Investigation of Supercavitation PhysicsSiyao 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 effects3. 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, σ c=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.

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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.

FacilitiesFigure 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 ConditionsThe 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:

D= 2√π

h

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.

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Figure 2 CNU Water Tunnel

Figure 3 SAFL Water Tunnel

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SAFLTest section 190x190

D [mm] 214.4dc [mm] 20.0 30.0 40.0

D/dc 10.72 7.15 5.36σ (min) 0.20 0.32 0.46

CNUCTTest section 100x100

D [mm] 　112.8dc [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:

Cq=Q

Ud2

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.

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Figure 4 Typical set of images over a range of ventilation rate

Figure 5. Choking Cavitation Number versus Blockage Ratio

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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.

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Figure 7 Forward Facing Model

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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 the natural supercavities formed by the backward facing model and forward facing model with the same cavitator size (30mm).

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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

Fr range 15.9-19.7 12.3-17.1

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Wake signature

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 EvolutionAn 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

ChokingAfter 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 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

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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

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Figure 13 Change in Cavity Shape After Choking

Figure 14 Choking Test with FFM

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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)

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Figure 16 Cavity Closure after Choking (40mm cavitator)

Physics of Natural CavitationAn 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.

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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.

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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.

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AppendixData

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

17

18

19

20

21

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

22

23

24

25

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

26

27

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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

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30

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

31

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

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