The document discusses optical flow measurement of cavitation in a converging-diverging nozzle using high-speed imagery. High-speed photography was used to visualize and measure cavitation onset and flow characteristics. It was found that cavitation onset occurred just past the nozzle throat, and areas of flow recirculation were observed. Choked flow conditions were also indicated, as the volumetric flow rate reached a maximum once cavitation began, regardless of downstream pressure changes. Particle tracking showed tracer velocities initially followed calculated profiles but accelerated past the throat.

1. 1 Copyright © 2015 by ASME
Proceedings of the ASME 2015 International Mechanical Engineering
Congress & Exposition
IMECE2015
November 13-19, 2015, Houston, Texas
IMECE2015-54172
OPTICAL FLOW MEASUREMENT OF CAVITATION IN A CONVERGING-DIVERGING
NOZZLE USING HIGH-SPEED IMAGERY
Alan Duong
Department of Mechanical and Nuclear
Engineering
Kansas State University
Manhattan, KS, United States of America
ABSTRACT
Cavitation is a phenomenon where liquids will vaporize
when subjected to low pressures. Essentially, the pressure is
reduced sufficiently such that the liquid boils at the given
temperature. The highest pressure at which cavitation could
occur is called the vapor pressure. However, the pressure
associated with the onset of cavitation could be lower than the
vapor pressure. This indicates the liquid exists under a meta-
stable condition.
The current research is investigating different aspects of
cavitation and cavitating flow characteristics. Particle tracking
using high-speed photography provided further insight as to
what the velocity profile of cavitating flow may resemble. The
research has shown that the cavitation that occurred in the
current nozzle appears to have a laminar velocity profile. In the
experiments that were conducted, it was also observed that as
the back pressure of the downstream decreased, the volumetric
flow rate would increase. However, a maximum volumetric
flow rate was measured once the flow had begun cavitation
regardless of the back pressure. This indicated that choked flow
conditions likely exist within the nozzle. Choked flow within
the nozzle indicates that near the region of the throat the fluid
velocity has reached the speed of sound. Using high-speed
photography, visualization of flow separation and recirculation
was recorded.
The information obtained from the research provides a
more detailed description of the velocity profile near the onset
of cavitation. The main objectives of this research were to
obtain measurements of the overall flow for support of on-going
research and analysis of nozzle flow cavitation. This study will
provide a foundation for further and more detailed research into
cavitation phenomena.
INTRODUCTION
Cavitation is the phenomenon where vapor cavities (liquid-
free zones or “bubbles”) form in a liquid at low pressures. The
highest pressure at which the liquid will begin cavitating is
often referred to as the vapor pressure. During cavitation, these
bubbles will form at low pressures and implode when the liquid
is subjected to a higher pressure [1]. Cavitation can occur in a
variety of engineering applications such as pumps, heat
exchangers, propellers, capillary tubes, and nozzles, all of
which share any combination of the following characteristics:
constricting geometries, large flow-rates, and low pressures [2].
Ever since cavitation was first studied by Lord Rayleigh in
the late nineteenth century, researchers, scientists, and engineers
around the world have tried to understand it. There have been
many studies attempting to model various aspects of cavitation
numerically, computationally, and conceptually. In these studies,
attempts have been made to put quantitative values on the
varying pressures of cavitation, void fraction, the force released
by the imploding bubbles, the velocity of cavitating flow, and
the onset of choked flow conditions.
The aforementioned areas of studies in cavitation are not
limited to water. Cavitation can occur in many different liquids;
the most common in engineering practices are fuels and
refrigerants.
As mentioned earlier, cavitation can occur in a variety of
applications. There is no shortage of cavitation research topics
when considering the different applications where cavitation
can occur, the various aspects of cavitation (i.e., velocity, void
fraction, etc.), and the different choices of working fluids.
One particular setup used in many applications involves
the use of a nozzle. A nozzle is used for many purposes, such as
controlling the flow of a fluid, decreasing the pressure of the

2. 2 Copyright © 2015 by ASME
system, throttling a working fluid, measuring the flow rate of a
system, etc. The use of a nozzle to induce cavitation is
relatively simple because of the geometry. A typical nozzle will
have a large inlet and a small throat. There are other nozzles,
such as a converging-diverging nozzle, that have a large inlet
and outlet but the small constriction of flow occurs somewhere
in-between at the so-called throat position.
For the present research, a converging-diverging nozzle
was chosen for analysis. There has been relatively little research
done on the detailed flow characteristics of cavitating liquids
near the onset of cavitation in nozzles. The main objectives are
to obtain measurements of both overall flow as well as more
detailed velocity profile characteristics of cavitation onset in a
converging-diverging nozzle using high-speed imagery. The
experimental setup places the nozzle oriented vertically
between two reservoirs. The upstream reservoir supplies liquid
water flow entering the nozzle is open to the atmosphere while
the downstream reservoir is partially evacuated.
Figure 1 illustrates the geometry of a typical converging-
diverging nozzle. The nozzle will generally have the same size
inlet and outlet; however the transition from the inlet to the
throat is much sharper than the transition from the throat to the
outlet.
Fig.1: Illustration of a converging-diverging nozzle
A gradual area expansion in the diffusing section of the
nozzle could reduce the extent of flow separation present in the
nozzle. This could also reduce the amount of losses in the
system in the diverging region of the nozzle.
Based on the Reynolds’ Transport Theorem and the law of
continuity, the mass flow rate of the fluid going into the system
is equal to the mass flow rate leaving the system. This means
that at any given point within the nozzle the mass flow rate is
the same, however, the velocities may be different. Taking this
into consideration means that the velocity at the throat of the
nozzle is highest. Now, applying Bernoulli’s Principle, indicates
that as the velocity increases the pressure decreases. This shows
that the location of the lowest pressure will also be at, or close
to, the throat at the nozzle. As mentioned earlier, cavitation
occurs when the pressure is lowered below its vapor pressure.
However, cavitation initiation could occur at pressures
much lower than the vapor pressure. This would indicate the
liquid is in a meta-stable state. The cavitation pressure can be
significantly below the vapor pressure and the lowest pressure
at which cavitation onset could occur is called the spinodal
pressure. Theoretically, the absolute pressure of the liquid could
be negative and the liquid itself is in tension [3].
When cavitation occurs, the use of a clear converging-
diverging nozzle (usually glass or plastic) makes it simpler to
see the exact location where cavitation occurs (although the
throat is close to the area of the lowest pressure, due to viscous
effects, cavitation can occur past the throat). Figure 2 shows
what happens to the working fluid past the onset of cavitation
[4].
Fig. 2: Cavitation of water within a converging-diverging
nozzle
Figure 2 clearly shows where cavitation starts to occur and
what happens to the water as it continues to travel down the
nozzle. It is observed from Figure 2 that there is multi-phase
flow that contains both liquid and vapor constituents. This is a
direct result of cavitation; the pressure of the water is
significantly low enough to where the water begins to vaporize.
The image in Figure 2 was taken by a hi-speed camera
developed by the company, Photron [4].
HIGH SPEED PHOTOGRAPHY
The use of high-speed photography is the least invasive
measurement method. A high-speed camera has capabilities of
taking photographs at rates from 60 frames per second to
756,000 frames per second. With a high-speed camera and
image viewing/processing software, high-speed photography
can provide not only images of the cavitation at intervals of
micro-seconds, but can also provide videos of flow
visualization. High-speed imaging will provide capabilities of
measuring various aspects of cavitating fluid flow; one of
special interest is the velocity.
Even though the use of a high-speed camera is non-
intrusive, it does have some disadvantages. One disadvantage is
that the frame rate and the resolution of a high-speed camera are
inversely related to each other. While it is desirable to take
images with a higher frame rate, the spatial resolution of the
image decreases with an increasing frame rate. With any high-
speed camera setup there is an optimal frame rate and resolution
setting, however, it will take some calibration to figure out the
optimal setup. Also, using a high frame rate means a shorter
window of opportunity to record high-speed videos. For
example, a setting of 2,000 frames per second could record for
10 seconds while a setting of 20,000 frames per second could
only record for 1 second. The ambient lighting of the test
environment could provide some issues with the high-speed
imaging as well. With the nozzle being made of glass or plastic,

3. 3 Copyright © 2015 by ASME
there is bound to be some reflection on the nozzle that could
potentially disrupt the quality of the photograph.
EXPERIMENTAL SETUP AND METHOD
A schematic of the experimental set up is shown in Figure
3. The upstream reservoir is open to atmospheric pressure while
the downstream reservoir will have a vacuum pump to reduce
the pressure. The pressure difference between the two reservoirs
will drive the water to flow from the upstream to the
downstream reservoir.
Fig. 3: Schematic of experimental setup
The nozzle was made of clear glass and measures
approximately 150 mm in length. The entrance and exit inside
diameters are the same with the throat diameter to be about 2.3
mm.
The measurements made of the nozzle were used with a
digitizing software takes an image of the object with a scale and
plots various points along the object. The data points taken are
coordinate points of the object and were used to determine the
inside diameter of the nozzle.
The length of the nozzle was measured to be 150 ± 1.0 mm
while the distance from the entrance to the throat was measured
to be 50 ± 1.0 mm. The inside diameters at the entrance and exit
of the nozzle was measured to be 9.7 ± 0.5 mm and the
diameter of the throat measured at 2.3 ± 0.3 mm.
The high-speed camera that was used is the FASTCAM
SA5 775K developed by Photron. It has a sensor resolution of
1,024 by 1,024 pixels. Its recording color depth is 12 bit with
an electronic shutter. Recording memory capacity is 8
gigabytes. It has a frame rate of 7,000 frames per second (fps)
in full frame and 775,000 fps in a frame segment. However, it
can go as low as 60 fps with a spatial resolution of 1,024 by
1,024 pixels.
Because the area of interest containing the throat and
downstream of the nozzle was relatively small, it was chosen to
use a resolution of 320 x 1024 at 20,000 fps.
The software that was used is the Photron FASTCAM
Viewer (PFV). The software processes the images and videos in
real time and allows for timely analysis. It was used to analyze
high-speed videos frame by frame with its many features.
The water was seeded with tracer particles which have
approximately the same density as water. High speed imagery
was then used to capture and measure the velocity of the flow.
The different tracer particles that were used were 50 micron
diameter plastic spheres and air bubbles that were injected into
the flow using a hypodermic needle.
RESULTS
Experiments were conducted using high-speed imagery in
order to characterize the velocity profile within the converging-
diverging nozzle. Both qualitative and quantitative results were
obtained.
Qualitative Flow Characterization
Theoretically, the location of the onset of cavitation would
be located at the throat of the nozzle. However, using high-
speed imagery, it was determined that the onset of cavitation
occurred just past the throat. This could be attributed to viscous
effects within the nozzle. At the onset of cavitation, the flow
displayed an effect similar to the Vena Contracta effect. Vena
Contracta is when the flow separates from the wall. Figure 4
illustrates the location of the onset of cavitation and flow
separation at varying pressures within the downstream reservoir.
Pabs = 30 ± 4 kPa Pabs = 17 ± 4 kPa Pabs = 4 ± 4 kPa
Fig. 4: Onset of cavitation at varying downstream pressures

4. 4 Copyright © 2015 by ASME
Looking further into flow separation within the nozzle, it
was observed that there are areas of flow recirculation. The
lower the pressure within the downstream reservoir, the more
apparent the recirculation areas become. Figure 5 shows where
the recirculation regions are located when the downstream
pressure is approximately 4 kPa absolute.
The areas circled in red contain residual bubbles that have been
separated from the main core of flow. However, instead of
continuing to flow upwards with the main core of flow, these
residual bubbles floated back down to the cavitation front or
have been carried by the recirculating flow.
Fig. 5: Areas of recirculation
Choked Flow Characterization
The study done by Davis [3] suggested the possibility of
choked flow. In order to investigate this, a simple experiment
was conducted to determine the relationship between the flow
rates of the water versus the downstream pressure. Figure 6
summarizes the results of the experiment.
Fig. 6: Relative (percent) flow rates versus downstream
pressure
The flowmeter that was used measures the flow rate as a
percentage of the maximum flow rate that it could measure
(0.81 gallons per minute). Varying the downstream pressure
showed that once the flow had begun cavitation that a maximum
volumetric flow rate would be recorded, regardless of the
increasing pressure difference.
In order to further verify choked flow within the nozzle, it
was necessary to increase the inlet pressure. While the upstream
reservoir is open to the atmosphere, elevating the reservoir to a
greater height would provide sufficient pressure increase at the
inlet. With an increased pressure at the inlet, the observed
relative flow rates were higher than the initial set of flow rate
measurements. However, once the flow began cavitating, the
volumetric flow rates would reach a maximum value regardless
of decreasing the downstream pressure.
This suggests that there are sonic conditions present within
the converging-diverging nozzle. While the speed of sound in
liquid water is very high (approximately 1,480 meters per
second at a temperature of 20°C) the speed of sound in two-
phase mixtures during phase transition decreases as the void
fraction increases [5]. The void fraction is defined as the
fraction of the cross-sectional area that is occupied by gas and
ranges from 0 to 1 [4].
Particle tracking with high-speed imagery
Information about the velocity of the two tracer particles,
50 micron plastic seeds and injected air bubbles, were obtained
by tracking their position frame by frame from the converging
region of the nozzle until they reached the onset of the
cavitation front. These velocities were then compared to the
calculated average velocities using a known volumetric flow
rate. Figure 7 summarizes these results.
Assuming that the flow had a laminar profile, the speeds of
the tracer particles were compared to the calculated average
velocities and two times the calculated average velocities. A
comparison was made between the maximum velocity (two
times the average velocity) and the speeds of the tracer particles
because the tracer particles were tracked along the centerline of
the nozzle.
The velocities of the tracer particles appear to follow the
maximum velocity of the water up to the throat of the nozzle.
However, once the tracer particles have flowed past the throat,
the particles continues to accelerate rather than slow down. This
could be due to different factors such as the resolution
uncertainty of the high-speed camera and that the tracer
particles are not neutrally buoyant.
CONCLUSION
Using high-speed imagery, qualitative and quantitative
measurements of the velocity characteristics of cavitation in a
converging-diverging nozzle have been made. These
measurements provide insight and verification of several flow
characteristics.
With the high-speed camera, qualitative observations of
recirculation and flow separation within the converging-

5. 5 Copyright © 2015 by ASME
diverging nozzle were made, an effect similar to the Vena
Contracta effect. The measurements using the high-speed
camera provided flow visualization that verifies the
recirculation and separation, both which were theoretically
discussed, but not experimentally determined in the converging-
diverging nozzle.
Fig. 7: Tracer particle centerline speed versus nozzle position
Choked flow conditions and a laminar velocity profile
were observed through two different experiments. The first
experiment involved measuring the volumetric flow rate as a
function of the downstream pressure. The second experiment
involved particle tracking of two tracer particles.
By varying the downstream pressure, measurements of the
volumetric flow rate were made. It was observed that once the
onset of cavitation occurred, the flow rate of the water would
reach a maximum, regardless of the downstream pressure. In
order to verify this, two different inlet pressures were tested.
While the overall flow rate of the system increased with an
increased inlet pressure, the flow would still reach a maximum
once cavitation began. This suggested that there are choked
flow conditions that exist within the converging-diverging
nozzle.
Using two tracer particles, 50 diameter plastic spheres and
injected air bubbles via hypodermic needle, velocity
measurements of the tracer particles were then compared to the
average and maximum velocities of the flow. The velocity of the
plastic spheres and air bubbles were made along the centerline
of the nozzle and were compared to the flow rates measured by
the flow meter. The average velocity was calculated from the
flow rates measured by the flow meter and the maximum
velocity was calculated by multiplying the average velocity by
two, assuming a laminar profile. Comparing the velocities of the
tracer particles to the maximum velocity for a laminar profile
showed a strong correlation between the different sets of
measurements.
Overall characterization of the velocity profile within the
converging-diverging nozzle has been made. This study was
done to provide a foundation for further and more detailed
research into the flow characteristics of cavitation within a
converging-diverging nozzle.
ACKNOWLEDGMENTS
The author would like to acknowledge Aaron Schmidt, a
graduate student working on the same project. The author and
Aaron Schmidt worked closely together conducting experiments
and data collection and analysis, however, did not contribute to
the actual writing of this paper. The author would also like to
acknowledge Dr. Terry Beck whom served as an advisor for the
project and provided a significant amount of support. With the
support and patience of the two aforementioned individuals,
that author would like to express his gratitude and thankfulness
for the opportunity to work and learn from this project.
REFERENCES
[1] Lu, J., Li, Z., Gong, X., Han, J., & Meng, J. (2013).
Resistance to cavitation erosion: Material selection John
Wiley and Sons. doi:10.1002/9781118562093.ch3
[2] Hammond, D. A., Amateau, M. F., & Queeney, R. A.
(1993). Cavitation erosion performance of fiber reinforced
composites. Journal of Composite Materials, 27(16), 1522-
1544.
[3] Brennan, C. (1995). Cavitation and Bubble Dynamics.
Oxford University Press
[4] Davis, M. P. (2008). Experimental Investigation of the
Cavitation of Aviation Fuel in a Converging-Diverging
Nozzle
[5] Schaber, K., Schnerr, G. (2010). M11 Spontaneous
Condensation and Cavitation. Springer