyancy conditions (~ 60 nm). the hfsb were generated with the orifice nozzle of dlr (bosbach et al. 2009) in combination with a commercial hfsb controller (lavision). the resulting hfsb have a mean diameter of 370 µm. however, while we tried as good as possible to maintain a continuous generation by the nozzle, the operation retained slightly intermittent with productive phases (see figure 2 (left)) and null phases changing at a rate of the order of 1 hz. as an added benefit the hfsb residence time in the sample can be evaluated from the lpt data, see section 4. hereto, we evaluated the number of tracked particles for a long-term run in figure 2. an exponential function is fitted to the data (dotted line), revealing an exponential decay of n(t) after an initial rise during the first 110 time-steps to a maximum of 560,000 particles. the time constant of the exponential fit indicates a mean hfsb residence time in the rbc experiment of r = (326  5) s. for a commercial bfs on the other hand, a mean lifetime of 97 s has been measured before (huhn et al. 2017), demonstrating, that the new bfs allows for a tremendous extension of the hfsb life time. figure 2: shadowgraph of hfsb generation (productive phase) (left). number of tracked particles n(t) and intensity of reconstructed particles ip(t) for run 30, evaluated at every 10th time-step (right). the dotted line is a fit of an exponential function with a time-constant of r = 326 s. the lpt data further revealed, that the residence time of the particles is not only influenced by the limited lifetime but also by a settling velocity of ~1.4 mm/s, which had to be accepted as a tradeoff between lifetime and achievable shell thickness. however, considering the measured settling velocity, we estimated the stokes number of the hfsb to amount �� = �� �� = (8.0 ± 1.7) ∙ 10��. (6) herewith, p denotes the well-known particle response time and  the mean kolmogorov time of the flow. as st < 10-3, the hfsb should be able to follow all turbulent fluctuations in our rbc experiment. looking at the intensity of the reconstructed particles given in figure 2, a decrease of the mean brightness by about 50% during the first ten minutes of the experiment can be detected. as the measurement continues, the intensity stays rather constant. we ascribe this effect to the secondary scattering of the hfsb at the initially high seeding densities, which diminishes as soon as the seeding density drops below about 0.1 hfsb per cubic centimeter. 2.3 optical set-up illumination of the tracer particles in the sample was enabled by an installation of 849 pulsed high-power leds above the transparent cooling plate. hereto, different arrays of led spots in either white or green color were used. by lifting the led array to a level of about ~ 1 m above the cooling plate we ensured that the gaps between the led modules were sufficiently filled with light in the sample volume. the leds were synchronized with the camera system and operated in pulsed mode with a pulse duration of 3 ms. to capture the images of the illuminated hfsbs, we used an inline ensemble of six scientific cmos cameras with a resolution of 2560 x 2159 pixels each, which we combined with zeiss distagon lenses (f = 35 mm). they were installed on a circle around the convection cell at a distance of about 3 m from the vertical center line and covered an aperture of 69°. sharp imaging of the particles was achieved by closing the apertures to f/9.5 and f/11. the mean magnification in the volume amounted to m = 0.012, corresponding to a resolution of 0.55 mm/px. accordingly, the geometric particle images would measure about 0.7 pixels in diameter. in contrast, the real particle image diameters ranged between 2 and 3 pixels due to diffraction limited imaging. these values allow for precise sub-pixel fitting, yet are not suited to resolve the glare points of the hfsbs. calibration of the camera system was done using a quadratically arranged dot pattern (spacing 25 mm) on an aluminum honeycomb plate, which we placed in three parallel planes with a consecutive distance of 230 mm within the cell. this geometrical calibration was further refined using volume self calibration (wieneke 2008) and calculation of the optical transfer function (schanz et al. 2013) using low density images from dedicated runs. both, image acquisition and synchronization of the cameras and the light source were controlled through the davis 10.0.5 software (lavision). 3 experimental conditions and measurement procedure preceding each measurement, the convection apparatus was given between three and four hours for thermal equilibration of the respective boundary conditions. herewith, the temperature levels of heating (th) and cooling plate (tc) were chosen such that the mean sample temperature t = (th + tc)/2 equaled the mean room temperature in the surrounding of the experiment. prior to the lpt measurements, we seeded the fluid with hfsbs by temporally inserting the hfsb nozzle through a small opening in the side wall for up to 4 minutes. in order to prevent induction of long-lasting flow structures, we changed the direction of the hfsb nozzle every 10 s. after seeding, the system was given between two and four minutes to allow for the turbulence induced in excess by the hfsb nozzle to decay. we conducted continuous and chunked (a multitude of short recordings with limited time-steps to attain a long overall runtime or statistical convergence) measurement runs with durations between 80 s and 30 minutes. in total, 30 experimental runs of varying duration and interval configuration were performed. while the heat impact by the lights sources was negligible during the short or chunked runs, the central heating element was switched off during the long-term measurements. hereto, the optical power of the leds was adjusted in order to exactly compensate for the heat flux of the central heating element. from the complete data of the measurement campaign, we selected two for this study in order to discuss the measurement procedure and the quality of the resulting data. the boundary conditions and measurement parameters for these runs, which comprise two ra, are denoted in table 1 and 2. as an indication of the range of lengthand time-scales to be expected, the volume-averaged kolmogorov lengthand time-scales are given (sugiyama et al. 2007). further, the nominal thickness of the thermal boundary layer, from which the thermal plumes are emitted, is calculated via the relation �� = 1/(2��) (chillà and schumacher 2012) and the "free-fall" velocity �� = �βgδ�� is added as a measure for the maximal velocities to expect (chillà and schumacher 2012). given the initial density of tracked particles between 0.32 and 0.56/cm³, the measurements begin with mean particle distances between 6.4 and 7.8 kolmogorov lengths. as the lifetime of the tracer particles was limited, the seeding density further decayed during the experimental runs. accordingly, data assimilation by flowfit is required in order to resolve the smallest spatial scales in the eulerian frame. the temporal oversampling, in turn, corresponds to 5.4 and 7.0 mean kolmogorov time constants, allowing to resolve the smallest temporal scales and the spatial scales along the lagrangian tracks. while the short experimental ‘run 09’ of 3384 time-steps has a duration of about 60 free fall times, the long-term ‘run 30’ spans more than 1,000 free fall times. according to the results in table 1, the smallest turbulent scales in the flow are already 4-5 times larger than the tracer particles and should be fully resolvable by the measurement system. the same holds for the thermal boundary layers, which measure more than ~ 20 nominal particle diameters. table 1: boundary conditions and fundamental parameters of the presented flow cases. t, k, , b and uf denote the mean sample temperature, kolmogorov length and time-scale, the thermal boundary layer thickness and free-fall velocity, respectively. for t, t and ra, the maximal deviations occurring during the stb measurement are denoted. run # t [k] t [°c] ra [108] pr k [mm]  [s] b [mm] uf [m/s] 09 4.03  0.06 22.00  0.06 5.25  0.06 0.70 2.3 0.35 11.5 0.38 30 11.8  0.2 22.14  0.17 15.3  0.3 0.70 1.7 0.18 8.5 0.66 table 2: experimental settings and measurement parameters for the flow cases given in table 1. herewith, facq, d and n denote the acquisition frequency, the duty cycle of the leds and number of instantaneous recordings, respectively. nf denotes the acquisition time in number of free fall times. finally, the maximal number of tracked particles n, the mean interparticle distance / k, and the temporal oversampling · f are specified. run # facq [hz] d n nf n [1/cm³] / k · f 09 20 0.15 3384 59 0.32 6.4 7.0 30 30 0.1 54528 1091 0.56 7.8 5.4 4 data processing the raw particle image data was processed using the "shake-the-box" lpt algorithm (schanz et al. 2016) after slight image pre-processing, which consisted of subtraction of the sliding minimum of 36 consecutive images as well as a constant. the stb method employs a predictor/corrector approach, in which known tracks are first extended to the next time-step and subsequently treated by a position correction method ('shaking' with image matching techniques). this way, the vast majority of particles can be tracked effortlessly, avoiding ghost particle generation, before the small portion of yet untracked particles is identified using iterative particle reconstruction ipr (wieneke 2013) on the residual images. images with locally up to 0.15 particles per pixel (ppp) were evaluated. due to the limited residence time of the hfsb, during the time-scale of the experiment, the number of tracks decays with time, see figure 2. while after the second stb pass, more than half a million of hfsb are tracked at the first time-step, only a few thousand tracked hfsb remain after around 30 minutes. with the second stb pass, running backward in time and using the particle positions and track information from the first pass, the number of tracked particles can be increased by about 10%. hereafter, the particle tracks were fitted with a cubic b-spline curve using the ‘trackfit’ algorithm (gesemann et al. 2016), smoothing the particle tracks according to the found optimal filter length over about 5 time-steps. as a result, a particle position accuracy of ~24 µm (0.043 pixel) and a velocity uncertainty of 0.34 mm/s (‘run 30’) could be estimated from the spatial spectrum of the tracks. the latter corresponds, depending on ra, to a dynamic velocity range of ~ 900:1 (‘run30’). as the final step, the data assimilation scheme ‘flowfit’ (gesemann et al. 2016) with continuity and navier-stokes-constraints was used to interpolate the scattered velocity and acceleration data by continuous 3d b-splines in a cubic grid at a grid spacing of 7 mm, corresponding to 0.06 0.1 particles per b-spine cell (ppc). as compared to earlier measurements with quite similar set-up and procedure (huhn et al. 2017), much longer time-series were recorded and evaluated in this study and the number of tracked particles could be further increased by a factor of two. 5 results 5.1 lagrangian particle tracks figure 3: volumetric particle distribution from ‘run 09’ (left), single particle trajectory of ~ 4.4·104 timesteps from ‘run 30’ (middle, right). vertical velocity component coded with color. figure 4: distribution of track lengths for ‘run 30’. frequency distribution (left). cumulated mean fraction of tracks per image (right). the green line indicates a value of 0.5 and the red line a track length of 1,300. an exemplary output of the stb method is depicted in figure 3 (left), which illustrates an instantaneous volumetric particle distribution of ‘run 09’ (godbersen et al. 2020). for the sake of the moderate ra, the lsc can be spotted well in the reconstructed distribution of ~ 300,000 tracer particles by looking at the color-coded vertical velocity. while the ability to perform long-time investigations is one of the assets of experimental studies of rbc, of course not all of the initially tracked hfsb could be observed over the full time-span of the measurement. the reasons for this are manifold. first, the hfsb have a limited residence time in the sample. however, this effect could only explain a minority of the track-endings. in fact, the majority of the tracks ends prior to reaching the end of residence of the according hfsb, which could be due to overlapping particle images, residual background reflections or high acceleration events. accordingly, ending as well as newly beginning tracks are observed to some extent in all time-steps during the evaluation. however, the median length of the tracks per image totals to ~ 1300 time-steps (~ 43 s). a few hfsb could be tracked over more than 30,000 and the longest trajectory found lasts 44,000 time-steps, which corresponds to about 900 free-fall times, 60 lsc turn-around times and a distance of 130 sample heights (143 m), see figure 3. this opens up the possibility to perform long-time lagrangian statistics with the larger fraction of the tracks over a significant number of time-steps. 5.2 global flow fields and large-scale circulation figure 5: visualization of instantaneous velocity fields during ‘run 09’. depicted are the iso-surfaces of the q-criterion and the vertical velocity (color). the first five images are sampled every 10 s in time. as the dense particle data impedes visualization of the turbulent structures, regularized data from flowfit was used in the current section. hereto, the flow is visualized by iso-surfaces of the q-criterion (haller 2005) in figure 5, where the grid spacing of the regularized data amounts to 3· k at a number of 0.06 tracer particles per cell (ppc). as different instances in time are depicted, the data shall give an impression of the dynamics of the turbulent flow structures. to give insight into an extensive range of turbulent structures with wide size and shape distribution the q-value for the iso-surfaces was set to 5/s². in each of the snapshots, the lsc can be spotted in terms of fluid rising in one part of the sample and moving down in another part. herewith, the axis of rotation is oriented near the y-axis. however, when trying to identify the morphology of the lsc, one has to state that there is no such thing and the lsc rather decomposes into an agglomerate of smaller turbulent structures with very small order. when looking at the vertical velocity data in the central plane, besides the rotation of the lsc, a sloshing motion can be observed, the lsc being located in the front, in the middle and in the back in the different instances. the fine-dynamics of the flow, however, is hidden in the turbulent fluctuations. regular structures to be observed are discussed in the following. first, at the position, where the lsc detaches from the heating / cooling plate, the turbulent structures rise up and align into the direction of the mean flow, building arrays of aligned structures, spanning more than 1/2 l eventually. at the opposite side, where the lsc reattaches, a corner roller, oriented parallel to the top / bottom plate and oriented perpendicular to the mean flow forms. the dynamics in the region in between the corner roll and the separation is governed by the interaction with the buoyant structures (thermal plumes) with the turbulent flow and shall be elucidated in the next section. w [m/s] x y z 5.3 thermal plumes and turbulent interactions having measured with an oblique view onto the heating plate, we were content to resolve the fingerprints of thermal line-plumes in our velocity data above both, heating and cooling plate. necessary preconditions to do so were the high scattering efficiency of the hfsbs and some treating of the heating plate with a surfactant to make the bubbles vanish quickly after occasional settling. figure 6 illustrates the vertical velocity component in a slice located 2.7 b above the heating plate. further, the iso-surfaces of the q-criterion are depicted in a layer of 55 mm thickness above the plate. among the most prominent features to be spotted are line plumes, indicated by locally increased vertical velocity values, which are accompanied by pair wise, elongated vortical structures. the latter are induced by the rising plumes and form the well-known mushroom shape, which evolves when line plumes detach from the top or bottom plate. further, vortical structures rising perpendicular from the heating plate and extending beyond the layer, in which the q-iso surfaces are plotted, can be spotted. they are caused by interactions of the aforementioned structures with the turbulent lsc flow. eventually, such structures organize to larger uprising vortical structures, resembling dust devils, known from atmospheric flows. figure 6: series with visualization of thermal plumes in instantaneous velocity fields above the heating plate of ‘run 30’. shown are the contours of the vertical velocity in a slice located 23 mm as well as iso-surfaces of the q-criterion, q = 12 s-², in a layer of 55 mm thickness above the heating plate. the interval between the snapshots amounts to one fourth of the lsc turnaround time, i.e. 6.25 s. 5.4 lagrangian statistics in order to improve the understanding of the lagrangian transport processes in our rbc experiment, we evaluated the autocorrelation functions of the different velocity components along the particle tracks, averaging over the 5,000 longest particle tracks of ‘run 30’. herewith, we computed the spatial autocorrelation along the tracks, see figure 7 (left). the finger print of the lsc can be observed as a strong and periodic correlation signal. the first side maximum is located at ~ 2.7 l, the mean perimeter of the lsc, corresponding to a lsc turn-around time of lsc = 25.9 s. it turns out that the residence time of particles in the lsc is quite limited. more precisely, we can conclude from figure 7, that the motion of the particles, which constitute the lsc, is dephasing in at most two cycles. obviously, already at the moderate ra studied in this experiment, the lsc is not to be imagined as a fixed set of fluid particles, which recirculate but rather by a turbulent transport of momentum information, which is exchanged between the particles joining and leaving the roller (very similar findings are reported for superstructures in a tbl by novara et al. contribution to this ispiv’21). as a consequence, and a matter of fact, visualization of the lsc at the studied ra is already quite challenging, because the lsc is mostly of a statistical nature rather than a topological feature of the flow. the conjugated view on these phenomena is given by the power spectral density computed along the tracks, see figure 7 (middle). the motion of the lsc leads to a prominent peak at about 0.0065 (0.037 hz), which overshadows the inertial subrange scaling at lower frequencies. at higher frequencies, damping of the turbulent structures increases strongly above ~  / 5, such that when the cut-off filter of the stb track w [m/s] fitting sets on, the structures are already attenuated due to turbulent dissipation by about three orders of magnitude. the onset of the cut-off filter can be clearly spotted and it is located at ~ 0.6 . we are thus confident to resolve all relevant turbulent structures up to the dissipation range. however, the aforementioned is valid for the temporal resolution along the tracks. as the particle density decreases with measurement time, the spatial resolution is, of course, decreasing with time. herewith, one of the assets of lagrangian measurements as compared to eulerian is the possibility to provide high track-wise spatial resolution via fast sampling of the particle motion, even at lower seeding densities, see figure 7 (right), which depicts a pdf of the propagated length in units of the volume averaged kolmogorov length. it peaks at a value of 2 and shows maximum values of ~ 5.5. figure 7: lagrangian statistics for ‘run 30’, evaluated over the 5,000 longest tracks: track-wise spatial autocorrelation functions (left) and power spectra (middle). for reference, the inertial subrange scaling is given (dotted line). the frequencies are normalized to the kolmogorov frequency. pdf of the propagated length in units of the volume averaged kolmogorov length (right). 5.5 dynamics of the large-scale circulation to obtain insight into the dynamics and long-term behavior of the lsc, spatial statistics were calculated from the particle data and plotted as time-series in figure 8 and 10. to clarify, how many tracer particles are required to sample the integral flow data, figure 8 (left) shows the number of tracked particles together with the total kinetic energy (tke) of the fluid as a function of time. obviously, the tke can be sampled well with only a few thousand particles, which remain at the end of the run, with fluctuations, which are typical of the turbulent rbc system. figure 8: spatial statistic data as a function of time for ‘run 30’. left: total kinetic energy (red) and number of tracks (blue). right: square of the total angular momentum (blue) and azimuth of the angular momentum (red). on the right-hand side of figure 8 the magnitude square and azimuth of the total angular momentum of the fluid is given with respect to the sample center, revealing the dynamic behavior of the lsc. besides slow meandering of the azimuth (‘rotation’), several events involving large angular reorientations, very often in combination with a breakdown of rotational energy, so-called ‘spontaneous reorientations’ can be spotted. ~ -5/3 co in order to further disclose the fine-dynamics of the lsc, the angular momentum was calculated individually for the upper and lower third of the sample. the azimuth between both, tb, is plotted in figure 10. clearly, the torsional oscillations of the lsc, known from indirect measurements of local wall temperatures (funfschilling et al. 2008; zhou et al. 2009), are disclosed by the periodic oscillation of tb with amplitudes up to 80°. to further unveil the sloshing mode (zhou et al. 2009) of the lsc from our data as well, we calculated the center of gravity of the projection of the angular momentum to the lsc axis, x cog (made dimensionless with l/2), see figure 10. the plot of x cog versus time reveals the sloshing motion of the lsc, which occurs at the same frequency as the twisting mode. by looking at the autocorrelations of each, x cog and tb, the time constant for these processes, which has been used to normalize the x-axis in figure 10, could be determined by measuring the first side maximum to be sl = 28.5 s (not shown). the latter is higher by about 10% as compared to the lsc turnaround time determined in the previous section by evaluation of the 5,000 longest tracks. the cross-correlation of x cog and tb shows, that twisting and sloshing mode are phase locked to each other with a phase shift of ~ /4 in contrast to the phase shift of ~ /2 deduced from wall-temperature measurements (zhou et al. 2009). in the velocity data, evaluated with the above-mentioned method, the maximal twist occurs already 1/8th of a full cycle after the maximal sloshing amplitude. figure 9: torsional oscillation and sloshing mode of the lsc during ‘run 30’: difference of azimuth of the total angular momentum in the upper and the lower third of the sample and center of gravity of the projection of the angular momentum on the lsc axis (left) as well as the cross-correlation of both quantities (right). 6 conclusions we have demonstrated that by combination of stb / lpt with long-lived hfsb simultaneous acquisition of lagrangian particle tracks and time-resolved eulerian velocity fields of turbulent rbc spanning the complete volume of a cylindrical sample becomes possible. with a temporal oversampling factor between 5 and 8 with respect to the kolmogorov frequency and measurement runs spanning up to 30 minutes, we were able to capture in one measurement short-term dynamics and long-time evolution of the turbulent rbc system. with initial inter-particle distances between 6 and 8 kolmogorov lengths, spatial resolutions in the assimilated vector fields of a few kolmogorov lengths could be derived using ‘flowfit’. the generated data sets allow for direct observation of the interaction between largeand small-scale turbulent structures by visualizations using the q-criterion. besides highly resolved views on the lsc, we have been able to detect the fingerprints of thermal plumes rising from the thermal boundary layers in the velocity fields just above the heating and cooling plates. with runs spanning more than 1,000 free-fall times, our data allows spatially and temporally resolved studies of the short and long-term dynamics of the lsc including torsional oscillations, sloshing modes, rotation and spontaneous reorientations. analysis of the determined time-constants and phase-relations in the light of the results from principal component analysis will be among the next steps of our study. the long-lived hfsbs developed in the course of the project with mean lifetimes of more than 5.5 minutes are an important technology for current and future studies of indoor air flow and thermal convection of gaseous fluids (see also paper 184 of this ispiv’21 by schröder et al.). acknowledgements support with hardand software for illumination and image acquisition by lavision gmbh is gratefully acknowledged. we thank j. lemarechal, t. kleindienst and c. fuchs for their contributions to the rbc sample and j. agocs for his support during set-up of the optical system. j.b. acknowledges several constructive conversations with s. weiss. we thank the max-planck-institute ds for provision of the refrigerated bath circulator. this work was supported by the deutsche forschungsgemeinschaft (dfg) through grant no. schr 1165/5-1 as part of the priority programme on turbulent superstructures (dfg spp 1881). references bodenschatz e, pesch w, ahlers g (2000) recent developments in rayleigh-bénard convection. annu rev fluid mech 32:709–778 bosbach j, kühn m, wagner c (2009) large scale particle image velocimetry with helium filled soap bubbles. exp fluids 46:539–547. https://doi.org/10.1007/s00348-008-0579-0 brown e, ahlers g (2006a) rotations and cessations of the large-scale circulation in turbulent rayleigh– bénard convection. j fluid mech 568:351. https://doi.org/10.1017/s0022112006002540 brown e, ahlers g (2006b) effect of the earth’s coriolis force on the large-scale circulation of turbulent rayleigh-bénard convection. phys fluids 18:125108. https://doi.org/10.1063/1.2402875 chillà f, schumacher j (2012) new perspectives in turbulent rayleigh-bénard convection. eur phys j e 35:58. https://doi.org/10.1140/epje/i2012-12058-1 funfschilling d, brown e, ahlers g (2008) torsional oscillations of the large-scale circulation in turbulent rayleigh–bénard convection. j fluid mech 607:119-139. https://doi.org/10.1017/s0022112008001882 gesemann s, huhn f, schanz d, schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in: 18th international symposium on the application of laser and imaging techniques to fluid mechanics. lisbon, portugal, july 4-7 gibeau b, gingras d, ghaemi s (2020) evaluation of a full-scale helium-filled soap bubble generator. exp fluids 61:28. https://doi.org/10.1007/s00348-019-2853-8 godbersen p, bosbach j, schanz d, schröder a (2020) video: the beauty of turbulent convection: a particle tracking endeavor. in: 73th annual meeting of the aps division of fluid dynamics gallery of fluid motion. american physical society, chicago, il haller g (2005) an objective definition of a vortex. j fluid mech 525:1–26. https://doi.org/10.1017/s0022112004002526 huhn f, schanz d, gesemann s, et al (2017) large-scale volumetric flow measurement in a pure thermal plume by dense tracking of helium-filled soap bubbles. exp fluids 58:116. https://doi.org/10.1007/s00348-017-2390-2 kühn m, bosbach j, wagner c (2009) experimental parametric study of forced and mixed convection in a passenger aircraft cabin mock-up. build environ 44:961–970. https://doi.org/10.1016/j.buildenv.2008.06.020 kühn m, ehrenfried k, bosbach j, wagner c (2012) large-scale tomographic piv in forced and mixed convection using a parallel smart version. exp fluids 53:91–103. https://doi.org/10.1007/s00348-012-1301-9 liot o, salort j, seychelles f, et al (2017) lagrangian measurements in turbulent thermal convection: about the inhomogeneity of the velocity and temperature fields. procedia iutam 20:112–119. https://doi.org/10.1016/j.piutam.2017.03.016 paolillo g, astarita t, greco cs, cardone g (2018) three-dimensional velocity measurements of rayleigh-bénard convection in a cylinder. 18th international symposium on flow visualization, zurich, switherland, june 26-29. https://doi.org/10.3929/ethz-b-000279194 scarano f, ghaemi s, caridi gca, et al (2015) on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments. exp fluids 56:42. https://doi.org/10.1007/s00348015-1909-7 schanz d, gesemann s, schröder a, et al (2013) non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. meas sci technol 24:024009. https://doi.org/10.1088/0957-0233/24/2/024009 schanz d, gesemann s, schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. exp fluids 57:70. https://doi.org/10.1007/s00348-016-2157-1 schanz d, novara m, geisler r, et al (2019) large-scale volumetric characterization of a turbulent boundary layer flow. 13th international symposium on particle image velocimetry. munich, germany, july 22-24 schiepel d, herzog s, wagner c (2018) experimental study of turbulent rayleigh-bénard convection using large-scale tomo-piv and high-density ptv. in: deville mo, couaillier v, estivalezes j-l, et al. (eds) turbulence and interactions. springer international publishing, cham, pp 225–231 spoelstra a, de martino norante l, terra w, et al (2019) on-site cycling drag analysis with the ring of fire. exp fluids 60:90. https://doi.org/10.1007/s00348-019-2737-y sugiyama k, calzavarini e, grossmann s, lohse d (2007) non–oberbeck-boussinesq effects in twodimensional rayleigh-bénard convection in glycerol. europhys lett epl 80:34002. https://doi.org/10.1209/0295-5075/80/34002 wieneke b (2008) volume self-calibration for 3d particle image velocimetry. exp fluids 45:549–556. https://doi.org/10.1007/s00348-008-0521-5 wieneke b (2013) iterative reconstruction of volumetric particle distribution. meas sci technol 24:024008. https://doi.org/10.1088/0957-0233/24/2/024008 zhou q, xi h-d, zhou s-q, et al (2009) oscillations of the large-scale circulation in turbulent rayleigh– bénard convection: the sloshing mode and its relationship with the torsional mode. j fluid mech 630:367–390. https://doi.org/10.1017/s0022112009006764 mytitle 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 particle detection by means of machine learning in defocusing ptv maximilian dreisbach1∗, robin leister1, matthias probst2, pascal friederich3,4, alexander stroh1, jochen kriegseis1 1 institute of fluids mechanics, karlsruhe institute of technology, germany 2 institute of thermal turbomachinery, karlsruhe institute of technology, germany 3 institute of theoretical informatics, karlsruhe institute of technology, germany 4 institute of nanotechnology, karlsruhe institute of technology, germany ∗ maximilian.dreisbach@kit.edu the accurate measurement of a fluid flow inside a measurement volume (mv) with limited optical access poses a challenge since the view on the mv is often partially obstructed for all but one viewing angle. defocusing particle tracking velocimetry (dptv) can be used to determine the instantaneous threedimensional velocity field of the flow with a standard piv setup, requiring only a single optical axis. current detection algorithms reach an out-of-plane accuracy in an order of magnitude lower than the planar accuracy, on top of a low rate of detected particles in comparison to other ptv approaches. these drawbacks originate from the low image quality due to noise, fluctuations in illumination, reflections and overlapping particle images. it has been shown that machine learning (ml) based detection is more robust against these adverse effects, due to the ability to leverage a higher amount of optical features for detection than conventional algorithms (lecun et al. (1998)). therefore, the present work addresses the applicability of ml algorithms in the post-processing of dptv experiments, which will be evaluated on the ground of the dptv experiments conducted by leister and kriegseis (2019). the setup of these experiments can be seen in figure 1(a) and a section of a raw image recorded during the experiments in figure 1(b). (a) dptv setup (b) raw image 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.6 0.7 0.8 0.9 1 recall [-] pr ec is io n [] faster r-cnn synthetic faster r-cnn munit faster r-cnn real hough transform retinanet synthetic retinanet munit retinanet real (c) detection results figure 1: (a) dptv setup in an open wet clutch; (b) recorded dptv raw image above the grooved region of an open wet clutch; (c) precision-recall diagram of the detection on dptv images. two established object detection frameworks, faster r-cnn by ren et al. (2017) and retinanet by lin et al. (2017) based on convolutional neural networks (cnn) are trained for particle detection by supervised learning. to fully exploit the capacity of these deep learning algorithms large datasets consisting of o(10000) images with annotated centre point location and diameter for each particle are necessary. since manual image annotation requires an unfeasible time effort and leads to the introduction of additional uncertainty and bias, two kinds of synthetic image data sets are used. the first training set da is generated from 2d-gaussian particle images with additional noise, while the second approach focuses on generating refined synthetic data db by employing ml algorithms for unsupervised image-to-image translation on the first training data set. the image-to-image translation method munit by huang et al. (2018) is used to train a mapping from an input domain consisting of the synthetic particle images to an output domain of real particle images via unsupervised learning. the objective of the image translation step is to generate particle images that represent the feature distribution of the real data while preserving the location and diameter information of the individual synthetic input images. mailto:maximilian.dreisbach@kit.edu overall, we find that the ml-based detection approach outperforms the current state-of-the-art conventional detection algorithm used by (leister and kriegseis, 2019) which detects particles through a hough transformation by up to 49 percent in terms of detection rate, depending on the image quality; see figure 1(c). especially on images with fluctuations in background illumination (e.g. fig. 1(b)) the ml approaches surpass the detection performance of the hough transform. the translation framework munit generates realistic synthetic representations of real particle images by reproducing small scale features. in particular, increasingly wide edges for higher diameters, noisy contours, distortions and intensity variations over the circumference of the particle images are generated, leading to visual similarity as shown in figure 2(a). as illustrated in figure 2(b) the radial intensity profile, which is a major characteristic of the real particle images, is approximated more closely by munit in comparison to the 2d-gaussian synthetic images. the object detection algorithms trained on the feature-rich synthetic data db from the image trans(a) particle images 5 10 15 20 26 30 0 0.2 0.4 0.6 0.8 1 1.2 radius [px] in te ns ity [] synthetic munit real (b) radial intensity distribution 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.25 0.5 m is s ra te [] faster r-cnn hough retinanet 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 1 2 overlap [iou] σ d [p x] (c) results on overlapping particles figure 2: (a) random synthetic (da), real and translation refined particle images (db) at ascending diameters; (b) averaged radial intensity profiles of synthetic (da) and refined synthetic (db) and real particle images with a diameter of d = 22.5±0.025px; (c) miss rate and uncertainty in diameter determination σd on synthetic particle images with increasing relative overlap, measured by intersection over union (iou). lation reach a higher detection rate combined with a lower rate of false positives as compared to the same algorithms trained on synthetic data da; see figure 1(c). this shows that the image translation algorithm successfully transformed the distribution of the synthetic dataset closer to the dptv image distribution, leading to a better generalization and real-world accuracy of the ml model trained on the refined images db compared to the fully synthetic images da. in experiments on synthetic images and artificial particle images produced through a pinhole aperture retinanet achieves a higher accuracy than the hough transformation. both faster r-cnn and retinanet resolve overlapping synthetic particle images with a higher accuracy and a lower miss rate as seen in figure 2(c). in summary, we showed that a machine learning approach based on synthetic data generation and data refinement using the munit images translation method leads to highly accurate particle detection. the high detection rate and accuracy even on overlapping synthetic particle images also renders the presented approach promising for significantly increased particle seeding densities in dptv experiments. furthermore, the insight of significant improvements by means of training-data refinement uncovers the impact of small scale features for ml-based particle detection, which in turn emphasizes the need for realistic training data. references huang x, liu my, belongie s, and kautz j (2018) multimodal unsupervised image-to-image translation. in computer vision eccv 2018. pages 179–196 lecun y, bottou l, bengio y, and haffner p (1998) gradient-based learning applied to document recognition. proceedings of the ieee 86:2278–2324 leister r and kriegseis j (2019) 3d-lif experiments in an open wet clutch by means of defocusing ptv. in 13th international symposium on particle image velocimetry (ispiv 2019), july 22-24, 2019, munich, germany lin t, goyal p, girshick r, he k, and dollár p (2017) focal loss for dense object detection. in 2017 ieee international conference on computer vision (iccv). pages 2999–3007 ren s, he k, girshick r, and sun j (2017) faster r-cnn: towards real-time object detection with region proposal networks. ieee transactions on pattern analysis and machine intelligence 39:1137–1149 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 flow characteristics analysis for flow past the porous spheres: wake structures likun ma13, sina kashanj2, shuliang xu1, mao ye1, david s nobes2∗ 1 dalian institute of chemical physics, chinese academy of sciences, dalian, p.r.china 2 university of alberta, department of mechanical engineering, edmonton, canada 3 university of chinese academy of sciences, beijing, p.r.china ∗ dnobes@ualberta.ca abstract flow past a permeable sphere is different from that of a solid sphere due to the penetration of the fluid within porous structures, which can arise a change of flow fields. in this work, flow past porous spheres with darcy numbers (da) ranging from [0,10−3] were measured using planar particle image velocimetry (piv). the whole flow fields, including both leading edge and trailing edge, were captured at six different reynolds numbers (re) varying from 400 to 1400. time-average flow fields were calculated based on instantaneous flow fields within fully-developed stages. local minimum method was used to search for stagnation point positions. the results show positions of stagnation points are nearly proportional to the logarithm of re. for most porous spheres, positions of stagnation points are extended to farther downstream positions than that of a solid sphere. however, at some certain darcy numbers, ranging from 5∗10−6 to 2∗10−5, positions of stagnation points are closer to the sphere centers than that of an impermeable one. 1 introduction the flow through and around a group of particles or a permeable body is widely seen in many industrial processes, including the motion of clusters in fluidized bed reactors, movement of coal particles in power stations and transport of porous microcarriers in bioreactors. understanding flow characteristics, especially wake structures and fluid-particle interaction forces, of permeable bodies which are different from solid bodies, is important for the control of these processes yu et al. (2012). theoretical analysis of flow characteristics for flow past a porous sphere has been limited to the creeping flow regime where inertial effects can be neglected. for higher reynolds numbers, many numerical simulations studies wu and lee (1999); wittig et al. (2017) have been carried out and it has been found yu et al. (2012) the length of wake for flow past a porous sphere is different from that of a solid sphere and varies with permeability. a detached or penetrating wake is also observed for a certain permeability range, which is different from the attached wake of a solid sphere. additionally, the changed wake structures can affect the force acting on the sphere, such as the pressure drag force. however, it’s difficult for numerical simulations to determine appropriate fluid-porous interface boundary conditions for porous spheres, which can significantly affect the simulation results. thus, there is a need for detailed experimental results of porous spheres as a benchmark to understand wake characteristics and validate numerical simulations results. piv is a non-intrusive measurement technique which can provide velocity field of full field with excellent temporal and spatial resolution. in this paper, the effect of the permeability for flow fields is investigated by applying piv technique to visualize the difference of the flow past a solid sphere and a porous one. 2 experimental setup in our experiments, all spheres are connected to a traverse moving in horizontal direction which can be controlled with a controller to be given a constant velocity with 400 ≤ re ≤ 1400. 2d-piv is used to capture time-dependent flow field and a double frame ccd camera is synchronized to a double pulse laser to capture images of fluid flow seeded with 18 µm hollow glass particles. both camera and the sphere are connected to the traverse to capture the images in an eulerian reference frame. 3 results and discussion figure 1: variation of stagnation points positions along re at nine different darcy numbers darcy numbers is dimensionless permeability, which can be written as da= k/d2 = d2 · ε3/ ( d2 ·180 ( 1− ε 2 )) . in this study, flow fields of porous spheres with darcy numbers ranging from [0,10−3] were captured at re = 400,600,800,1000,1200,1400. instantaneous frames in fully-developed stage were used to calculate time-average flow fields. local minimums of the vector field were regarded as stagnation point positions. it can be found for a high permeability when da is more than 5.05 ∗ 10−4, as shown in figure 1, positions of stagnations points from sphere centers are significantly increased compared with that of a solid sphere. for most porous spheres, positions of stagnation points are extended to farther downstream positions than that of a solid sphere while it is only increased slightly for the low permeability spheres. however, at some certain darcy numbers, ranging from 5 ∗ 10−6 to 2 ∗ 10−5, positions of stagnation points are closer to the sphere centers than that of an impermeable one. these phenomena are because, for a large permeability, a higher percentage of fluid will go through rather than flow around the porous sphere, causing a decrease on the effective re with a closer position of stagnation point. the penetrating flow also pushes the stagnation point’s position away from the porous sphere, causing farther stagnation points. thus, the final position of stagnation points are depended on the combination of the above two opposite effects. it is also clear that positions of stagnation points are nearly proportional to the logarithm of re for all different permeability. acknowledgements this work was finished in university of alberta, canada, supported from a scholarship by the university of chinese academy of sciences, china. references wittig k, nikrityuk p, and richter a (2017) drag coefficient and nusselt number for porous particles under laminar flow conditions. international journal of heat and mass transfer 112:1005–1016 wu r and lee d (1999) highly porous sphere moving through centerline of circular tube filled with newtonian fluid. chemical engineering science 54:5717–5722 yu p, zeng y, lee t, chen x, and low h (2012) numerical simulation on steady flow around and through a porous sphere. international journal of heat and fluid flow 36:142–152 introduction experimental setup results and discussion 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 1 physics-based universal outlier detector for flow statistics e. saredi1*, a. sciacchitano1 and f. scarano1 1faculty of aerospace engineering, delft university of technology, delft, the netherlands * e.saredi@tudelft.nl abstract outlier detection for piv velocity fields is still nowadays an active field of research. in the last decades, several image pre-processing and processing algorithms have been developed aiming at increasing the dynamic velocity range of piv measurements and reducing the measurement uncertainty. nevertheless, piv velocity fields are still often characterised by the presence of outliers, which potentially hamper the correct interpretation of the flow physics and negatively affect the evaluation of the flow statistics. the outlier detection strategies presented in literature are mainly based on the statistical analysis of the velocity vector with its immediate neighbour. most of these algorithms have been demonstrated to be effective for instantaneous flow fields, where the errors associated with the outliers are order of magnitude larger than the expected measurement uncertainty. however, these approaches are not as effective for the flow statistics, where the outliers yield errors of the same order of the measurement uncertainty. to overcome this limitation, this paper proposed an outlier detection approach based on the agreement of the flow statistics to the constitutive equations, more specifically to the turbulent kinetic energy (tke) transport equation. the focus is posed on the ratio between the local advection terms of tke and a robust estimation of the tke production along the local streamline. it is demonstrated that, in presence of outliers, the proposed principle yields a clear separation between the correct and the erroneous vectors. in order to assess the performance of the proposed principle, three different test cases are considered. for all of them, the results are compared with a reference outlier detection methodology, namely the universal outlier detection method proposed by westerweel and scarano (2005). the proposed turbulence transport-based approach exhibits higher performance in terms of percentage of outliers correctly identified in the flow statistics. 1 introduction in particle image velocimetry (piv), outliers are spurious vectors that exhibit large unphysical variations in magnitude and direction from neighbouring valid vectors (westerweel, 1994). several factors can lead to the appearance of outliers. among them, unwanted light reflections, lack of seeding and inadequate processing methodology are the main ones (hart, 2000; lazar et al., 2004; sciacchitano, 2019; among others). several methods for outlier detection have been presented in the literature, with the focus on the analysis of instantaneous flow fields. the most common approach relies on the analysis of the difference between a vector and its neighbours, either in the temporal or in the spatial domain. in this category of outlier detection algorithms, the approach proposed by westerweel and scarano (2005) is nowadays widely applied. the latter approach builds upon the median filter presented by westerweel (1994) and achieves a larger degree of mailto:e.saredi@tudelft.nl 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 2 generality by introducing a normalisation of the median residual with respect to an estimate of the local velocity variation. the authors proved the applicability of their normalised median test in a wide range reynolds numbers from 10-1 to 107. duncan et al. (2010) extended this approach for unstructured data as those obtained by particle tracking velocimetry (ptv) or adaptive interrogation algorithms. these methodologies proved to be effective for isolated outliers, whereas they suffer from under-detection of outliers when a cluster of false vectors is present in the data. this phenomenon is common when low-seeding areas, if cross-correlation based algorithms are employed, or strong reflections on objects are present in the raw images (masullo and theunissen, 2016). in order to overcome this limitation, masullo and theunissen (2016) presented a new method based on the combination of a first spatial coherence test and a modified gaussianweighted distance-based averaging median. the introduction of the former parametrises the extent of the region inside which the vectors are tested. this methodology showed a gain in the achievable spatial resolution and outlier detection probability, at a cost of an increased computational burden. in addition to the spatial domain, also the time domain has been exploited to identify erroneous vector in piv data. proper orthogonal decomposition (pod) has been considered as a filter to detect outlier (wang et al., 2015; raiola et al., 2015). in these cases, the low-order pod modes are used in order to reconstruct the velocity field at each time step and the difference between the original velocity and the reconstructed field is used as flag for the erroneous vector. this approach has shown a higher effectiveness for detecting clustered outliers with respect to the normalized median test approach. the advent of shake-the-box (stb, schanz et al., 2016) has established a new state-of-the-art to perform volumetric measurements. particles are tracked individually across frames and the temporal information is used then to improve the accuracy of the estimation of the particle position at the various time-steps. the result of this operation is an ensemble of particle tracks inside the measurement volume. several techniques have been presented to obtain the instantaneous velocity field 𝐮 or the time-averaged velocity field �̅� on a cartesian grid, such as ensemble averaging (agüera et al. , 2016) or functional binning (godbersen and schröder, 2020). the aforementioned outlier detection strategies are typically effective for the instantaneous velocity when the latter is expressed on a cartesian grid. in contrast, when the ensemble-average operation is conducted to determine the time-average velocity field, the magnitude of the outliers often decreases significantly because of their unsteady nature. as a consequence, the outliers’ magnitude can become of the same order of that of the correct vectors, thus decreasing the effectiveness of the aforementioned outlier detection methods and potentially leaving a large percentage of invalid vectors undetected. considering the constitutive equations is another possible approach to the outlier detection problem. song et al. (1999) made use of the continuity equation calculated on a delaunay tessellation in order to detect spurious vectors. due to the presence of outliers, unphysical nonzero values of the velocity divergence appear in the incompressible flow field. the outliers can be identified based as regions of high velocity divergence magnitude; however, for this purpose, the definition of a user-defined threshold is necessary, so as to limit the occurrence of false positive (as deductible from the data presented by azijli and dwight, 2015). inspired by the two works above, in the present work a robust physics-based approach is proposed that employs the turbulent kinetic energy transport equation to detect the outliers in the flow statistics. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 3 2 physics-based outlier detection principle this work proposes an outlier detection approach for flow statistics. the measured velocity is expressed via reynolds decomposition in terms of mean and fluctuating component: 𝑢𝑖 = �̅�𝑖 + 𝑢′𝑖 (1) where the subscript i indicates the component of the velocity (𝑖 = 1,2,3 in a three-dimensional flow). in the following discussion, an outlier is defined as a velocity vector whose time-average value or its fluctuations depart from the exact value to an extent exceeding the measurement uncertainty. from the fluctuating component of equation 1, 𝑢′𝑖, the turbulent kinetic energy (tke), expressed as 𝑘 = 1/2(𝑢1 ′ 2̅̅ ̅̅̅ + 𝑢2 ′ 2̅̅ ̅̅ ̅ + 𝑢3 ′ 2̅̅ ̅̅ ̅), can be obtained. its behaviour is described by the associated transport equation (hinze, 1975): 𝐷𝑘 𝐷𝑡 = 𝑃 + 𝒯 − 𝜀 (2) where: 𝐷𝑘 𝐷𝑡 = 𝜕𝑘 𝜕𝑡 + 𝐴 is the material derivative of k, (3) 𝐴 = �̅�𝑖 𝜕𝑘 𝜕𝑥𝑖 is the transport by advection, (4) 𝑃 = −𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ̅ 𝜕𝑢𝑖̅̅ ̅ 𝜕𝑥𝑗 is the production, (5) 𝒯 contains all the transport terms of turbulence, (6) 𝜀 = 𝜈 𝜕𝑢𝑖 ′ 𝜕𝑥𝑗 𝜕𝑢𝑖 ′ 𝜕𝑥𝑗 ̅̅ ̅̅ ̅̅ ̅̅ is the pseudo-dissipation. (7) many studies have focused the attention on the description of the relative importance of the different terms of the tke equation. in ikhennicheu et al. (2020) a list of the most recent works is reported where the tke budget has been experimentally evaluated. in this work, turbulent shear flows are considered, such as jets, mixing layers, channel flows and boundary layers. for this kind of flows, the turbulent quantities change slowly together with the mean flow; the production and the dissipation of the turbulent kinetic energy are in balance, i.e. 𝑃 ≈ 𝜀 (pope, 2000). furthermore, equation 2 can be further simplified since in many flows the turbulent transport of 𝑘 is negligible (nieuwstadt et al., 2016). from this, it is possible to conclude that 𝑃 acts as upper bound of the variation of tke along a streamline, since, neglecting the transport term, a non-null dissipation can yield only to a reduction of tke. in order to explain the proposed outlier detection principle, it is here considered a time-average velocity field around an airfoil described by �̅�, 𝐮′ and 𝑘, whose streamline are schematically represented in figure 1. the airfoil is set at high angle of attack, which causes the separation of the flow along the suction side of the airfoil. the edges of the separated region are characterized by a high shear and then, as consequence, a high turbulence production. in this case, the presence of four regions of outliers is hypothesized: region a, in front of the airfoil; regions b and c, caused by the shadow created by the light refraction at leading and trailing edges of the (transparent) airfoil, and region d, located in the shear region. along any time-average streamline of the flow, the evolution of 𝑘 must comply with equation 2. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 4 figure 1: schematic representation of the outlier detection principle based on turbulent transport. based on the above considerations, the normalized admissible tke transport 𝜌𝑇𝑇 is defined which accounts for the variation of the turbulent kinetic energy along a streamline, relative to the tke production: 𝜌𝑇𝑇 = |𝐴| |𝑃| < 𝑇ℎ𝑟 (8) values of 𝜌𝑇𝑇 larger than a threshold thr (theoretically close to unity, in practice larger than 1 to account for the noise in the measurements) are physically inadmissible and therefore correspond to the presence of outliers. in order to increase the robustness of the evaluation of 𝑃 with respect to the presence of spurious measurement data, the production term in equation 8 is substituted by 𝑃𝑚, that represents the median of its neighbourhood. furthermore, to avoid elevated values of 𝜌𝑇𝑇 in regions where 𝑃 tends to zero, a minimum normalization level 𝛾𝑇𝑇 is assumed that represents the uncertainty on the determination of the numerator of equation 8, similarly to what proposed by westerweel and scarano (2005). with these two modifications, equation 8 becomes: 𝜌𝑇𝑇 = |𝐴| |𝑃𝑚|+𝛾𝑇𝑇 < 𝑇ℎ𝑟 (9) equation 9 is proposed in this work as a means to identify outliers in statistical data from piv or lpt. in regions of valid vectors, the normalised ratio 𝜌𝑇𝑇 remains below the threshold, meaning that the variation of the kinetic energy due to the advection along a streamline is smaller than the kinetic energy production (multiplied by the parameter 𝑇ℎ𝑟). instead, values of 𝜌𝑇𝑇 larger than 𝑇ℎ𝑟 indicate a variation of the turbulent kinetic energy greater than its production, which is physically inadmissible. assuming an uncertainty level on the measured velocity of the order of 5% of uꝏ, the term tt can be estimated: 𝛾𝑇𝑇 = (0.05𝑈∞)3 δ (10) 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 5 being δ the vector pitch of the velocity field. in the next section, the approach is assessed using three different datasets comprising both planar and volumetric piv measurements. 3 experimental assessment in order to assess the proposed principle, three different experimental datasets have been considered: the 2d velocity field around a two-dimensional wing with naca 0012 section, the near-wake of a truncated cylinder and the near wake of the ahmed body. figure 2 shows three instantaneous raw images of the three considered datasets. the three datasets have been acquired with different systems: in the 2d-wing case, a single-camera two-component piv system has been used (adatrao et al, 2021); the images for the near-wake of the cylinder have been acquired with four cameras placed at a large tomographic aperture (schneiders et al., 2016); finally, the nearwake of the ahmed body has been investigated using the robotic volumetric piv system (jux et al., 2018), which is composed by four cameras placed at a low tomographic angle (saredi et al., 2020). in order to assess the performance of the turbulence transport-based principle, its results are compared to the ones obtained by the universal outlier detection, hereafter referred as uod, proposed by westerweel and scarano (2005). in their work, the authors proposed to identify outliers based on the value of a normalized residual 𝑟0 ∗ defined as: 𝑟0 ∗ = |𝑈0−𝑈𝑚| 𝑟𝑚+𝛾𝑈𝑂𝐷 (11) where 𝑈0 is the velocity vector considered, 𝑈𝑚 the median of its neighbours, 𝑟𝑚 the median of the neighbour residuals defined as 𝑟𝑖 = |𝑈𝑖 − 𝑈𝑚| and 𝛾𝑈𝑂𝐷 the minimum normalization level, set to 0.1 pixel. in the original paper, velocity measurements were considered outliers when the normalized residual 𝑟0 ∗ exceed the value of 2; the same threshold is used in this analysis. figure 2: raw images of the three experimental datasets considered in this work. left: flow around a 2d-wing naca 0012; center: near-wake of a truncated cylinder; right: near-wake of the ahmed body. the sources of outliers differ among the considered test cases. for the 2d-wing case (figure 2, left) the presence of the wing body and the shadow created by the refraction at the leading edge create outlier regions in the velocity field, as it can be seen in figure 3 (top-left), where the instantaneous velocity field is presented. considering the case of the cylinder, a strong reflection on the object surface is visible in the raw image presented in figure 2 (center). this reflection cannot be eliminated with pre-processing and causes the appearance of outlier instantaneous tracks along the line of sight of the considered camera, as visible in the highlighted region in figure 3 (centerleft). for the ahmed body flow, studied with a coaxial system (schneiders et al., 2018), an excess of particles coupled with the background noise in the middle of the images causes the appearance of spurious tracks at the center of the measured volume close to the cameras (figure 3, bottom-left). the outliers that appear in the instantaneous fields, represented by the velocity vector on a 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 6 cartesian grid in the 2d-wing case and particle tracks for the other two cases, corrupt the correspondent time-average and ensemble-average velocity fields, presented for all the cases in the right column of figure 3. for the 2d-wing case, the region correspondent to both the shadow and the perspective section of the wing are characterized by erroneous low velocity. this effect is clearly visible in the area correspondent to the shadow. for the cylinder case, the detrimental effect of laser reflections that generates invalid vectors inside the cylinder geometry is evident. furthermore, a region of flow characterized by quasi-null streamwise velocity can be spotted in the area correspondent to the erroneous tracks, indicated with an ellipse in figure 3 (center-left). this can be explained by the fact that the erroneous particles generated by the surface reflection yield random tracks whose mean velocity is approximately null. similarly, the presence of spurious tracks in the near-wake of the ahmed body produces an unphysical region of deceleration and acceleration at x = 0.2 m in the free-stream region of the ensemble-averaged flow field (figure 3, bottom-right). ure 3: left column: instantaneous streamwise velocity field 𝑢 represented on a cartesian grid and at particle locations for the planar case and for the 3d cases, respectively. in all the cases, the areas interested by erroneous measurements are highlighted. right column: time-averaged and ensemble-averaged velocity field �̅� for the 2d case and the 3d cases, respectively. for the nearwake of the ahmed body, the region labelled a indicates the area considered correct for the determination of 𝜂𝑓𝑝, presented in figure 6. 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 7 the presence of outliers in the instantaneous velocity fields does not influence only the timeaveraged field �̅� but also the fluctuating component of the velocity 𝒖′. in order to evaluate this effect along all the three velocity components, the turbulent kinetic energy is here considered, in the form of √𝑘/𝑈∞. for all the cases analysed, the outlier regions present a sharp increase of turbulent kinetic energy with respect to the surrounding (figure 4). it can be noted that the extension and the shape of the outlier regions result more visible in the flow fluctuations, visualised by means of the turbulent kinetic energy in figure 4, than in the time-averaged flow fields (figure 3-right). nevertheless, the turbulent kinetic energy alone can hardly be used as a criterion for outliers detection, because its physically admissible values vary greatly among the experiments. figure 4: contour of normalized turbulent kinetic energy √𝑘/𝑈∞ for the three experimental datasets: 2d-wing (left), cylinder (centre) and ahmed body (right). for the near-wake of the ahmed body, the region labelled b indicates the area considered erroneous for the determination of 𝜂𝑑, presented in figure 6. in order to assess the performance of the proposed principle, the two outliers indicators, namely the normalized admissible tke variation of the current turbulence transport-based approach (𝜌𝑇𝑇 of equation 9 and the residual 𝑟0 ∗ of westerweel and scarano (2015) are presented in figure 5 for all the three considered cases. when considering the universal outlier detection, it should be remembered that the presence of false vectors is flagged by the residual 𝑟0 ∗ exceeding the value of 2. for both the 2d case and the cylinder case, the universal outlier detection fails to detect the outlier region. in the former, only a small region at the leading edge of the shadow is flagged as erroneous. in the latter, the area affected by reflection is not detected as erroneous, with only some vectors at the edges of the flow domain indicated as outliers. the uod shows better results when applied to the data of the near-wake of the ahmed body. in this case, a portion of the erroneous region in the free-stream is correctly detected. the right column of figure 5 presents the spatial distribution of the ratio 𝜌𝑇𝑇 for all the considered cases. for all of them, 𝜌𝑇𝑇 reaches the highest value at the edges of the erroneous region, with 𝜌𝑇𝑇 > 10, an order of magnitude difference with respect to the adjacent correct region. considering the 2d-wing case, the edges of the shadow region and the front and top edges of the area occupied by the prospective view of the wing body are clearly detected as faulty vectors. when the cylinder case is considered, the edges of the erroneous region are clearly detected. it is remarked that the indicator 𝜌𝑇𝑇 exhibits a large separation between the erroneous region (𝜌𝑇𝑇 typically exceeding 10) and the correct portion of the flow (𝜌𝑇𝑇 < 1). when the third case is considered, the near-wake of the ahmed body, the proposed method correctly detects the boundary of the erroneous region highlighted in 4 (right). also in this case, the separation in terms of 𝜌𝑇𝑇 between the correct and the erroneous region is larger than one order of magnitude. in addition, two regions close to the ahmed body are highlighted as 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 8 erroneous. unfortunately, their validity cannot be determined since both the velocity field presented in figure 3 (bottom-right) and the tke presented in figure 4 (right) do not show unphysical behaviour. this suggests the presence of false positives in those regions. figure 5: (left column) normalized residual 𝑟0 ∗ of the universal outlier detection algorithm proposed by westerweel and scarano (2005) for all the considered datasets. top: 2d-wing; center: near-wake of a truncated cylinder; bottom: near-wake of an ahmed body. (right column) normalized admissible tke variation 𝜌𝑇𝑇 defined by equation 9 for all the considered datasets. top: 2d-wing; center: near-wake of a truncated cylinder; bottom: near-wake of an ahmed body. in order to quantitatively evaluate the performance of the turbulence transport-based principle in comparison with the reference methodology, results are presented in terms of detection and false positive rates 𝜂𝑑 and 𝜂𝑓𝑝, respectively. the former is defined as the number of spurious vectors correctly flagged as erroneous divided by the total number of outliers. the false positive rate 𝜂𝑓𝑝 is defined as the ratio between the number of correct vectors flagged as outliers and the total number of correct vectors in the considered portion of the flow. to evaluate the robustness of the two methodologies, the two ratios have been evaluated varying the thresholds between 0 and 4 for the uod, and between 0 and 10 for the turbulence transport-based approach. to perform this analysis, the dataset regarding the near-wake of the ahmed body has been considered. the calculation of 𝜂𝑓𝑝 requires the knowledge of the number of correct vectors that are wrongly flagged as outliers. in order to evaluate this, a volume containing only correct vectors has been selected by visual inspection. the planar section of the considered volume is indicated as region a in figure 3 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 9 (bottom-right). on the contrary, the calculation of 𝜂𝑑 requires the knowledge of the erroneous vectors. for this purpose, the area circled and indicate as region b in figure 4 (right) has been considered. since the proposed principle aims to detect the edges of erroneous regions, only the vectors located at the edge of the faulty area have been considered. once isolated this group of vectors, the amount of them flagged as erroneous by the uod and by the turbulence transportbased outlier detection has been calculated. the results obtained in terms of 𝜂𝑑 and 𝜂𝑓𝑝 by the two methods varying the correspondent threshold is presented in figure 6. it has to be noted that the optimal values of 𝜂𝑓𝑝 and 𝜂𝑑 are 0 and 1, respectively. it is expected that, when increasing the value of the threshold of the two algorithms, both correct detection probability and the false positive rate decrease. both the methodologies presents the expected behaviour. however, for the uod approach the correct-detection and false-positive curves decrease at similar rates, whereas for the turbulence transport-based approach the false-positive curve drops much more rapidly. as a consequence, when the typical threshold of 𝑟0 ∗ = 2 is used for the uod method, only 5% of the correct vectors are detected as outliers (5% over-prediction), but less than 50% of the outliers are identified (only 45% correct prediction). conversely, using the turbulence transport-based approach with a threshold of 5 yields 5% over-prediction and 95% correct prediction. this result supports the conclusion that the median test based on the velocity field is not able to detect outliers when the flow statistics are considered, while the proposed turbulence transport-based approach is able to detect the outliers in the flow statistics. figure 6: comparison of the detection ratio 𝜂𝑑 and the false positive ratio 𝜂𝑓𝑝 obtained by universal outlier detection and the turbulence transport-based approach proposed in this paper. the data are referred to the near-wake of ahmed body dataset. 4 conclusions a novel outlier detection criterion is presented that invokes the physical principle of turbulence transport and applies to the flow statistics evaluated by piv or ptv. the approach relies on the fact that the measured flow field should satisfy the turbulent kinetic energy transport equation. however, outliers often produce un imbalance between the terms of the transport equation. the ratio between the measured turbulent kinetic advection rate and the production term along a trajectory (𝜌𝑇𝑇) is introduced to define a criterion for the detection of the boundaries of regions of erroneous data. in order to guarantee the robustness of the method, the production term is substituted with the median of its neighbours. the approach has been tested on three different datasets, obtained with three different techniques: planar piv, large-aperture 3d-lpt and small14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 10 aperture 3d-lpt the proposed turbulence transport-based outlier detection principle compares favourably with the state-of-the-art universal outlier detection when considering diverse experimental cases. in order to compare quantitively the performance of the proposed method with the reference, the dataset regarding the near-wake of the ahmed body has been considered. considering the two optimal threshold, 𝑟0 ∗ = 2 for uod of westerweel and scarano (2005) and 𝜌𝑇𝑇 = 5 for the turbulence transport-based approach, the results of the two methods are compared in terms of detection ratio 𝜂𝑑 and false positive ratio 𝜂𝑓𝑝. both of the methods yielded a similar over-prediction of the outliers (about 5%); however, while the algorithm from westerweel and scarano could only detect less than 50% of the outliers, the proposed turbulence transport-based outlier detector was capable to identify 95% of the outliers. in case of large regions of outliers, once the boundary of the outlier regions has been identified with the proposed methodology, standard contour tracing algorithms can be applied in order to isolate the of the erroneous regions. references adatrao s, bertone m, sciacchitano a (2021) multi-δt approach for peak-locking error correction and uncertainty quantification in piv. measurement science and technology 32:054003 agüera n, cafiero g, astarita t and discetti s (2016) ensemble 3d ptv for high resolution turbulent statistics. measurement science and technology 27:12 azijli i, dwight rp (2015) solenoidal filtering of volumetric velocity measurements using gaussian process regression. experiments in fluids 56:198 duncan j, dabiri d, hove j, gharib m (2010) universal outlier detection for particle image velocimetry (piv) and particle tracking velocimetry (ptv) data. measurement science and technology 21:057002 godbersen p and schröder p (2020) functional binning: improving convergence of eulerian statistics from lagrangian particle tracking. measurement science and technology 31:095304 ikhennicheu m, druault p, gaurier b, germain g (2020) turbulent kinetic energy budget in a wallmounted cylinder wake using piv measurements. ocean engineering 210:107582 hart dp (2000) piv error correction. experiments in fluids 29:13–22 hinze j (1975) turbulence, second ed. mcgraw-hill, new york jux c, sciacchitano a, schneiders jfg, scarano f (2018) robotic volumetric piv of a full-scale cyclist. experiments in fluids 59:74 lazar e, deblauw b, glumac n, dutton c, elliott g (2010) a practical approach to piv uncertainty analysis. aiaa paper 4355:30 masullo a, theunissen r (2016) adaptive vector validation in image velocimetry to minimise the influence of outlier clusters. experiments in fluids 57:33 nieuwstadt ftm, boerma bj, westerweel j (2016) turbulence, introduction to theory and applications of turbulent flows. springer international publishing pope sb (2000) turbulent flows. cambridge university press raiola m, discetti s, ianiro a (2015) on piv random error minimization with optimal pod-based low order reconstruction. experiments in fluids 56:75 saredi e, sciacchitano a, scarano f (2020) multi-δt 3d-ptv based on reynolds decomposition. measurement science and technology 31:084005 schanz d, gesemann s, schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:70 schneiders jfg, caridi gca, sciacchitano a, scarano f (2016) large‑scale volumetric pressure from tomographic ptv with hfsb tracers. experiments in fluids 57:164 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 11 schneiders jfg, scarano f, jux c, sciacchitano a (2018) coaxial volumetric velocimetry. measurement science and technology 29:065201 sciacchitano a (2019) uncertainty quantification in particle image velocimetry. measurement science and technology 30:092001 song x, yamamoto f, iguchi m, murai y (1999) a new tracking algorithm of piv and removal of spurious vectors using delaunay tessellation. experiments in fluids 26:371-380 wang hp, gao q, feng lh, wei rj, wang jj (2015) proper orthogonal decomposition based outlier correction for piv data. experiments in fluids :56:43 westerweel j (1994) efficient detection of spurious vectors in particle image velocimetry data. experiments in fluids : 16:236-247 westerweel j and scarano f (2005) universal outlier detection for piv data. experiments in fluids 39:1096–1100 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 volumetric velocimetry for small seeding tracers in large volumes y. zhang1∗, h. abitan1, s. l. ribergård1, c. m. velte1 1 technical university of denmark, department of mechanical engineering, kgs. lyngby, denmark ∗ yiszh@mek.dtu.dk abstract this paper presents the volumetric velocity measurement method of small seeding tracer with diameter 5µm ∼ 100µm for volumes of ≥ 500cm3. the size of seeding tracer is between helium-filled soap bubbles (hfsb) and di-ethyl-hexyl-sebacic acid ester(dehs) droplets. the targeted measurement volume dimension is equivalent to the volume of hfsb, which will give a higher resolution of turbulence study. the relations between particle size, imaging and light intensity are formulated. the estimation of the imaging results is computed for the setup design. finally, the methodology is demonstrated for turbulence velocity measurements in the jet flow, in which the velocities of averaged diameter 15µm air filled soap bubbles are measured in a volume of 7200cm3. 1 introduction there is a strong push for large volumetric velocity measurement using small tracers in barros et al. (2021). normally, due to light scattering and characterics length scale considerations, big tracers are used for tracing large eddies in big volumes, and smaller tracers are applied for microscale eddies in smaller volumes. as can be expected from figure 1, there is a noticeable gap between attainable volumetric domains for large (≥ 300cm3) and small (1µm∼ 20µm) tracers in the range between 102 cm3 ∼ 104 cm3. as part of a long-term combined theoretical and experimental initiative, we are setting out to experimentally test the degree of locality of the interactions between wavenumber components. this requires measurements that cover the ‘global’ dynamics of the flow, while also capturing as wide a bandwidth of the turbulent (temporal and spatial) spectrum as possible. soap bubbles of diameter ∼ 15µm can follow the flow accurately to the degree of spatio-temporal resolution in the experimental design while at the same time they are highly resilient and long-lived and therefore the most viable option from a practical point of view. therefore, these smaller seeding particles are the key factor to these experiments. discetti and coletti (2018) summarized methods that have been developed to measure the full volumetric velocity (3d–3c, i.e. three-dimensional and three-component). in the past two decades, volumetric velocimetry has evolved from experiments at moderate scale of 10 cm3 up to large scales of 104 cm3 by various experiments. the initial tomo-piv experiment done by elsinga et al. (2006) was conducted with 1µm droplets in a volume of 13 cm3. later the larger measurement volumes were obtained by volumetric velocimetry in air conducted by schröder et al. (2009), humble et al. (2009), violato et al. (2011), ghaemi and scarano (2011), schröder et al. (2011) and atkinson et al. (2011), which did not exceed 102 cm3 measurement volume with micron-scale seeding tracers. the main factors limiting the scale up of piv to macroscopic dimensions summarized by scarano et al. (2015) are the limited illumination energy from the illumination source, the scattering efficiency of the tracers, the small optical aperture (due to large depth of field), and the sensitivity and spatial resolution of the camera sensors. with low repetition rate (prolonging exposure time) and millimeter scale hfsb (increasing scattering efficiency), larger measurement volumes can be observed to characterize large scale flow structure in the experiments of lobutova et al. (2009) and kühn et al. (2011). for turbulent flows, the inherent instability and three dimensions requires high resolution time-resolved volumetric velocimetry. it is impossible to utilize millimeter scale tracers to measure the same scale turbulent structure, because the length scale of the structure is smaller than the tracer diameter, and the cut-off figure 1: compilation of volumetric velocimetry investigations in air flows: the particle diameter and the imaged volume. the labeled points refers to the researches in the references: 1, atkinson et al. (2011); 2, kühn et al. (2011); 3,cafiero et al. (2015); 4, caridi et al. (2016); 5, boushaki et al. (2017); 6, pröbsting et al. (2013); 7, schneiders et al. (2016); 8,schneiders and scarano (2016); 9, schneiders and scarano (2016); 10, elsinga et al. (2006); 11, schröder et al. (2007); 12, humble et al. (2009); 13, terra et al. (2017); 14, scarano et al. (2015); 15, michaelis et al. (2012); 16, hou et al. (2021); 17, barros et al. (2021); 18, bosbach et al. (2009). the red square is the current study and the red area is the interested study area. diameter of the particles deduced from cut-off frequency could be micron-scale (see mei (1996)). the current investigation aims at characterizing both the ’global’ flow structure and millimeter scale structure with micron-scale tracers. with the capabilities of low resolution cameras,, the only option to capture the turbulence structure is to observe small tracers in a small measurement volume. now with the development of camera sensor techniques, the high resolution cameras in recent years provide the possibility of capturing the intermediate-size turbulence structure in a larger volume, in which the whole evolution process of the turbulent spectrum can be observed. however, there is still a problem between the visibility of seeding tracers and the following effect of intermediate-size turbulence structure. in order to visualize small structures in the turbulence flow, micron-scale tracers are needed to follow the unstable and three dimensional millimetre scale structures. and as the result of reducing the tracer dimension, the signal from seeding tracers to camera would drop in quadratic proportion. for the purpose of solving this problem, this paper thus details the computation of particle image size with tracers, lens and camera parameters. then with the desired turbulent scales, the relation among camera, light source and measurement volume is formulated to make sure that the particle images cannot travel across pixels (to avoid streaky particle images). two examples of approximate 15µm particles in a 7200 cm3 volume, that are 10 times larger than barros et al. (2021), are demonstrated at an acquisition frequency of ∼ 2khz. the current work thus documents how to design a time-resolved volumetric velocimetry experiment in a manner that the gap of smaller seeding particles for the target turbulent micro-scale structure in big volume for ’global’ flow is filled. the paper is organized as follows. in the section 2, the methodology that related from flow characteristics, seeding, illumination and imaging was formulated. to demonstrate the computation, a jet flow example was computed in section 3, where we use the all the formulas in section 2. the setup and experiment result corresponding to the computation in section 3 was provided in section 4. finally, our conclusion and perspectives are presented. 2 methodology 2.1 flow characteristics the target smallest structure in the flow is characterized with length-scale ` and characteristic velocity u(`). the timescale of these structure (see pope (2000)) is: τ(`)≡ ` u(`) . (1) based on the timescale, the interested frequency is fi = 1 τ(`) . (2) according to the shannon’s sampling theorem, the camera minimum repetition rate fc should be more than twice of the interested frequency fc ≥ 2 fi. both the spatial resolution and the camera repetition are based on the flow length-scale and timescale. 2.2 seeding there are six factors that affects the particles to follow the flow from the study of mei (1996), adrian and westerweel (2011) and raffel et al. (2018). response time and stokes number are related to the fidelity of tracer particles accurately following the flow. response time (τt) represents the characteristic time required for a tracer particle to reach an equilibrium condition after a flow disturbance. the response time is commonly calculated using the following form τt = d2 p ρp 18ν (3) where dp is the particle diameter, ρp is the particle density and ν is the kinematic viscosity of the ambient fluid. the stokes number (sk) is defined as the ratio of the characteristic time of a particle to a characteristic time of the flow (τ f ), sk = τt τ f (4) because the smallest eddies are characterized the timescale τ(`), the flow characteristic time equals to the timescale τ f = τ(`). in general, a stokes number of 0.1 or less given by tropea et al. (2007) could return an acceptable flow tracing accuracy with errors below 1%. in dynamic conditions like turbulent flows studied by mei (1996), the particle frequency response function hp that is defined as the sinusoidal response of particle to a sinusoidal oscillation of the flow relates to the bias between the particle velocity and flow velocity, v̂(ω) = hp(ω)û(ω) (5) where v̂(ω) is the particle velocity amplitude at frequency ω, and û(ω) is the flow velocity amplitude, both of which are deduced from particle oscillation function v(t) = v̂(ω)e−iωt and flow oscillation function u(t) = û(ω)e−iωt . defining stokes number in frequency domain ε with the frequency variable ω (see mei (1996)), ε = √ ωd2 p 2ν , (6) the energy transfer function deduced from the particle frequency response function is |hp(ω)|= |hp(ε)|= (1+ ε)2 +(ε+ 2 3 ε2)4 (1+ ε)2 +[ε+ 2 3 ε2 + 4 9(ρ−1)ε2]2 . (7) where, ρ is the density ratio of particles and ambient flow ρ = ρp/ρ f , and ρ f is the density of the ambient flow. in the study of mei (1996), the cut-off frequencies of the particles are based the 50% and 200% energy response, which means that 0.5 < |hp(ω)|2 < 2 implies very good response of the seeding particles. so the cut-off frequencies fcuto f f , the cut-off stokes number εcuto f f and the cut-off particle diameter dcuto f f can be computed from the follow equations: εcuto f f = {ε : |hp(ω)|2 = 0.5 or 2} εcuto f f ≈ [2.3800.93 + ( 0.659 0.561−ρ −1.175 )0.93 ] 1 0.93 , for ρ < 0.561 εcuto f f ≈ [ ( 3 2ρ1/2 )1.05 + ( 0.932 ρ−1.621 )1.05 ] 1 1.05 , for ρ > 1.621 fcuto f f ≈ ν π ( εcuto f f dp )2 dcuto f f ≈ εcuto f f √ π fcuto f f ν (8) however, in practice the computation process is the reversed version: a. find the particle parameter like diameter dp and density ρp; b. compute the density ratio ρ and stokes frequency domain number ε; c. get the energy transfer function result |hp(ω)|2 and decide if the seeding type is suitable for the flow; d. compute the cut-off frequency to see if it can cover the interested frequency range. to emphasize the unit of the parameters in the equations, kinematic viscosity in the equation 8 and 6 is expressed in terms of cm2/s, and the diameter of particles is in the term of µm. 2.3 imaging the observed volume v = l×h ×w is imaged by cameras with the fixed optical magnification based on the sensor size. defining the pixel resolution ls, pixel pitch ∆pix, and aperture number fs, the optical magnification of the imaging system can be deduced from the ratio of the focal lens to the working distance. m = ls∆pix l = di do . (9) where do is the distance from the object geometrical center to the lens center and di is the distance from the image geometrical center to the lens center. the particle image τp on camera sensor can be computed from: τp = √ d2 op +d2 s +d2 f ∆pix (10) where dop = mdp is the particle diameter; ds is diffraction limit spot diameter, which can be computed with aperture stop number fs and light wave length λ by ds = 2.44(1+m) fsλ; and d f is the blur circle diameter. the depth of focus (dof) δz is δz = 2ds fs 1+m m2 = 4.88 f 2 s λ (1+m)2 m2 (11) 2.4 scattered light in the piv experiment, part of the incident light is scattered by the tracers onto the camera sensors. the light scattering properties of a homogeneous and isotropic sphere in a plane wave, which leads to the lorenz-mie theory, are well documented in van de hulst (1981), thus only related final results are presented to obtain the light source budget. the first step is to project the incident wave vector onto the scattering plane. from camera lens, the received electric field vector can be expressed as er = e−ikωrp kωrp mβmsmϕe0 (12) where e0 is incident plane wave vector, kω is the incident wave vector, and rp is the scattering vector between the particle center and lens center, the angle between kω and rp is ϑ, the scattering plane lies at an angle of ϕ, ms is the scattering matrix with sum of scattering functions, mβ, and mϕ is plan transform matrix (details to see albrecht et al. (2003) pages:79-126). one dimensionless parameter defined as mie parameters is important to the scattering intensity, xm = πdp λ . (13) for particles with mie parameter xm > 10, the scattered intensity increases with the second power of the particle diameter, which means geometrical optics can be applied for approximate computation. for the lorenz-mie region with 1≤ xm ≤ 10, the scattered intensity exhibits strong oscillations. the received light intensity is ir(λ,r,ϑ) = cε 2 |e0|2 (14) where ε is the permittivity of the medium, c is the speed of light. the photons signal ic received by the cameras is the inner product of the light intensity distribution function and the camera sensor quantum efficiency function φqe(λ), ic = ∫ ∫ φqe(λ)ir(λ,r,ϑ)dλda. (15) the integral of the area depends on the aperture diameter. if the distance between particle and lens is much larger than the efficient aperture r� d and the scattering angle is in the range of geometrical optics, the scattering angle can be consider as constant. thus the integral is only the constant intensity multiply the efficient aperture area. the signal-to-noise ratio snr in this paper follows the definition of scharnowski and kahler (2016), which used standard deviations of the image intensity and the noise: snr = σa σn , (16) where σn is the standard deviation of the noise level, and σa is the standard deviation of the signal level, which can be approximated with number particle images per pixel nppp, σa = ic 2 √ nppp · ( π 4 τ2 p−1) (17) the loss-of-correlation due to image noise fσ is defined as, fσ = σ2 a σ2 a +σ2 n = ( 1+ 1 snr2 )−1 . (18) before experiments start, the noise level σn can be estimated from the camera manuals. from the theory analysis and experimental evaluation in scharnowski and kahler (2016), the loss-of-correlation fσ increase strongly from 0.4 to 0.8 with linearly increment of light power. so the main focus of the light design is to pursuit the higher fσ below 0.8 under the limited light source budget. 3 measurement computation in a jet flow example in this section, we demonstrate the computation process of the visibility problem in a jet flow with approximate 15µm diameter air-filled bubbles in a volume of 30cm×30cm×8cm. the whole estimation is carried out under the condition of international standard atmosphere (isa). 3.1 axisymmetric jet flow the axisymmetric jet flow is one of the best canonical flow for understanding the turbulence. it has been interrogated using both experimental and theoretical methods. we model the jet velocity field based on the experimental investigation results by hussein et al. (1994). according to measurement result in buchhave and velte (2017), for 1 cm jet at re= 19868, the length taylor microscales are 2.2mm and the temporal taylor microscales are 1ms at the center line at 30d downstream location and , which requires particle cut-off frequency higher than 1khz and camera repetition rate higher than 2khz. from 13mm radial distance off the jet centerline, the temporal taylor microscales are 2ms, which requires particle cut-off frequency 500hz. 3.2 seeding computation the seeding tracers that we use to verify the method are the air-filled micron-scale bubble tracers, which have mean diameters of approximately 15µm. barros et al. (2021) investigated the characteristics of the seeding in a wind tunnel experiment. the theoretical response time computed from equation 3 is 20µs, and the measured mean response time was 40µs. more details of the microbubble tracer and the bubble generator can be found in barros et al. (2021). the reason we choose this type of seeding is that the tracers size is big enough to reflect light signal, and is small enough to show trajectory of taylor micro-scale, and the response time is small enough to follow taylor micro-scales. as the temporal taylor micro-scales measured by buchhave and velte (2017) is 1ms at the center line at 30d downstream location for 1 cm jet at re = 19868, the stokes number of the microbubbles was found to be 0.04, which is in the acceptable upper limit of 0.1 given by tropea et al. (2007). according to kerho and bragg (1994) and afanasyev et al. (2011), the wall thickness of soap bubbles lies in the range 0.1µm∼ 0.3µm, the density of the bubbles is 20∼ 70kg ·m−3 in barros et al. (2021). taking the visible bubble diameter from 10µm ∼ 30µm, which have the frequency domain stoke number at 0.26 and 0.47, the cut-off frequencies varies from 752.2hz for large high density bubbles to 6.77khz for small low density bubbles. and the mean cut-off frequency is 2.21khz for 15µm particles with 0.2µm wall thickness. so in the radial range of 13mm at 30d downstream, only minor parts of the tracers (2.5% computed from statistics in barros et al. (2021)), of which the diameter is larger than 30µm and the wall thickness is thicker than 0.3µm, cannot represent the taylor microscale in the 10mm jet. out the radial range of 13mm at 30d downstream, all the tracers follows the taylor microscale eddies well. for the average diameter particles, the energy transfer function in equation 7 equals to 0.7088, which is in the efficient response range. 3.3 imaging computation considering the sensor size 27.6mm×26.3mm with resolution 2048 × 1944px and pixel pitch 13.5µm, the magnification is 0.0875. only computing the aperture number with λ = 625 that is the highest quantum efficient point of the camera used in the section 4.2, the aperture number 13 is as dof=8cm. so the f-stop is set at 16 due to the discrete number. the particle image τp is 1.97. to avoid to interfere the flow, the lens and the jet nozzle are in the same plane parallel to the front plane of the investigated volume, thus the distance from the object geometrical center to the lens center do is 35cm with the camera angle at 30°. so the focal length f is 28.16mm. the 35mm lens is adapted due to discrete product models. 3.4 light budget computation the emission spectra of a white light led consists of a wide wavelength band from 440-760 nm. in order to simplify the estimation of the image signal, we consider the optical power as if it is emitted at the single wavelength λ = 625nm. i.e. the following computation is based on λ = 625 nm and corresponding photon energy of 3.2×10−19 joules. at this wavelength the mie parameters xm equals 75.4, which is in the range of geometrical optics approximate computation. at the scattering angle of 90°, the light brightness at the target is 106 lux per led. the averaged mie scattering coefficient is about 8.6× 10−12m−2. the received light energy of the cmos detector is 2.95×10−18 joules. the quantum efficiency of the cmos detector of the camera at this photon energy is 0.95. plugging these parameters into the aforementioned model for estimating, the signal from one particle gives 8.8 counts for one led set. if a led can be pivoted to the cameras for acquiring a better scattering angle like , for example, 75°, the received light energy would be 1.39× 10−17 joules, and the particle signal on (a) drawing of the current ff setup (preliminary). (b) drawing of the current ff setup (preliminary). figure 2: the current setup in the full field section in turbulence research laboratory at technical university of denmark. the sensor is about 41.6 counts for each led set. the noise level of the cmos detector is σn = 7.2, the signal level is 10.8 and the required light density ic is 148 counts with assuming nppp = 0.01. so the number of required led sets is 3.5. because all the computation are conserved, we choose to use 3 leds in the experiment. 4 experiment and results experiments are conducted in a facility of the turbulence research laboratory (trl) of the department of mechanical engineering at technical university of denmark. the trl consists of two separate test cells – the high-resolution experiment test cell and the full-field (ff) experiment test cell (see ribergaard et al. (2021)). the experiment in this paper are implemented in the full-field testcell. 4.1 jet facility in the full-field test cell, a jet with 10mm diameter nozzle was placed in the center of injection wall. at the end of jet downstream direction, a sucking plate was mounted on the wall. the whole full-field test cell has a volume of 4600mm (streamwise length) ×4010mm (width) ×4930mm (height). outside of the test section, there is an air recirculation controlling the air flow and the seeding density without influencing flow in the test cell. 4.2 camera the visualization system that we used is a commercial lavision piv/ptv system, which consists of four 2048 × 1944px cmos high-speed video cameras (v2640), a programmable timing unit(ptu) and system software davis10. the sensor size is 27.6mm× 26.3mm, and the pixel pitch is 13.5µm with 12-bit depth. the cameras were arranged symmetrically facing the volume of interest(voi), as shown in figure 2(b). the cameras were angled at α = 30◦ to the jet center line. the cameras were mounted on a 4 degree of freedom frame, which help to adjust the view angle at the minimum point independently. according to computation from section 3, the lens focal length is 35mm, and the aperture is set at f# 8. (a) the sub-image of the measurement. (b) the signal intensity is 80-160 counts. figure 3: a sample image acquired from one camera. 4.3 lights the light sources we use in the experiment are an array of flashlight 300 leds, which is produced by lavision gmbh. these high power leds consist of 72 diodes each. the opening angle is 10°. in the pulsed-overdrive mode, the leds are operated above the nominal led current to generate short pulses at about 5 times high light intensities than the free trigger mode. but to protect the leds at such high current, the duty cycle is limited to a maximum of 10%. the brightness can be measured above 106 lux at 1m distance. in order to acquire better light conditions, forward scattering is applied by rotating the leds to the camera. 4.4 bubble generator the air-filled soap bubble generator used in this paper was developed by tsi and had been applied for several wind tunnel experiements. it consists of a 57 liter reservoir filled with a 5% surfactant-water solution. the surfactant was common non-color and non-perfume pure dish-washing detergent. at bottom of the reservoir, a piston pump is used to draw and pressurize the solution through a high pressure tube with a set of 10 nozzles. the outlet diameter of the nozzles is 0.2mm, and could be blocked with special blank nozzle heads to reduce the seeding generating rate. the air-filled-soap-bubble tracers have mean diameter of 14.7µm, response time 40µs with a dispersion of 30µm. the bubbles can be generated at high rates of 50 tracers per cm3. the stokes number of the microbubbles was 0.04, which could show the flow trajectory faithfully. 4.5 result for each snapshot, the number of the traced particles was in the range 7000–9000. a sample image acquired by one camera was shown in fig. 3(a), in which the particles can be clearly identified by the lavison davis system. the particle size is 2-4 pixels, in agreement with computation. as shown in fig. 3(b), the signal intensity from the camera sensor is about 80-160 counts, which is in the same level with the estimated 147 counts in section 3. the main difference may be due to the different angle of led to different cameras. 5 conclusions to cover the whole range from the global eddies to the smallest interested eddies, the relations of particle size, imaging, light intensity are formulated. from the characteristic timescale and length scale of the smallest interested eddies, the tracer type can be chosen by the diameter and density. then the light intensity can be estimated from the particle and the necessary minimum distance of the setup. with all the computed parameters, one setup for jet flow measurement was prepared for the volumetric velocimetry in the volume of ≥ 5000 cm3. the selected seeding tracer is air-filled soap bubbles with diameter of approximately 15µm, of which the size of seeding tracer is between millimeter scale hfsb and 1µm scale dehs. the targeted measurement volume dimension is equivalent to the volume of hfsb, which will give a higher resolution of turbulence study. the evaluation method in section 2 can successfully predict the visibility of the small tracers. our furthur work is to observe taylor micro-scale in the same time to catch the global eddies at re= 15×103 in the 1 cm jet flow. a higher reynolds number is possible to be achieved with well designed illumination source. acknowledgements this project has received funding from the european research council (erc) under the european unions horizon 2020 research and innovation program (grant agreement no 803419). the department of mechanical engineering at the technical university of denmark is also acknowledged for their generous additional support in establishing the laboratory. references adrian rj and westerweel j (2011) particle image velocimetry. cambridge university press afanasyev y, andrews g, and deacon c (2011) measuring soap bubble thickness with color matching. american journal of physics 79:1079–1082 albrecht h, borys m, damaschke n, and tropea c (2003) laser doppler and phase doppler measurement techniques. springer-verlag berlin heidelberg atkinson c, coudert s, foucaut j, stanislas m, and soria j (2011) the accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer. experiments in fluids 50:1031–1056 barros dc, duan y, troolin dr, and longmire ek (2021) air-filled soap bubbles for volumetric velocity measurements. experiments in fluids 62 bosbach j, kühn m, and wagner c (2009) volumetric velocity measurements (v3v) on turbulent swirling flows. experiments in fluids 46:539–547 boushaki t, koched a, mansouri z, and lespinasse f (2017) volumetric velocity measurements (v3v) on turbulent swirling flows. flow meas instrum 54:46–55 54:46–55 buchhave p and velte cm (2017) measurement of turbulent spatial structure and kinetic energy spectrum by exact temporal-to-spatial mapping. physfluids 29:085109 cafiero g, discetti s, and astarita t (2015) flow field topology of submerged jets with fractal generated turbulence. phys fluids 27:115 caridi g, ragni d, sciacchitano a, and scarano f (2016) hfsb-seeding for large-scale tomographic piv in wind tunnels. experiments in fluids 52:190 discetti s and coletti f (2018) volumetric velocimetry for fluid flows. meas sci technol 29 elsinga g, scarano f, wieneke b, and van oudheusden b (2006) tomographic particle image velocimetry. experiments in fluids 41:933–947 ghaemi s and scarano f (2011) counter-hairpin vortices in the turbulent wake of a sharp trailing edge. journal of fluid mechanics 689:317–356 hou j, kaiser f, sciacchitano a, and rival de (2021) a novel single-camera approach to large-scale, three-dimensional particle tracking based on glare-point spacing. experiments in fluids 63 humble r, elsinga g, scarano f, and van oudheusden b (2009) three dimensional instantaneous structure of a shock wave/turbulent boundary layer interaction. journal of fluid mechanics 622:33–62 hussein h, capp s, and george w (1994) velocity measurements in a high-reynolds-number, momentumconserving, axisymmetric, turbulent jet. journal of fluid mechanics 285:31–75 kerho m and bragg m (1994) neutrally buoyant bubbles used as flow tracers in air. experiments in fluids 16:393–400 kühn m, ehrenfried k, bosbach j, and wagner c (2011) large-scale tomographic particle image velocimetry using helium-filled soap bubbles. experiments in fluids 50:929–948 lobutova e, resagk c, rank r, and müller d (2009) extended three dimensional particle tracking velocimetry for large enclosures. in imaging measurement methods for flow analysis. springer mei r (1996) velocity fidelity of flow tracer particles. experiments in fluids 22:1–13 michaelis d, bomphrey r, henningsson p, and hollis d (2012) reconstructing the vortex skeleton of the desert locust using phase averaged pod approximations from time resolved thin volume tomographic piv. in 16th international symposium on applications of laser techniques to fluid mechanics, lisbon, portugal pope sb (2000) turbulent flows. cambridge university press pröbsting s, scarano f, bernardini m, and pirozzoli s (2013) on the estimation of wall pressure coherence using time-resolved tomographic piv. experiments in fluids 54:1567 raffel m, willert c, scarano f, kähler c, wereley s, and kompenhans j (2018) particle image velocimetry: a practical guide third edition. springer international publishing ribergaard s, zhang y, abitan js hand nielsen, jensen n, and velte c (2021) a novel laboratory pushing the limits for optics-based basic turbulence investigations. in 14th international symposium on particle image velocimetryispiv 2021, chicago, illinois, usa, august 1-5 scarano f, ghaemi s, caridi g, bosbach j, dierksheide u, and sciacchitano a (2015) on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments. experiments in fluids 56 scharnowski s and kahler c (2016) on the loss-of-correlation due to piv image noise. experiments in fluids 57 schneiders j, caridi g, sciacchitano a, and scarano f (2016) largescale volumetric pressure from tomographic ptv with hfsb tracers. experiments in fluids 57 schneiders jf and scarano f (2016) dense velocity reconstruction from tomographic ptv with material derivatives. experiments in fluids 57 schröder a, geisler r, elsinga g, scarano f, and dierksheide u (2007) investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic piv. experiments in fluids 44:305–316 schröder a, geisler r, sieverling a, wieneke b, henning a, scarano f, elsinga g, and poelma c (2009) lagrangian aspects of coherent structures in a turbulent boundary layer flow using tr-tomo piv and ftv. in 8th international symposium on particle image velocimetry schröder a, geisler r, staack k, elsinga g, scarano f, wieneke b, and westerweel j (2011) eulerian and lagrangian views of a turbulent boundary layer flow using time-resolved tomographic piv. experiments in fluids 50:1071–1091 terra w, sciacchitano a, and scarano f (2017) aerodynamic drag of a transiting sphere by large-scale tomographic-piv. experiments in fluids 58 tropea c, foss j, and yarin a (2007) springer handbook of experimental fluid mechanics. springer van de hulst h (1981) light scattering by small particles. dover publications violato d, moore p, and scarano f (2011) lagrangian and eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic piv. experiments in fluids 50:1057–1070 introduction methodology flow characteristics seeding imaging scattered light measurement computation in a jet flow example axisymmetric jet flow seeding computation imaging computation light budget computation experiment and results jet facility camera lights bubble generator result conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 aerodynamics of a cycling wheel in crosswind by coaxial volumetric velocimetry c. jux1∗, a. sciacchitano1, f. scarano1 1 delft university of technology, dept. of aerospace engineering aerodynamics, delft, the netherlands ∗ c.jux@tudelft.nl abstract the aerodynamic characteristics of a modern road cycling wheel in crosswind are studied through force measurements and 3d velocimetry in tu delft’s open jet facility. the performance of the 62 mm deep rim is evaluated for two tire profiles, and yaw angles up to 20◦. all measurements are executed at 12.5 m/s (45 km/h) freestreamand wheel-rotational velocity. the wheel’s rim-tire section in crosswind is found to behave similar to an airfoil at incidence, ultimately resulting in a reduction of the wheel’s aerodynamic resistance with increasing yaw angle magnitude. this trend, also referred to as the sail-effect, is limited by the stall angle of the tire-rim profile. the stall angle is found to be dependent on the tire surface texture and varies between 14◦ and 20◦. 1 introduction aerodynamic drag is the major resistance a cyclist needs to overcome at speeds of 40 km/h and beyond. in fact, the aerodynamic drag accounts for approximately 90% of a rider’s total resistance in this speed regime which is typical for road racing (kyle and burke, 1984). the wheels contribute to about 10% of the total aerodynamic drag (greenwell et al., 1995), making them a crucial element in any cycling-performance optimization. focusing on road cycling, a rider is exposed to a variety of wind conditions, affecting the perceived yaw angle. the concept of wind-averaged drag (wad, cooper, 2003) accounts for the statistically anticipated yaw-angle distribution experienced by a ground vehicle. the higher the vehicle velocity, the smaller the maximum yaw angle perceived for a given wind speed. for professional road cycling speeds, the probability of exceeding 20◦ yaw angle is reported to be less than 10% (brownlie et al., 2010; barry, 2018). vice versa, a rider spends 90% of the time at yaw angles below 20◦. aerodynamically designed wheels used in road racing (thus, excluding time-trial and triathlon specific multi-spoke and disc wheels) are characterized by a 40-80 mm deep rim section, that connects via a multitude of thin spokes to a cylindrical hub. in comparison to classical, shallow rim profiles, the deep-section rim fulfills two functions: on one hand, it streamlines the tire shape, effectively reducing the tire-rim drag coefficient. on the other hand, it generates —similar to a sail —a side force perpendicular to the relative wind direction. a component of this force points in the riding direction, effectively “pulling” the wheel forwards and thereby further reducing its drag coefficient for non-zero yaw angles. the latter effect is known as the “sail-effect” in literature, and it can result in a negative net drag force for wheels at high yaw angles (lukes et al., 2005; barry et al., 2012; malizia and blocken, 2020a). designing a wheel for optimal performance is, however, not solely about minimizing (wind-averaged) drag. as barry et al. (2012) point out, large side forces on wheels yield strong steering moments and can be a concern of maneuverability. similar concerns can be expressed when discussing the stall behavior for wheels at large yaw angles. in addition to the rim-geometry, the aerodynamic characteristics of a wheel depend on the interaction of rim and tire. crane and morton (2018) investigate this interaction with specific attention to tire width relative to the rim. besides tire width, data from wheel manufacturers suggests that the tire profile is equally decisive for the rim-tire interaction, because the tire’s surface texture conditions the boundary layer development for the flow over the wheel (cant, 2014). complementing the analysis of crane and morton (2018), this work includes the comparison of a slick tire to a slightly profiled tire for a fixed tire width. in the discussion of cycling wheel aerodynamics it is common practice to study wheels in isolation. experimental studies in the field focus predominantly on balance measurements (e.g. zdravkovich, 1992; greenwell et al., 1995; tew and sayers, 1999), whereas flow topology data remains undocumented to the best of the authors’ knowledge. such data is readily available from computational fluid dynamics (cfd) analysis, which presents an active line of research in the context of cycling wheel aerodynamics (godo et al., 2010; malizia et al., 2019; malizia and blocken, 2020b). authors developing numerical tools for the aerodynamic analysis of cycling wheels, however, have to rely on the experimentally documented force data for validation of their simulations. this practice becomes problematic when reported drag measurements for the same wheel show variations of up to 300%, as observed by godo et al. (2010). the large force sensitivity is ascribed to variations in the experimental setup, including tire choice, free-stream turbulence, wheel support design and wind tunnel blockage. in view of the gaps and discrepancies in literature, the present work provides an experimental analysis of the flow topology on a state-of-the-art bicycle wheel in crosswind by means of coaxial volumetric velocimetry (cvv, schneiders et al., 2018). the change in flow topology with yaw angle and tire selection is documented. additionally, the hypothesized “sail-effect” theory is scrutinized by analysis of the pressure distribution near the rim-tire surface. 2 definitions & terminology prior to presentation of the experimental apparatus and procedures in the subsequent section, we provide clear definitions of the relevant variables and coordinate systems. the provided definitions largely follow the work of tew and sayers (1999). figure 1: definition of axes systems, flow angles and velocities for a cyclist moving at a velocity vbg relative to the ground (left). relation of forces in wind and bike reference frames, illustrated on a bicycle wheel in top view (right). figure 1 (left) shows a cyclist moving at a velocity vbg relative to the ground. the direction of travel defines the main reference frame xb, pertaining to the bicycle, with the x-axis pointing opposite to the motion direction. in an external environment, the wind velocity vext and its direction (γ, the crosswind angle) relative to the cyclist’s direction of motion are relevant for the definition of the aerodynamic problem. the vector difference of external wind vext and bicycle ground velocity vbg determines the relative wind velocity vrel experienced by the cyclist. the angle between the cyclist’s motion axis and the relative wind velocity defines the yaw angle β. let us define a second coordinate system xwt whose x-axis is aligned with vrel . the subscript ‘wt’ signals that this reference frame pertains to the wind-tunnel when testing in a laboratory environment, where the x-axis is always aligned with the relative wind direction. figure 1 (right) illustrates the resistive and lateral forces acting on a bicycle wheel. classically, the drag force d acts parallel to the free-stream direction defined by vrel , whereas the lift force l points perpendicular to it, combining to the resultant force ftot . more relevant for a cyclist, however, are the force components in the reference frame xb connected to the direction of motion. the side force fs and the axial force fa are expressed as geometrical projections of l and d: fa = dcos(β)−lsin(β) (1) fs = dsin(β)+lcos(β) (2) it follows that a situation can arise in which lsin(β) > dcos(β), resulting in a thrusting force which supports the cyclist’s motion —the sail effect. in the remainder of this work, forces are always provided and discussed in the bicycle reference frame. 3 experimental apparatus and procedures wind tunnel measurements are conducted at tu delft’s open jet facility, an open jet, atmospheric wind tunnel with a 2.85×2.85 m2 exit section. all measurements are executed at a freestream velocity of 12.5 m/s (45 km/h). the turbulence intensity in the test section, with a large-scale piv seeding system installed in the settling chamber, is reported with 0.8% by giaquinta (2018). an overview of the test setup is provided in figure 2. figure 2: experimental setup in the open jet facility (left). details of the mechanical systems installed in the wind tunnel, with surrounding floor plates removed (right). 3.1 wheel model & mechanical setup a dt swiss arc 1100 dicut db 62 front wheel is installed in the test section. the 28” (700 mm diameter with tire fitted) wheel features a 62 mm deep and 27 mm wide carbon rim. while the wheel is designed to run with disc brakes, no brake discs were installed during the wind tunnel test. the clincher rim is fitted with a 25 mm tire, inflated at 7 bar. a continental gp 5000 tire featuring a mild periodic surface pattern is chosen as a baseline tire, which is compared to a slick tire, a continental gp tt. the difference in tire profile is shown in figure 3. the grooved texture element on the baseline tire model is approximately 35 mm long, and 12 mm wide, with a 35 mm gap along the circumference between two subsequent elements. the wheel is connected to the support structure using a standard 12×100 mm through axle. the singlesided support holding the wheel from the left hand side is designed to enhance optical access for the velocimetry measurements. the tire rests on two 70 mm diameter (60 mm width) rollers embedded in the wooden ground plate. the rearward roller is driven by a variable speed dc motor to control wheel rotation. the wheel rotational speed is kept constant at 348 rpm, matching a ground velocity (vbg) of 12.5 m/s equal to the freestream velocity. wheel rotational speed and freestream velocity are both maintained constant at all times, and only the yaw angle is adjusted during the measurements. the wheel branding is covered by black adhesive foil to limit background reflections in the piv acquisition. a few circular (2 mm diameter) targets on the rim serve as reference markers to locate the model in the piv data, as well as a means to verify the wheel rotational speed. (a) baseline tire, continental gp 5000, with approximate indication of texture element size. (b) option tire, continental gp tt figure 3: fotographs of the tested tires mounted on the wheel. 3.2 force measurement system the wheel model including the mechanical support and drive mechanism is installed on a 6-axis force balance situated underneath the ground plate. the balance acquires data at a frequency of 2 khz, and its accuracy is reported with 0.06% (0.15 n) of its full 250 n load capacity (alons, 2008). force data is acquired and averaged over 20 s. the balance is placed on a turntable that controls the yaw angle. as such, the force measurements delivered by the balance system pertain to the bicycle wheel reference frame (xb). the yaw angle is varied in a range of β between -22◦ and +22◦ in steps of 2◦. the arrangement of the components is illustrated in figure 2 (right). prior to force measurements on the wheel, the forces on the isolated support are recorded for all yaw angles of interest. this data is subsequently subtracted from the measurements with the wheel installed to identify the forces generated by the wheel only. 3.3 velocimetry system three-dimensional (3d) particle image velocimetry data is acquired by a coaxial volumetric velocimetry (cvv, schneiders et al., 2018) system. a lavision minishaker aero cvv probe acquires image quadruples of 640×476 px2 at a frequency of 821 hz. 16,400 images are acquired for each yaw angle, equaling an acquisition period of 20 s. the velocimeter is mounted on a universal robots ur5 robotic arm, allowing to keep a similar imaging position and distance relative to the wheel for all yaw angles. neutrally-buoyant helium filled soap bubbles (hfsb, scarano et al., 2015) of 300 500 µm diameter serve as tracer particles, which are provided by a 0.6×0.8 m2 seeding rake installed in the wind tunnel settling chamber. the measurement domain spans a 30×20×20 cm3 volume near the most upstream section of the wheel. data is only acquired on the leeward, respectively, the suction-side of the rim. 3.3.1 velocity measurement the wheel rotation results in unsteady reflections which are filtered from the particle images by means of a butterworth frequency filter (sciacchitano and scarano, 2014), followed by a directional minimum filter on a local 5×5 px2 kernel. pre-processed images are analyzed by the 3d lagrangian particle tracking algorithm “shake-the-box” (stb, schanz et al., 2016) as implemented in davis 10.1. the scattered stb tracks are subsequently ensemble averaged by a linear fit of the velocity data in ellipsoidal cells of 6×6×30 mm3 (x× y× z), analogous to the approach presented by agüera et al. (2016). anisotropic cells are selected to enhance spatial resolution in the horizontal directions, where velocity gradients are anticipated be stronger as compared to the vertical direction, for the section of the wheel imaged by the velocimetry system. the grid spacing is maintained constant at 1.5 mm in all axes. 3.3.2 pressure evaluation based on the time-averaged velocity data, the static pressure is evaluated following a dual-model approach previously presented by the authors (jux et al., 2020). in the region of irrotational flow, bernoulli’s equation provides the local pressure and the necessary dirichlet condition for the subsequent spatial integration of the pressure gradient in the rotational flow domain. lastly, the static pressure in the flow is mapped onto rim and tire surface, using the local pressure gradient information. 4 results and discussion the analysis of the measurement data starts with the force measurements. subsequently, the velocimetry data is analyzed, leading to the discussion of the pressure distribution. 4.1 force measurement figure 4 compares the axial and lateral forces as function of yaw angle for the two tested tire options. the side force fs in figure 4a features a linear trend of decreasing force magnitude with increasing yaw for moderate angles within |β| ≤ 10◦. in this range, the lateral force reduces by approx. 0.85 n/◦, independent of the selected tire. interestingly, the point of zero side force is found at a small positive yaw angle of about 2◦. for large yaw angle magnitudes beyond 10◦, the slope tapers off with a clear difference between the tires: the (slick) option tire reaches higher side force magnitudes for both, large negative and positive yaw angles, whereas the side force for the (profiled) baseline tire tapers off at slightly smaller yaw angle magnitudes. this trend is well illustrated around β = 14◦ where the force curves cross each other. (a) lateral force (b) axial force figure 4: force measurements on the isolated wheel versus yaw angle. the axial force fa in figure 4b indicates a plateau of maximum resistance for small yaw angles (2◦ ≤ β ≤ 6◦). the peak resistance of 1.12 n is found at 2◦ yaw, corresponding with the location of zero side force in figure 4a. outside the indicated range, the axial force rapidly reduces for increasing yaw angle magnitudes. for negative yaw angles the tires behave similarly, with the axial force decreasing until -10◦ yaw, where a negative resistive force is measured, meaning the wheel is generating a propulsive force in this condition, albeit small in magnitude with about 0.1 n. the trend of decreasing axial force is stagnating in the range of -14◦ ≤ β ≤ -10◦, before the axial force rapidly increases again for even lower yaw angle values. this suggests that the flow over the wheel separates around β = -12◦. for yaw angles below -10◦ the (slick) option tire shows a lower axial force as compared to the baseline tire. differences between the two tire options are stronger for large positive yaw angles. the baseline tire initially shows a steeper reduction of the axial force with increasing yaw until β = 12◦, where the trend turns, and the resistive force increases again for β > 14◦. for positive yaw angles, the resistive force on the wheel with the baseline tire is always positive. in contrast, the axial force on the wheel with the option tire keeps reducing until β = 18◦, although at a slightly slower rate. an increase in axial force is only observed for the highest tested yaw angle of 22◦. negative resistance is observed for 18◦ ≤ β ≤ 20◦. despite the differences between the tire configurations, both cases show an asymmetric behavior against yaw angle: (1) the point of maximum axial force and minimum side force is found at β = 2◦ rather than 0◦. (2) minima in axial force are different in magnitude and occur at different yaw angle magnitudes when comparing behavior in negative and positive yaw. potential sources of this asymmetry are the non-symmetric wheel support, holding the wheel only from the left-hand-side (lhs); the blockage caused by the support structure of the piv system on the wheel’s right-hand-side (rhs); and the asymmetric design of the wheel’s hub and spokes to accommodate a (centerlock) brake disc on its lhs. the above analysis of the force data suggests nonetheless that the aerodynamic performance of the wheel is strongly dependent on the tire choice. the two tires behave similarly in the range of -10◦ ≤ β ≤ 10◦, whereas for larger yaw angles the option tire features lower axial resistance, which even becomes negative, and thus acts as a (small) propulsive force. the lower resistive force of the option tire comes with an increase in lateral force, which is approximately 10% higher as compared to the wheel with the baseline tire for |β| > 14◦. in the following we scrutinize the velocimetry data to link the observed differences to changes in the flow topology. 4.2 time-average velocity field for analysis of the flow topology, we extract slices of the 3d velocimetry data in a horizontal plane at hubheight (z = 342.5 mm). the data shown in figure 5 contains the velocity field upstream and past the leeward (suction) side of the rim. the velocity contours show the normalized axial velocity component in the bicycle wheel reference frame xb, u∗ b = ub ub∞ = ub uwt∞ cos(β) (3) where the subscript ‘∞’ indicates free-stream conditions upstream of the wheel. the velocity contours are complemented by streamlines in the 2d planes. additionally, for each yaw angle, the aerodynamic effect of the tire is illustrated by plotting the difference in the axial velocity component between the baseline and the option tire. in straight ahead conditions (β = 0◦, figure 5a) the inflow decelerates towards the most upstream point of the tire. while one would expect the streamwise velocity component to stagnate at the tire surface, the finite velocity measurement reduces only to u∗ b ≈ 0.6, which is attributed to spatial resolution effects. alongside the rim-tire profile the flow accelerates reaching streamwise velocities in excess of u∗ b = 1.2 at the thickest section of the rim. the wake of the rim is not well captured by the velocimetry data. the streamlines, however, suggest the presence of a separated wake zone just downstream of the rim. the differences between the tire options are very mild at 0◦ yaw, in line with the balance data discussed previously. the region of accelerated flow past the wheel gains in size and magnitude as the yaw angle increases. consider e.g. figure 5c (β = 8◦) where for both cases the axial velocity exceeds 130% of the inflow velocity as it passes the wheel. comparing back to the straight ahead case in figure 5a it is also noted that the location of maximum velocity moved upstream, approximately to the junction of rim and tire, whereas at 0◦ yaw the maximum velocity is observed further downstream at the thickest point of the rim. likewise, the zone of decelerated flow upstream of the wheel rotates towards the windward side as the yaw angle increases. the latter is seen well by following the unity contour of axial velocity (u∗ b = 1) which follows a counter-clockwise motion with increasing yaw angle. the described trend continues for both tire cases until β = 12◦ (figure 5d). for greater yaw angles there is a substantial difference in the flow topology for the different tire options. comparing the data in figures 5e and 5f, the streamlines pertaining to the (slick) option tire in the right-hand-side plots suggest that the flow follows the largest part of the wheel contour. instead, for the (textured) baseline tire in the left-hand-side plots, the streamlines only bend slightly around the tire but continue diverging from the rim surface as the flow passes the wheel. the different behavior is also visible in the delta plot in figure 5f, which indicates that the flow around the wheel with the option tire attains far greater axial velocity. while flow data closer to the rim surface is lacking for the baseline tire at these high yaw angles, the streamlines indicate that the flow separates from the tire, similar to a leading edge separation on aeronautical airfoil profiles at high angle of attack. such leading edge separation results in a loss of lift (here, side force) and a simultaneous increase in drag (here, axial force) which is in line with the observations from the force data above. (a) β = 0◦ (b) β = 4◦ (c) β = 8◦ (d) β = 12◦ figure 5: time-average velocity contours in xy-planes at hub height (z = 342.5 mm), along with 2d surface streamlines. velocity contours show the normalized axial velocity component in the bicycle wheel reference frame. (left) baseline tire. (right) option tire. (center) delta = ubaseline −uoption. (continues on next page) (e) β = 16◦ (f) β = 18◦ figure 5: (continued) time-average velocity contours in xy-planes at hub height (z = 342.5 mm), along with 2d surface streamlines. velocity contours show the normalized axial velocity component in the bicycle wheel reference frame. (left) baseline tire. (right) option tire. (center) delta = ubaseline −uoption. 4.3 pressure data following the analysis of the velocity data, we briefly investigate the pressure distribution over tire and rim profile. similar to the previous assessment, the analysis starts in a horizontal xy-plane at hub height (z = 342.5 mm). because both tire options behave similar for moderate yaw angles, and data close to the figure 6: cp profiles over the tire-rim surface at hubheight (z = 342.5 mm) for the option tire (gp tt). surface is lacking for high yaw angles on the baseline tire, we limit ourselves to the study of the (slick) option tire here. figure 6 shows the pressure profiles on the leeward side of the wheel for β = [0, 8, 16]◦. the pressure profiles are characterized by a steep pressure reduction over the upstream tire section. as the yaw angle increases, the pressure reduction gains in magnitude, signifying greater suction with increasing yaw angle. the location of minimum cp moves downstream as the yaw angle grows. at 0◦ yaw the minimum pressure of cp = -0.7 is recorded at x/c = 0.06, before approaching an approximately constant value of cp = -0.5 further downstream. at 8◦ yaw instead, the minimum pressure coefficient exceeds a value of -1, and it is obtained slightly further downstream (x/c = 0.13). increasing the yaw angle further to 16◦, the pressure coefficient drops to a minimum of cp = -1.75 at x/c = 0.26, followed by an adverse pressure gradient approaching cp = -0.5 at x/c = 0.6. complementing the above pressure profiles in the wheel center plane, 3d iso-surfaces of pressure coefficient are shown for the three selected cases in figure 7, along with axial velocity contours on the upper and lower boundary of the measurement volume. for each case, two iso-surfaces are plotted: the first, at cp = 0.35 (red) indicates the volume of increased pressure resulting from the flow deceleration upstream of the wheel. the second, at cp = -0.6 (blue) is selected to visualize the volume of reduced pressure induced by the flow acceleration alongside the wheel. comparing the latter iso-surface for the three yaw angles confirms the growth of the low-pressure region with increasing yaw angle, signaling a likewise increase in side force. figure 7: axial velocity contours in horizontal planes at z = [242.5, 442.5] mm along with 3d pressure iso-surfaces of cp = 0.35 (red) and -0.6 (blue). data shown for wheel fitted with option tire at β = 0◦ (left), 8◦ (center) and 16◦ (right). the observed trend is qualitatively in line with the force data presented in section 4.1 which indicated a monotonically increasing side force magnitude with increasing yaw angle in this range. it further supports the theory that the tire-rim profile in crosswind indeed behaves like an airfoil at incidence, thereby making the wheel work like a sail. 5 conclusions the aerodynamic characteristics of a state-of-the-art road cycling wheel in cross wind have been assessed experimentally by means of force measurements and a full-scale 3d velocimetry investigation. additionally, the interaction of rim and tire is studied by comparison of a textured and a slick tire. the resistive force on the isolated wheel is highest at moderate yaw angles of β = 2◦ ± 4◦. outside this range, the aerodynamic resistance of the wheel is reduced as the yaw angle magnitude increases. analysis of the velocimetry data confirms that the reduction in resistance measured by a force balance is indeed a consequence of the “saileffect”, resulting from a substantial side-force on the wheel at yaw incidence. the benefit of this effect is limited by the stall angle of the tire-rim combination, which is found to be dependent on the tire choice. the two tested tires behave similarly for negative yaw angles, with the flow separating around β = -14◦. for positive yaw angles, the slick tire performs significantly better, increasing the separation angle from 14◦ to 20◦ with respect to the profiled baseline tire. acknowledgements we thank thomas koep on behalf of dt swiss for providing the wheels for the study. likewise, we thank dennis bruikman, peter duyndam and frits donker duyvis for the invaluable technical support. this research is supported by lavision gmbh. references agüera n, cafiero g, astarita t, and discetti s (2016) ensemble 3d ptv for high resolution turbulent statistics. measurement science and technology 27:124011 alons hj (2008) ojf external balance. report nlr-cr-2008-695. nederlands luchten ruimtevaartcentrum (national aerospace laboratory, nlr) barry n (2018) a new method for analysing the effect of environmental wind on real world aerodynamic performance in cycling. in 12th conference of the international sports engineering association. volume 2. page 211 barry n, burton d, crouch t, sheridan j, and luescher r (2012) effect of crosswinds and wheel selection on the aerodynamic behavior of a cyclist. in engineering of sport conference 2012. volume 34. pages 20–25 brownlie l, ostafichuk p, tews e, muller h, briggs e, and franks k (2010) the wind-averaged aerodynamic drag of competitive time trial cycling helmets. procedia engineering 2:2419–2424 cant g (2014) back to the wind tunnel. www.swissside.com/blogs/news/back-to-the-wind-tunnel accessed on 17.05.2021 cooper kr (2003) truck aerodynamics reborn-lessons from the past. sae transactions 112:132–142 crane r and morton c (2018) drag and side force analysis on bicycle wheel-tire combinations. journal of fluids engineering-transactions of the asme 140 giaquinta d (2018) the flow topology of the ahmed body in cross-wind: an experimental investigation by means of robotic volumetric piv. msc thesis, tu delft godo m, corson d, and legensky s (2010) a comparative aerodynamic study of commercial bicycle wheels using cfd. in 48th aiaa aerospace sciences meeting including the new horizons forum and aerospace exposition. page 1431 greenwell di, wood nj, bridge ekl, and addy rj (1995) aerodynamic characteristics of low-drag bicycle wheels. aeronautical journal 99:109–120 jux c, sciacchitano a, and scarano f (2020) flow pressure evaluation on generic surfaces by robotic volumetric ptv. measurement science and technology kyle cr and burke e (1984) improving the racing bicycle. mechanical engineering 106:34–45 lukes ra, chin sb, and haake sj (2005) the understanding and development of cycling aerodynamics. sports engineering 8:59–74 malizia f and blocken b (2020a) bicycle aerodynamics: history, state-of-the-art and future perspectives. journal of wind engineering and industrial aerodynamics 200:104134 malizia f and blocken b (2020b) cfd simulations of an isolated cycling spoked wheel: the impact of wheel/ground contact modeling in crosswind conditions. european journal of mechanics b-fluids 84:487–495 malizia f, montazeri h, and blocken b (2019) cfd simulations of spoked wheel aerodynamics in cycling: impact of computational parameters. journal of wind engineering and industrial aerodynamics 194 scarano f, ghaemi s, caridi gca, bosbach j, dierksheide u, and sciacchitano a (2015) on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments. experiments in fluids 56:42 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:70 www.swissside.com/blogs/news/back-to-the-wind-tunnel schneiders jfg, scarano f, jux c, and sciacchitano a (2018) coaxial volumetric velocimetry. measurement science and technology 29:065201 sciacchitano a and scarano f (2014) elimination of piv light reflections via a temporal high pass filter. measurement science and technology 25:084009 tew gs and sayers at (1999) aerodynamics of yawed racing cycle wheels. journal of wind engineering and industrial aerodynamics 82:209–222 zdravkovich m (1992) aerodynamics of bicycle wheel and frame. journal of wind engineering and industrial aerodynamics 40:55–70 introduction definitions & terminology experimental apparatus and procedures wheel model & mechanical setup force measurement system velocimetry system velocity measurement pressure evaluation results and discussion force measurement time-average velocity field pressure data conclusions paperispiv2021_sciacchitano_da_july052021 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 main results of the first data assimilation challen ge a. sciacchitano 1*, b. leclaire 2, a. schröder 3 1 delft university of technology, faculty of aerospace engineering, delft, the netherlands 2 onera, department of aerodynamics, aeroelasticity and acoustics, meudon, france 3 dlr, institute of aerodynamics and flow technology, göttingen, germany *corresponding author: a.sciacchitano@tudelft.nl abstract this work presents the main results of the first data assimilation (da) challenge, conducted within the framework of the european union’s horizon 2020 project homer (holistic optical metrology for aero-elastic research), grant agreement number 769237. the challenge was jointly organised by the research groups of dlr, onera and tu delft. the same synthetic test case as in the lagrangian particle tracking (lpt) challenge (also presented in this symposium) was considered, reproducing the flow in the wake of a cylinder in proximity of a flat wall. the participants were provided with three datasets containing the measured particles locations and their trajectories identification numbers, at increasing tracers concentrations from 0.04 to 1.4 particles/mm3. the requested outputs were the three components of the velocity, the nine components of the velocity gradient and the static pressure, defined on a cartesian grid at one specific time instant. the results were analysed in terms of errors of the output quantities and their distributions. additionally, the performances of the different da algorithms were compared with that of a standard linear interpolation approach. although the velocity errors were found to be in the same range as those of the linear interpolation algorithm, typically between 3% and 12% of the bulk velocity, the use of the da algorithms enabled an increase of the measurement spatial resolution by a factor between 3 and 4. the errors of the velocity gradient were of the order of 10-15% of the peak vorticity magnitude. accurate pressure reconstruction was achieved in the flow field, whereas the evaluation of the surface pressure revealed more challenging. 1 introduction in the recent years, three-dimensional velocity measurements by particle image velocimetry (piv) have evolved from crosscorrelation-based volume analysis (elsinga et al., 2006; scarano, 2012) to tracking of individual particles (particle tracking velocimetry, ptv, malik et al., 1993; lagrangian particle tracking, lpt, schanz et al., 2016). one of the main advantages of the particle tracking approaches lays in the increased measurement spatial resolution, because a velocity (and acceleration) vector is determined for each and every reconstructed particle, without averaging such information within a spatial subdomain. however, the particle tracking approaches return velocity vectors at the scattered locations where the tracer particles are present. for data reduction purposes, it is often convenient to map such information onto a regular (cartesian) grid, so as to facilitate the operations required for the computation of relevant flow properties such as the vorticity, the qor λ2-criteria for vortex identification and the shear rate, among others. additionally, the evaluation of the pressure field via the direct integration of the pressure gradient or the solution of the poisson equation for pressure (van oudheusden, 2013) is typically performed on a regular grid, although grid-less approaches for the solution of the poisson equation have also been proposed (kunhert and tiwari, 2001). the conventional techniques to map scattered flow information onto a regular grid involve the use of interpolation (usually linear or cubic interpolation) or spatial averaging of the particles’ velocities and accelerations over sub-domains or bins (e.g. adaptive gaussian windowing technique, agw, agüí and jimenez, 1987). however, these approaches suffer from low spatial resolution, because are incapable to resolve flow wavelengths smaller than the interparticle distance or the bin linear size. as a result, they lead to spatial modulation of the flow field and unresolved or underresolved length-scales, especially for the study of turbulent flows where a wide range of length-scales is present. the use of prior information on the flow physics, e.g. by imposing the conservation of mass for incompressible flows via application of a solenoidal filter to the retrieved velocity field (schiavazzi et al., 2014; azijli and dwight, 2015), has been shown as a viable methodology to attenuate the measurement noise and enhance the accuracy of the measured flow field. more advanced data assimilation approaches have been recently proposed to enforce the compliance of the resulting flow field with the governing equations of fluid motion, aiming at increasing the range of length-scales resolved, possibly beyond the limit of nyquist criterion. in the flowfit algorithm introduced by gesemann et al. (2016), the velocity field is divided into cubic volumes, where it is represented as a weighted sum of 3rd order 3d base splines. the spline functions are evaluated by solving an optimisation problem, where a cost function is minimised that imposes physical constraints such as the conservation of mass and momentum for incompressible flows. alternative approaches involve the use of vortex methods (christiansen, 1973), which make use of the vorticity transport equation at one time instant (schneiders et al., 2016) or during a short time sequence (jeon et al., 2018; scarano et al., 2021; jeon, 2021) to retrieve a vorticity field compatible with the measured particles’ velocities and accelerations. four-dimensional data assimilation has been proposed recently within the framework of variational methods for computational fluid dynamics (chandramouli et al., 2020). 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 the discussion above highlights the presence of a multitude of approaches aiming at combining flow measurements by lpt and background information on the flow physics to accurately reconstruct the flow field on a regular grid. the aim of the first data assimilation challenge, whose main results are presented in this work, is to comparatively assess the different data assimilation approaches using a database from a simulated experiment, so as to shed light on the capabilities of these approaches and on which parameters and error sources have the largest influence on their performance. 2 database description the database used for the data assimilation challenge is described in detail in the contribution from leclaire et al. (2021), also presented at the ispiv 2021. for sake of completeness, a short description of the database is reported hereafter. the database contains the particles’ velocities from a synthetic experiment on a wall-bounded wake flow behind a cylinder. the cylinder had a diameter d = 0.01 m, and was located at 0.01 m distance from the wall. the fluid used in the simulations was air, but scaling was applied to simulate an experiment in water at a bulk velocity of vꝏ = 0.667 m/s, yielding a turbulent boundary layer of thickness δ ≈ 60 mm and a momentum thickness reynolds number of reθ = 4,500. the flow domain for the da challenge was the same as the one used in the lpt challenge (sciacchitano et al., 2021), and had dimensions of 0.1 � × 0.05 � × 0.03 � (∆x × ∆y × ∆z, being x, y and z the streamwise, spanwise and wall-normal directions respectively; see figure 1). figure 1: side view (left) and top view (right) of the flow domain. the dashed rectangle indicates the domain used for the da challenge. iso-contours of the instantaneous streamwise velocity component are shown; the flow is in the positive x direction. the origin of the system of axes used for the da challenge is indicated with o in the figure. the particles’ positions in 3d space and their trajectories identification numbers were provided to the participants for a sequence of 50 equally-spaced time instants at time separation ∆t = 600 µm. the particles’ positions were affected by a 0.1 back-projected pixel ��� random error (information not disclosed to the participants). the database comprised three different datasets at increasing tracer particles concentrations, as reported in table 1. table 1: main parameters of the datasets composing the da database. dataset # equivalent ppp1 # of particles in the fluid domain particles concentration c [particles/mm3] average interparticle spacing l [mm] normalised interparticle spacing l /h 1 0.005 6,422 0.043 1.61 4.0 2 0.025 31,847 0.212 0.94 2.3 3 0.160 204,280 1.362 0.52 1.3 the participants were requested to provide 13 output quantities on a cartesian grid of spacing h = 0.4 mm composed of 251 grid locations along x (from –50 mm to +50 mm), 126 along y (from –25 mm to +25 mm) and 76 along z (from +0.01 mm to +30.01 mm), for a total of 2,403,576 grid points. the 13 output quantities were: the three components of the velocity vector (� , ��, ��), in m/s; the nine components of the velocity gradient tensor ( �� ��⁄ , �� ��⁄ , �� ��⁄ , ��� ��⁄ , ��� ��⁄ , ��� ��⁄ , ��� ��⁄ , ��� ��⁄ , ��� ��⁄ ) in s–1; the static pressure p in pa, relative to the point (�, �, �) = (0, 0.2, 0.01) mm. all output quantities were requested at the time instant number 25. the data were analysed in terms of errors of the output quantities (viz. difference from the actual value from the les simulation at each grid location), their distributions and spectral content. 1 the equivalent ppp is evaluated considering a synthetic experiment as that of the lpt challenge described in leclaire et al. (2021) and sciacchitano et al. (2021). 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 3 participants and approaches four research groups participated to the da challenge, namely the german aerospace centre from göttingen (dlr), the kutateladze institute of thermophysics in russia (iot), delft university of technology in the netherlands (tu delft, shortly tud) and the german instrumentation company lavision gmbh. the approaches employed by these groups are briefly summarised hereafter. as reported in table 2, differences among the algorithms are already present in the way the particles’ locations are fitted to retrieve the positions, velocities and accelerations at time instant t = 25, which constitute the inputs for the da approaches. table 2: types and kernel sizes of the fit used to determine the particles’ positions, velocities and accelerations. participant (approach) track fit type track fit kernel size dlr cubic b-spline adaptive, based on the spectral analysis of the particles’ tracks iot cubic b-spline adaptive, based on the spectral analysis of the particles’ tracks lavision (vic#-3d) 2nd order polynomial 7/7/9 at ppp = 0.005/0.025/0.160 lavision (vic#-4d) 2nd order polynomial 7/7/9 at ppp = 0.005/0.025/0.160 tud (vic+) 2nd order polynomial, 3 iterations 9 tud (tsa) 2nd order polynomial, 3 iterations 9 3.1 dlr: flowfit2 the approach employed by the dlr group is based on the trackfit and flowfit2 algorithms, which are described in detail in gesemann et al. (2016). the main processing steps are the following: a) determination of the particles’ trajectories according to the provided locations and track-id data; b) spectral analysis of the location-over-time signals to estimate the optimal trackfit parameters; c) trackfit: estimation of the particle trajectories as uniform cubic b-spline curves; d) sampling of the particle track b-spline functions at the specified time step (namely 25), including first and second derivatives (velocity and acceleration), as input to flowfit; e) flowfit2: non-linear estimation of velocity and pressure fields as 3d uniform cubic b-splines based on a weighted least-square optimisation that minimises the sum of several squared errors. those include: the divergence of the velocity field, the gradient of the divergence of the velocity field, deviations between measured and fitted velocities and accelerations, deviations from the pressure poisson equation, velocity vector laplacian. before the flowfit2 step, additional virtual particles with zero velocity and acceleration are generated at the wall (z = 0 m) to comply with the no-slip boundary condition. 3.2 iot the stb algorithm from the openlpt project (tan et al. 2020) with slight modifications is used by the iot group. the processing algorithms employed are described in bobrov et al. (2021) and consists of four main stages: a) track approximation by weighted cubic cardinal b-splines (gesemann et al., 2016), where the weighting coefficients were determined by minimisation of a cost function using the gradient descent method. the velocity and acceleration along the tracks were computed via analytical derivation in time of the b-splines using previously obtained weights; b) calculation of the spatial derivatives of the velocity and acceleration via the least-squares method on an unstructured grid, using the approach proposed by kuhnert and tiwari (2001); c) calculation of the pressure field via iterative joint solution of the navier-stokes equations and the poisson equation for pressure (kuhnert and tiwari, 2001); d) kriging interpolation of the resulting data onto the output cartesian grid. to enhance the accuracy of the estimated pressure field at low seeding concentrations, virtual particles were inserted into the flow domain, using kriging interpolation of the values from the known particles’ positions. 3.3 tud: vic+ and tsa the tu delft team made use of two approaches, both based on the vortex-in-cell method (christiansen, 1973). the first approach, named vic+ (schneiders and scarano, 2016), seeks a vorticity field defined at the output cartesian grid such that a cost function is minimised. the latter depends on the difference between the measured and reconstructed velocities and lagrangian accelerations at the particles’ locations. the velocity field is then obtained from the reconstructed vorticity field via the solution of the poisson equation. the second approach, named time-segment assimilation (tsa, scarano et al., 2021) is an evolution of the vic+ concept which exploits the temporal information from time-resolved measurements. in this case, the vorticity dynamics equation is used to march forward and backward for a finite number of exposures (in total 31 at ppp = 0.005 and 21 at ppp = 0.025) the first guess of the vorticity field at time t = 0. the cost function is built as the difference 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 between the measured and the reconstructed velocity at the particles’ locations along the entire time segment. it should be noted that, due to the high computational cost, the tsa results were only produced for ppp = 0.005 and 0.025, and not for ppp = 0.160. also, the pressure field was evaluated only for the vic+ analysis (and not for the tsa analysis), by solving the poisson equation for pressure (van oudheusden, 2013), using neumann boundary conditions at all boundary points. 3.4 lavision: 3d and 4d vic# also lavision gmbh made use of two approaches, one relying only on instantaneous data (3d) and one exploiting the information on the time evolution from time-resolved measurements (4d). the approaches, indicated with vic#-3d and vic#-4d, respectively, are based on an evolution of the vic+ algorithm (schneiders and scarano, 2016) where additional physical constraints on the divergence of velocity, vorticity, eulerian acceleration, lagrangian acceleration and on the momentum equation are imposed (jeon et al., 2018; jeon, 2021). a multi-grid approximation was performed so as to decrease the computational cost due to large number of elements in the output cartesian grid. 4 results 4.1 velocity components the results of the data assimilation algorithms are expected to exhibit an increasing uncertainty for decreasing seeding concentration, as a consequence of the larger inter-particle distance and therefore lower spatial resolution. for the lowest seeding concentration case (ppp = 0.005), figure 2 compares the streamwise velocity component along several planes in the measurement domain, as well as an iso-surface of the q-criterion (q = 80,000 s-2) among ground truth (top-left), participants’ results, and linear interpolation of the particles’ velocities (bottom right). from the ground truth flow field, the decrease of the velocity towards the wall (z = 0) due to the presence of the boundary layer is evident. the flow field is clearly turbulent, with small coherent vortical structures visualised via the q-criterion mainly in the region x < 0. the results of the different algorithms are overall rather similar to the ground truth, in that they correctly reproduce the turbulent nature of the boundary layer and close-to-zero velocity at the wall. the result from tud tsa exhibits more edge effects especially towards the lower limit of y, where the streamwise velocity component decreases to unphysical values close to zero. the linear interpolation result correctly reproduces the main characteristics of the flow field, although with a larger spatial modulation, thus resulting in smoother velocity contours. however, when the small vortical structures are compared in terms of iso-surfaces of q-criterion, it is clear that none of the data assimilation algorithms (nor the linear interpolation) is able to correctly capture those due to the limited spatial resolution of the measurement. figure 2: slices of the streamwise velocity component and of iso-surfaces of q criterion (q = 80,000 s–2) for the ppp =0.005 case. the ground truth flow field from the numerical simulations is shown on the top-left. the result from the linear interpolation of the particles velocities onto the cartesian grid is shown on the bottom-right. a quantitative analysis of the bias and random errors of the velocity magnitude as a function of the seeding concentration is conducted in the entire measurement domain excluding 4 mm (ten grid points) from all the outer edges to avoid edge effects. such analysis is presented in figure 3. the bias error (figure 3-left) exhibits little dependence on the ppp, and it typically 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 attains values within 0.5% of the fluid bulk velocity vꝏ; such errors increase slightly at the lowest ppp, reaching values of 2% of vꝏ. the highest errors are encountered with the tud tsa algorithm, attaining values of up to 4% of vꝏ. also, it is remarked that the linear interpolation algorithm yields similar but slightly larger bias errors to most data assimilation algorithms. the random error, illustrated in (figure 3-left), shows the expected decrease with increasing seeding concentration. at the lowest ppp, the random error is between 0.06 and 0.085 m/s (or 9% and 13% of vꝏ), and decreases to about 0.025 m/s (roughly 4% of vꝏ) at the highest ppp. at each seeding concentration, small but systematic differences of about 0.01-0.02 m/s among the different algorithms are recorded. it is noticed that the linear interpolation approach yields random error values of the same order as those of the data assimilation algorithms. figure 3: bias (left) and random (left) error of the velocity magnitude as a function of the ppp. the symbol keys apply to both plots. to further assess the capabilities of the data assimilation approaches to resolve small scales in the flow field, a spectral analysis is conducted in a region of the flow domain away from the wall, namely for 20 mm ≤ z ≤ 30 mm. the average power spectral density in such region of the wall-normal velocity component vz is illustrated in figure 4 for the three ppp values. as expected, the different algorithms agree well with the ground truth results (thick grey lines) at the lower wavenumbers k (larger wavelengths λ), whereas the agreement worsens for increasing wavenumbers. also expected is the improved agreement with increasing seeding concentration. at the lowest ppp of 0.005 (figure 4-left), the linear interpolation result departs from the ground truth already at a wavenumber of 50 m-1 (or wavelength of 20 mm, that is more than 12 times larger than the average inter-particle distance). in contrast, the data assimilation algorithms follow the ground truth result up to k ≈ 200 m–1 (λ ≈ 5 mm), thus yielding an increase of the range of resolved length scales by factor 4 with respect to the linear interpolation. similar trends are retrieved also at the higher seeding concentrations (figure 4-middle and -right), with improved agreement with the ground truth result. in particular, at the highest ppp of 0.16, most data assimilation algorithms capture correctly the power spectrum up to k ≈ 300 m-1 (λ ≈ 3 mm), whereas the linear interpolation result starts departing from the ground truth already around k ≈ 100 m-1 (λ ≈ 10 mm). hence, based on this spectral analysis, it can be concluded that the data assimilation algorithms increase the range of resolvable length scales by factor 3 to 4 with respect to the standard interpolation, and that the smallest fluctuations correctly captured occur at a length scale that is 3 to 6 time larger than the average inter-particle distance. figure 4: power spectral density of the wall-normal velocity component vz, averaged in the region 20 mm ≤ z ≤ 30 mm. left: ppp = 0.005; middle: ppp = 0.025; right: ppp = 0.16. the bottom horizontal axis represents the wavenumber, while the top horizontal axis represents the corresponding wavelength. the dashed vertical line, when present, corresponds to the wavenumber (or wavelength) associated with the average inter-particle spacing. the symbol keys apply to all plots. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 4.2 velocity gradient components the evaluation of the components of the velocity gradient is notoriously more challenging than that of the velocity itself for two main reasons: first, under-resolved or unresolved length scales result in the underestimation of the spatial derivatives of the velocity; second, the spatial derivative operator acts as a high-pass filter onto the velocity field, thus yielding a decrease of the measurement signal-to-noise ratio in presence of uncorrelated noise. the accuracy of the evaluation of the velocity gradient components is assessed in figure 5 via the analysis of the vorticity magnitude for the case ppp = 0.005. the ground truth vorticity field presents vorticity peaks up to 1000 hz attributed to small-scale vortical structures especially in the region closer to the cylinder (x < 0). all considered algorithms exhibit a significant modulation of the vorticity field, yielding vorticity peak values seldom exceeding 500 hz. the highest modulation occurs with the iot algorithm and, as expected, when using the linear interpolation approach. figure 5: slices of the vorticity magnitude for the ppp =0.005 case. the ground truth flow field from the numerical simulations is shown on the top-left. the vorticity result from the linear interpolation of the particles velocities onto the cartesian grid is shown on the bottomright. figure 6: error of the vorticity magnitude obtained with the different algorithms, for the case ppp = 0.005. the contours of the vorticity error magnitude, presented in figure 6, confirm that the vorticity errors are of the order of 100 hz or 10% of the peak vorticity. these errors are mainly negative because the algorithms tend to underestimate the actual vorticity. the maximum errors are encountered closer to the cylinder, that is at lower values of the streamwise coordinate x, where small vortical structures of high swirling strength are present. from the visual analysis of the contours of figure 6, 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 small differences are noticed among the different algorithms, with lower vorticity errors for dlr and lavision 4d algorithms and larger errors for the iot and the linear interpolation approaches. similar to the velocity, a quantitative analysis of the vorticity magnitude error is conducted in terms of mean bias and random components in the entire measurement domain, excluding a region of 4 mm thickness at the outer edges. the results of this analysis are shown in figure 7. as expected, there is a clear trend of increasing performance when increasing the seeding concentration. as discussed above, the mean bias errors (figure 7-left) are negative as a consequence of the spatial modulation of the velocity field that yields underestimated vorticity values. the dlr algorithm exhibits the best performance in terms of mean bias errors, with error values between -80 hz at the lowest ppp and -20 hz at the highest ppp. similar values are retrieved also with the lavision algorithms and the tu delft vic+ approach. in contrast, the iot algorithm and the linear interpolation approach return bias error values between -120 and -80 hz. the random error component, illustrated in figure 7-right, exhibits values of around 150 hz at ppp = 0.005, with small differences among the different algorithms. at higher seeding concentrations, a significant error reduction is retrieved down to 80 hz with the dlr and lavision algorithms; in contrast, for the other algorithms the random errors remain above 110 hz (iot algorithm) or even close to 130 hz (tu delft vic+ and linear interpolation approaches). considering that the ground truth peak vorticity attains values of about 1000 hz, it can be concluded that, using the best data assimilation algorithms at the highest ppp level of 0.160, the vorticity error values are of the order of 2% and 8% for the bias and random components, respectively. however, these errors increase to 8% and 13%, respectively, when less performing data assimilation algorithms are employed. figure 7: bias (left) and random (left) error of the vorticity magnitude as a function of the ppp. the symbol keys apply to both plots. for sake of completeness, the histograms of the velocity divergence are computed, so as to evaluate the accuracy also of the diagonal terms of the velocity gradient tensor. being the flow incompressible, the velocity divergence is expected to be null, and the histograms are theoretically dirac pulses centered at zero. the results, illustrated in figure 8, show that the lavision 3d and 4d algorithms achieve close-to-zero divergence at all ppp values. larger values of the velocity divergence are estimated with the dlr algorithm and the tu delft approaches, typically within 1 or 2 hz. in contrast, the iot and the linear interpolation approaches return a much broader distribution of the velocity divergence, which implies a lower degree of agreement of the measured flow field with the continuity equation. figure 8: histograms of the velocity divergence for ppp = 0.005 (left), 0.025 (middle) and 0.16 (right). the symbol keys apply to all plots. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 4.3 static pressure the pressure gradient is related to the lagrangian acceleration via the navier-stokes equations, and then integrated either directly or solving the poisson equation for pressure (van oudheusden, 2013). hence, errors in the lagrangian acceleration propagate to the pressure, although the integration operator is expected to attenuate the contribution of the random errors. figure 9 illustrates the static pressure field in a plane close to the centerline (y = –0.2 mm) for the lowest seeding density case (ppp = 0.005), along with the corresponding error fields. the ground truth field shows the presence of two large lowpressure blobs, at x = –0.03 m and x = 0.015 m respectively, associated with vortices shed by the cylinder. the minimum pressure within these regions is of about -110 pa and -70 pa, respectively, corresponding to 50% and 30% of the free-stream dynamic pressure (qinf = 221.8 pa). additionally, small flow features with low pressure are present near the upstream edge of the measurement domain. all algorithms are capable to reproduce the largest low-pressure blob at x = –0.03 m, although not always with the correct pressure magnitude. in particular, the iot algorithm yields a minimum pressure attenuated by 50%, whereas the linear interpolation result2 overestimates the pressure peak by 100%. the other algorithms return correct values of the pressure peak typically within 10%. the second pressure blob, located at x = 0.015 m, is not captured by the iot algorithm, whereas all other algorithms correctly reproduce it. the error fields, presented in the second column of figure 9, show that the errors are mainly random, with peaks as high as 50 pa or over 20% of the free-stream dynamic pressure. the iot algorithm and the linear interpolation approach exhibit larger bias errors in correspondence of the pressure peak at x = -0.03 m, which is respectively underestimated and overestimated by the two approaches. the quantitative analysis of the errors, illustrated in figure 10, confirms that the random errors dominate over the bias errors. the latter are typically in the range [5, 5] pa, except for the iot algorithm, exceeding the values of ±5 pa for ppp = 0.025, and the linear interpolation approach, exceeding the values of ±5 pa for all the concentrations. as expected, the accuracy of the pressure reconstruction increases with the seeding density, thus yielding a reduction of the random error component (figure 10-middle). however, the random errors curves decrease rapidly up to ppp = 0.025, whereas they flatten for higher seeding concentrations. at ppp = 0.16, the random errors from the different algorithms range between 4 pa (less than 2% of qinf, achieved with the dlr algorithm) and 18 pa (8% of qinf, obtained with the linear interpolation approach). also, it is noticed that the use of temporal information in the data assimilation algorithm slightly improves the pressure reconstruction (see comparison between lavision 3d and lavision 4d results, where the latter always yields lower random errors).the cross-correlation coefficients between the participants’ results and the ground-truth pressure field (figure 10-right) confirm the capability of the data assimilation algorithm to accurately reconstruct the larger-scale features in the pressure field. for the two higher seeding concentrations, the cross-correlation coefficient is close to or above 0.8, with values even exceeding 0.95 especially at ppp = 0.160. as anticipated, the pressure reconstruction is more challenging at the lowest seeding concentration due to the low measurement spatial resolution; in these conditions, the cross-correlation coefficients range between 0.5 (iot algorithm) and 0.93 (lavision 4d algorithm). 2 the linear interpolation result is obtained by first computing the velocity and lagrangian acceleration fields based on linear interpolation of the particles’ information, then computing the pressure gradient as ∇ = −� �� ��⁄ , and finally solving the poisson equation for pressure. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 figure 9: static pressure field (left column) and error of the static pressure (right column) at the plane y = -0.2 mm, for the case ppp = 0.005. first row: ground truth result. the values in the colorbars are in pascal. figure 10: mean bias error (left), random error (middle) and cross-correlation coefficient with respect to the ground truth (right) of the static pressure, evaluated at plane y = -0.2 mm, as a function of the ppp. the errors and cross-correlation coefficient are evaluated over the entire measurement domain, excluding a border of 4 mm (10 grid points) at the outer edges. the symbol keys apply to all plots. the evaluation of the static pressure on the surface of solid objects is of great relevance in aerodynamics and fluid-structure interaction problems, because it enables to characterize the spatial distribution of the aerodynamic loads. unfortunately, computing the surface pressure often involves even more challenges than evaluating the static pressure in the flow field, because of the small magnitude of the wall-pressure fluctuations, the large velocity gradients in the boundary layer, and the presence of unwanted light reflections. the ground-truth surface pressure field, illustrated in figure 11-top for the case ppp = 0.005, confirms that indeed the pressure variations on the surface are a small fraction of those in the flow field; smallscale flow structures are visible, with pressure values varying between –30 and 30 pa, with the pressure generally decreasing along the streamwise direction. the results of the different participants, shown in the first column of figure 11, confirm the complexity of the surface pressure reconstruction problem. at this low seeding concentration value, none of the algorithms is able to correctly reconstruct the small-scale pressure fluctuations encountered in the ground-truth flow field. the dlr result is the closest to the actual pressure field and reproduces the increase of pressure along the streamwise direction, although with strong modulation of the small flow structures. the results from the lavision 3d and lavision 4d algorithms strongly attenuate the pressure fluctuations to the range between –5 and 5 pa. the other approaches, instead, yield a very noisy surface pressure field, with limited agreement with the actual pressure field. for those algorithms, the errors on the estimated pressure, illustrated in the second column of figure 11, even exceed the actual pressure fluctuations. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 figure 11: surface static pressure field (left column) and error of the static pressure (right column), evaluated at z = 0.01 mm from the wall, for the case ppp =0.005. first row: ground truth result. the values in the colorbars are in pascal. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 the quantitative analysis of the mean bias error, random error and cross-correlation coefficient with the ground-truth surface pressure field is presented in figure 12. the surface pressure errors are in a similar range as the errors in the rest of the flow field shown in figure 10 (bias errors: between –10 and 10 pa; random errors: between 5 and 20 pa). however, as a consequence of the smaller magnitude of the surface pressure fluctuations, the cross-correlation coefficient drops significantly to values below 0.8. the largest cross-correlation coefficient (0.8) is obtained with the dlr algorithm, and is rather independent of the seeding density; in contrast, the other approaches return cross-correlation coefficient values below 0.6, which further drop at the lowest seeding concentration, confirming the poor surface pressure reconstruction accuracy in this condition. finally, the results of the spectral analysis on the surface pressure are illustrated in figure 13 for the three ppp levels. a clear trend is visible of increasing agreement between ground-truth and participants’ results at increasing seeding concentration. however, some algorithms (dlr, lavision 3d and lavision 4d) underestimate the pressure fluctuations at all wave numbers, whereas others (iot and linear interpolation) tend to overestimate them, thus resulting in more noisy pressure fields. the pressure spectrum of the tud vic+ algorithm agrees well with the ground-truth result at the two larger seeding concentrations, whereas at ppp = 0.005 it overestimates the pressure fluctuations at the lower wave numbers (k < 20 m-1), and underestimates them at the higher wave numbers. figure 12: mean bias error (left), random error (middle) and cross-correlation coefficient with respect to the ground truth of the surface pressure, evaluated in the plane z = 0.01 mm, as a function of the ppp. the symbol keys apply to all plots. figure 13: power spectral density of the surface static pressure, evaluated in the plane z = 0.01 mm. left: ppp = 0.005; middle: ppp = 0.025; right: ppp = 0.16. the bottom horizontal axis represents the wavenumber, while the top horizontal axis represents the corresponding wavelength. the dashed vertical line, when present, corresponds to the wavenumber (or wavelength) associated with the average interparticle spacing. the symbol keys apply to all plots. 5 conclusions this work presents the main results of the data assimilation challenge organised within the framework of the european union’s horizon 2020 project homer (holistic optical metrology for aero-elastic research). the challenge made use of a synthetic experiment, presented in another contribution to this symposium (leclaire et al., 2021), reproducing the wallbounded flow in the wake of a cylinder. the particles’ positions along their trajectories were provided to the participants, in three datasets reproducing the seeding concentration levels corresponding to ppp = 0.005, 0.025 and 0.16. the output quantities were the three velocity components, the nine components of the velocity gradient tensor and the static pressure, all defined in a cartesian grid of h = 0.4 mm grid spacing. four research groups took part to the da challenge, namely dlr, iot, lavision gmbh and tu delft. the latter two groups submitted results with two algorithms each. for what concerns the estimated velocity, errors between 3% and 12% of the bulk velocity vꝏ were obtained, depending on the seeding concentration and the data assimilation algorithm. these errors are of similar magnitude as those achieved when using the conventional linear interpolation of the particles’ velocities onto the 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 output cartesian grid. however, the spectral analysis revealed that the use of the data assimilation algorithms enables to increase the range of resolved length scales by factors 3 to 4 with respect to the linear interpolation approach. the analysis of the velocity gradients highlighted the presence of bias and random errors of 100-150 hz, or 10-15% of the typical vorticity magnitude peaks. as expected, both error components decrease with increasing seeding concentration; however, even at the highest ppp of 0.16, bias and random errors exceeding 20 hz and 80 hz, respectively, are obtained. finally, the evaluated pressure featured bias errors within ±10 pa and random errors between 5 pa and 20 pa. a better agreement with the actual pressure field (cross-correlation coefficient exceeding 0.95) was achieved away from the wall, whereas on the solid surface the agreement decreased (cross-correlation coefficient below 0.8) due to the lower magnitude of the pressure fluctuations. acknowledgments this work has been carried out in the context of the homer (holistic optical metrology for aero-elastic research) project, funded by the european union’s horizon 2020 research and innovation programme under grant agreement no 769237. the data processing performed by the research groups who participated in the challenge is kindly acknowledged. references agüí j and jimenez j (1987) on the performance of particle tracking velocimetry. journal of fluid mechanics 185:447-468 azijli i and dwight rp (2015) solenoidal filtering of volumetric velocity measurements using gaussian process regression. experiments in fluids 56(11), 1-18 bobrov m, hrebtov m, ivashchenko v, mullyadzhanov r, seredkin a, tokarev m, zaripov d, dulin v and markovich d (2021) pressure evaluation from lagrangian particle tracking data using a grid-free least-squares method. measurement science and technology 32, 084014 chandramouli p, mémin e and heitz d (2020). 4d large scale variational data assimilation of a turbulent flow with a dynamics error model. journal of computational physics 412, 109446 christiansen ip (1973) numerical simulation of hydrodynamics by the method of point vortices. journal of computational physics 13(3), 363-379 elsinga ge, scarano f, wieneke b and van oudheusden bw (2006) tomographic particle image velocimetry. experiments in fluids 41(6), 933-947. gesemann s, huhn f, schanz d and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser and imaging techniques to fluid mechanics, lisbon, portugal (pp. 4-7) jeon yj, schneiders jfg, müller m, michaelis d and wieneke b (2018) 4d flow field reconstruction from particle tracks by vic+ with additional constraints and multigrid approximation. in proceedings 18th international symposium on flow visualization, eth zurich jeon yj (2021) eulerian time-marching in vortex-in-cell (vic) method: reconstruction of multiple time-steps from a single vorticity volume and time-resolved boundary condition. in 14th international symposium on particle image velocimetry – ispiv 2021, august 1–5, 2021 kuhnert j and tiwari s (2001) grid free method for solving the poisson equation. fraunhofer-institut für technound wirtschaftsmathematik, https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-12885 leclaire b, mary u, liazun c et al. (2021) first lagrangian particle tracking and data assimilation challenge: datasets description and evolution to an open online benchmark. in 14th international symposium on particle image velocimetry – ispiv 2021, august 1–5, 2021 malik na, dracos t and papantoniou da (1993) particle tracking velocimetry in three-dimensional flows. experiments in fluids 15(4), 279-294 scarano f (2012) tomographic piv: principles and practice. measurement science and technology 24(1), 012001 scarano f, schneiders jfg, gonzalez saiz g and sciacchitano a (2021) dense velocity reconstruction with vic-based timesegment assimilation, under review in experiments in fluids schanz d, gesemann s and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57(5), 1-27 schiavazzi d, coletti f, iaccarino g and eaton jk (2014) a matching pursuit approach to solenoidal filtering of threedimensional velocity measurements. journal of computational physics 263, 206-221 schneiders jfg and scarano f (2016) dense velocity reconstruction from tomographic ptv with material derivatives. experiments in fluids 57(9) 1-22 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 sciacchitano a, leclaire b and schröder a (2021) main results of the first lagrangian particle tracking challenge. in 14th international symposium on particle image velocimetry – ispiv 2021, august 1–5, 2021 tan s, salibindla a, masuk a u m and ni r (2020) introducing openlpt: new method of removing ghost particles and high-concentration particle shadow tracking. experiments in fluids 61: 47 van oudheusden bw (2013) piv-based pressure measurement. measurement science and technology 24(3), 032001 paperispiv2021_sciacchitano_lpt_july052021 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 main results of the first lagrangian particle track ing challenge a. sciacchitano 1*, b. leclaire 2, a. schröder 3 1 delft university of technology, faculty of aerospace engineering, delft, the netherlands 2 onera, department of aerodynamics, aeroelasticity and acoustics, meudon, france 3 dlr, institute of aerodynamics and flow technology, göttingen, germany *corresponding author: a.sciacchitano@tudelft.nl abstract this work presents the main results of the first lagrangian particle tracking challenge, conducted within the framework of the european union’s horizon 2020 project homer (holistic optical metrology for aero-elastic research), grant agreement number 769237. the challenge, jointly organised by the research groups of dlr, onera and tu delft, considered a synthetic experiment reproducing the wall-bounded flow in the wake of a cylinder which was simulated by les. the participants received the calibration images and sets of particle images acquired by four virtual cameras, and were asked to produce as output the particles positions, velocities and accelerations (when possible) at a specific time instant. four different image acquisition strategies were addressed, namely two-pulse (tp), four-pulse (fp) and time-resolved (tr) acquisitions, each with varying tracer particle concentrations (or number of particles per pixel, ppp). the participants’ outputs were analysed in terms of percentages of correctly reconstructed particles, missed particles, ghost particles, correct tracks and wrong tracks, as well as in terms of position, velocity and acceleration errors, along with their distributions. the analysis of the results showed that the best-performing algorithms allow for a correct reconstruction of more than 99% of the tracer particles with positional errors below 0.1 pixels even at ppp values exceeding 0.15, whereas other algorithms are more prone to the presence of ghost particles already for ppp < 0.1. while the velocity errors remained contained within a small percentage of the bulk velocity, acceleration errors as large as 50% of the actual acceleration magnitude were retrieved. 1 introduction since the introduction of tomographic particle image velocimetry (shortly tomo-piv, elsinga et al., 2006, scarano, 2012) for volumetric flow velocity measurements, much research has been conducted aiming at enhancing the measurement accuracy and spatial resolution, as well as reducing the computational cost of the image analysis. in the first years of tomo-piv development, the three-dimensional distribution of tracer particles in the measurement domain was performed via a voxelbased reconstruction of their intensities, using the mart approach (herman and lent 1976) or one of its evolutions (multiplicative first guess mfg, worth and nickels, 2008; multiplicative-line of sight mlos-mart, atkinson and soria, 2009; motion tracking enhancement mte-mart, novara et al., 2010, among others). the three-dimensional velocity field was then evaluated via cross-correlation analysis (scarano, 2012), similar to planar piv. the sparsity of the particles distribution in three-dimensional space has been exploited to enhance the reconstruction accuracy (champagnat et al., 2014) as well as to increase the computational efficiency (cornic et al., 2015). for double-frame recordings, cornic et al. (2020) recently introduced the double-frame tomographic ptv (df-tptv) approach that first uses voxel grids to find the possible position of particle candidates and obtain a coarse predictor of their displacements via a correlation analysis, and finally determines the individual particles’ intensities and exact positions via a global optimisation procedure. wieneke (2013) proposed an iterative particle reconstruction (ipr) algorithm where the distribution of the tracer particles in the volumetric measurement domain is represented from the beginning by three-dimensional positions and intensity values rather than by a voxel-based intensity distribution. the ipr algorithm requires detailed knowledge of the spatially varying optical transfer function (otf) between the locations in the physical domains and the cameras pixels, which is achieved via the calibration and application of a non-uniform otf as introduced by schanz et al. (2012). the ipr approach was compared with the conventional three-dimensional triangulation, mlos, and mart, exhibiting higher performances than the former two approaches and similar performances to mart up to ppp =0.05. schanz et al. (2016) combined the iterative particle reconstruction from wieneke (2013) with the temporal information from time-resolved measurements to predict the particles’ locations at successive time instants and correct their positions by a local image matching (‘shaking’) step, which therefore identifies particles’ tracks thus performing lagrangian particle tracking (lpt). the approach, named shake-the-box (stb), enables the evaluation of the velocity and lagrangian acceleration of individual tracer particles at high particle image densities exceeding 0.1 ppp. comparison with the conventional correlation-based tomo-piv processing showed higher performance of the stb approach in terms of number of correctly reconstructed particles, accuracy of the reconstruction, and suppression of ghost particles (kähler et al., 2016). for high-speed flows, where time-resolved image recording is often unfeasible due to hardware limitations, the applicability of the stb approach has been recently extended via the concept of multi-pulse stb employing multiple systems (novara et al., 2016a) or exposures (novara et al., 2019). 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 alternative solutions to the problem of particles reconstruction and flow field evaluation have been proposed over the years. yang et al. (2018) proposed modification to the “shaking” phase of the stb algorithm and resolved the optimization with the ensemble technique. this technique is further integrated into the kernelized lagrangian particle tracking (klpt) approach in yang and heitz (2021), in which a sampling-learning-detection strategy is adopted. a dataset describing an ensemble of the possible state of one particle with their back-projections is firstly sampled. then a function is learned from this sampled dataset that maps the image intensities to the physical coordinates. finally, the particle position is detected by applying the learned function to image recordings. to improve the initialisation accuracy of stb and klpt, khojasteh et al. (2021) proposed using lagrangian coherent structure (lcs) to check if an initialised particle is locally coherent with its neighbour coherent motions. lasinger et al. (2018) introduced an approach for particle reconstructions based on the joint minimisation of an energy function accounting for the deviation between reconstructed particles and image recordings as well as for the sparsity of the particles in the three-dimensional space. in the same work, the velocity field was evaluated using a variational model that included physical information on the flow, such as incompressibility and viscosity. the approach was further developed in lasinger et al. (2019), where the tracer particles’ distribution and the velocity field were jointly reconstructed via an integrated energy minimisation process. in the lagrangian piv approach proposed by yang et al. (2019), an eulerian description of the velocity field is sought which minimises the positional difference between the particle image recordings at time k and the back-projected particles reconstructed from the information at previous time instants. from the discussion above, it emerges that the evaluation of the three-dimensional flow fields from particle image recordings is a topic of active research, and that different research groups have tackled this problem with different approaches. the aim of the first lpt challenge, whose main results are summarised in this work, is to comparatively assess the different approaches in terms of the accuracy of the particles’ reconstruction and of their velocities and accelerations via the use of a dedicated synthetic database. 2 dataset and test cases 2.1 dataset description this section provides a brief description of the dataset employed in the lpt challenge. a more detailed description of the simulation parameters is reported in the communication of leclaire et al. (2021), also presented at the ispiv 2021 symposium. the synthetic experiment reproduces the turbulent wall-bounded flow in the wake of a cylinder, considered representative of many turbulent flows where large fluctuations both in the velocity and the pressure take place. whereas the simulation was performed for an air flow in quasi-incompressible conditions, scaling was conducted to transpose it to the virtual experimental context of water at bulk velocity vꝏ = 0.667 m/s. the cylinder had a diameter d = 0.01 m, and was located at a gap distance g = 0.01 m from the wall, where a turbulent boundary layer was present with thickness δ ≈ 60 mm; the momentum thickness reynolds number 10 mm upstream of the cylinder was reθ = 4,150. according to literature (wang and tan 2008), these conditions lead to vortex shedding in ground effect, thus yielding large pressure fluctuations on the wall. a sample of the instantaneous flow field is shown in figure 1. the flow region used for the lpt challenge has dimensions of 0.1 � × 0.05 � × 0.03 � (∆x × ∆y × ∆z, being x, y and z the streamwise, spanwise and wall-normal directions respectively). such domain is centred in span, with its upstream face located 0.035 � downstream of the cylinder centre, and its bottom face located at the wall. figure 1: snapshot of the instantaneous flow field, illustrating iso-surfaces of the q-criterion colour-coded by streamwise velocity u, and contours of the static pressure. synthetic particle images were generated considering four virtual cameras with sensor size of 1920×1200 pixels and 10 μm pitch, using pinhole projection. no scheimpflug nor image distortion were simulated. the cameras viewed the measurement domain mainly from above, and were located along the x-axis at y = 0 and height of about 600 mm above the wall, at angles of [-30, -10, 10, 30] degrees respectively. based on the simulated cameras’ locations and lenses’ focal lengths (100 mm), each 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 back-projected pixel ( ���) (defined with a value close to the average size of pixel back-projections through the volume) corresponded to 60 µm in the object space. the particles were given a poly-disperse intensity distribution; the particle images were produced with a gaussian (σ = 0.6) point-spread function to model diffraction limited imaging. thermal and shot noise were also added to the images. 2.2 test cases three different image acquisition strategies were considered, namely two-pulse (tp), four-pulse (fp) and time-resolved (tr). the tp case consisted of only one image pair with time separation ∆t = 600 µs, corresponding to a maximum pixel displacement of about 7 pixels in the camera images. in the fp case, the time separations between the four exposures t0, t1, t2, t3 of a sequence were [2∆t, ∆t, 2∆t] (again, with ∆t = 600 µs), with the first two exposures captured in the first image and the last two exposures captured in the second image. finally, for the tr case, sequences of 50 or 100 images were considered depending of the number of particles per pixels (ppp), with time separation between two successive images of ∆t = 600 µs. the datasets were generated at ppp values of 0.005, 0.025, 0.05, 0.08, 0.12, 0.16 for the tp and fp cases, and also of 0.2 ppp for the tr case. the corresponding tracers’ concentrations was in the range between 0.043 particles/mm3 (ppp = 0.005) and 1.7 particles/mm3 (ppp = 0.2). calibration data, namely list of calibration points with their coordinates in the physical domain and the projections in the four camera images, were provided to the participants without any error. in the tp case, the participants were asked to produce as output the positions of the tracer particles at the time instants t0 (x0, y0, z0) and t1 (x1, y1, z1), respectively. in the fp case, the requested output consisted of the raw particles’ positions at the four time instants, plus the three components of the position (xm, ym, zm), velocity (vx, vy, vz) and acceleration (ax, ay, az) at the intermediate time instant � = ��� + ��� 2⁄ . in the tr case, the participants needed to provide the raw particles’ positions (x, y, z) as well as the fitted positions (xfit, yfit, zfit), the velocity (vx, vy, vz) and the acceleration (ax, ay, az) at time instant 40 for ppp ≤ 0.12 and 90 for ppp ≥ 0.16. the results could be submitted for any of the three cases, analysing the datasets from ppp = 0.005 to the maximum ppp value handled by the participants’ algorithms. the datasets were publicly released for download on march 9th, 2020 (https://w3.onera.fr/first_lpt_and_da_challenge/). participants were then requested to upload their processed results by july 17th, 2020. 2.3 data analysis the data uploaded by the participants were analysed via the evaluation of the following parameter: percentage of correct particles: a reconstructed particle was defined as “correct” if its location fell within 60 µm ( or 1 ���) from a true particle; percentage of false particles (or ghost): a reconstructed particle was defined as “false” (or ghost) if its distance from a true particle exceeded 60 µm (or 1 ���); percentage of false negatives (or missed particle): a true particle was considered missed when no particle was reconstructed within 60 µm (or 1 ���) from the former; percentage of correct tracks: a track was defined correct when composed by all correct particles; percentage of wrong tracks: a track was defined wrong when at least one particle of the track was not correct (either missed or ghost); error of the particles’ position (for all cases), velocity and acceleration (only for the fp and tr cases), in terms of the mean error magnitude, as well as error distribution to detect the presence of any bias. it should be noted that the errors were evaluated only for the correct particles (not for the ghost particles), as the difference between the reconstructed particle position, velocity or acceleration and the actual values of the corresponding true particles. 3 participant and approaches a total number of six research groups participated to the lpt challenge, namely the swiss federal institute of technology in zürich (ethz), the german aerospace centre from göttingen (dlr), the french national research institute for agriculture, food & environment (inrae), the kutateladze institute of thermophysics in russia (iot), the french aerospace lab (onera) and the german instrumentation company lavision gmbh. a summary of the participating groups and the algorithms used is reported in table 1. table 1: list of cases of the lpt challenge, participants and their algorithms. case participant algorithm reference tp dlr multi-pulse shake-the-box novara et al. (2019) ethz 3d fluid flow estimation with integrated particle reconstruction lasinger et al. (2019) inrae lagrangian piv yang et al. (2019) lavision multi-pulse shake-the-box novara et al. (2019) onera iterative double frame tomographic ptv cornic et al. (2020) fp dlr multi-pulse shake-the-box novara et al. (2019) lavision multi-pulse shake-the-box novara et al. (2019) tr dlr (time-resolved) shake-the-box schanz et al. (2016) 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 inrae kernelized lagrangian particle tracking yang and heitz (2021) inrae lagrangian piv yang et al. (2019) inrae lagrangian coherent track initialization khojasteh et al. (2021) iot openlpt tan et al. (2020) lavision (time-resolved) shake-the-box schanz et al. (2016) 3.1 two-pulse test case the following groups participated to the tp case of the lpt challenge: dlr, ethz, inrae, lavision and onera. all participants processed the data in the entire data of ppp values from 0.005 to 0.16, with the exception of onera and inrae that processed the data only up to ppp = 0.08. the algorithms used are briefly summarised hereafter. 3.1.1 dlr: multi-pulse shake-the-box the approach used by the dlr group is the multi-pulse shake-the-box from novara et al. (2019). the approach first reconstructs the particles in three-dimensional space via the use of an advanced iterative particle reconstruction (ipr) from jahn et al. (2021), based on wieneke (2013). then, a displacement predictor is obtained via the application of the particle space correlation algorithm (psc, novara et al., 2016b) between the reconstructed particles of the two frames. for each particle in the first frame ipr reconstruction, a search radius δ2p is established around the predicted location to generate twopulse track candidates. possible ambiguities between track candidates are solved by selecting the candidate that exhibits the lowest value of a cost function, which accounts for the variation of the peak intensity along a track and the difference with respect to the predicted position. two iterations are performed, with δ2p = 1 pixel and 10 pixels, respectively. 3.1.2 ehtz: integrated particle reconstruction the ethz group used a variational approach to jointly estimate the sparse 3d particle locations at the reference time step and the dense flow field on a regular grid. particles at the reference time step are triangulated iteratively, similar to ipr (wieneke, 2013). the individual iteration steps are alternated with the optimization of the energy function: ( ) ( ) ( ) ( )1 , , , , 2 2d s spe p c u e p c u e u e c λ µ≡ + + (1) where p, c and u represent the set of particles positions, the set of particles intensities, and the estimated flow field, respectively. the data term ed penalizes deviations between predicted and observed images by evaluating the 2d reprojection error in all camera views for both time steps. for the second time step, the particles are displaced by the estimated flow field u. the smoothness term es is derived from the stationary stokes equations and enforces a divergence-free flow field as well as a quadratic regularization per component of the flow gradient. the sparsity term esp enforces sparsity of the reconstructed particle set by suppressing low-intensity ghost particles. for camera calibration, the polynomial camera model of soloff et al. (1997) (38 parameters) is fitted. the output of this approach is a dense flow field on a regular grid. particle locations for the second time step were, thus, obtained from displacements interpolated from the estimated flow field. for higher seeding densities (ppp from 0.05 to 0.16) a grid resolution of 200×100×60 was used, while for lower seeding densities (0.005, 0.025), a coarser grid of 167×84×50 was employed. further details on the algorithm are reported in lasinger et al. (2019). 3.1.3 inrae lapiv the inrae group processed the tp data with the lagrangian piv algorithm (lapiv) from yang et al. (2019). the algorithm first builds the particle positions in object space from the first frame using an ipr-like method (wieneke, 2013). then, the best eulerian velocity field is sought that minimises a cost function accounting for the discrepancy between the image recording at the second time instant and the back-projected image using the optical transfer function otf (schanz et al., 2012). the particle positions in the second frame are reconstructed by integrating the interpolated eulerian velocity field, thus finding a temporal link between the two frames in accordance with the flow. finally, the particles positions at the second frame are further optimised using one step of the kernelized lpt approach (klpt, yang et al., 2018) to further increase accuracy. for the two-pulse case, the algorithm is reported to diverge for seeding concentrations beyond ppp = 0.08, because it is unable to accurately reconstruct the initial particles field due to the high seeding density. 3.1.4 lavision: two-pulse shake-the-box similarly to the dlr group, lavision employed the two-pulse shake-the-box algorithm (jahn et al., 2017), which makes use of an iterative combination of ipr and particle tracking. with respect to dlr, lavision used more iterations, namely from 8 to 20 depending on the ppp value. for ppp > 0.12, an intermediate filtering of the trajectories via the use of a median filter was also performed to remove spurious trajectories. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 3.1.5 onera: iterative double-frame tomographic ptv the algorithm used by onera for processing the tp data is an improved version of the double frame tomographic ptv (df-tptv) algorithm from cornic et al. (2020). the df-tptv approach involves three stages. firstly, particles reconstruction is performed on a fine voxel grid with a sparsity-based algorithm (needell and tropp, 2009) for each time step. secondly, these reconstructions are expanded on a coarser grid, on which 3d correlation is performed (cheminet et al., 2014), yielding a predictor displacement field that allows to efficiently match particles at the two time instants. as these particles are still located on a voxel grid, the final step achieves particle position refinement to their actual sub-voxel position by a global optimisation process, also accounting for their intensities. residual images are built based on the unmatched particles; the three stages of the df-tptv approach are then iterated on the residual images, using a predictor estimated from the previously optimised particles. 3.2 four-pulse test case only dlr and lavision processed the data of the fp test case, both using their implementations of the multi-pulse shakethe-box (mp-stb) algorithm from novara et al. (2019). similarly to the algorithm described in section 3.1.1 for the tp case, the approaches make use of advanced ipr (jahn et al. 2021) and ipr (wieneke, 2013) and a displacement predictor by particle space correlation (psc, novara et al., 2016b). as for the tp case, for each particle in the first frame ipr reconstruction, a search radius δ2p is established around the predicted location to generate two-pulse track candidates. the latter are then extrapolated backwards and forwards and an additional search radius (δ4p) is adopted to identify four-pulse track candidates. the cost function used to solve ambiguities between candidates accounts not only for the variation of the particle peak intensity along the track and the distance from the predicted position as in the tp case, but also for the mean acceleration magnitude. while dlr used 21 iterations of the mp-stb algorithm, lavision used a number of iterations from 10 to 100 depending on the ppp. both groups made use of a second order polynomial regression on the reconstructed particles positions to extract the position, velocity and acceleration at the intermediate time instant (time tm). additionally, lavision employed an intermediate spatial filtering of the trajectories via a median filter for ppp > 0.08 to remove spurious trajectories. also, for ppp> 0.12 lavision applied a time-average reference velocity field as a predictor for the initial reconstruction. in addition to the data processed by dlr and lavision, a “hacker” participant was also considered, following the approach of the 4th piv challenge (kähler et al., 2016). hacker used the exact particle positions at times t0, t1, t2, and t3, and fitted a second order polynomial through the particles of a track to determine the position, velocity and acceleration at the intermediate time instant. the comparison between the results from hacker and those from the other participants allows to evaluate to which extent the errors on position, velocity and acceleration are caused by errors in the particles reconstruction and due to the applied image noise, rather than by the temporal resolution of the simulated experiments. 3.3 time-resolved test case four research groups processed the data of the tr test case, namely dlr, inrae, iot and lavision. the inrae group used three different algorithms (kernelized lpt, lagrangian piv, and lagrangian coherency-based tracks initialisation), which are explained in the reminder of this section. additionally, as for the fp case, a “hacker” participant made use of the exact particle positions at three time instants centred around the time instant of interest, and evaluated the velocity and acceleration via a second order least-square polynomial regression and analytical time derivation. the range of datasets processed by each participant are summarised in table 2. table 2: datasets (ppp cases) processed by the participants for the tr case. 0.005 0.025 0.050 0.080 0.120 0.160 0.200 dlr        inrae klpt        inrae lapiv        inrae lcti        iot        lavision        hacker        3.3.1 dlr: time-resolved shake-the-box the dlr group processed the images of the tr case using a three-pass shake-the-box algorithm (schanz et al., 2016). the processing chain was optimised for the highest seeding density (0.2 ppp) and then applied to all other cases. for all seeding densities, the final 25 images of the time series were processed (25-49 for ppp ≤ 0.12; 75-99 for ppp ≥ 0.16). the first five images of the first pass used an extensive particle reconstruction via an advanced ipr approach (jahn et al., 2021; wieneke, 2013). the allowed triangulation radius was gradually increased from 0.4 to 1.0 pixels. after each triangulation iteration, 16 sub-iterations of particle shaking using an image matching scheme with analytic cost function (jahn et al., 2021) were carried 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 out. the tracks selection was based on a wiener-filter-type fit. starting from the fifth time step, a predictor for the identification of new tracks was constructed from the average velocity from the six closest neighbouring tracked particles, with a search radius of 4.5 pixels. after the stb processing, the raw particle positions were fitted using the trackfit approach (gesemann et al., 2016), which employs a system of 1d cubic-b-splines to yield a continuous and smooth function for each dimension of the track. 3.3.2 inrae: klpt, lapiv and lcti the inrae group made use of three algorithms. the kernelized lpt (klpt) approach (yang and heitz, 2021) initializes the tracer particle distribution in physical space via the ipr method (wieneke, 2013). then, klpt adopts a sampling strategy that firstly forecasts a cloud of one particle’s possible position at time k from the particle’s sampled history up to time k–1, followed by projecting the ensemble prediction into image space using the otf. successively, a function mapping the image pixel intensities to the particles’ 3d coordinates is learned by minimizing a regularized empirical risk. this risk measures the discrepancy between the sample-predicted position at time k and the mapping function output value taking the sampled image projection as input. finally, the learned function is applied to the image recording at time k to yield the best flow variable. such optimisation problem is solved using kernel methods (hofmann et al., 2008). the raw particles positions were then regularised using a spline method. the velocity and acceleration were computed via analytical derivation in time of the spline curves. for track lengths smaller than five samples, the finite difference method was used instead of the spline regularisation. at the highest seeding densities (ppp ≥ 0.12), the images were processed also with the lagrangian piv approach (lapiv, yang et al., 2019), which has been described already in section 3.1.3 for the image analysis of the tp case. finally, the lagrangian coherent tracks initialisation (lcti) approach from khojasteh et al. (2021) was also employed. the method initialises new tracks at every iteration of the stb or klpt processing based on the local lagrangian information of the particles. in particular, the concept of the finite-time lyapunov exponent (ftle, ott, 2002) is exploited locally to identify lcs ridges (e.g. boundaries) in the flow field, and ensure that the newly-added and the recovered lost tracks are coherent with the neighbouring existing tracks. 3.3.3 iot: open-lpt the iot group processed the tr data via the stb algorithm c++ implementation from the openlpt project (tan et al. 2020). the following stb parameters were used: 2d particle image detection with intensity threshold of 24 counts and 3point gaussian subpixel interpolation; maximum triangulation error of 0.015 mm (0.255 pixels); 4 outer and inner loop iterations, with the shaking step of 0.04 mm (0.68 pixels). the possible particle’s shift between two consecutive frames was limited to 0.42 mm (7.14 pixels). the search radius for particles detection based on a predictor was 0.1 mm (1.7 pixels). three initial predictor fields were obtained by particle space correlation on a cartesian grid with 1.25 mm spacing, using spherical interrogation windows of 2 mm radius. the resulting velocity at the particles’ locations were validated via a spatial moving average filter. the particles positions at successive time instants were predicted using a wiener filter. weighted cardinal b-splines (gesemann et al. 2016) were employed to regularise the particles’ positions and in turn determine their velocities and accelerations. 3.3.4 lavision: time-resolved shake-the-box lavision made use of the davis 10 implementation of the shake-the-box algorithm (schanz et al., 2016), employing fourframe track search initialisation. for ppp > 0.12, spatial filtering of the trajectories via a median filter was conducted during the stb iterations to remove spurious tracks. for ppp = 0.2, the particles’ reconstruction was carried out marching both forward and backward to enhance its accuracy. the particles’ raw positions were regularised with a second order polynomial least square regression over a kernel of 7 samples, from which the velocity and acceleration were determined via analytical differentiation in time. 4 results 4.1 two-pulse test case it is well established that the particles’ reconstruction accuracy is dependent on the particles’ concentration or number of particles per pixels (ppp) (scarano, 2012), with decreasing quality of reconstruction for increasing ppp. figure 2 illustrates the true particles (red crosses) and the reconstructed particles (black circles) in sub-domains of the measurement volume, for selected increasing ppp values from 0.005 (top row) to 0.16 (bottom row). at the lowest ppp value, most algorithms succeed in correctly reconstructing almost the totality of the true particles, with no ghost particles or missed particles appearing in the considered sub-volume. the only exception is the result from ethz, which presents several ghost particles and a few missed particles. when the ppp value is increased to 0.08, the difference in performance among the processing algorithms becomes more noticeable. the dlr and lavision implementations of stb enable to reconstruct correctly a very high percentage of the true 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 particles without the appearance of ghost particles. also, the inrae lapiv approach shows good particles reconstruction capabilities, with only a few ghost and missed particles present. the other processing algorithms, instead, are more prone to ghost particles (ethz) or missed particles (onera). the dlr and lavision algorithms retain their high performances even at the highest ppp value of 0.16, where only a few ghost and missed particles appear in the domain. conversely, the result from the ethz algorithm maintains a large amount of ghost particles in the analysed sub-domain. figure 2: comparison between true particles (red crosses) and reconstructed particles (black circles) in sub-domains of the entire measurement volume, for the two-pulse (tp) case. top: ppp = 0.005. middle: ppp = 0.08. bottom: ppp = 0.16. notice that, for sake of clarity, smaller sub-volumes are selected for the ppp = 0.08 and ppp = 0.16 cases. the results in terms of percentages of correctly reconstructed particles and false positives (ghosts) are illustrated in figure 3. the percentages are computed relative to the number of true particles in the measurement domain, averaged over the two time instants. it can be noticed that the results from dlr and lavision exhibit a close-to-perfect reconstruction, with nearly all particles correctly reconstructed at all ppp values, and no ghost particles. also, the ethz algorithm correctly reconstructs more than 90% of the true particles at all the ppp values; however, the number of ghost particles is equal to or even exceeding that of the true particles. the results of the onera and inrae lapiv algorithms have been submitted only up to ppp = 0.08; within these range of seeding concentrations, the approaches exhibit good particle reconstruction capabilities, with over 95% of the true particles correctly reconstructed. the inrae algorithm is found to be more prone to ghost particles, with up to 5% false negatives recorded at ppp = 0.08. the positional mean error magnitude as a function of the ppp is illustrated in figure 4. at the lowest ppp (equal to 0.005), all algorithms exhibit a positional error of around 0.04 ���, except the ethz algorithm which features an error of 0.28 ���. in general, the positional error increases with the seeding concentration, although the slope of the increase varies depending on the algorithm. for the dlr approach, the increase is very mild and the error value reaches 0.06 ��� at the highest ppp of 0.16. the error increase is slightly higher for the lavision implementation of the two-pulse shake-the-box algorithm, with the error reaching 0.10 ��� at ppp = 0.16. the inrae lapiv result follows closely that of lavision up to ppp = 0.08. the onera algorithm exhibits a higher error increase with ppp, with error values of 0.17 pixels at ppp = 0.08. the error from the ethz approach is in the range 0.2-0.3 ��� at all seeding concentration analysed and shows a non-monotonic variation with the ppp. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 figure 3: left: percentage of the correct particles (relative to the number of true particles), as a function of the number of particles per pixels (ppp) in the images. right: percentage of false particles (ghosts) as a function of the ppp. the symbol keys apply to all figures. all results are for the two-pulse (tp) test case. figure 4: mean positional error magnitude (considering all three position components, and both time instants) as a function of the ppp, for the tp test case. the analysis of the histograms of the positional errors (not shown here) highlights that the positional errors along the z-direction are two to three times larger than those along the xand y-directions due to the given limitation of the camera system aperture (+/30 °), and that the random errors dominate over the bias errors. the latter are typically null, except for the x-position component with the onera algorithm and the z-position component with the lavision algorithm, where they remain within 0.02 ���. additionally, the errors appear to be uniformly distributed in the entire measurement domain, with no significant spatial variations. 4.2 four-pulse test case the distribution of true particles (red crosses) and reconstructed particles (black circles) in sub-domains of the measurement volume for two sample ppp values, namely 0.050 and 0.160, are shown in figure 5. at the lower seeding concentration of the two, both the dlr and the lavision algorithm correctly reconstruct all the particles in the visualised sub-volume, with neither ghost nor missed particles. at the highest ppp of 0.160, the two algorithms still retain their high performance in particles reconstruction; only a few particles are missed by the lavision algorithm, whereas the dlr algorithm correctly reconstructs all of them. even at this high value of the seeding concentration, no ghost particles appear. the quantitative analysis of the percentages of correctly reconstructed particles, false particles (ghosts), correct tracks and wrong tracks is presented in figure 6. the dlr algorithm exhibits outstanding performances, with nearly all particles and tracks correctly reconstructed at all the analysed seeding concentrations, and percentages of ghost particles and wrong tracks below 0.05% and 0.15%, respectively. the lavision implementation features a slightly higher sensitivity to the seeding 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 concentration, with a small decrease of the performance at the highest ppp. nevertheless, the percentages of correctly reconstructed particles and tracks remain above 90% even at the highest ppp, and the amount of ghost particles and wrong tracks does not exceed 0.15% and 0.6%, respectively. figure 5: comparison between true particles (red crosses) and reconstructed particles (black circles) in sub-domains of the entire measurement volume, for the four-pulse (fp) case. top: ppp = 0.05. bottom: ppp = 0.16. notice that, for sake of clarity, a smaller subvolume is selected for the ppp = 0.16 case. figure 6: percentages of correct particles (top-left), missed particles (ghosts, top-right), correct tracks (bottom-left) and wrong tracks (bottom-right) as a function of the ppp. the symbol keys apply to all figures. all results are for the four-pulse (fp) test case. the mean error magnitudes of position, velocity and acceleration, all evaluated at the intermediate time instant tm, are illustrated in figure 7 for varying seeding concentrations. as explained in section 3.2, also the results from a fictitious participant “hacker” are shown for reference; the latter made use of the exact particles positions and a second-order polynomial regression to retrieve position, velocity and acceleration at the intermediate time instant. hence, the results from hacker are regarded to as the minimum errors attainable in case of perfect particles reconstructions. from figure 7 top-left, it is clear that the minimum positional error of the dlr and lavision algorithms is almost one order of magnitude larger than that from hacker, indicating a clear margin for further improvement of the reconstruction accuracy. the positional error 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 increases linearly with the seeding concentration. the error increase is mild with the dlr algorithm, with maximum errors below 0.05 ��� at the highest ppp; a steeper increase occurs with the lavision algorithm, although the errors remain well below 0.1 ��� even at ppp = 0.16. instead, the positional errors from hacker are independent of the seeding concentration and attain a value of about 0.005 ���. the velocity retrieved with the dlr algorithm exhibits an error of about 0.4% of vꝏ (figure 7 top-right), with negligible variations with the ppp. such error is of the same order as that of hacker (0.3% of vꝏ), thus indicating that the temporal modulation due to the finite temporal resolution plays a significant role. the velocity error of the lavision algorithm shows more pronounced variations with the seeding concentration, increasing from 0.4% to about 0.6% of vꝏ at the highest seeding concentration. the mean acceleration error magnitude (figure 7 bottom-left) is of the order of 10 m/s2, or 22.5% of the reference acceleration vꝏ 2/d. the values of the two algorithms are very close to those of hacker, and show only minor variations with the amount of particles per pixel. as for the velocity, this result suggests that the error is mainly dominated by the temporal resolution effects, rather than by the uncertainty in the particles positions. for reference, the mean acceleration magnitude is plotted as a thick grey line, which attains a value of 15 m/s2. hence, it can be concluded that the errors of the measured acceleration are as large as 60% to 80% of the mean acceleration magnitude. figure 7: mean error magnitude of position (top-left), velocity (top-right) and acceleration (bottom-left) as a function of the ppp. all quantities are computed at the intermediate time instant tm and only for the correct tracks. the symbol keys apply to all figures. the thick grey line in the acceleration error plot represents the mean acceleration magnitude. 4.3 time-resolved test case the use of temporal information is expected to enhance the quality of the particles’ reconstruction, thus enabling accurate particles’ reconstructions at higher ppp values. figure 8 illustrates the distribution of true particles (red crosses) and reconstructed particles (black circles) in sub-domains of the measurement volume, for values of the ppp equal to 0.005, 0.08 and 0.2. at the lowest seeding concentration, all algorithms are able to reconstruct the large majority of the particles, with only a few particles missed by the approach submitted by iot (first row of figure 8). similar performances are achieved also at ppp = 0.08, with almost no missed or ghost particles for all algorithms, except for the iot result. at the highest ppp level of 0.2, larger differences among the algorithms are reported. the iot submission correctly reconstructs only a small percentage of the true particles, and exhibits a large number of false negatives (missed particles). the inrae lapiv algorithm yields large amounts of both false positives (ghost particles) and false negatives. conversely, the dlr and the lavision algorithms maintain high reconstruction accuracy even at such high concentration, with a limited number of missed particles (higher for the lavision algorithm) and no ghost particle. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 figure 8: comparison between true particles (red crosses) and reconstructed particles (black circles) in sub-domains of the entire measurement volume, for the time-resolved (tr) case. top: ppp = 0.005. middle: ppp = 0.08. bottom: ppp = 0.20. notice that, for sake of clarity, a smaller sub-domain is selected for ppp = 0.08 and 0.20. the quantitative analysis of the particles reconstruction at all the ppp values is reported in figure 9. the percentage of correctly reconstructed particles is very close to 100% in the entire range of ppp values for both the dlr and lavision algorithms, as well as for the inrae klpt and lcti algorithms in the range of submitted results (up to ppp = 0.08) and for the inrae lapiv result at ppp = 0.12. the latter algorithm shows a significant degradation of its performance for larger ppp values; in particular, at ppp = 0.2, only 10% of the true particles are correctly reconstructed, and the number of ghost particles exceeds 70%. the iot submission exhibits a high sensitivity to the tracers’ concentration, with the percentage of particles correctly reconstructed decreasing progressively from 95% to 10% in the considered range of ppp values; nevertheless, the number of ghost particles remains always well below 1%. figure 9: left: percentage of the correct particles (relative to the number of true particles), as a function of the number of particles per pixels (ppp) in the images. right: percentage of false particles (ghosts) as a function of the ppp. all results are for the time-resolved (tr) test case, and considered the fitted particles’ positions. the symbol keys apply to both figures. 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 the mean error magnitudes of the fitted position, velocity and acceleration for all ppp values are shown in figure 10. the velocity and acceleration errors are also compared with the result from hacker to assess the role of the temporal discretisation. the positional errors range between 0.02 and 0.5 ��� depending on the algorithm and the seeding concentration, with a general trend of increased error values for increasing ppp. such increase is very mild for the dlr algorithm, where the error remains below 0.05 ��� at ppp = 0.2. the inrae klpt, inrae lcti and the lavision algorithms exhibit a slightly larger error increase, with the latter approach yielding an error above 0.1 ��� at the largest ppp. the inrae lapiv algorithm features a much higher sensitivity to the ppp value beyond 0.12, indicating that the algorithm diverges for high seeding concentrations. finally, the iot approach shows a steep error increase already from the lowest analysed ppp value. the velocity errors range between 0.3% and 2.5% of the bulk velocity vꝏ for all cases except for the inrae lapiv algorithm beyond ppp = 0.12. as already discussed, in the latter case the algorithm diverges thus yielding invalid results. the dlr algorithm provides the lowest errors, always below 0.5% of vꝏ, which are very close to the minimum attainable values (hacker errors: 0.25% of vꝏ). the other algorithms exhibit a slightly more pronounced sensitivity to the seeding density, yielding velocity errors that increase from below 1% of vꝏ at ppp = 0.005 to above 1.5% of vꝏ at the highest ppp. the acceleration errors from hacker, dlr, lavision and iot show very little dependence on the ppp value. the hacker result already exhibits an error of the order of 8 m/s2 or 18% of the reference acceleration vꝏ 2/d: this is a clear indication that, in the current test case, modulation errors due to the finite temporal resolution are predominant with respect to the random errors. most of the algorithms provide acceleration errors between 25% and 35% of vꝏ 2/d, with the lower errors achieved with the dlr algorithm. nevertheless, these acceleration error values are between 50% and 100% of mean magnitude of the actual acceleration, thus highlighting the inadequacy of the algorithms to correctly resolve the flow acceleration in the current test case. the inrae algorithms return the highest acceleration errors, which increase with the seeding density well above of the actual acceleration magnitude. figure 10: mean error magnitude of position (top-left), velocity (top-right) and acceleration (bottom-left) as a function of the ppp. the position error is evaluated based on the fitted particles positions. the symbol keys apply to all figures. the thick grey line in the acceleration error plot represents the mean acceleration magnitude. 5 conclusions the main results of the lagrangian particle tracking challenge organised within the framework of the european union’s horizon 2020 project homer (holistic optical metrology for aero-elastic research) are presented. the challenge employed a synthetic experiment where the wall-bounded flow in the wake of a cylinder was simulated. particle images were acquired with four synthetic cameras at different seeding concentrations corresponding to a range of particles per pixel between 0.005 and 0.20. three different image acquisition strategies were considered, namely two-pulse, four-pulse and time14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 resolved acquisitions. six research groups participated to the challenge. the submitted results were analysed in terms of accuracy of particles reconstruction (namely percentages of correct particles, false positives and false negatives), as well as based on the errors on position, velocity and acceleration. the analysis of the two-pulse case showed that the best algorithms are capable to reconstruct correctly nearly all the particles in the entire range of considered ppp values, with a negligible percentage of missed or ghost particles (less the 0.1%). for those algorithms, the positional errors were in the range between 0.05 and 0.1 ���. for the other algorithms, the percentage of correctly reconstructed particles remained well above 80%, although some of the algorithms such as that of ethz exhibited a large amount of ghost particles, of the same order of the true particles. positional errors up to 0.3 ��� were recorded. only two research groups participated to the four-pulse test case of the challenge, namely dlr and lavision, using slightly different implementations of the same multi-pulse shake-the-box algorithm. the results showed the very high performance of this algorithm, with over 90% correctly reconstructed particles and tracks at all ppp values (close to 100% for the dlr implementation), and less than 0.2% and 0.6% ghost particles and wrong tracks, respectively. the positional errors were in the range between 0.03 and 0.08 ���, showing a slight increase with the seeding concentration. velocity errors of about between 0.4% and 0.6% vꝏ have been retrieved, slightly larger than the minimum admissible ones (0.3%) obtained by the hacker participant. conversely, much larger acceleration errors were found, between 60% and 80% of the acceleration magnitude, a large part of them being ascribed to temporal truncation. the results of the time-resolved test case showed that the best algorithms are capable to perform a close-to-perfect particle reconstruction up to ppp = 0.2, with nearly all particles correctly reconstructed and less than 0.1% ghost particles. for those algorithms, the positional errors remain below 0.05 ��� at all ppp values. other algorithms exhibited larger sensitivity to the seeding density, either already from ppp = 0.005 (iot submission) or only at the higher ppp values (inrae lapiv algorithm). positional errors exceeding 0.3 ��� were found for these algorithms at the highest ppp. the velocity errors range from below 0.5% vꝏ for the best algorithm to beyond 4% vꝏ for the least-performing algorithm. instead, much larger acceleration errors were retrieved, from 50% to several times the acceleration magnitude, also due to the limited temporal resolution of this test case. acknowledgments this work has been carried out in the context of the homer (holistic optical metrology for aero-elastic research) project, funded by the european union’s horizon 2020 research and innovation programme under grant agreement no 769237. the data processing performed by the research groups who participated in the challenge is kindly acknowledged. references atkinson c and soria j (2009) an efficient simultaneous reconstruction technique for tomographic particle image velocimetry. experiments in fluids, 47(4), 553-568 champagnat f, cornic p, cheminet a, leclaire b, le besnerais g and plyer a (2014) tomographic piv: particles versus blobs. measurement science and technology, 25(8), 084002 cheminet a, leclaire b, champagnat f, plyer a, yegavian r and le besnerais g (2014) accuracy assessment of a lucaskanade based correlation method for 3d piv. in 17th international symposium on applications of laser techniques to fluid mechanics. cornic p, leclaire b, champagnat f, le besnerais g, cheminet a, illoul c and losfeld g (2020) double-frame tomographic ptv at high seeding densities. experiments in fluids, 61(2), 1-24 elsinga ge, scarano f, wieneke b and van oudheusden bw (2006), tomographic particle image velocimetry. experiments in fluids, 41(6), 933-947 gesemann s, huhn f, schanz d and schröder a (2016) from noisy particle tracks to velocity, acceleration and pressure fields using b-splines and penalties. in 18th international symposium on applications of laser and imaging techniques to fluid mechanics, lisbon, portugal (pp. 4-7) herman gt and lent a (1976) iterative reconstruction algorithms. computers in biology and medicine, 6(4), 273-294 hofmann t, schölkopf b and smola aj (2008) kernel methods in machine learning. the annals of statistics, 1171-1220 jahn t, schanz d, gesemann s and schröder a (2017) 2-pulse stb: 3d particle tracking at high particle image densities. in 12th international symposium on piv-piv17, busan, korea jahn t, schanz d and schröder a (2021) advanced iterative particle reconstruction for lagrangian particle tracking. accepted for publication in experiments in fluids. kähler cj, astarita t, vlachos pp, sakakibara j, hain r, discetti s, ... & cierpka c (2016) main results of the 4th international piv challenge. experiments in fluids, 57(6), 97 khojasteh ar, yang y, heitz d and laizet s (2021) lagrangian coherent track initialisation (lcti). arxiv:2106.11049. lasinger k, vogel c, pock t and schindler k (2018) variational 3d-piv with sparse descriptors. measurement science and technology, 29(6), 064010 14th international symposium on particle image velocimetry – ispiv2021 august 1–4, 2021 lasinger k, vogel c, pock t and schindler k (2019) 3d fluid flow estimation with integrated particle reconstruction. international journal of computer vision, 1-16 leclaire b, mary u, liazun c et al. (2021) first lagrangian particle tracking and data assimilation challenge: datasets description and evolution to an open online benchmark. in 14th international symposium on particle image velocimetry – ispiv 2021, august 1–5, 2021 needell d and tropp ja (2009) cosamp: iterative signal recovery from incomplete and inaccurate samples. applied and computational harmonic analysis, 26(3), 301-321 novara m, batenburg kj and scarano f (2010) motion tracking-enhanced mart for tomographic piv. measurement science and technology, 21(3), 035401 novara m, schanz d, gesemann s, lynch kp and schröder a (2016b) lagrangian 3d particle tracking for multi-pulse systems: performance assessment and application of shake-the-box. in: 18th international symposium on applications of laser techniques to fluid mechanics, pp 4–7 novara m, schanz d, reuther n, kähler cj and schröder a (2016a) lagrangian 3d particle tracking in high-speed flows: shake-the-box for multi-pulse systems. experiments in fluids, 57(8), 1-20 novara m, schanz d, geisler r, gesemann s, voss c and schröder a (2019) multi-exposed recordings for 3d lagrangian particle tracking with multi-pulse shake-the-box. experiments in fluids, 60(3), 1-19 ott e (2002) chaos in dynamical systems. cambridge university press scarano f (2012) tomographic piv: principles and practice. measurement science and technology, 24(1), 012001 schanz d, gesemann s and schröder a. (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids, 57(5), 1-27 schanz d, gesemann s, schröder a, wieneke b and novara m (2012) non-uniform optical transfer functions in particle imaging: calibration and application to tomographic reconstruction. measurement science and technology, 24(2), 024009 soloff sm, adrian rj and liu zc (1997) distortion compensation for generalized stereoscopic particle image velocimetry. measurement science and technology, 8(12), 1441 tan s, salibindla a, masuk aum and ni r (2020) introducing openlpt: new method of removing ghost particles and highconcentration particle shadow tracking. experiments in fluids, 61(2), 1-16 van gent pl, michaelis d, van oudheusden bw, weisspé, de kat r, laskari a, ... and schrijer, ffj (2017) comparative assessment of pressure field reconstructions from particle image velocimetry measurements and lagrangian particle tracking. experiments in fluids, 58(4), 33 wang xk and tan sk (2008) comparison of flow patterns in the near wake of a circular cylinder and a square cylinder placed near a plane wall. ocean engineering, 35(5-6), 458-472 wieneke b (2012) iterative reconstruction of volumetric particle distribution. measurement science and technology, 24(2), 024008 worth na and nickels tb (2008) acceleration of tomo-piv by estimating the initial volume intensity distribution. experiments in fluids, 45(5), 847-856 yang y, heitz d and mémin e (2018) an ensemble filter estimation scheme for lagrangian trajectory reconstruction. in 16ème congrès francophone de techniques laser pour la mécanique des fluides (p. 8) yang y, heitz d and mémin e (201). lagrangian particle image velocimetry. in ispiv2019-13th international symposium on particle image velocimetry (pp. 1-9) yang y and heitz d (2021) kernelized lagrangian particle tracking. ⟨hal-03212696⟩ 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 aerodynamics of a cycling wheel in crosswind by coaxial volumetric velocimetry c. jux1∗, a. sciacchitano1, f. scarano1 1 delft university of technology, dept. of aerospace engineering aerodynamics, delft, the netherlands ∗ c.jux@tudelft.nl abstract the aerodynamic characteristics of a modern road cycling wheel in crosswind are studied through force measurements and 3d velocimetry in tu delft’s open jet facility. the performance of the 62 mm deep rim is evaluated for two tire profiles, and yaw angles up to 20◦. all measurements are executed at 12.5 m/s (45 km/h) freestreamand wheel-rotational velocity. the wheel’s rim-tire section in crosswind is found to behave similar to an airfoil at incidence, ultimately resulting in a reduction of the wheel’s aerodynamic resistance with increasing yaw angle magnitude. this trend, also referred to as the sail-effect, is limited by the stall angle of the tire-rim profile. the stall angle is found to be dependent on the tire surface texture and varies between 14◦ and 20◦. 1 introduction aerodynamic drag is the major resistance a cyclist needs to overcome at speeds of 40 km/h and beyond. in fact, the aerodynamic drag accounts for approximately 90% of a rider’s total resistance in this speed regime which is typical for road racing (kyle and burke, 1984). the wheels contribute to about 10% of the total aerodynamic drag (greenwell et al., 1995), making them a crucial element in any cycling-performance optimization. focusing on road cycling, a rider is exposed to a variety of wind conditions, affecting the perceived yaw angle. the concept of wind-averaged drag (wad, cooper, 2003) accounts for the statistically anticipated yaw-angle distribution experienced by a ground vehicle. the higher the vehicle velocity, the smaller the maximum yaw angle perceived for a given wind speed. for professional road cycling speeds, the probability of exceeding 20◦ yaw angle is reported to be less than 10% (brownlie et al., 2010; barry, 2018). vice versa, a rider spends 90% of the time at yaw angles below 20◦. aerodynamically designed wheels used in road racing (thus, excluding time-trial and triathlon specific multi-spoke and disc wheels) are characterized by a 40-80 mm deep rim section, that connects via a multitude of thin spokes to a cylindrical hub. in comparison to classical, shallow rim profiles, the deep-section rim fulfills two functions: on one hand, it streamlines the tire shape, effectively reducing the tire-rim drag coefficient. on the other hand, it generates —similar to a sail —a side force perpendicular to the relative wind direction. a component of this force points in the riding direction, effectively “pulling” the wheel forwards and thereby further reducing its drag coefficient for non-zero yaw angles. the latter effect is known as the “sail-effect” in literature, and it can result in a negative net drag force for wheels at high yaw angles (lukes et al., 2005; barry et al., 2012; malizia and blocken, 2020a). designing a wheel for optimal performance is, however, not solely about minimizing (wind-averaged) drag. as barry et al. (2012) point out, large side forces on wheels yield strong steering moments and can be a concern of maneuverability. similar concerns can be expressed when discussing the stall behavior for wheels at large yaw angles. in addition to the rim-geometry, the aerodynamic characteristics of a wheel depend on the interaction of rim and tire. crane and morton (2018) investigate this interaction with specific attention to tire width relative to the rim. besides tire width, data from wheel manufacturers suggests that the tire profile is equally decisive for the rim-tire interaction, because the tire’s surface texture conditions the boundary layer development for the flow over the wheel (cant, 2014). complementing the analysis of crane and morton (2018), this work includes the comparison of a slick tire to a slightly profiled tire for a fixed tire width. in the discussion of cycling wheel aerodynamics it is common practice to study wheels in isolation. experimental studies in the field focus predominantly on balance measurements (e.g. zdravkovich, 1992; greenwell et al., 1995; tew and sayers, 1999), whereas flow topology data remains undocumented to the best of the authors’ knowledge. such data is readily available from computational fluid dynamics (cfd) analysis, which presents an active line of research in the context of cycling wheel aerodynamics (godo et al., 2010; malizia et al., 2019; malizia and blocken, 2020b). authors developing numerical tools for the aerodynamic analysis of cycling wheels, however, have to rely on the experimentally documented force data for validation of their simulations. this practice becomes problematic when reported drag measurements for the same wheel show variations of up to 300%, as observed by godo et al. (2010). the large force sensitivity is ascribed to variations in the experimental setup, including tire choice, free-stream turbulence, wheel support design and wind tunnel blockage. in view of the gaps and discrepancies in literature, the present work provides an experimental analysis of the flow topology on a state-of-the-art bicycle wheel in crosswind by means of coaxial volumetric velocimetry (cvv, schneiders et al., 2018). the change in flow topology with yaw angle and tire selection is documented. additionally, the hypothesized “sail-effect” theory is scrutinized by analysis of the pressure distribution near the rim-tire surface. 2 definitions & terminology prior to presentation of the experimental apparatus and procedures in the subsequent section, we provide clear definitions of the relevant variables and coordinate systems. the provided definitions largely follow the work of tew and sayers (1999). figure 1: definition of axes systems, flow angles and velocities for a cyclist moving at a velocity vbg relative to the ground (left). relation of forces in wind and bike reference frames, illustrated on a bicycle wheel in top view (right). figure 1 (left) shows a cyclist moving at a velocity vbg relative to the ground. the direction of travel defines the main reference frame xb, pertaining to the bicycle, with the x-axis pointing opposite to the motion direction. in an external environment, the wind velocity vext and its direction (γ, the crosswind angle) relative to the cyclist’s direction of motion are relevant for the definition of the aerodynamic problem. the vector difference of external wind vext and bicycle ground velocity vbg determines the relative wind velocity vrel experienced by the cyclist. the angle between the cyclist’s motion axis and the relative wind velocity defines the yaw angle β. let us define a second coordinate system xwt whose x-axis is aligned with vrel . the subscript ‘wt’ signals that this reference frame pertains to the wind-tunnel when testing in a laboratory environment, where the x-axis is always aligned with the relative wind direction. figure 1 (right) illustrates the resistive and lateral forces acting on a bicycle wheel. classically, the drag force d acts parallel to the free-stream direction defined by vrel , whereas the lift force l points perpendicular to it, combining to the resultant force ftot . more relevant for a cyclist, however, are the force components in the reference frame xb connected to the direction of motion. the side force fs and the axial force fa are expressed as geometrical projections of l and d: fa = dcos(β)−lsin(β) (1) fs = dsin(β)+lcos(β) (2) it follows that a situation can arise in which lsin(β) > dcos(β), resulting in a thrusting force which supports the cyclist’s motion —the sail effect. in the remainder of this work, forces are always provided and discussed in the bicycle reference frame. 3 experimental apparatus and procedures wind tunnel measurements are conducted at tu delft’s open jet facility, an open jet, atmospheric wind tunnel with a 2.85×2.85 m2 exit section. all measurements are executed at a freestream velocity of 12.5 m/s (45 km/h). the turbulence intensity in the test section, with a large-scale piv seeding system installed in the settling chamber, is reported with 0.8% by giaquinta (2018). an overview of the test setup is provided in figure 2. figure 2: experimental setup in the open jet facility (left). details of the mechanical systems installed in the wind tunnel, with surrounding floor plates removed (right). 3.1 wheel model & mechanical setup a dt swiss arc 1100 dicut db 62 front wheel is installed in the test section. the 28” (700 mm diameter with tire fitted) wheel features a 62 mm deep and 27 mm wide carbon rim. while the wheel is designed to run with disc brakes, no brake discs were installed during the wind tunnel test. the clincher rim is fitted with a 25 mm tire, inflated at 7 bar. a continental gp 5000 tire featuring a mild periodic surface pattern is chosen as a baseline tire, which is compared to a slick tire, a continental gp tt. the difference in tire profile is shown in figure 3. the grooved texture element on the baseline tire model is approximately 35 mm long, and 12 mm wide, with a 35 mm gap along the circumference between two subsequent elements. the wheel is connected to the support structure using a standard 12×100 mm through axle. the singlesided support holding the wheel from the left hand side is designed to enhance optical access for the velocimetry measurements. the tire rests on two 70 mm diameter (60 mm width) rollers embedded in the wooden ground plate. the rearward roller is driven by a variable speed dc motor to control wheel rotation. the wheel rotational speed is kept constant at 348 rpm, matching a ground velocity (vbg) of 12.5 m/s equal to the freestream velocity. wheel rotational speed and freestream velocity are both maintained constant at all times, and only the yaw angle is adjusted during the measurements. the wheel branding is covered by black adhesive foil to limit background reflections in the piv acquisition. a few circular (2 mm diameter) targets on the rim serve as reference markers to locate the model in the piv data, as well as a means to verify the wheel rotational speed. (a) baseline tire, continental gp 5000, with approximate indication of texture element size. (b) option tire, continental gp tt figure 3: fotographs of the tested tires mounted on the wheel. 3.2 force measurement system the wheel model including the mechanical support and drive mechanism is installed on a 6-axis force balance situated underneath the ground plate. the balance acquires data at a frequency of 2 khz, and its accuracy is reported with 0.06% (0.15 n) of its full 250 n load capacity (alons, 2008). force data is acquired and averaged over 20 s. the balance is placed on a turntable that controls the yaw angle. as such, the force measurements delivered by the balance system pertain to the bicycle wheel reference frame (xb). the yaw angle is varied in a range of β between -22◦ and +22◦ in steps of 2◦. the arrangement of the components is illustrated in figure 2 (right). prior to force measurements on the wheel, the forces on the isolated support are recorded for all yaw angles of interest. this data is subsequently subtracted from the measurements with the wheel installed to identify the forces generated by the wheel only. 3.3 velocimetry system three-dimensional (3d) particle image velocimetry data is acquired by a coaxial volumetric velocimetry (cvv, schneiders et al., 2018) system. a lavision minishaker aero cvv probe acquires image quadruples of 640×476 px2 at a frequency of 821 hz. 16,400 images are acquired for each yaw angle, equaling an acquisition period of 20 s. the velocimeter is mounted on a universal robots ur5 robotic arm, allowing to keep a similar imaging position and distance relative to the wheel for all yaw angles. neutrally-buoyant helium filled soap bubbles (hfsb, scarano et al., 2015) of 300 500 µm diameter serve as tracer particles, which are provided by a 0.6×0.8 m2 seeding rake installed in the wind tunnel settling chamber. the measurement domain spans a 30×20×20 cm3 volume near the most upstream section of the wheel. data is only acquired on the leeward, respectively, the suction-side of the rim. 3.3.1 velocity measurement the wheel rotation results in unsteady reflections which are filtered from the particle images by means of a butterworth frequency filter (sciacchitano and scarano, 2014), followed by a directional minimum filter on a local 5×5 px2 kernel. pre-processed images are analyzed by the 3d lagrangian particle tracking algorithm “shake-the-box” (stb, schanz et al., 2016) as implemented in davis 10.1. the scattered stb tracks are subsequently ensemble averaged by a linear fit of the velocity data in ellipsoidal cells of 6×6×30 mm3 (x× y× z), analogous to the approach presented by agüera et al. (2016). anisotropic cells are selected to enhance spatial resolution in the horizontal directions, where velocity gradients are anticipated be stronger as compared to the vertical direction, for the section of the wheel imaged by the velocimetry system. the grid spacing is maintained constant at 1.5 mm in all axes. 3.3.2 pressure evaluation based on the time-averaged velocity data, the static pressure is evaluated following a dual-model approach previously presented by the authors (jux et al., 2020). in the region of irrotational flow, bernoulli’s equation provides the local pressure and the necessary dirichlet condition for the subsequent spatial integration of the pressure gradient in the rotational flow domain. lastly, the static pressure in the flow is mapped onto rim and tire surface, using the local pressure gradient information. 4 results and discussion the analysis of the measurement data starts with the force measurements. subsequently, the velocimetry data is analyzed, leading to the discussion of the pressure distribution. 4.1 force measurement figure 4 compares the axial and lateral forces as function of yaw angle for the two tested tire options. the side force fs in figure 4a features a linear trend of decreasing force magnitude with increasing yaw for moderate angles within |β| ≤ 10◦. in this range, the lateral force reduces by approx. 0.85 n/◦, independent of the selected tire. interestingly, the point of zero side force is found at a small positive yaw angle of about 2◦. for large yaw angle magnitudes beyond 10◦, the slope tapers off with a clear difference between the tires: the (slick) option tire reaches higher side force magnitudes for both, large negative and positive yaw angles, whereas the side force for the (profiled) baseline tire tapers off at slightly smaller yaw angle magnitudes. this trend is well illustrated around β = 14◦ where the force curves cross each other. (a) lateral force (b) axial force figure 4: force measurements on the isolated wheel versus yaw angle. the axial force fa in figure 4b indicates a plateau of maximum resistance for small yaw angles (2◦ ≤ β ≤ 6◦). the peak resistance of 1.12 n is found at 2◦ yaw, corresponding with the location of zero side force in figure 4a. outside the indicated range, the axial force rapidly reduces for increasing yaw angle magnitudes. for negative yaw angles the tires behave similarly, with the axial force decreasing until -10◦ yaw, where a negative resistive force is measured, meaning the wheel is generating a propulsive force in this condition, albeit small in magnitude with about 0.1 n. the trend of decreasing axial force is stagnating in the range of -14◦ ≤ β ≤ -10◦, before the axial force rapidly increases again for even lower yaw angle values. this suggests that the flow over the wheel separates around β = -12◦. for yaw angles below -10◦ the (slick) option tire shows a lower axial force as compared to the baseline tire. differences between the two tire options are stronger for large positive yaw angles. the baseline tire initially shows a steeper reduction of the axial force with increasing yaw until β = 12◦, where the trend turns, and the resistive force increases again for β > 14◦. for positive yaw angles, the resistive force on the wheel with the baseline tire is always positive. in contrast, the axial force on the wheel with the option tire keeps reducing until β = 18◦, although at a slightly slower rate. an increase in axial force is only observed for the highest tested yaw angle of 22◦. negative resistance is observed for 18◦ ≤ β ≤ 20◦. despite the differences between the tire configurations, both cases show an asymmetric behavior against yaw angle: (1) the point of maximum axial force and minimum side force is found at β = 2◦ rather than 0◦. (2) minima in axial force are different in magnitude and occur at different yaw angle magnitudes when comparing behavior in negative and positive yaw. potential sources of this asymmetry are the non-symmetric wheel support, holding the wheel only from the left-hand-side (lhs); the blockage caused by the support structure of the piv system on the wheel’s right-hand-side (rhs); and the asymmetric design of the wheel’s hub and spokes to accommodate a (centerlock) brake disc on its lhs. the above analysis of the force data suggests nonetheless that the aerodynamic performance of the wheel is strongly dependent on the tire choice. the two tires behave similarly in the range of -10◦ ≤ β ≤ 10◦, whereas for larger yaw angles the option tire features lower axial resistance, which even becomes negative, and thus acts as a (small) propulsive force. the lower resistive force of the option tire comes with an increase in lateral force, which is approximately 10% higher as compared to the wheel with the baseline tire for |β| > 14◦. in the following we scrutinize the velocimetry data to link the observed differences to changes in the flow topology. 4.2 time-average velocity field for analysis of the flow topology, we extract slices of the 3d velocimetry data in a horizontal plane at hubheight (z = 342.5 mm). the data shown in figure 5 contains the velocity field upstream and past the leeward (suction) side of the rim. the velocity contours show the normalized axial velocity component in the bicycle wheel reference frame xb, u∗ b = ub ub∞ = ub uwt∞ cos(β) (3) where the subscript ‘∞’ indicates free-stream conditions upstream of the wheel. the velocity contours are complemented by streamlines in the 2d planes. additionally, for each yaw angle, the aerodynamic effect of the tire is illustrated by plotting the difference in the axial velocity component between the baseline and the option tire. in straight ahead conditions (β = 0◦, figure 5a) the inflow decelerates towards the most upstream point of the tire. while one would expect the streamwise velocity component to stagnate at the tire surface, the finite velocity measurement reduces only to u∗ b ≈ 0.6, which is attributed to spatial resolution effects. alongside the rim-tire profile the flow accelerates reaching streamwise velocities in excess of u∗ b = 1.2 at the thickest section of the rim. the wake of the rim is not well captured by the velocimetry data. the streamlines, however, suggest the presence of a separated wake zone just downstream of the rim. the differences between the tire options are very mild at 0◦ yaw, in line with the balance data discussed previously. the region of accelerated flow past the wheel gains in size and magnitude as the yaw angle increases. consider e.g. figure 5c (β = 8◦) where for both cases the axial velocity exceeds 130% of the inflow velocity as it passes the wheel. comparing back to the straight ahead case in figure 5a it is also noted that the location of maximum velocity moved upstream, approximately to the junction of rim and tire, whereas at 0◦ yaw the maximum velocity is observed further downstream at the thickest point of the rim. likewise, the zone of decelerated flow upstream of the wheel rotates towards the windward side as the yaw angle increases. the latter is seen well by following the unity contour of axial velocity (u∗ b = 1) which follows a counter-clockwise motion with increasing yaw angle. the described trend continues for both tire cases until β = 12◦ (figure 5d). for greater yaw angles there is a substantial difference in the flow topology for the different tire options. comparing the data in figures 5e and 5f, the streamlines pertaining to the (slick) option tire in the right-hand-side plots suggest that the flow follows the largest part of the wheel contour. instead, for the (textured) baseline tire in the left-hand-side plots, the streamlines only bend slightly around the tire but continue diverging from the rim surface as the flow passes the wheel. the different behavior is also visible in the delta plot in figure 5f, which indicates that the flow around the wheel with the option tire attains far greater axial velocity. while flow data closer to the rim surface is lacking for the baseline tire at these high yaw angles, the streamlines indicate that the flow separates from the tire, similar to a leading edge separation on aeronautical airfoil profiles at high angle of attack. such leading edge separation results in a loss of lift (here, side force) and a simultaneous increase in drag (here, axial force) which is in line with the observations from the force data above. (a) β = 0◦ (b) β = 4◦ (c) β = 8◦ (d) β = 12◦ figure 5: time-average velocity contours in xy-planes at hub height (z = 342.5 mm), along with 2d surface streamlines. velocity contours show the normalized axial velocity component in the bicycle wheel reference frame. (left) baseline tire. (right) option tire. (center) delta = ubaseline −uoption. (continues on next page) (e) β = 16◦ (f) β = 18◦ figure 5: (continued) time-average velocity contours in xy-planes at hub height (z = 342.5 mm), along with 2d surface streamlines. velocity contours show the normalized axial velocity component in the bicycle wheel reference frame. (left) baseline tire. (right) option tire. (center) delta = ubaseline −uoption. 4.3 pressure data following the analysis of the velocity data, we briefly investigate the pressure distribution over tire and rim profile. similar to the previous assessment, the analysis starts in a horizontal xy-plane at hub height (z = 342.5 mm). because both tire options behave similar for moderate yaw angles, and data close to the figure 6: cp profiles over the tire-rim surface at hubheight (z = 342.5 mm) for the option tire (gp tt). surface is lacking for high yaw angles on the baseline tire, we limit ourselves to the study of the (slick) option tire here. figure 6 shows the pressure profiles on the leeward side of the wheel for β = [0, 8, 16]◦. the pressure profiles are characterized by a steep pressure reduction over the upstream tire section. as the yaw angle increases, the pressure reduction gains in magnitude, signifying greater suction with increasing yaw angle. the location of minimum cp moves downstream as the yaw angle grows. at 0◦ yaw the minimum pressure of cp = -0.7 is recorded at x/c = 0.06, before approaching an approximately constant value of cp = -0.5 further downstream. at 8◦ yaw instead, the minimum pressure coefficient exceeds a value of -1, and it is obtained slightly further downstream (x/c = 0.13). increasing the yaw angle further to 16◦, the pressure coefficient drops to a minimum of cp = -1.75 at x/c = 0.26, followed by an adverse pressure gradient approaching cp = -0.5 at x/c = 0.6. complementing the above pressure profiles in the wheel center plane, 3d iso-surfaces of pressure coefficient are shown for the three selected cases in figure 7, along with axial velocity contours on the upper and lower boundary of the measurement volume. for each case, two iso-surfaces are plotted: the first, at cp = 0.35 (red) indicates the volume of increased pressure resulting from the flow deceleration upstream of the wheel. the second, at cp = -0.6 (blue) is selected to visualize the volume of reduced pressure induced by the flow acceleration alongside the wheel. comparing the latter iso-surface for the three yaw angles confirms the growth of the low-pressure region with increasing yaw angle, signaling a likewise increase in side force. figure 7: axial velocity contours in horizontal planes at z = [242.5, 442.5] mm along with 3d pressure iso-surfaces of cp = 0.35 (red) and -0.6 (blue). data shown for wheel fitted with option tire at β = 0◦ (left), 8◦ (center) and 16◦ (right). the observed trend is qualitatively in line with the force data presented in section 4.1 which indicated a monotonically increasing side force magnitude with increasing yaw angle in this range. it further supports the theory that the tire-rim profile in crosswind indeed behaves like an airfoil at incidence, thereby making the wheel work like a sail. 5 conclusions the aerodynamic characteristics of a state-of-the-art road cycling wheel in cross wind have been assessed experimentally by means of force measurements and a full-scale 3d velocimetry investigation. additionally, the interaction of rim and tire is studied by comparison of a textured and a slick tire. the resistive force on the isolated wheel is highest at moderate yaw angles of β = 2◦ ± 4◦. outside this range, the aerodynamic resistance of the wheel is reduced as the yaw angle magnitude increases. analysis of the velocimetry data confirms that the reduction in resistance measured by a force balance is indeed a consequence of the “saileffect”, resulting from a substantial side-force on the wheel at yaw incidence. the benefit of this effect is limited by the stall angle of the tire-rim combination, which is found to be dependent on the tire choice. the two tested tires behave similarly for negative yaw angles, with the flow separating around β = -14◦. for positive yaw angles, the slick tire performs significantly better, increasing the separation angle from 14◦ to 20◦ with respect to the profiled baseline tire. acknowledgements we thank thomas koep on behalf of dt swiss for providing the wheels for the study. likewise, we thank dennis bruikman, peter duyndam and frits donker duyvis for the invaluable technical support. this research is supported by lavision gmbh. references agüera n, cafiero g, astarita t, and discetti s (2016) ensemble 3d ptv for high resolution turbulent statistics. measurement science and technology 27:124011 alons hj (2008) ojf external balance. report nlr-cr-2008-695. nederlands luchten ruimtevaartcentrum (national aerospace laboratory, nlr) barry n (2018) a new method for analysing the effect of environmental wind on real world aerodynamic performance in cycling. in 12th conference of the international sports engineering association. volume 2. page 211 barry n, burton d, crouch t, sheridan j, and luescher r (2012) effect of crosswinds and wheel selection on the aerodynamic behavior of a cyclist. in engineering of sport conference 2012. volume 34. pages 20–25 brownlie l, ostafichuk p, tews e, muller h, briggs e, and franks k (2010) the wind-averaged aerodynamic drag of competitive time trial cycling helmets. procedia engineering 2:2419–2424 cant g (2014) back to the wind tunnel. www.swissside.com/blogs/news/back-to-the-wind-tunnel accessed on 17.05.2021 cooper kr (2003) truck aerodynamics reborn-lessons from the past. sae transactions 112:132–142 crane r and morton c (2018) drag and side force analysis on bicycle wheel-tire combinations. journal of fluids engineering-transactions of the asme 140 giaquinta d (2018) the flow topology of the ahmed body in cross-wind: an experimental investigation by means of robotic volumetric piv. msc thesis, tu delft godo m, corson d, and legensky s (2010) a comparative aerodynamic study of commercial bicycle wheels using cfd. in 48th aiaa aerospace sciences meeting including the new horizons forum and aerospace exposition. page 1431 greenwell di, wood nj, bridge ekl, and addy rj (1995) aerodynamic characteristics of low-drag bicycle wheels. aeronautical journal 99:109–120 jux c, sciacchitano a, and scarano f (2020) flow pressure evaluation on generic surfaces by robotic volumetric ptv. measurement science and technology kyle cr and burke e (1984) improving the racing bicycle. mechanical engineering 106:34–45 lukes ra, chin sb, and haake sj (2005) the understanding and development of cycling aerodynamics. sports engineering 8:59–74 malizia f and blocken b (2020a) bicycle aerodynamics: history, state-of-the-art and future perspectives. journal of wind engineering and industrial aerodynamics 200:104134 malizia f and blocken b (2020b) cfd simulations of an isolated cycling spoked wheel: the impact of wheel/ground contact modeling in crosswind conditions. european journal of mechanics b-fluids 84:487–495 malizia f, montazeri h, and blocken b (2019) cfd simulations of spoked wheel aerodynamics in cycling: impact of computational parameters. journal of wind engineering and industrial aerodynamics 194 scarano f, ghaemi s, caridi gca, bosbach j, dierksheide u, and sciacchitano a (2015) on the use of helium-filled soap bubbles for large-scale tomographic piv in wind tunnel experiments. experiments in fluids 56:42 schanz d, gesemann s, and schröder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:70 www.swissside.com/blogs/news/back-to-the-wind-tunnel schneiders jfg, scarano f, jux c, and sciacchitano a (2018) coaxial volumetric velocimetry. measurement science and technology 29:065201 sciacchitano a and scarano f (2014) elimination of piv light reflections via a temporal high pass filter. measurement science and technology 25:084009 tew gs and sayers at (1999) aerodynamics of yawed racing cycle wheels. journal of wind engineering and industrial aerodynamics 82:209–222 zdravkovich m (1992) aerodynamics of bicycle wheel and frame. journal of wind engineering and industrial aerodynamics 40:55–70 introduction definitions & terminology experimental apparatus and procedures wheel model & mechanical setup force measurement system velocimetry system velocity measurement pressure evaluation results and discussion force measurement time-average velocity field pressure data conclusions 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 particle image velocimetry measurements of a dry powder inhaler flow v. chaugule1∗, l. g. dos reis2, d. f. fletcher3, p. m. young2,4, d. traini2,5, j. soria1 1 laboratory for turbulence research in aerospace and combustion (ltrac), department of mechanical and aerospace engineering, monash university, clayton, victoria 3800, australia 2 respiratory technology, woolcock institute of medical research, nsw 2037 sydney, australia 3 school of chemical and biomolecular engineering, the university of sydney, sydney, australia 4 department of marketing, macquarie business school, macquarie university, nsw 2109, australia 5 department of biomedical sciences, faculty of medicine, health and human sciences, macquarie university, nsw 2109, australia ∗ vishal.chaugule@monash.edu abstract inhalation therapy for respiratory disorders is being increasingly delivered via dry powder inhalers (dpis), which are breath-actuated devices that deliver pharmaceutical drug particles to the lungs. the motion of inhalation air, produced when a patient inhales through this device, supplies all energy for the entrainment, de-agglomeration, and dispersion of powder drug agglomerates into a fine drug particle aerosol. the aerosol performance is directly related to the fluid-mechanics of a given dpi device. these flow mechanisms are complex as they depend on the device design, inhalation flow rate, and the properties of the dry powder formulation used. among these, the role of device design is crucial as it significantly affects not only the generation and properties of delivered aerosol, but also the capability of targeted regional drug deposition. figure 1: dpi model examined and schematic of the experimental set-up a common design feature in several dpi devices is the provision of tangential inlets to generate a swirling inhalation flow for the entrainment and de-agglomeration of the drug powder. a typical dpi model based on this design is shown in fig. 1. it is a hollow circular pipe with two diametrically opposite tangential inlets placed above a hemispherical drug-dosing cup at the bottom, while the open top forms the device mouthpiece. two component-two dimensional (2c-2d) piv measurements have been performed on this model using water-based experiments under geometrically and dynamically similar conditions to actual dpis operating in air (dos reis et al., 2021). a schematic of the experimental set-up is shown in fig. 1. the dpi model is placed in the bottom of a tank, both of which are made of clear perspex, with a closed-loop steady water flow-rate of 12 l/min maintained through the system. piv measurements are taken in longitudinal and transverse planes, both inside and outside the dpi mouthpiece. the transverse plane measurements are taken by imaging the ccd camera through a 45° mirror mounted inside the tank onto the observation plane defined by the laser sheet. the piv images are analyzed using the multi-grid/multi-pass cross-correlation digital particle image velocimetry (mccdpiv) introduced by soria (1996). the coordinate system adopted is also shown in fig. 1, with its origin just outside the centre of the dpi mouthpiece-exit. the flow re = 8400 is defined based on the mouthpiece-exit inner diameter d = 30 mm and the average axial-exit flow velocity uw. the mean axial u , lateral v , and tangential w velocity profiles inside and outside the dpi mouthpiece are shown in fig. 2 (a), (b) and (c), respectively. the mean axial velocities in the central flow region become increasingly negative as we move from inside to the outside of the mouthpiece. the regions around the mouthpiece edges, y/d =±0.5, have high positive mean axial velocities, accompanied by high mean lateral velocities. these characteristics are attributes of a strongly swirling pipe flow inside the dpi mouthpiece which transforms into a swirling jet emerging from it. the mean tangential velocities inside the dpi at x/d =−3 attain a maximum value of about 2.7uw, which shows the strongly swirling nature of the internal flow, and the swirl level reduces as we move towards the mouthpiece-exit. figure 2: mean velocities inside and outside the dpi mouthpiece in: (a) axial; (b) lateral; (c) tangential directions. figure 3: flow-field vectors on transverse planes inside the dpi mouthpiece at: (a) x/d = −3; outside at (b) x/d = 0; and on a (c) longitudinal plane outside the dpi mouthpiece. the velocity vectors in the transverse planes (y−z) inside the dpi mouthpiece, at x/d=−3, and outside, at x/d = 0, are illustrated in fig. 3 (a) and (b), respectively, while those in the longitudinal plane (x− y) outside are shown in fig. 3 (c). these outline a strongly swirling dpi flow which acts on the drug particles, forcing them into a spiralling trajectory towards the periphery, where they undergo de-agglomeration due to action of fluid forces and particle collisions. the dispersed flow leaving the mouthpiece spreads laterally from the edges and has a central reverse flow region, which is identified as vortex breakdown. the deagglomerated particles conform to these flow features and cause significant drug losses due to impaction in a patient’s mouth-throat region (fletcher et al., 2021). the aforementioned results unravel the dpi flow characteristics, and thus provide valuable insight into aerosol generation from these inhalers – the knowledge of which has been limited until now. acknowledgments: the research was supported by the australian research council. the research also benefited from computational resources provided through the ncmas, supported by the australian government, and the multi-modal australian sciences imaging and visualisation environment (massive) at monash university. references dos reis lg, chaugule v, fletcher df, young pm, traini d, and soria j (2021) in-vitro and particle image velocimetry studies of dry powder inhalers. international journal of pharmaceutics 592:119966 fletcher df, chaugule v, dos reis lg, young pm, traini d, and soria j (2021) on the use of computational fluid dynamics (cfd) modelling to design improved dry powder inhalers. pharmaceutical research 38:277–288 soria j (1996) an investigation of the near wake of a circular cylinder using a video-based digital crosscorrelation particle image velocimetry technique. experimental thermal and fluid science 12:221–233 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 a study on piv-based pressure measurements using cfd techniques f. felis-carrasco1, b. b. watz1, d. hess1∗, m. a. mendez2 1 dantec dynamics a/s/company, copenhagen, denmark 2 von karman institute for fluid dynamics, sint-genesius-rode, belgium ∗ dhs@dantecdynamics.com abstract this work discusses an approach to compute pressure fields from planar piv measurement using standard cfd tools. in particular, we propose a combination of interpolation and mesh adaptation to import the piv measurements on a grid that is morphed around objects, and is fine enough to solve the poisson equation accurately. the whole process of meshing, interpolation and pressure computation is carried out using the popular open-source solver openfoam®. the method is tested and validated on a classic benchmark test case, namely, the unsteady flow past a cylinder. a 3d multiphase flow simulation is used to generate the reference data and analyze the impact of both, the piv interrogation and the interpolation on the morphed grid. the simulation uses an euler-lagrangian one-way coupling approach to simulate the flow field and the dynamics of seeding particles. the analysis compares the pressure field from the 3d cfd simulation with the solution of a 2d poisson equation based on the 2d velocity field obtained by either down-sampling the cfd data or by piv interrogation of synthetic images built from the cfd data. finally, we challenge the proposed method with the pressure reconstruction in a tr-piv experiment in similar conditions. 1 introduction measuring the flow field by planar or volumetric piv is often the first step towards the solution of many aerodynamics, acoustics, and fluid-structure interaction problems. phenomena such as boundary layer separation or travelling vortices can be identified within the measurement domain and linked to noise emission or aerodynamic loads. further insights on many of these phenomena are possible if the pressure fields can be retrieved from the measurement domain. for example, aerodynamic loads, force balances and momentum exchanges can be evaluated by integrating pressure distributions along boundaries. jakobsen et al. (1997) were among the first to estimate forces from piv flow fields; since then, many approaches have been presented (see, van oudheusden, 2013). regardless of the required input (either averaged fields or time-resolved sequences of instantaneous fields), most methods are based on the integration of a poisson equation, derived from the momentum and mass conservation equations(see also, van gent et al., 2017; van oudheusden, 2013). standard techniques from cfd (computational fluid dynamics) offers powerful and efficient tools to compute pressure fields from velocity fields (gunaydinoglu and kurtulus, 2020; regert et al., 2011). however, the main challenge in the use of these tools is that piv fields are generally noisy and available on grids that are often too coarse to reproduce accurately curved boundaries. adaptive piv interrogation methods (see for example, masullo and theunissen (2017)) offer a valuable solution but are not yet widely diffused. in this work, we propose a combination of interpolation and mesh adaptation to compute pressure fields from planar piv using the popular open-source cfd package openfoam®. in particular, we analyze the impact of the interpolation and mesh adaptation and the piv interrogation by testing the algorithm on a test case, for which the ground truth is available. the selected test case is the unsteady flow past a cylinder, which was first simulated using a 3d euler-lagrangian simulation. this allows reproducing the flow field and the seeding particle dynamics. besides providing the reference data, the cfd results were also used to extract a set of 2d fields on grid step sizes similar for piv and reproduce a set of synthetic piv images. the first was used to analyze the impact of the velocity field interpolation; the second was used to analyze the impact of the piv interrogation area size. the numerical methods are discussed in section 2 while section 3 presents the test case and the related computation. finally, we close in section 4 with an assessment of the method on time-resolved piv experiment in a similar configuration, where the additional challenge of a limited region of interest and unknown boundary conditions are included. conclusions and perspectives are given in section 5. 2 numerical method for pressure calculation the starting point for the pressure calculation is the set of mass and momentum conservation equations. considering an incompressible flow with constant density ρ and constant kinematic viscosity ν, the continuity equation imposes the divergence-free (solenoidal) condition to the velocity field. in cartesian coordinates, denoting the velocity components as ui with i = 1,2,3, and using einstein notation, this reads ∂ui/∂xi = 0. with the same notation, the momentum conservation equations read: ∂ui ∂t + ∂uiu j ∂x j =− ∂p ∂xi + ∂ ∂x j [ ν ( ∂ui ∂x j + ∂u j ∂xi − 2 3 ∂uk ∂xk δi j )] , (1) where p is here the kinematic pressure (i.e. p/ρ, with p the static pressure). the link between the velocity field and the pressure field is given by the poisson equation obtained by taking the divergence of (1): ∂2p ∂x2 i = ∂ ∂xi [ ∂ui ∂t ] ︸ ︷︷ ︸ time source + ∂ ∂xi [ ∂uiu j ∂x j ] ︸ ︷︷ ︸ convective source + ∂ ∂xi [ ∂ ∂x j ν ( ∂ui ∂x j + ∂u j ∂xi − 2 3 ∂uk ∂xk δi j )] .︸ ︷︷ ︸ diffusive source (2) in its general form, this equation includes three source terms on the right hand side. the first is related to the flow unsteadiness, the second to the advection term and the last to the viscous diffusion. the divergencefree condition from the continuity equation significantly simplifies this equation. however, when working with 2d measurements, the assumption of solenoidal 2d fields implies that the out-of plane component is identically null and is thus an important source of errors. 2.1 numerical solver in openfoam® an integration scheme and adequate boundary conditions are needed to solve the poisson eq. (2) for the pressure. many approaches have been explored over the years, from direct integration using finite differences methods to complete implementations of cfd solvers like simple or piso, where both the pressure and the velocity fields are calculated and corrected in an iterative process (gunaydinoglu and kurtulus, 2020; regert et al., 2011). a direct approach is used in this work, namely a standard poisson solver using finite-volume method (fvm) from openfoam®. in this solver, the velocity field ui and hence all terms on the right hand side of eq. (2) are assumed to be known. the solver was implemented in a custom solver inherited from a piso solver from the openfoam® tools. within this, a gamg (geometric algebraic multi-grid) solver is applied, with a maximum of 10 non-orthogonal correction steps, until a residual of 1e−9 is reached. the boundary conditions consist of a mixture of dirichlet and neumann conditions. dirichlet conditions p = 0 are set to all ‘open’ boundaries of the domain that are sufficiently far from the solid walls (e.g. the cylinder surface). the classic zero gradient ∂p/∂n along the normal direction n is imposed at solid walls. a different approach consists of using the velocity field along a boundary to compute the pressure gradient from eq. (1), and finally set neumann conditions accordingly. nevertheless, this approach was not implemented in this study. the pseudo-code to solve eq. (2) is detailed in the appendix list. 1, where the step-by-step construction for the know source terms is shown using fvm classes in openfoam® (opencfd-limited, 2019a). from a syntax point-of-view, the same steps are taken when moving from eq. (1) into eq. (2). 2.2 mesh adaptation via snappy hex mesh the main challenge in computing the pressure field past a curved object is that standard piv interrogation provides the flow field ui on a coarse grid. usually, this grid is not capable of representing a curved surface as the cylinder in the proposed test case. in this work, we test the snappyhexmesh utility from openfoam® to construct a mesh that conforms to the curved boundary. this utility uses hexahedra and split-hexahedra mesh elements which are iteratively refined and morphed to the curved surface (opencfd-limited, 2019b). the process begins with a structured mesh which acts as a ‘background mesh’ and defines both the domain and the base level of mesh density. this is typically generated using the blockmesh utility. in the piv-based pressure computation, the background mesh is provided by the piv grid. the main steps are illustrated in figure 1, using a down-sampled version of the cfd results to mimic the piv field as discussed in section 3. figure 1-a shows the initial coarse mesh and the expected pressure field, while figure 1-b shows the velocity fields interpolated on the morphed mesh. note that the original grid in figure 1-a is incapable of describing the cylinder surface. figure 1-c shows the adapted mesh and the results the solution of the poisson equation together with the velocity field interpolation. finally, once the solution for the pressure is found in the adapted mesh, the result is interpolated back into the original piv grid. the results are shown in figure 1-d, which is to be compared, as discussed in section 3, with figure 1-a. a) b) c) d) a b c a b c figure 1: steps for the mesh adaptation and pressure computation around an object. for validation purposes, as described in sec. 3, figure a) shows the pressure field available over a coarse grid. figure b) shows the 2d velocity vector field (green arrows) interpolated from the original downsampled 3d cfd simulation. figure c) shows the morphed mesh around a re-inserted cylinder object together with the pressure solution (pe) from the solver. figure d) shows the interpolation of the result back to the original coarse grid. 3 case study for proof-of-concept: flow past a cylinder the procedure to validate the proposed methodology is illustrated in figure 2. the cfd simulation, described in section 3.1, allows for controlled numerical experiments in which both velocity and pressure fields are available on a fine grid and in a large domain. the cfd results are used for two purposes. first, a coarse velocity vector field is extracted by down-sampling the 3d cfd results along with a 2d coarse mesh that mimics a piv grid (grey boxes in figure 2). this is used to re-compute the pressure fields using the poisson solver described in the previous section. details of these computations are reported in section 3.2. this test case provides the “best-case” scenario for the solver (orange boxes in figure 2) and allows evaluating the impact of the 2d assumption. second, the results from the lagrangian tracking are used to generate synthetic 2d-2c piv images. these are then processed using standard piv interrogation algorithms, and the resulting velocity fields are also used to calculate the pressure field (blue boxes in figure 2). details of these computations are reported in section 3.3. this test case allows for testing the impact of the piv interrogation. finally, section 3.4 reports on the results of this comparison. cfd simulation 3d: eulerian field (p, u) lagrangian particles 3d field: roi original velocity (u) original pressure (p) 2d planar field: velocity (u) 2d planar field: velocity (u) to coarser structured mesh particle imaging: time series adaptive piv temporal smooting piv processing: eulerian field (u) to coarser mesh to morphed mesh using snappyhexmesh pressure solver 2d planar field: velocity (u) pressure solver 2d planar field: pressure (pe) 2d planar field: pressure (pe) 2d planar field: pressure (pe) 2d slice field: pressure (p) 2d planar field: pressure (pe) to morphed mesh using snappyhexmesh interpolation to structured mesh interpolation to structured mesh openfoam solver openfoam solver figure 2: flowchart of the proposed study case. the boxes in gray show the steps to obtain the reference data from the 3d transient cfd simulation. the boxes in orange show the steps to extract 2d pressure planes from the 3d data. the boxes in blue trace the step to obtain piv based pressure evaluation from the cfd data, using synthetic images. 3.1 3d transient euler-lagrange simulation the simulation case consist on a 3d transient flow around a fixed cylinder. the domain is a box of [−50, 200] mm in the x direction, [−50, 50] mm in the y direction and [−125, 125] mm in the z direction. the cylinder is centered at the origin (0,0,0) and oriented in the z direction, with a diameter dc = 5 mm and a length of lc = 30dc. a snapshot of the 3d domain, illustrating also the mesh refinement along the middle plane z = 0 is shown in figure 3-a. the inlet free stream velocity is set to u∞ = 0.5m/s at the inlet plane x = 0. the fluid properties for air are taken as ρ = 1.2047kg/m3 and ν = 15.11× 10−6 m2/s, leading to a diameter-referenced reynolds number of re = u∞d/ν = 170. the flow is thus in the laminar unsteady regime. a) b) figure 3: 3d transient cfd euler/lagrange simulation of the flow past a cylinder. fig a) shows the calculation domain 3d iso-contours pressure surfaces around the cylinder. fig b) shows a slice in the center plane of a), showing the mesh grading towards the 3d cylinder. the iso-contours pressure surfaces in figure 3-a indicate that the flow has a complex 3d topology downstream the cylinder, where the effect of the edges develops, reaching the center-plane (z = 0) for x/dc > 5. figure 3 shows a snapshot of the pressure field and the mesh refinements close to the cylinder. the simulation is enriched with lagrangian tracking of particle tracers in the eulerian fields. as described in figure 2, these provides the required information to build synthetic piv fields and assess the complete chain. the lagrangian solver uses a one-way coupling, meaning that the particles move according to the eulerian field, but these do not alter the main flow. the simulations are carried out using the uncoupledkinematicparcelfoam in openfoam®. a total of 20×106s−1 particles are injected in the domain inlet with initial velocity equal to 5% of the local velocity. these are injected at randomly selected location and are assumed to be spherical and mono-dispersed with a diameter of dp = 1µm. the particle density is set equal to the fluid flow to let them follow the flow accurately. their interaction with surfaces is set to rebound, taking a stiffness young’s module of 6×106 pa. particles leaving the domain are set to disappear. in both the 2d pressure field evaluation and the piv-based reconstruction, the selected domain is taken as −4 ≤ x/dc ≤ 4, namely in a region which is fairly bi-dimensional. to simulate a piv experiment, the velocity field is assumed bi-dimensional, i.e. with u3 = 0: regions in which this assumption is invalid produce out-of plane motion which cannot be quantified in a planar, single camera, piv experiment. these invalidate the assumption of solenoidal 2d fields and prevents simplifications of eq. (2). 3.2 pressure reconstruction from 2d field following the work flow in the orange boxes of figure 2, 2d fields simulating 2d-2c piv measurements are obtained by under-sampling the 3d data on the plane z = 0. the original velocity field ui and the pressure fields are linearly interpolated from the 3d grid onto a coarser regular 2d grid. in the process, we force u3 = 0 to have 2d fields. however, we do not impose the condition of divergence free for the 2d flow u1,u2 and hence the pressure eq. (2), here solved in its 2d form, has the three source terms on the right hand side. however, it is worth noticing, that the region close to the cylinder (−4≤ x/dc ≤ 4) is characterized by nearly solenoidal 2d fields. the results were shown in figure 1-a and 1-b. given the position and the diameter of the cylinder, this is introduced in the flow field (red circle in figure 1-a) in order to recreate a surface patch for the cfd calculation. the snappyhexmesh utility is used to morph and adapt the original regular background grid into a grid capable of well representing the cylinder and the associated boundary conditions. the velocity field is then linearly interpolated again into this mesh, as shown in figure 3-c. the poisson solver described in section 2 is used to compute the pressure field and the result is interpolated back into the original background mesh (figure 3-d). 3.3 pressure reconstruction from piv measurements the results from the lagrangian tracking are used as input for a synthetic image generation engine. this procedure is based on the work of lecordier and westerweel (2004). the synthetic images with the size of 2400× 1600 px represents a domain of [−26,52] mm in x direction and [−26,26] mm in y direction. the center of the cylinder is aligned with the [0,0] coordinate leaving 5-diameters upstream and 10 diameters downstream for the flow to develop. the synthetic camera sensor has a 10 µm pixel size and is paired with a 100 mm lens positioned 325 mm away from the measurement plane. the particles are modelled with gaussian intensity profiles with the size of 0.02 mm, resulting in a particle diameter of 2.4 px. the resulting seeding density is approximately 0.01 particles per pixel (ppp). piv snapshots were generated with a frequency of 1000 hz, imitating a tr-piv acquisition in “single-exposure” mode. the piv velocity fields are available at the same time instance of the simulation, which are sampled with twice the frequency. the velocities from the particle images are computed in dynamicstudio using an adaptive piv algorithm (theunissen, 2010) with a smallest size of 32×32 px using 50% overlap, resulting in a vector spacing of 0.48 mm. the vectors are filtered in time and space with a multiscale proper orthogonal decomposition (mpod) (mendez et al., 2020) analysis and mpod reconstruction with 98.5 % of the highest energetic modes. this is necessary since the velocities close to cylinder are more noisy, probably because of the lower seeding concentration in this area. thereafter, the pressures are computed as in the previous section. 3.4 analysis figure 4 shows the pressure profiles sampled along the circumference c and the line a−b from figure 1. the comparison along the circumference c is performed in a polar plot in which θ = 180o is the front stagnation point and θ = 0o is the rear stagnation point (see also figure 1). four profiles are shown. black continuous lines are used for the pressure profiles extracted from the 3d simulation. these can be considered as the ground truth. the profiles with the round blue markers are extracted from the down-sampled grid, onto which the pressure fields were interpolated. the excellent matching between these two curves shows that the morphed mesh is, in principle, well suited to reproduce the pressure fields in this configuration. the profiles with the red round markers are obtained by integrating eq. (2) on the coarse (piv-live) grid, using the velocity available over it. the discrepancy is everywhere significant and is clearly because the grid is way too coarse. besides introducing errors in the derivative computation, this grid is incapable of correctly describing the cylinder surface and does not allow, therefore, to set the boundary conditions of the problem correctly. the results are significantly improved if eq. (2) is solved over the morphed grid, with velocity fields linearly interpolated from the coarse mesh, as shown by the profiles with the orange square markers. this result is primarily due to the constraint of the no-slip condition on the cylinder, which helps the interpolation overcoming the limitations of linear support. of course, more complex interpolations schemes might be needed for problems characterized by more significant gradients, but for the scopes of this work, the agreement is sufficient to prove the feasibility of the proposed approach. moreover, these results highlight the importance of correctly defining the object geometry, both because of the required mesh refinement and because of the need to correctly impose the boundary conditions. finally, the profiles with green triangles are the ones obtained by integrating eq. (2) over the morphed grid using velocity fields obtained via piv interrogation. although some discrepancies appear on the pressure profile along the line a−b in the rear stagnation region, the agreement between the pressure distribution in the 2d pressure re-calculation and the piv-based pressure evaluation is overall acceptable. this shows that the piv evaluation, enhanced by the mpod-based filter, provides fields that are sufficiently accurate. additional mesh refinements, finer interrogation windows and/or better interpolation might be needed in the regions close to the boundary layer separation (θ ≈ ±120o), in which the velocity gradients are more pronounced. figure 4: comparison of the pressure field in the vicinity of the cylinder. a) pressure around the cylinder object at δ = 0.1dc from the surface. b) pressure along the x axis centerline across the cylinder. 4 an experimental test case while the previous test cases allow for evaluating the impact of all the different steps in the pressure evaluation, we here consider an experimental test case. this is the time-resolved piv measurement of the flow around a cylinder, using the same set set-up are the same used in mendez et al. (2020). the experiments are carried out in the l-10 low speed wind tunnel of the von karman institute. the tunnel offers a cross-section of 20 cm and the cylinder has a diameter of 5 mm. seeding particles were injected in the intake manifold of the tunnel from a laskin nozzle operated with ondina shell 91 mineral oil. these are illuminated by the physics instruments nd:ylf laser, offering up to 20 mj/pulse at 1 khz. the time resolved piv system, from dantec dynamics, is completed by a speedsense 9090 camera running at 7200 hz. dynamicstudio 7.3 is used for acquisition and analysis. the 1280×800 px camera with its 100 mm macro lens for this measurement has a pixel resolution of 50 µm/px and the total field of view is 64×40 mm. the image interrogation was carried out using adaptive piv (theunissen, 2010) with a final window size of 24× 24 px and a vector spacing of 8 px, resulting in one vector every 0.4 mm. for temporal and spatial filtering a mpod analysis and mpod reconstruction with 97 % of the total energy is applied prior to the pressure computations. these 97 % of the total energy are represented by the 101 modes (including the mean) with the highest energy. the free stream velocity is measured to u∞ = 1.25 m/s resulting in a reynolds number of re= 400. with a vortex formation frequency of approximately f = 48 hz, the strouhal number is st = f d/u∞ = 0.192. this is in the typical range for a vortex street behind a cylinder at the reynolds number considered. figure 5: result of the pressure computation from a conducted piv experiment of a cylinder flow. unfortunately, this experimental test case was designed to focus on the wake dynamics and not on the flow in proximity of the cylinder. because of a large shadow cast on the bottom side of the flow, the roi for the piv analysis can only be placed downstream the cylinder. the investigated roi and the result from the pressure computation can be seen in figure 5. from these velocity fields, the pressures are computed using the explicit pressure computations using the methodology previously described. the main challenge here is the definition of the boundary conditions, particularly on the left edge of the roi. in this first proof of concept, this was set to zero gradients, while zero pressure is set to all the other boundaries. these conditions on the left and right boundaries are not appropriate given the presence of non-negligible velocity gradients, and future studies will implement more sophisticated neumann boundary conditions by reconstructing the pressure gradient from eq.(1) and the velocity close to the integration boundaries. nevertheless, the results far from these boundaries appear realistic (with pressure minima correctly located at the centre of the vortices) and are therefore encouraging. 5 conclusion and perspectives this work analyzed the implementation of a poisson solver, using the popular cfd package openfoam®, to compute pressure fields from 2d-2c piv data. the novelty of the approach lies in the treatment of objects immersed in the flow: by using the snappyhexmesh routine from openfoam®, an adapted mesh can be created around the object and refined starting from the piv grid. the piv field can then be interpolated on this grid. the morphed mesh allows to better impose the no-slip boundary condition for the velocity and the zero-gradient for the pressure field, increasing the velocity interpolation and pressure integration accuracy. a 3d transient multiphase simulation of a flow around a cylinder was used to benchmark the method and analyze the impact of the correct boundary definition, the interpolation and the piv interrogation. in particular, the simulations reproduced both the flow field and the seeding distribution and was used for providing the reference data, for testing the impact of the velocity interpolation and the piv interrogation, evaluated by reconstructing synthetic images from the cfd results. among all the investigated factors, it appears that the correct definition of the curved wall plays the most important role: it allows for better reproducing the gradient of the flow and essential boundary conditions in the integration. finally, a first implementation on an experimental data-set was presented, although better treatment of the boundary conditions is still to be implemented. the proposed method could be further extended with (1) more advanced interpolation schemes (e.g. radial basis functions), which potentially enable for additional constraints to the velocity interpolation, (2) by the use of more advanced piv interrogation schemes to better resolve gradients along walls, which allows for better sample the flow and (3) by the use of an implicit solver that corrects the flow divergence while computing the pressures. these three research directions are currently being investigated. appendix openfoam c++ pseudo-code for the pressure solver implemented. listing 1: pressure from piv pseudo-code solver using openfoam® tools. / / momentum e q u a t i o n e x p l i c i t t e r m s ( v e c t o r f i e l d s ) v o l v e c t o r f i e l d ddtu ( ” ddtu ” , r d e l t a t *(u−uold ) ) ; v o l v e c t o r f i e l d divu ( ” divu ” , f v c : : d i v ( phi , u ) ) ; v o l v e c t o r f i e l d d i f f u ( ” d i f f u ” , f v c : : d i v ( t u r b u l e n c e −>nu ( ) * dev ( twosymm ( f v c : : g r ad (u ) ) ) ) ) ; / / apply d i v e r g e n c e and s i g n f o r p o i s s o n e q u a t i o n ( s c a l a r f i e l d s ) v o l s c a l a r f i e l d divddtu ( ” divddtu ” , − f v c : : d i v ( ddtu ) ) ; v o l s c a l a r f i e l d divdivu ( ” divdivu ” , − f v c : : d i v ( divu ) ) ; v o l s c a l a r f i e l d d i v d i f f u ( ” d i v d i f f u ” , f v c : : d i v ( d i f f u ) ) ; / / p o i s s o n e q u a t i o n s o l u t i o n f o r pe whi le ( p i s o . c o r r e c t n o n o r t h o g o n a l ( ) ) { f v s c a l a r m a t r i x pexpeqn ( fvm : : l a p l a c i a n ( pe ) == divddtu + divdivu + d i v d i f f u ) ; pexpeqn . s e t r e f e r e n c e ( prefce l l , prefvalue ) ; pexpeqn . s o l v e ( ) ; } references gunaydinoglu e and kurtulus df (2020) pressure–velocity coupling algorithm-based pressure reconstruction from piv for laminar flows. experiments in fluids 61:1–20 jakobsen ml, dewhirst tp, and greated ca (1997) particle image velocimetry for predictions of acceleration fields and force within fluid flows. measurement science and technology 8:1502–1516 lecordier b and westerweel j (2004) the europiv synthetic image generator (s.i.g.) in: particle image velocimetry: recent improvements. springer berlin heidelberg masullo a and theunissen r (2017) on the applicability of numerical image mapping for piv image analysis near curved interfaces. measurement science and technology 28 mendez ma, hess d, watz bb, and buchlin jm (2020) multiscale proper orthogonal decomposition (mpod) of tr-piv data—a case study on stationary and transient cylinder wake flows. measurement science and technology 31 opencfd-limited (2019a) openfoam programmer’s guide version v1912 opencfd-limited (2019b) openfoam user’s guide version v1912 regert t, chatellier l, tremblais b, and david l (2011) determination of pressure fields from time-resolved data. in 9-th international symposium on particle image velocimetry theunissen r (2010) adaptive resolution in piv image analysis application to complex flows and interfaces. doctoral thesis von karman institute van gent pl, michaelis d, van oudheusden bw, weiss pe, de kat r, laskari a, jeon yj, david l, schanz d, huhn f, gesemann s, novara m, mcphaden c, neeteson nj, rival de, schneiders jfg, and schrijer ffjj (2017) comparative assessment of pressure field reconstructions from particle image velocimetry measurements and lagrangian particle tracking. experiments in fluids 58 van oudheusden bw (2013) piv-based pressure measurement. measurement science and technology 24:484–497 introduction numerical method for pressure calculation numerical solver in openfoam® mesh adaptation via snappy hex mesh case study for proof-of-concept: flow past a cylinder 3d transient euler-lagrange simulation pressure reconstruction from 2d field pressure reconstruction from piv measurements analysis an experimental test case conclusion and perspectives 14th international symposium on particle image velocimetry – ispiv 2021 august 1–5, 2021 lagrangian strainand rotation-rate tensor evaluation based on multi-pulse particle tracking velocimetry (mptv) and radial basis functions (rbfs) lanyu li1, prabu sellappan2, peter schmid3, louis n. cattafesta2∗, jean-pierre hickey1 and zhao pan1† 1 university of waterloo, department of mechanical and mechatronics engineering, on n2l 3g1, canada 2 florida center for advanced aero-propulsion (fcaap), famu-fsu college of engineering, tallahassee, florida, 32310, us 3 department of mathematics, imperial college london, london, uk ∗ lcattafesta@fsu.edu † zhao.pan@uwaterloo.ca abstract physical conservation laws are inherently lagrangian. however, analyses in fluid mechanics using the lagrangian framework are often forgone in favor of those using the eulerian framework. this is perhaps due to a lack of experimental techniques with high temporal and spatial resolution that track the movement of fluid tracers in a flow domain. the development of time-resolved particle tracking velocimetry/accelerometry (tr-ptv/a) that measures flows with high seeding density has made the use of the lagrangian framework more accessible. a challenge facing ptv/a is the need for robust mesh-free numerical schemes that handle random particle locations. such a scheme can be created with high-order accuracy using radial basis functions (rbfs). rbfs allow direct evaluation of derivatives of vector and scalar fields at random locations with infinite-order smoothness. the current work uses rbf-based differential schemes to develop a post-processing tool for ptv/a data, which can accurately evaluate spatial derivatives directly from lagrangian particle tracks. this rbf-based strain/rotation-rate tensor evaluation tool is validated with two and three-dimensional flows from analytical solutions and is then tested with experimental data measured by a multi-pulse ptv/a system. 1 introduction classic textbooks in fluid mechanics often start with the concept of a fluid parcel and eulerian versus lagrangian descriptions of fluid motion (panton, 2006). in addition to the inherent conservation laws developed in a lagrangian framework, particle tracking is perhaps the most intuitive means to probe a fluid flow. a common example is examining the motion of tea leaves in a cup. however, examples of lagrangian methods in the experimental fluid dynamics literature pale in comparison to eulerian approaches. this is perhaps due to a lack of experimental techniques with sufficient temporal and spatial resolution that can track the threedimensional motion of many fluid parcels in a flow domain. this deficiency has persisted until the recent development of time-resolved particle tracking velocimetry/accelerometry (tr-ptv/a) that can measure lagrangian tracer particle tracks with high seeding density (schanz et al., 2016). in addition to the above experimental challenge, robust mesh-free numerical schemes that handle randomly scattered vector field are lacking in the experimental fluid mechanics community. one of the basic tasks for data analysis is evaluating the three-dimensional (3d) velocity gradient tensors, namely the strain-rate and rotation-rate tensors. strain/rotation-rate tensors are essential to understand the kinematics of complex flows (e.g., coherent structures and invariants). for example, kitzhofer et al. (2010) developed an algorithm based on least squares matching to estimate the strain/rotation-rate tensor using tomo-piv. although this work successfully extended kinematic analysis from two dimensions (2d) to 3d, it used an eulerian framework because the velocity data on a structured mesh are from piv. methods such as vic+ can handle scattered velocity data on ‘unstructured mesh’ from ptv (jeon et al., 2018). however, interpolating scattered data to a structured mesh before any other analysis is a common practice. this step can introduce unnecessary numerical error; more importantly, such a procedure may ‘degrade’ the often sparse but accurate ptv-based lagrangian data to piv-like eulerian data on a regular mesh. direct analysis of velocity fields on scattered data relies on a mesh-free numerical scheme. recent progress by rosi et al. (2015) used voronoi tessellation to evaluate spatial gradients for lagrangian coherent structure identification. this work introduced a direct analysis tool for lagrangian data. but, it was limited to 2d, and extending to 3d would be much more difficult (in terms of implementation and computation) due to the nature of the voronoi diagram. as another example, takehara and etoh (2009) reconstructed the 2d vorticity field directly from ptv data using a moving least square (mls) method. the authors applied this algorithm to visualize fluid motion and vortices in wind-driven waves (takano et al., 2012). however, the algorithm was not extended to 3d. consequently, some parameters in the algorithm were limited to 2d. for example, particle distribution was quantified by particle per pixel (ppp). this is a standard measure of image resolution in planar piv or ptv, and ppp is also a global indicator of average particle seeding density in 2d physical space with proper calibration. however, the particle data layout is important for a mesh-free method, and the local spatial particle density in 3d must be considered when applying such methods. as such, a robust, accurate, and convenient mesh-free method is much needed to directly compute spatial velocity gradients in 3d. in the current work, we establish a three-step data analysis method, which can accurately evaluate spatial derivatives (and then strain/rotation-rate tensors) directly from lagrangian velocimetry data. the three-step method consists of i) a data processing step that calculates spatial derivatives using a stable mesh-free method based on radial basis functions (rbfs), ii) a pre-processing step that improves the data quality by leveraging the data layout and smoothing the potential noise from the experiments, and iii) a post-processing that removes possibles outliers. this data analysis method is verified using simulated ptv data in 2d and 3d and then tested on experimental data from an mptv system in 3d. 2 data processing: rbf-qr and pum for stable gradient evaluation 2.1 rbf-qr as stable mesh-free method radial basis functions (rbfs) are a class of mesh-free methods that are increasingly applied in many fields, such as computational physics and machine learning. rbfs are often used as an interpolation and approximation tool that can handle high-dimensional scattered data. a typical rbf-based interpolation problem can be stated as follows. given the known scalar data f c i ∈ r at n scattered node centers xxxc i ∈ rd , i = 1,2,3, ...n, (d is the number of dimension of xxxc i ), we look for a reconstructing function s(xxx) that interpolates these known data (also called centers). this function is a linear combination of n rbfs in the form of s(xxx) = n ∑ i=1 λiφ(ε,ri) = n ∑ i=1 λiφ(ε,‖xxx− xxxc i ‖), (1) where φ(ε,ri) is a rbf, and ε is a parameter called the ‘shape factor’ that controls the shape (e.g., spiky or flat) of the rbf, and ri = ‖xxx− xxxc i ‖ is the euclidean distance from a location in the domain to a center. one of the common choices for φ(ε,r) is the gaussian rbf (i.e., φ(r) = exp(−ε2r2)). the coefficient λi can be determined by enforcing s(xxxc i ) = f c i . the corresponding linear system is fff = hhhλλλ , where hhh has entries hi j = φ ( ε, ∥∥∥xc i − xc j ∥∥∥), λλλ = (λ1,λ2, ...,λn) t , and fff = ( f c 1 , f c 2 , ..., f c n) t . by inverting hhh, λλλ = hhh−1 fff can be solved for eq. (1). derivatives of s(xxx) can be easily calculated by applying a corresponding differential operator to φ(ε,‖xxx− xxxc i ‖). for example, sy(xxx) = ∑ n i=1 λiφy(ε,ri) is the spatial derivative of s(xxx) with respect to coordinate y. this straightforward approach is commonly called ‘rbf-direct’. for data interpolation using a smooth function, small ε corresponding to flat rbfs leads to accurate interpolation. however, if the rbf-direct approach is used, a flat rbf also results in an ill-conditioned hhh and, thus, numerical instability. to overcome this problem, there are currently three primary versions of stable rbf algorithms (wright and fornberg, 2016): the contour-padé (rbf-cp), rbf-ga, and rbfqr methods. rbf-cp was the first algorithm that removed the restriction that the shape factor must be a real number (fornberg and wright, 2004). in rbf-cp, a basis function incorporates a rational function of ε , and stable computing can be achieved with flat rbfs. a recent extension to rbf-cp is the rbfra (wright and fornberg, 2016), which is more accurate and efficient compared to rbf-cp. rbf-ga is specifically based on the gaussian kernel (fornberg et al., 2013). it transforms an ill-conditioned basis to well-conditioned ones which include the incomplete gamma function instead of a truncated numerical approximation. rbf-qr was introduced by fornberg et al. (2011) and can handle a relatively large number of points than rbf-ga and rbf-cp/ra. these methods are all stable at flat limit of rbfs (e.g., ε → 0 for gaussian rbfs) and can calculate derivatives on scattered data (larsson et al., 2013) in high dimensions with a finite number of data points. rbf-cp and rbf-ra are limited to about a hundred and a few hundred points in 2d and 3d, respectively (fornberg and wright, 2004; fornberg et al., 2013; wright and fornberg, 2016). rbf-ga can increase these to a few hundred in 2d and greater than 500 in 3d (fornberg et al., 2013), while rbf-qr can use hundreds of points in 2d and thousands of points in 3d with double precision (fornberg et al., 2011). in the current work, we use rbf-qr as the core numerical method to compute gradients on scattered data. implementation details of rbf-qr in 2d and 3d can be found in fornberg et al. (2011); larsson et al. (2013). 2.2 localization by partition of unity method (pum) as mentioned above, flat rbfs are often used to achieve high accuracy reconstruction at the expense of illconditioning. however, this is not only caused by using flat rbfs (or the choice of value of shape factor). for a fixed value of shape factor, a large number of data points can also lead to numerical instability. the same issue persists for stable rbf-based methods. in addition, computing a large number of data points in a domain at once can be prohibitively expensive. there are two popular strategies to overcome the challenge associated with large data: i) rbf-generated finite differences (fornberg and wright, 2004; wright and fornberg, 2016), and ii) the partition of unity method (pum) (larsson et al., 2013) as a localization approach. in the current work, we use pum to localize the rbf-qr to handle large data. first, a set of overlapped sub-domains (ω j, j = 1, ...,p, called pum patches) are constructed to cover the whole domain ω. figure 1 shows examples where 9 circular and 8 spherical pum patches cover the domain1 in 2d and 3d, respectively. each patch is then assigned a weight function wj(xxx) so that i) for a certain patch, the weight function outside that patch is zero (i.e., wj(xxx) = 0, for xxx /∈ ω j), and ii) the summation of all weight functions from all the patches is unity at any location in the domain (i.e., ∑ p j=1wj(xxx) = 1). the weights can be constructed by applying shepard’s method (shepard, 1968): wj(xxx) = ψ j(xxx)/∑ p k=1 ψk(xxx), j = 1,2,3...p, where ψ(xxx) is a compactly supported generating function such as the wendland c2 function (wendland, 1995). a global function s(xxx) on the domain ω can then be assembled by a weighted summation of local functions on ω j: s(xxx) = ∑ p j=1wj(xxx)s j(xxx). for example, if s j(xxx) is a spatial gradient of a velocity component of a flow, when s j(xxx) is calculated using rbf-qr in every patch, then a localized stable rbf that can handle a large number of data points is achieved. in addition, combining pum and rbf-qr also reduces computational cost and memory requirements. example implementations of rbf and pum can be found in, for example, larsson et al. (2017). figure 1: example pum patch layout in 2d, (a) and 3d, (b). the grey lines indicate the edges of domain ω (square for 2d and cube for 3d). circles and spheres in transparent light blue are pum patches for 2d and 3d, respectively, whose centers are marked by green dots. reds dots indicate the locations of scattered data points in the domain. 1the domain ω does not have to be regular-shaped boxes, and the pum patches do not have to be regular-shaped circles or spheres. 3 pre-processing: data layout enhancing and smoothing velocity from a real experiment is imperfect. in addition to contamination due to measurement noise, ptv data may not be well distributed. the location of single tracer particle cannot be controlled and local seeding density may be too high or too low, which may lend difficulties to rbf-based gradient computation. thus, before data processing, pre-processing may be necessary to improve the data quality. in the current work, we suggest a two-stage pre-processing including i) data layout enhancement and ii) smoothing before processing experimental data. a mesh-free method (including rbfs) in general performs better on quasi-uniformly distributed data (fasshauer, 2007). although rbfs can in principle evaluate gradients on arbitrarily scattered data, randomly distributed data can lead to results with low accuracy. this challenge arises from the ‘conflicting’ nature of ptv experiments and mesh-free numerical methods. we here use a simple example to demonstrate this particular issue. we use rbf-qr with pum to directly calculate velocity gradient (∂u/∂x) in a 2d domain based on simulated ptv data (see §5 and fig. 3 for more details about the simulated data and the flow field). here, 1×104 virtual tracing particles are injected in the domain so that they are either randomly distributed (coordinates of particle locations are generated using random numbers with uniform distribution) or have a much more uniformly distributed particle layout (particle locations are generated using a halton sequence). we want to emphasize that the particle layout generated from random numbers with uniform distribution is not quasi-uniform. uniform distribution generated random particles, similar to the particle distribution in a well-seeded ptv experiment, have high randomness in particle location leading to excessive local sparse or dense particle layout. the relative errors of the gradient calculation on the velocity data contaminated by small noise (zero mean gaussian noise with a standard deviation of 1% of maximum corresponding velocity component) on each data layout are examined. figure 2 shows the relative error (e , defined by eq. (2)) in the calculated velocity gradient against the distance of every two neighboring particles (dn). figure 2: relative error (e ) of the computed gradient (∂u/∂x) on each data point vs. distance of two neighboring data points (dn), on random (a) and halton points (b). the light red and blue point clouds indicate the relative error in the computed gradient at each simulated ptv particles with and without artificial noise, respectively. the overlaid crosses with darker colors summarize the trend of point clouds in groups. the left and right end of a horizontal bar represents ±1 standard deviation band of log10(dn) for a group of data, and the vertical bar represents the ±1 standard deviation band of log10(e ) for the same group of data. the intersection of vertical and horizontal bars indicates the mean of the error for the group of the data. the results show that the gradient calculation based on randomly distributed particles (figure 2(a)), which is close to the particle distribution of real ptv data, in general has higher error than that based on a halton particle distribution (figure 2(b)). as shown in fig. 2(a), when dn is too large, too sparse data cannot resolve the fine flow structures and lead to high error, which is intuitive. when dn is too small (implying that high local particle density), elevated error also results. this is due to low uniformity of the particle layout, which is unfriendly to the rbfs. this observation may not be surprising either. it resembles a low quality mesh, in the context of finite element analysis, caused by neighboring nodal points that are too close and lead to high-aspect ratio cells. to enhance the data layout, we interrogate neighboring particle pairs in each pum patch, and iteratively mask out one of the two neighboring points if the distance between them is much closer than the rest of neighbors. in our tests, a few iterations are sufficient to significantly improve the performance of rbf-based calculation. it is worth noting that when the velocity data is contaminated by noise, the observation about the data layout is even more obvious (see the red data points and error bars in figure 2): random noise on close data points further exacerbates the effect of non-uniformity on numerical differentiation. however, being noisy is unfortunately the case of real experimental data. in addition, numerical differentiation of noisy data may significantly amplify the noise especially when the ‘grid spacing’ is small and/or the order of the differentiation scheme is high. for example, fig. 2 shows that small artificial noise in the velocity field can significantly corrupt the gradient calculation. thus, we propose applying a smoother to the velocity data in each pum patch after data layout enhancement. in the current work, a two layer neural network (‘newrbe’, a matlab built-in function) is used to smooth out potential noise. an adaptive spread parameter (sp) is used in the ’newrbe’ function is used: sp = kdmin n / d √ n, where dmin n is the closest distance between two neighboring points within a pum patch after data layout enhancing, n is the number of points in that patch, d is dimension of domain. we tested on isotropic turbulent flows (see §5) and found that k = 1000 and 250 are robust choices for 2d and 3d computation, respectively. 4 post-processing: outlier detection and removal it is possible to have few extreme values (likely suffering large error) in the calculated gradient fields, even if pre-processing is applied and the overall accuracy of the calculation is significantly improved. thus, an outlier detector and remover may be necessary for post-processing. in the current work, we adopt an adaptive outlier detector developed by cheng and wang (2019), which labels an extreme value in a neighborhood as an outlier and removes it for the final result. 5 validation on simulated ptv data we next validate the performance of our data analysis method. a direct numerical simulation (dns) of forced isotropic turbulence is used as ground truth to validate the algorithm. the simulations were conducted using the pencil code (brandenburg et al., 2021). the solver uses a high-order, explicit finite-difference scheme combined with a hyperviscosity filter for stability. a solenoidal forcing is applied to randomly selected low-wave numbers in the velocity spectrum to sustain the turbulence at a reynolds number (based on the taylor length scale) of reλ ≈ 80. an overly conservative grid resolution of 5123 was selected to adequately resolve all relevant dynamic scales in the flow. pseudo-particles are injected in the domain at random locations. the velocity and velocity gradients at the particle locations are obtained using linear interpolation from the dns data. small artificial noise is introduced to each velocity component at a particle to simulate the noise in experiments. the noise is zero mean gaussian noise with a standard deviation of 1% of the maximum corresponding velocity component, and we use this noise throughout the current paper. we use this contaminated synthetic ptv data as the input to test the performance of the data analysis tool. a baseline algorithm based on rbf-direct with adaptive shape factor from literature jeon et al. (2018) is also used for compression (i.e., φ(r) = exp(− r2 2.4h2 ), where we define h as the average distance between the particles). the relative error in the quantity of interest is used to assess the accuracy of the computation. for example, when calculating the vorticity of a 2d flow field, the relative error at each particle is defined as e = |ω− ω̃| ||ω||l∞(ω) ×100%, (2) where ω is the true value of the vorticity, and ω̃ is the computed value that may have error. note, we found that the distribution of error is close to logarithm-normal. figure 3 shows a 2d validation calculating vorticity from simulated 2d ptv data, where uuu = (u,v) is the velocity field measured at 1×104 randomly distributed particles on a (x,y) ∈ [−π,π]× [−π,π] domain. the velocity (fig. 3(a)) and vorticity (fig. 3(b)) fields are based on a slice of the aforementioned 3d dns data. calculated vorticity field based on simulated ptv data with (fig. 3(c3 and c4)) and without (fig. 3(c1 and c2)) noise are shown. the corresponding relative error at each particle is presented in fig. 3(d1 – d4) accordingly, and summarized as histograms in fig. 3(e1 – e4). when no artificial noise is introduced to the velocity field, both the baseline algorithm and our method can evaluate the vorticity accurately. the median figure 3: 2d validation on simulated ptv data. (a) velocity field of the simulated ptv data. quivers indicate the direction of the flow field and particles are colored by the amplitude of the velocity. particles are down-sampled to 25% of the actual seeding density for clear illustration. (b) ground truth of vorticity, colored at each particle. computed vorticity based on the simulated ptv data without noise contamination using the baseline algorithm (c1) and our three-step method (c2). computed vorticity based on the simulated ptv data with artificial noise introduced, using the baseline algorithm (c3) and our three-step method (c4). (d1–d4) relative error in the computed vorticity, corresponding to c1–c4, respectively. only particles with error in vorticity higher than 20% are shown. (e1–e4) histogram of relative error in the computed vorticity, corresponding to d1–d4. the vertical magenta and blue dashed lines indicate the median and +2 standard deviation above the mean, respectively. values of the relative error are 0.52% and 0.24%, as shown in fig. 3(e1 and e2), respectively. however, when the velocity is slightly contaminated by random noise, our method is significantly more robust. we next validate the algorithm in 3d with the simulated data on a cropped domain, x×y× z ∈ [−π,0]× [−π,0]× [−π,−0.75π], of the dns result. noise contaminated velocity field at 2× 104 randomly distributed particles in the domain is used to reconstruct strain-rate tensor (s̃i j, fig. 4(b)) and rotation-rate tensor (r̃i j, fig. 5(b)). the velocity gradient tensor in 3d is ui, j = ∂ui/∂x j, where ui, i = 1,2,3 are the velocity components, and x j, j = 1,2,3 are the cartesian coordinates, which can be directly evaluated at each particles using our method. ui, j can be decomposed into symmetric and anti-symmetric parts (blazek, 2015) as follows: ui, j = 1 2(ui, j + u j,i)+ 1 2(ui, j− u j,i). the first part is strain-rate tensor si j = 1 2(ui, j + u j,i) and the second part is rotation-rate tensor ri j = 1 2(ui, j−u j,i). compared to the ground truth (fig. 4(a) for si j) against the computed values from noisy ptv data (fig. 4(b) for s̃i j). the median values of relative error in s̃i j are less than 2% and two standard deviations above average of are less than about 20%. therefore, our method can compute the gradients and the tensor with robustness and sufficient accuracy. the flow structures are well visualized with the iso-surfaces. figure 5 shows the ground truth (ri j, fig. 5(a)) of the rotation-rate tensor and the computed results (r̃i j, fig. 5(b)). noting that ri j =−r ji, the iso-surfaces in fig. 5(a) and fig. 5(b) have the almost the same shape for the corresponding components, but with reversed color. the relative error in r̃i j, as examples, are summarized in fig. 5(c1–c3). the median of the relative error is around 2% and two standard deviation above average of the error is less than 15%. figure 4: visualization of the strain-rate tensor (si j) of a 3d turbulent flow. (a) lower six components of the strain-rate tensor (si j, i ≥ j), ground truth from dns. (b) upper six components of strain-rate tensor, s̃i j, i ≤ j, computed from simulated ptv data with artificial noise introduced in the velocity field. (a) and (b) are separated by the blue dashed line. the surface iso-values are +0.3 for red and −0.3 for blue. figure 5: visualization of the rotation-rate tensor (ri j) of a 3d turbulent flow. (a) lower three components of rotation-rate tensor (ri j, i > j), ground truth from dns. (b) upper three components of rotation-rate tensor, r̃i j, i < j, computed from simulated ptv data with artificial noise introduced in the velocity field. the surface iso-values are +0.3 for red and −0.3 for blue. (c1–c3) histogram of the relative error in the computed r̃i j in (b), r̃23, r̃13, r̃12, respectively. 6 application to experimental data finally, we apply our method to real experimental data. velocity field of a free jet issuing from a circular nozzle (diameter d = 2.54 cm) at mach 0.3 is obtained using multi-pulse shake-the-box (fig. 6). details of the setup and data can be found in sellappan et al. (2020). our three-step method is used to process ∼ 2.6×104 particles in a volumetric domain (average seeding density is 0.25 particles/mm3) and evaluate strain/rotation-rate tensors (fig. 7 and fig. 8, respectively). in s12,s21 and r12,r21, two stripes with different colors (opposite signs of iso-values for iso-surfaces) are shown as they are dominated by ∂u/∂y. the similar large scale strip are also shown in s13,s31 and r13,r31 for the dominant ∂u/∂ z contribution. in s11 = ∂u/∂x, we observe blue and red bands appearing alternatively in the steam-wise direction, which is from roll-up due to strong shear and can be better visualized by a vortex identification method. figure 9 shows vortical structures of the jet flow identified by q-criterion, where q = 1 2 (∣∣r2 ∣∣− ∣∣s2 ∣∣)> 0. toroidal vortex structures of the high speed jet present near the nozzle due to kelvin-helmholtz instabilities, and break up downstream. figure 6: nondimensionalized velocity field of a ma 0.3 free jet shooting from left to right. the side view of the velocity field is projected to the left. figure 7: nondimensionalized strain-rate tensor of the ma 0.3 free jet. surface iso-values for s12, s21, s13, s31 are ±0.2, and other tensor components adopt iso-values of ±0.1. red surfaces for positive iso-values and blue for negative. figure 8: nondimensionalized rotation-rate tensor of the ma 0.3 free jet. surface iso-values for r23, r32 are ±0.1, and other tensor components adopt iso-values of ±0.2. red surfaces for positive iso-values and blue for negative. figure 9: iso-surface of q-criterion (q = 0.025), colored by ma, of the ma 0.3 jet flow. 7 conclusion and discussions we propose a three-step method to calculate spatial velocity gradients and strain/rotation-rate tensors for volumetric ptv/a data. rbf-qr with pum, serving as the core of the processing step, ensures that the method can handle large scattered data in 3d with numerical stability. pre-processing improves data quality by enhancing data layout and reducing potential noise from experimental data. the post-processing detects and removes potential outliers for more robust final results. validation on simulated data in 2d and 3d show that this method is robust and accurate enough to be applied to real volumetric ptv/a data, where particle layout may not be ideal and the velocity is uncertain. our method directly reads, operates, and stores lagrangian data for each particle, and only some visualization may require interpolation on eulerian mesh. lastly, we want to point out a special issue that the data layout (local particle distribution) can significantly affect a gradient calculation, especially when noise is present in the ptv data. to be more specific, tracer particles with quasi-uniform layout is preferred by our method, and many other mesh-free schemes. however, a quasi-uniform distribution of particles may never be achieved in a real ptv measurement for many reasons. examples include agglomeration of tracer particles in high shear flows, low seeding densities near the wall, and non-uniform illumination and scattering, etc. due to the non-uniformity of the particle layout, raw ptv data has low efficiency in terms of resolving flow structures. local high-density seeding may appear at low gradient regions, where high spatial resolution sampling is not needed. moreover, excessively high-density seeding in a local region may corrupt a mesh-free numerical scheme, despite the fact that global high seeding density is much preferred to resolve small scale structures in the flow. even for a well-seeded flow, randomly distributed particles do not yield the most friendly data layout for a mesh-free scheme and data layout enhancement is perhaps needed. acknowledgements we acknowledge the support of the natural sciences and engineering research council of canada (nserc) and the u.s. office of naval research grant n00014-21-1-2454 (monitored by dr. david gonzalez) and insightful discussions with prof. larsson at uppsala university and prof. wright from boise state university. references blazek j (2015) computational fluid dynamics: principles and applications. butterworth-heinemann brandenburg a, johansen a, bourdin pa, dobler w, lyra w, rheinhardt m, bingert s, haugen nel, mee a, gent f, babkovskaia n, yang cc, heinemann t, dintrans b, mitra d, candelaresi s, warnecke j, käpylä pj, schreiber a, chatterjee p, käpylä mj, li xy, krüger j, aarnes jr, sarson gr, oishi js, schober j, plasson r, sandin c, karchniwy e, rodrigues lfs, hubbard a, guerrero g, snodin a, losada ir, pekkilä j, and qian c (2021) the pencil code, a modular mpi code for partial differential equations and particles: multipurpose and multiuser-maintained. journal of open source software 6:2807 cheng z and wang j (2019) quantification of the strain field of sands based on x-ray micro-tomography: a comparison between a grid-based method and a mesh-based method. powder technology 344:314–334 fasshauer ge (2007) meshfree approximation methods with matlab. volume 6. world scientific fornberg b, larsson e, and flyer n (2011) stable computations with gaussian radial basis functions. siam journal on scientific computing 33:869–892 fornberg b, lehto e, and powell c (2013) stable calculation of gaussian-based rbf-fd stencils. computers & mathematics with applications 65:627–637 fornberg b and wright g (2004) stable computation of multiquadric interpolants for all values of the shape parameter. computers & mathematics with applications 48:853–867 jeon y, schneiders j, müller m, michaelis d, and wieneke b (2018) 4d flow field reconstruction from particle tracks by vic+ with additional constraints and multigrid approximation. in proceedings 18th international symposium on flow visualization. eth zurich kitzhofer j, westfeld p, pust o, nonn t, maas h, and brücker c (2010) estimation of 3d deformation and rotation rate tensor from volumetric particle data via 3d least squares matching. in proc. 15th int. symp. on applications of laser techniques to fluid mechanics larsson e, lehto e, heryudono a, and fornberg b (2013) stable computation of differentiation matrices and scattered node stencils based on gaussian radial basis functions. siam journal on scientific computing 35:a2096–a2119 larsson e, shcherbakov v, and heryudono a (2017) a least squares radial basis function partition of unity method for solving pdes. siam journal on scientific computing 39:a2538–a2563 panton rl (2006) incompressible flow. john wiley & sons rosi ga, walker am, and rival de (2015) lagrangian coherent structure identification using a voronoi tessellation-based networking algorithm. experiments in fluids 56:1–14 schanz d, gesemann s, and schrder a (2016) shake-the-box: lagrangian particle tracking at high particle image densities. experiments in fluids 57:70 sellappan p, alvi fs, and cattafesta ln (2020) lagrangian and eulerian measurements in high-speed jets using multi-pulse shake-the-box and fine scale reconstruction (vic#). experiments in fluids 61:1–17 shepard d (1968) a two-dimensional interpolation function for irregularly-spaced data. in proceedings of the 1968 23rd acm national conference. pages 517–524 takano y, etoh gt, and tsujimoto g (2012) measurements of vortex generation and motion at wind wave surfaces. coastal engineering proceedings pages 28–28 takehara k and etoh t (2009) accurate estimation of vorticty from ptv velocity distribution. in proc. of 8th international symposium on particle image velocimetry-piv09. volume 185 wendland h (1995) piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. advances in computational mathematics 4:389–396 wright gb and fornberg b (2016) stable computations with flat radial basis functions using vector-valued rational approximations. journal of computational physics 331 introduction data processing: rbf-qr and pum for stable gradient evaluation rbf-qr as stable mesh-free method localization by partition of unity method (pum) pre-processing: data layout enhancing and smoothing post-processing: outlier detection and removal validation on simulated ptv data application to experimental data conclusion and discussions