Hydrodynamic Properties of Annular Cavitator

College of Aerospace Sci. & Tech. National University of Defense TechnologyChangsha, CHINA

Presenter: Ming-dong LIN

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Contents

1. Backgrounds

2. Numerical Method

3. Results & Discussion

4. Conclusion

CAV2012, Singapore

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CAV2012, Singapore

Backgrounds

Fully Wetted Drag V∝ 3

Propellor

Low speed (<70Kn)

Navigation styles underwater

Supercavitating

Drag V∝ 2

Rocket propulsed

Ultrahigh speed (>200Kn)

Revolution

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Backgrounds

Studies of supercavitating flow

Logvinovich (IHM, Ukraine) proposed the theorem of Independence of Caivity Section Expension, which is testified by many experiments.

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CAV2012, Singapore

Backgrounds

Studies of supercavitating flow

Kunz, Lindau, et.al (APL, The Pennsylvania State University, US) improved numerical method for both partial and fully developed supercavities, and coupled the flow simulation with the vehicle trajectory.

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Backgrounds

Studies of supercavitating flow

Hydrodynamic properties of different cavitators were tested by Kuklinski (NUWC, US).

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Backgrounds

Critical technologies of long distance supercavitating flight

Supercavitating hydrodynamics

Water ramjet propulsion system

Advanced motion control strategy

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Backgrounds

Hydrodynamic properties

of annular cavitator?

Supercavity

water ramjetannular cavitator

with water injectionof “Shkval-E”

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LOGONumerical Method

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

The continuity equation of the vapor:

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

LOGONumerical Method

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B. Rayleigh-Plesset cavitation model2

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

v

c v

B

3 2,

3v v

l

p pm C p p

R

C. Standard turbulence model

( ) ( ) [( ) ]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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Numerical Method

Vehicle model

Computational gridsvehicle

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2m

10cm 20cm

100 /inv m s 0.2p MPa

500,000 grids

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Numerical Method

Computation setting

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Case Pout[MPa] Dtube[cm] Case Pout[MPa] Dtube[cm]

1 4.0 2.0 5 3.0 4.0

2 4.0 3.0 6 3.5 4.0

3 4.0 4.0 7 4.0 4.0

4 4.0 5.0 8 4.5 4.0

Table 1. Differenct CFD models and boundary conditions

LOGOResults & Discussions

Hydrodynamicproperties of

annular cavitator Cavitysize

Pressure field

Injectingflow

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Drag

LOGOResults & Discussions

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Pressure field

0 1 2 3 4 50

1

2

3

4

5

6

Pre

ssur

e (M

Pa)

r (cm)

Case 0 Case 1 Case 2 Case 3 Case 4

0 1 2 3 4 50

1

2

3

4

5

6

Pre

ssur

e (M

Pa)

r (cm)

Case 0 Case 5 Case 6 Case 7 Case 8

Pressure distributions on cavitator surface

Stagnation ring moves outward

Stagnation ring is stable

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Drag

Case Fcav[N] Ftube[N] Ftotal[N] Increment[%]

0 30608 0 30608 0

1 30260 1565.4 31825.4 3.98

2 28720 3408 32128 4.97

3 26480 5870 32350 5.69

4 23480 8886 32366 5.74

5 26740 5488 32228 5.29

6 26640 5676 32316 5.58

7 26480 5870 32350 5.69

8 26260 6076 32336 5.65

Table 2. Forces acted on cavitator region

Increasewith

tube size

Increasewith outlet

pressure

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Injecting flow

1 2 3 4 5 60

20

40

60

80

100 Mass flow Velocity

Tube Diameter (cm)

Mas

s flo

w (

kg/s

)

10

20

30

40

50

60

Velocity (m

/s)2.5 3.0 3.5 4.0 4.5 5.0

0

20

40

60

80

100

Mass flow Velocity

Pressure Out (MPa)

Mas

s flo

w (

kg/s

)

10

20

30

40

50

60

Velocity (m

/s)

Mass flow and velocities in different cases

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Cavity size

Decreasewith

tube size

Increasewith outlet

pressure

LOGOConclusions

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Pressure distribution changes significantly on cavitator surface which results in the increase of the drag.

The injecting flow is proportional to the tube size, and decreases with the outlet pressure.

Compare with disk, the annular cavitator generates smaller cavity. The cavity size decreases with the tube size and increases with the outlet pressure.

College of Aerospace Science and TechnologyNational University of Defense Technology