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 volumet- ric 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 chan- nel 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 stream- gaging. 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 bina- rization 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 kine- matic 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 assist- ing 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 ve- locity profiles. Water Resources Research 53:7521–7535 Thielicke W and Stamhuis E (2014) PIVlab – Towards User-friendly, Affordable and Accurate Digital Par- ticle Image Velocimetry in MATLAB. Journal of Open Research Software 2:e30 Introduction Methodology Results & discussion Conclusions