st.master thesis prentation
TRANSCRIPT
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7/23/2019 ST.master Thesis Prentation
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Numerical Study of Free Surface Effect on S
upercavitating Flows
Student: Dang Son TungSupervisor: Prof. Park Warn yu
!"#$%#!%"&
Sc'ool of (ec'anical Engineering
Pusan National )niversity
(aster T'esis Presentation
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*ontents
+ntroduction
overning e,uation
-F met'od
Simulation results
*onclusions
1
2
3
4
5
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+ntroduction
Supercavitating flow / p'enomenon occurs w'en t'e cavity develop large enoug' to cover an o01ect travelling
t'roug' t'e li,uid. Classififcation:
1. Natural supercavity2 w'ic' t'e 0u00le is filled 0y pure vapor
2. Ventilated supercavity, w'ic' is artificially created 0y in1ecting gas to t'e cavity +n reality2 most of supercavitating applications operate under t'e free surface 0etween
li,uid and air suc' as torpedo or underwater ve'icle.
Figure 1. Supercavitating flow Figure 2. The application of supercavitation
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+ntroduction
Supercavitating flow Computational methods:
1. Two-fluid model Simulates eac' p'ase separately 0y employing two sets of conservation e,uations
governing t'e 0alance of t'e mass2 momentum2 and energy of eac' p'ase.
2. Homogeneous mixture model(H!" /ssumes t'at t'e temperature2 pressure2 and velocity are in e,uili0rium 0etween t'e
p'ases. *onse,uently2 t'e governing e,uations for t'e mass2 momentum2 and energy
conservation reduce to a form similar to t'ose for a single3p'ase flow
Vapor volume fraction
Mixturespeedofsound(m/s)
0 0.25 0.5 0.75 110
0
101
102
103
104
427.9 m/s
1503.0 m/s
3.741 m/s
Preconditioning method
(ultip'ase flow
4.56 m%s 7 c 7 #$"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" !
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+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
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+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 $"*ective of this stud+
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overning E,uation
T'e compressi0le two3p'ase 'omogeneous
F=
?E=
>F=
?E=
@A=
BtA=
B
vv
e =+++
=
g
v
C
C
T
v
u
p
A=
+
+
=
)DC
)DC)'D
p?v)D
p?u)D
)2DC
#E=
mg
mv
tm
pym
pm
mG
+
+
=
-DC
-DC-'D
pE>v-D
pE>u-D
-DC
#F=
mg
mv
tm
pym
p:m
mG
v>u>-Hv?u?) y:y: +=+=
pE
( ) ( )
++++
+
=
"
"
,v@u@?,v@u@?
@?@?
@?@?
"
#E=
yyyyyy
yyyy
yy
v
( ) ( )
++++
+
=
"
"
,v@u@>,v@u@>
@>@>
@>@>
"
#F=
yyyyyy
yyyy
yy
v
+
++
+
=
+
+
y
vDCc
y
vDCcmm
y
,v@u@v'D3c
y@
yvDc
y
@
y
uvDc
y
vDCcmm
S=
mg
a
mva
yyyytm
a
yy
!
ma
yma
mGa
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overning E,uation
T'e flu aco0ian matri and preconditioning matri
w'ere2
*avitation model I(erkle !""6J:
=
;CC""C
CC""C
FEDvu*
v v v"v
uuu"u
PKC""C
B
mCvgmTg
L
mpg
mCgvmTv
L
mpv
mm
mCgmCvmTm
L
mp
mCgmCvmTm
L
mp
mTG
L
mpG
=
;CC""C
CC""C
FEDvu*
v v v"v
uuu"u
PKC""C
B
mCvgmTgmpg
mCgvmTvmpv
mm
mCgmCvmTmmp
mCgmCvmTmmp
mTGmpG
e
C;2C
''F'2'E
''D2''*
C3P2C3K
mCggmmCvvm
CgmmCgtCvmmCvt
TmmTtppmmpt
mCgGmmCvGm
+=+=
+=+=
+=+=+=+=
( )
( )"2ppmat)
!
#
M*m
"2ppmint)
!
#
M*
m
v
vvprod
v
lldest
=
=
+
L
m m L! !
# #
p p c c
= +
T
D
p
'D
p
D
T
'D
T
'D
cm
mp
m
m
mp!
+
=
!! ! ! !
p- cL min c 2ma:I ) 2) J = =
r
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-F met'od
T'e location of interface 0etween two p'ases is defined t'roug' a li,uid void fraction
+f # : t'e cell contains only li,uid
+f " : t'e cell contains only t'e ot'er p'ase +f " 7
7 #: t'e cell contains 0ot' two p'ases
T'e advection e,uation: +n *artesian coordinates:
+n generali9ed curvilinear coordinates:
w'ere2
Figure ,. Modelling interface
through #$F
"l l lu vt x +
+ + =
l
l l
F - ! #.
t . .
+ + = +
lF !.
=
l- #.
=
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-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 *#+
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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
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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
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Simulation results
Dam0reak test
Figure 11. The tan' shape at front view and side view
Figure 12. The computation domain
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Simulation results
Dam0reak test
Figure 13. i0uid void fraction calculated "+ #$F method
and 45M method
Figure 1(. The shape of fluid versus non6dimensional time
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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 primary wave
arrival of
t'e second wave
arrival of t'e primary 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
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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')
*ensor 2 &umerical result(#M)*ensor 2 xperiment
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')
*ensor 4 &umerical result(#M)*ensor 4 xperiment
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'
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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'
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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
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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
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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
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Simulation results
Supercavitating flow under free surface effects
&% 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
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Simulation results
Supercavitating flow under free surface effects
*/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
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*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
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+H,-. /!0 F!
/!0 ,++E-+!-