1. The document summarizes an investigation into supercavitation physics conducted in two laboratories. It included studies of ventilated cavitation, configuration effects, and a comparison of ventilated and natural supercavitation. 2. Key findings included that results from the two laboratories for ventilated cavitation agreed well, and that a backward facing model provided better visualization of natural supercavitation compared to a forward facing model. 3. The formation and evolution of natural supercavitation was observed, including four stages of cavity development. Choking behavior, where cavity size remains constant despite pressure changes, was demonstrated and used to measure minimum cavitation numbers.

1. 1
Investigation of Supercavitation Physics
Siyao Shao, Ashish Karn, Jiarong Hong and Roger E.A. Arndt
Final Report
To
Professor Byoung-Kwon Ahn,
Flow Induced Noise & Cavitation Control Lab. (FINCL)
Introduction
Supercavitation is of interest because of the large reduction in drag that can be achieved,
allowing for considerably higher operating speeds for various hydrodynamic vehicles. Although
there have been a considerable number of investigations of supercavitation carried out in many
institutions around the world, there have been few studies in which comparable results have been
achieved.
This is a collaborative study with the Flow Induced Noise & Cavitation Control Lab. (FINCL),
Dept. of Naval Architecture and Ocean Engineering, in Chungnam National University in
Daejon, 34134, Korea. The study reported herein has three parts:
1. A study of ventilated cavitation in which direct comparison is made with the results
obtained in Korea
2. An investigation of configuration effects
3. A comparison between ventilated and vaporous supercavitation
The operation of supercavitating vehicles poses unique challenges. Only small regions at the
nose (cavitator) and possibly on the afterbody are in contact with water. Unlike for a fully wetted
vehicle, there is an absence of lift on the body. In addition, the vehicle has significant start-up
issues requiring special attention to methods for reaching high enough velocity to operate in the
supercavitating mode. A precise knowledge of cavity shape is very important when computing
the fin and planing forces acting on a supercavitating vehicle. In addition, cavity-vehicle
interaction also exhibits strong memory effects (cavity shape is a function of the history of the
vehicle motion). Ventilation is an important issue due to the paucity of both experimental data
and reliable modeling of ventilation demand.
The role of ventilation is illustrated in Figure 1. Here air demand is shown for a vehicle operating
at a depth of 10 m and at a constant cavitation number, 𝜎𝑐 =
2( 𝑃∞−𝑃𝑐)
𝜌𝑈∞
2 = 0.05. Note that amount
of ventilation required varies with speed until the vehicle achieves a velocity high enough obtain
supercavitation without the aid of ventilation. Figure 1 illustrates the need for ventilation data
over a wide range of operating conditions. Since ventilation demand is an important factor, one
of the aims of this study is to determine whether comparable results can be achieved in similar
facilities.

2. 2
Figure 1 Schematic of ventilation demand for an accelerating vehicle designed to operate
at a cavitation number of 0.05 and a depth of 10m.
Facilities
Figure 2 is an illustration of the water tunnel at Chungnam University. By comparison the Saint
Anthony Falls Laboratory (SAFL) Water Tunnel is shown in Figure 3. Both tunnels have test
sections with a square cross section with the SAFL tunnel having a larger cross section (190mm
X 190mm versus 100mm X 100 mm. Both tunnels have a maximum operating speed of 20 m/s.
A unique feature of the SAFL tunnel is the ability to remove large quantities of injected air,
allowing for continuous operation with high rates of ventilation air.
Test Conditions
The first phase of our study was a comparison of the ventilation rates obtained in the two
facilities. The size of cavitators used were adjusted so that the relative size, D/dc was the same
for a series of tests. This is illustrated in Table 1. In both cases the tunnel diameter was defined
as the diameter of a circular cross section with the same cross sections area:
hD

2

where h is the tunnel cross section height. 20mm, 30mm and 40mm cavitators were used in the
experiments to study the effect of blockage on the cavity geometry and closures. Cavity images
including the cavity closure region were captured with a Nikon D-610 digital camera. The
highest flow velocity was set as 12m/s.

3. 3
Figure 2 CNU Water Tunnel
Figure 3 SAFL Water Tunnel

4. 4
SAFL
Test section 190x190
D [mm] 214.4
dc [mm] 20.0 30.0 40.0
D/dc 10.72 7.15 5.36
σ (min) 0.20 0.32 0.46
CNUCT
Test section 100x100
D [mm] 112.8
dc [mm] 10.5 15.8 21.1
D/dc 10.72 7.15 5.36
σ (min) 0.20 0.32 0.46
Table 1. Comparison of test conditions for ventilation studies
Ventilation Studies Forward Facing Model
Since the Chungnam facility is only equipped with a forward facing model, comparison are made
with this configuration first. The forward facing model was similar in design to the one used in
Korea. A typical set of data is shown in Figure 4. In this plot the size of a cavity varies with the
ventilation rate. Here the ventilation rate is normalized with flow velocity and cavitator diameter:
2
Ud
Q
Cq 
Cavitation number is defined as the equivalent cavitation number for free stream conditions
(Kawakami and Arndt 2011, p). The results are similar to those obtained in Korea.
The minimum cavitation number agrees well with the predictions of Brennen (1969) as shown in
Figure 5. Further, the measured geometry agreed well with simulations of Ahn et al (2012). Here
the original data was converted to show the cavity geometry, D/dc in terms of the equivalent
cavitation number for unbounded flow (Kawakami and Arndt 2011).
The overall conclusion is that results of the present study and the earlier results of Kawakami and
Arndt agree very well with Chungnam University data.
A full summary of all the data is given in the appendix.

5. 5
Figure 4 Typical set of images over a range of ventilation rate
Figure 5. Choking Cavitation Number versus Blockage Ratio

6. 6
Figure 6 Comparison of measured geometry with the simulations of Ahn et al (2012)
Configuration Effects
Our initial experiments with forward facing cavitators (FFM) indicated some issues:
 It was found to be difficult to establish a natural supercavity with the FFM, especially
with the 10 mm cavitator and 20mm cavitator.
 Difficult to observe cavity closure.
 Later experiments with natural supercavitation were difficult to carry out because large
vibrations in the strut were encountered while carrying out experiments at high
tunnel velocities.
To circumvent these issues a backward facing model (BFM) was developed. A favorable feature
was the ease of observing cavity closure without the encumbrance of a supporting body. A
negative was the influence of a supporting hydrofoil strut, mounted upstream of the cavity. The
two types of models are compared in Figures 7 and 8.
A comparison of the performance of the two types of models is shown in Figure 9. Note that the
biggest drawback with BFM is the influence of the wake from the hydrofoil support.

7. 7
Figure 7 Forward Facing Model

8. 8
Figure 8 Backward Facing Model
Figure 9 Comparison of two types of models.
A typical set of backward facing model is shown in Figure 10.
Figure 10 Typical set of images over a range of ventilation rate
Natural Supercavitation
The backward facing model provided a good starting point for observing natural cavitation. The
experimental conditions are shown in Table 2. And a much smaller experimental range of
forward facing model natural supercavitation was achieved after the stabilization of the model
from outside of the test section which is shown in Table 3. Figure 10 provides a comparison of

9. 9
the natural supercavities formed by the backward facing model and forward facing model with
the same cavitator size (30mm).
Figure 10 Comparison of two types of models (natural supercavitation).
Table 2 Experimental Conditions with BFM
SAFL
Test section 190x190
D (mm) 214.4
dc (mm) 30.0 40.0
D/dc 7.15 5.36
Velocity range, V (m/s)* 8.7-10.7 7.7-10.7
Wake signature

10. 10
Fr range 15.9-19.7 12.3-17.1
Lowest stable operation pressure, P
(kPa)
15
σmin, theory 0.3174 0.4556
σv, attainable 0.3205 0.4594
Table 3 Experimental Conditions with FFM
Formation and Evolution
An important question is whether there are any differences between ventilated and natural
supercavitation. It was observed that, for a backward facing model, a bubbly flow undergoes four
different stages to generate a clear supercavity which are dense bubbly flow, bubbly flow with
spiraling bubble jets, foamy cavity and a supercavity. Figure 11 illustrates the process of the
cavity’s evolution.
Figure 11 Evolution of Cavity Formation
Choking
After reaching supercavitation, the cavitation index can be further reduced by pressure reduction.
However, there is a minimum below which the cavitation index cannot be further reduced. The
minimum value is dictated by blockage (Brennen, 1969, Tulin, 1961). Under choking, further

11. 11
pressure reduction does not influence the cavitation number. Instead, a constant velocity drop
occurs to satisfy this constant minimum/choking cavitation number, as shown in Figure 11. This
provides a practical way to measure minimum cavitation number in restrained water tunnel
experiments. The cavity size remained constant after choking, as seen in Figure 12 (rc is the
cavitator radius and (L/2) is the length from cavitator to the cavity’s maximum diameter).
Similar results are found with the forward facing model as shown in Figure 13.
Figure 12 Choking Test

12. 12
Figure 13 Change in Cavity Shape After Choking
Figure 14 Choking Test with FFM

13. 13
An interesting characteristic is the change in cavity closure with choking. Figure 15 shows the
characteristic cavity closure before choking and Figure 16 portrays the evolution of cavity
closure after choking. The variation of the closure geometry with velocity after choking is an
interesting new phenomenon that should be studied further. A published theory (Karn et al. 2015)
of closure types’ dependence on the closure region’s ambient pressure for the artificial
supercavities could be applied to the explanation of the natural supercavities’ closure evolution
and it requires a systematic measurement of the downstream pressure for both ventilated and
natural supercavities.
Figure 15 Cavity closure observed with the BFM (40mm cavitator)

14. 14
Figure 16 Cavity Closure after Choking (40mm cavitator)
Physics of Natural Cavitation
An interesting insight into the physics of natural cavitation can be inferred from inspection of
Figures 17 and 18. Figure 17 compares natural and ventilated cavitation at the same sigma
whereas Figure 18 displays a comparison for the same size cavity1. The reason the natural and
ventilated cavities are so different in Figure 17 is that v should be calculated on the basis of
vapor pressure within the cavity not the value corresponding to the temperature of the liquid
external to the cavity. There is a temperature gradient across the cavity wall that is necessary to
supply vapor to maintain the cavity. Hence the vapor pressure within the cavity is lower. Thus
the actual v is higher. Hence a lower value of v, based on the temperature in the test section is
required to achieve comparable conditions. Based on the experiment condition of Figure 17,
using ventilated supercavity’s pressure and shape data as a reference, a required pressure drop of
roughly 1kPa is required to maintain the similar cavity geometry. However, a theoretical
calculation indicates a pressure drop less than 500Pa (Gelder et al. 1966). Further studies into the
physics of natural cavitation are required from both the theoretical and experimental views to
resolve this discrepancy of the natural supercavities and artificial supercavities.
1 Actually a slightly smaller value of sigma is required to obtain equal cavity size.

15. 15
Figure 17
Figure 18
REFERENCES
Ahn, B-K, Jang, H-G, Kim, H-T and Lee, C-S 2012 “Numerical Analysis of Axisymmetric
Supercavitating Flows” Proceedings of the Eighth International Symposium on Cavitation (CAV
2012)
Brennen, C., 1969, “A Numerical Solution of Axisymmetric Cavity Flows,” J.Fluid Mech., 37
(4), pp. 671–688.
Kawakami, E and Arndt, REA , 2011 “Investigation of the Behavior of Ventilated Supercavities”
J. Fluids Engineering, 33, 091305-1-11 September
Tulin, M.P., 1961, “Supercavitating Flows,” Handbook of Fluid Dynamics, Streeter, V. (ed.),
McGraw-Hill, New York, pp. 1224–1246.

16. 16
Karn, A., Arndt, R., & Hong, J. “An experimental investigation into the physics of supercavity
closure,” Journal of Fluid Mechanics (In press).
Gelder. T., Ruggeri R., Moore. Royce, 1966 “Cavitation similarity considerations based on
measured pressure and temperature and temperature depression in cavitated regions of Freon
114”, NASA TN D-3509.

17. 17
Appendix
Data
Observations with the FFM
dc [mm] 20
V [m/s] 4 5 6 7 8 9
Fn 9.00 11.24 13.56 17.84 18.06 20.32

18. 18

19. 19

20. 20

21. 21

22. 22
dc [mm] 30
V [m/s] 4 5 6 7 8 9
Fn 7.38 9.22 11.03 12.93 14.75 16.5

23. 23

24. 24

25. 25

26. 26
dc [mm] 40
V [m/s] 4 5 6 7 8 9
Fn 6.39 7.99 9.58 11.13 12.78 14.42

27. 27

28. 28

29. 29
Observations from BFM
dc [mm] 20
V [m/s] 4 5 6 7 8 9
Fn 9.00 11.24 13.56 17.84 18.06 20.32

30. 30

31. 31
dc [mm] 30
V [m/s] 4 5 6 7 8 9
Fn 7.38 9.22 11.03 12.93 14.75 16.57

32. 32
dc [mm] 40
V [m/s] 4 5 6 7 8 9
Fn 6.39 7.99 9.58 11.13 12.78 14.42

33. 33