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 high-
speed 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 ab-
sorb 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 autocorre-
lation 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 cor-
responding 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 im-
pinging 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 devel-

opment 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 velocime-
try. 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