ST.master Thesis Prentation

7/23/2019 ST.master Thesis Prentation

1/24

Numerical Study of Free Surface Effect on S

upercavitating Flows

Student: Dang Son TungSupervisor: Prof. Park Warn yu

!"#$%#!%"&

Sc'ool of (ec'anical Engineering

Pusan National )niversity

(aster T'esis Presentation


2/24

*ontents

+ntroduction

overning e,uation

-F met'od

Simulation results

*onclusions

1

2

3

4

5


3/24

+ntroduction

Supercavitating flow / p'enomenon occurs w'en t'e cavity develop large enoug' to cover an o01ect travelling

t'roug' t'e li,uid. Classififcation:

1. Natural supercavity2 w'ic' t'e 0u00le is filled 0y pure vapor

2. Ventilated supercavity, w'ic' is artificially created 0y in1ecting gas to t'e cavity +n reality2 most of supercavitating applications operate under t'e free surface 0etween

li,uid and air suc' as torpedo or underwater ve'icle.

Figure 1. Supercavitating flow Figure 2. The application of supercavitation


4/24

+ntroduction

Supercavitating flow Computational methods:

1. Two-fluid model Simulates eac' p'ase separately 0y employing two sets of conservation e,uations

governing t'e 0alance of t'e mass2 momentum2 and energy of eac' p'ase.

2. Homogeneous mixture model(H!" /ssumes t'at t'e temperature2 pressure2 and velocity are in e,uili0rium 0etween t'e

p'ases. *onse,uently2 t'e governing e,uations for t'e mass2 momentum2 and energy

conservation reduce to a form similar to t'ose for a single3p'ase flow

Vapor volume fraction

Mixturespeedofsound(m/s)

0 0.25 0.5 0.75 110

0

101

102

103

104

427.9 m/s

1503.0 m/s

3.741 m/s

Preconditioning method

(ultip'ase flow

4.56 m%s 7 c 7 #$"4 m%s

Preconditioning

(ac'8#

Supersonic flow

(ac'7#

Su0sonic flow

*onverge faster *onverge slowly

c *onverge 0etterFigure 3. Mixture speed of sound versus

vapour fraction

CFt

=

sup ! su" ! ?

sup su" !


5/24

+ntroduction

Free surface flow T'e surface of a fluid t'at is su01ect to constant perpendicular normal stress and 9ero parallel s'ear

stress2 suc' as t'e 0oundary 0etween two 'omogeneous fluids2 in t'is case2 is li,uid water and t'e air. Computational methods:

1. #nterface trac$ing met%od (&agrangian sc%eme" (odels t'e free surface 0y attac'ing computational grid on t'e moving 0oundary

2. #nterface capturing met%od (ulerian sc%eme" Employs a fied mes' formulation and reconstructs t'e interface 0etween two p'ases from

t'e value of appropriate flow field varia0les #$F method models t'e free surface t'roug' li,uid void fraction.

+nterface s'arpening tec'ni,ue

+nterface reconstruction tec'ni,ue

a%&nterface trac'ing method "% &nterface capturing method

Figure (. &nterface modeling method


6/24

+ntroduction

HE

/ir

Water-apor

VOF

!"#ective of this stud$ +nvestigate t'e effect of free surface on supercavitating flow in term of

T'e s'ape of supercavity T'e deformation process of supercavity

/pply -F met'od to model t'e free surface and ;E( met'od to simulate

t'e multip'ase flows

Figure ). Schematic of $"*ective of this stud+


7/24

overning E,uation

T'e compressi0le two3p'ase 'omogeneous

F=

?E=

>F=

?E=

@A=

BtA=

B

vv

e =+++

=

g

v

C

C

T

v

u

p

A=

+

+

=

)DC

)DC)'D

p?v)D

p?u)D

)2DC

#E=

mg

mv

tm

pym

pm

mG

+

+

=

-DC

-DC-'D

pE>v-D

pE>u-D

-DC

#F=

mg

mv

tm

pym

p:m

mG

v>u>-Hv?u?) y:y: +=+=

pE

( ) ( )

++++

+

=

"

"

,v@u@?,v@u@?

@?@?

@?@?

"

#E=

yyyyyy

yyyy

yy

v

( ) ( )

++++

+

=

"

"

,v@u@>,v@u@>

@>@>

@>@>

"

#F=

yyyyyy

yyyy

yy

v

+

++

+

=

+

+

y

vDCc

y

vDCcmm

y

,v@u@v'D3c

y@

yvDc

y

@

y

uvDc

y

vDCcmm

S=

mg

a

mva

yyyytm

a

yy

!

ma

yma

mGa


8/24

overning E,uation

T'e flu aco0ian matri and preconditioning matri

w'ere2

*avitation model I(erkle !""6J:

=

;CC""C

CC""C

FEDvu*

v v v"v

uuu"u

PKC""C

B

mCvgmTg

L

mpg

mCgvmTv

L

mpv

mm

mCgmCvmTm

L

mp

mCgmCvmTm

L

mp

mTG

L

mpG

=

;CC""C

CC""C

FEDvu*

v v v"v

uuu"u

PKC""C

B

mCvgmTgmpg

mCgvmTvmpv

mm

mCgmCvmTmmp

mCgmCvmTmmp

mTGmpG

e

C;2C

''F'2'E

''D2''*

C3P2C3K

mCggmmCvvm

CgmmCgtCvmmCvt

TmmTtppmmpt

mCgGmmCvGm

+=+=

+=+=

+=+=+=+=

( )

( )"2ppmat)

!

#

M*m

"2ppmint)

!

#

M*

m

v

vvprod

v

lldest

=

=

+

L

m m L! !

# #

p p c c

= +

T

D

p

'D

p

D

T

'D

T

'D

cm

mp

m

m

mp!

+

=

!! ! ! !

p- cL min c 2ma:I ) 2) J = =

r


9/24

-F met'od

T'e location of interface 0etween two p'ases is defined t'roug' a li,uid void fraction

+f # : t'e cell contains only li,uid

+f " : t'e cell contains only t'e ot'er p'ase +f " 7

7 #: t'e cell contains 0ot' two p'ases

T'e advection e,uation: +n *artesian coordinates:

+n generali9ed curvilinear coordinates:

w'ere2

Figure ,. Modelling interface

through #$F

"l l lu vt x +

+ + =

l

l l

F - ! #.

t . .

+ + = +

lF !.

=

l- #.

=


10/24

-F met'od

Numerical met'od /pplying Operator Split /dvection /lgorit'm. T'e governing e,uation is split into

T'e discretisation of t'e e,uations

w'ere2

: t'e volume of fluid in t'e cell

+n present researc'2 PG+*tec'ni,ue is applied to reconstruct t'e free surface in order to

compute t'e flu across t'e cell 0oundary.

SG+*

PG+*

Figure /. &nterface reconstruction

techni0ue

l

l

F !.

t .

+ =

l

l

- #.

t .

+ =

( ) #%! #%!2 2 #%! #%!#%! #%!

Qt Q

Q? Q% #n i il i * il i

i i

! !tF F

. .. .

+ +

+

= +

( )#%! #%!# #%! #%!#%! #%!

Q Qt

Q#

t

Q

* *n

l * *

* *

l . .# #

- -. .

+ +

++

+

= +

( )#%!2 #%! #%!2 #%!%Qt Q>i * i i * iF ! # !+ + + +=

#%!2i *#+


11/24

Simulation results

Simple test case

-F (et'od ;omogeneous (odel I;E(J

: Eact interface

Figure . Schematic of Flow Field

Figure . Time se0uence of the interface movement


12/24

Simulation results

Simple test case

+nterface position:

".!

+nterface position: ".&

+nterface position:

".5

+nterface position:

#."

Figure 1. i0uid void fraction distri"ution in various interface locations


13/24

Simulation results

Dam0reak test

Figure 11. The tan' shape at front view and side view

Figure 12. The computation domain


14/24

Simulation results

Dam0reak test

Figure 13. i0uid void fraction calculated "+ #$F method

and 45M method

Figure 1(. The shape of fluid versus non6dimensional time


15/24

Simulation results

Dam0reak test

!ime

"avefront

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

2

2.5

3

3.5

4# $ 0.3% &umericalresult(V')# $ 0.% &umericalresult(V')# $ 0.3% &umerical result(#M)# $ 0.3% !*+& experiment

# $ 0.% !*+& experiment# $ 0.220% ,ressler1 954

# $ 0.110% ,ressler1 954# $ 0.055% ,ressler1 954# $ 0.114% Martin-Moce 1952

h%H

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1 # $ 0.3% &umericalresult(V')# $ 0.3% &umerical result(#M)

# $ 0.3% !*+& 01# $ 0 .% ee et al. 2002# $ 0.% ucner 2002

h%H

0 2 4 6 8 10 12

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 # $ 0.3% &umerical esult(V')# $ 0.3% &umericalesult(#M)

# $ 0.3% !*+& 01# $ 0.3% !*+& 02# $ 0.% /ee et al. 2002# $ 0.% ucner 2002

h%H

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 # $ 0.3% &umerical result(V')# $ 0.3% &umerical result(#M)

# $ 0.3% !*+& 01# $ 0.3% !*+& 02# $ 0.% /ee et al. 2002# $ 0.% ucner2002

1/#

0 2 4 6 8 10 120

0.2

0.4

0.6

0.8

1

1.2 # $ 0.3% &umericalresult(V')

# $ 0.3% &umericalresult(#M)

# $ 0.3% !*+&01

# $ 0.3% !*+& 02

# $ 0.% /ee et al. 2002# $ 0.% urcer 2002

arrival of

t'e second wave

arrival of

t'e second wave

arrival of t'e primary wave

arrival of

t'e second wave


arrival of

t'e second wave


Figure 1,. The position of wave front versus time

Figure 1). The water height at various locations versus the non6dimensional time

Gi,uid 'eig't at ;# Gi,uid 'eig't at ;!

Gi,uid 'eig't at ;4 Gi,uid 'eig't at ;&t&g%H'1%2 t&g%H'1%2

t&g%H'1%2 t&g%H'1%2


16/24

Simulation results

Dam0reak test

0 2 4 6

0

0.5

1

1.5

2

2.5

3

3.5

4 *ensor 1 &umerical result(V')

*ensor 1 &umerical result(#M)*ensor 1 xperiment

0 2 4 6

0

0.5

1

1.5

2

2.5 *ensor 2 &umerical esult(V')


0 2 4 6

0

0.5

1

1.5

2 *ensor 3 &umerical result(V')*ensor 3 &umerical result(#M)*ensor 3 xperiment

0 2 4 6

0

0.5

1

1.5

2 *ensor 4 &umerical esult(V')


Figure 1/. T+pical impact pressure at all four pressure sensors at 4 7 .3m

t&g%H'1%2 t&g%H'1%2

t&g%H'1%2 t&g%H'1%2

(%

&)gH'

(%

&)gH'

(% &)gH'

(% &)gH'


17/24

Simulation results

Dam0reak test

0 1 2 3 4 5

0

0.5

1

1.5

2

2.5

3

3.5*ensor 1 &umericalresult

*ensor 1 xperiment result

0 1 2 3 4 5

0

1

2

3*ensor 2 &umerical result

*ensor 2 xperimentalresult

0 1 2 3 4 5

0

1

2

3*ensor 3 &umericalresult

*ensor 4 xperimetal result

0 1 2 3 4 5

0

0.5

1

1.5

2*ensor 4 &umerical result

*ensor 4 xperiment result

Figure 1. T+pical impact pressure at all four pressure sensors at 4 7 .,m

t&g%H'1%2 t&g%H'1%2

t&g%H'1%2 t&g%H'1%2

(%

&)gH'

(%&)gH'

(%

&)gH

'

(%

&)gH'


18/24

Simulation results

S'eet cavitation flows over a #%R cali0er30lunt 0ody

*/,

4p

0 2 4 6 8-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2&umerical result a.no $ 0.3

&umerical result a.no $ 0.4xperiment a.no $ 0.3

xperiment a.no $ 0.4

Figure 1. Time se0uence of unstead+ cavitating flows over the 18

cali"er6"lunt "od+

Figure 2. the pressure coefficient


19/24

Simulation results

Non3slip wall

+nletutlet

S'eet cavitation flows over a divergent% convergent no99le

Figure 21. -rid of divergent8convergent no99le: 1/x1

Figure 22. Time se0uence of the c+clic process of "u""le formation


20/24

Simulation results

Supercavitating flow under free surface effects

Figure 23. The shape of h+drofoil and computational domain

Figure 2(. The time se0uence of "u""le formation for supercavitation at angle of attac' 7 12o:

cavitation num"er 7 .1/): water level from .3c to 1.c


21/24

Simulation results


&% Ca.no 7 .1) &&% Ca.no 7 .2

Figure 2). The maximum cavit+ shape at cavitation num"er 7 .1) and .2

Ta"le 1. The maximum cavit+ length


22/24

Simulation results


*/c-10 -5 0 5 10 15 20

-0.4

-0.2

0

0.2

0.4 # $ 0.3c

# $ 1.5c

# $ 3.0c

# $ 5.0c# $ 10.0c

*/c-10 -5 0 5 10 15 20

-0.4

-0.2

0

0.2

0.4 # $ 0.3c

# $ 1.5c

# $ 3.0c

# $ 5.0c# $ 10.0c

*/c-10 -5 0 5 10 15 20

-0.4

-0.2

0

0.2

0.4 # $ 0.3c

# $ 1.5c

# $ 3.0c

# $ 5.0c

# $ 10.0c

*/c-10 -5 0 5 10 15 20

-0.4

-0.2

0

0.2

0.4 6n7le of attac8 $ 10

6n7le of attac8 $ 126n7le of attac8 $ 14

Figure 2,. The pressure contour at four

different water levels

Figure 2/. The wave profile at angle of attac' e0ual to 1(o

Figure 2. The wave profile at three different angles of attac'

in case of ca.no 7 .1/)

Ca.no =

0.2

Ca.no =

0.175

Ca.no =

0.15

*h%c

*h%c

*h%c

*h%c


23/24

*onclusion

+n t'is t'esis2 t'e -F met'od and ;E( met'od are successfully implemented2 t'e

conclusions can 0e drawn as follows:

T'e simulation tests performed in various cases s'ow t'at t'e -F sc'eme can predict,uite accurately t'e movement of interface 0etween air and li,uid.

*omparing wit' t'e ;E( met'od2 t'e -F sc'eme produces a s'arper contacting layer

0y eliminating t'e numerical error t'roug' computing a cell 0oundary flu applying t'e

interface reconstruction.

T'e dynamics tests indicate t'at a diffusive interface make t'e ;E( met'od predict t'e

impact pressure peak less accurately t'an t'e -F sc'eme.

T'e presence of free surface affect strongly not only to t'e maimum cavity lengt' 0ut

also to t'e 0reaking process of 0u00le.

T'e wave elevation also depends on t'e distance from t'e o01ect to free surface. Future works:

/pplying -F met'od and ;E( met'od for t'ree3dimensional applications

+mproving -F met'od to track t'e interface 0etween t'ree p'ases suc' as t'e miture

of li,uid2 air2 and vapor in t'e ventilated supercavitation pro0lems


24/24

+H,-. /!0 F!

/!0 ,++E-+!-

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ST.master Thesis Prentation