Numerical simulation of supercavitating flow created by cavitators

with different shapes

Presenter ： Shuai Zhang

Institute of Aerospace and Material Engineering National University of Defense Technology

Changsha 410073, P.R. China

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Introduction

Contents

11

Modeling and computational approaches 22

Results and discussions33

Conclusion44

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Introduction

Supercavitation, which could decrease more than 90% of the

drag, is an outstanding method of anti-drag for high speed fully-

submerged vehicles. As a result, it has attracted more and more

interests resently.

Cavitator is an important facility of supercavitating vehicle, its

performance has a deep influence on cavitation effects and drag

of the vehicle.

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Introduction

High-Speed Projectile

Drag Analysis

Experimental methods

Water tunnel

High-Speed

Numerical methods

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Introduction

Singhal et.al established natural cavitating rate model based

on once order Rayleigh-Plesset equation, successfully simulated

the supercavity in comparison with the results of experiments.

Then, plenty of natural supercaviting simulations are carried out

based on the Singhal’s model. Especially, the model of Bakir et

al. was utilized by the generic CFD code ANSYS CFX, which is

the basement of this paper.

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Modeling and computational approaches

A. Governing equations The continuity, momentum equations of the mixture phase:

The continuity equation of the vapor phase:

The mixture property:

( )( ) 0m

mt

u

T T( )( ) [ ( )]m

m m mpt

u

u u u u g

( )( )v v

v v m mt

u

m l l v v

1l v

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Modeling and computational approaches

B. Natural cavitation model

The Rayleigh-Plesset equation which provides the basis for

the rate equation controlling vaporization and condensation is

given by:2

2B BB 2

B

3 2( )2

v

l v

p pd R dRR

dt dt R

ve v

B

3 2,

3nuc l v

l

p pm C p p

R

vc v

B

3 2,

3v v

l

p pm C p p

R

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Modeling and computational approaches

C. Turbulence model The standard turbulence model is used in this study:

( ) ( ) [( ) ]tm m k m

k

k vk k Gt

1 2( ) ( ) [( ) ] ( )tm m k mv C G C

t k

k

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Modeling and computational approaches

D. Computational approaches

The generic CFD code ANSYS CFX was utilized to investigate

the supercavitation flow. The governing equations discretized

by the Finite Volume Method(FVM). The convection terms were

approximated by a high order resolution scheme while the

diffusion terms were approximated by the second-order central

difference scheme.

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Results and discussions

Figure 1 Schematic of the vehicle

Figure 2 Mesh of the simulation for supercavitation

For the sake of simulating that the vehicle is navigating at the 10m depth underwater with the velocity of 100m/s and no angle of attack. The velocity of the incoming flow is 100m/s, with no angle of attack, and the pressure of the environment is 0.2MPa.

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Results and discussions

Figure 3 Shapes of supercavity

Shape 1

Shape 2

Shape 3

Shape 4

Shape 1 Shape 2

Shape 3 Shape 4

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Results and discussions

Figure 4 Pressure distribution on the front surface of the cavitator

Shape 1

Shape 2

Shape 3

Shape 4

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Results and discussions

Figure 5 Water volume fraction distribution along the surface of the vehicle body

Shape 1

Shape 2

Shape 3

Shape 4

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Results and discussions

Figure 6 Friction coefficient distribution along the surface of the vehicle body

Shape 1

Shape 2

Shape 3

Shape 4

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Results and discussions

Table 1 Drag data under different cavitator conditions (N)

Shape 1

Shape 2

Shape 3

Shape 4

  Shape 1 Shape 2 Shape 3 Shape 4PC

(relative decrease)

14520.8 

13432.3(7.5%)

10561.2(27.3%)

8581(40.9%)

TP 14831.1 14210.9 11345 9375.3

Percentage of TP from

PC97.9% 94.5% 93.1% 91.5%

TF 15.9 196.5 320.2 1141.3

RD 14847 14407.4 11665.2 10516.6

Percentage of RD from

TF0.1% 1.4% 2.7% 10.9%

PC: the pressure drag force acting on the cavitatorTP: the total pressure drag force acting on the vehicleTF: the total friction acting on the vehicleRD: the resultant drag force consisting of TP and TF

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Conclusion

A.

Under the same conditions of diameter and income flow, disk

cavitator owns the highest cavitating capability, but the

pressure drag on cavitator is the largest of all. Convex conical

cavitator has a opposite performance, there is wet part at the

tail of the vehicle ,but the the pressure drag on cavitator

decrease 40.9% relatively. The other two perform between disk

cavitator and convex conical cavitator.

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Conclusion

B.

The pressure drag on cavitator is higher than 90 percents of

total pressure drag, indicating that the pressure drag on

cavitator is the key part of total pressure drag, it is significant to

reduce the total pressure drag through optimal design of the

shape of cavitator.

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Conclusion

C.

Good positive correlation is found between water volume

fraction and friction coefficient distribution along the surface of

vehicle body. If the surface touches water, the friction will jump

sharply, indicating that the cavitating method of anti-drag is

outstanding to reduce the friction of the underwater vehicle.

Thank you