Comparison of Parasite Current Reduction Methods in Simulation of Two Phase Flow with VOF [in Persian]

Abstract

One of the obstacles in simulation of two phase flow is parasite currents. These currents cause
unphysical distortion at interface which impairs interface capturing and numerical results. In the
present study, two methods (using Filter and s-CLSVOF) are implemented in OpenFOAM two
phase flow solver called interFoam to reduce parasite current. Three filters are added to color
function volume of fluid (CF-VOF) method. These filters reduce parasite current in different ways,
one smoothes color function, one smoothes curvature and the other one compresses the interface.
The original and the modified solvers are tested with quiescent bubble bench mark to
investigate the effect of each filter on parasite currents. Then, the optimum arrangement of filters
is compared with s-CLSVOF method and interFoam. Present study shows parasite current
magnitude can be reduced at least up to 50% in the modified solvers. Also, the comparison of
pressure jump from numerical results and analytical result with Young-Laplace equation shows
modified solvers can predict pressure jump better than original solver. The pressure jump error is
reduced up to 400% in the modified solvers. The present study also shows filters have better
performance than s-CLSVOF method and can be considered as suitable alternative for coupled
methods.

Full text

   139415 2  243-252


  
mme.modares.ac.ir
:
Pleasecitethisarticleusing:
N.Samkhaniani,M.R.Ansari,ComparisonofParasiteCurrentReductionMethodsinSimulationofTwoPhaseFlowwithVOF,ModaresMechanicalEngineering Vol.15,No.2,
pp.243-252,2015(InPersian)



1

2*

1-         2-        *   111-14115 mra_1330@modares.ac.ir
 

:11  1393 :10  1393 :20 1393


 .

 . . :1- ) s-CLSVOF (2- 
 . .
    .
 . -
s-CLSVOF  .50 %
 .) 
s-CLSVOF (
-400 . %
s-CLSVOF  


  
   
 
 

ComparisonofParasiteCurrentReductionMethodsinSimulationofTwo
PhaseFlowwithVOF
NimaSamkhaniani,MohamadRezaAnsari*
DepartmentofMechanicalEngineering,TarbiatModaresUniversity,Tehran,Iran.
P.O.B.14115-111,TehranIran,mra_1330@modares.ac.ir
A
RTICLE
I
NFORMATION


A
BSTRACT

OriginalResearchPaper
Received02September2014
Accepted01November2014
AvailableOnline10January2015

Oneoftheobstaclesinsimulationoftwophaseflowisparasitecurrents.Thesecurrentscause
unphysicaldistortionatinterfacewhichimpairsinterfacecapturingandnumericalresults.Inthe
presentstudy,twomethods(usingFilterands-CLSVOF)areimplementedinOpenFOAMtwo
phaseflowsolvercalledinterFoamtoreduceparasitecurrent.Threefiltersareaddedtocolor
functionvolumeoffluid(CF-VOF)method. Thesefiltersreduceparasitecurrent indifferentways,
onesmoothescolorfunction,onesmoothescurvatureandtheotheronecompressestheinterface.
Theoriginalandthemodifiedsolversaretestedwith  quiescentbubblebenchmarkto
investigatetheeffectofeachfilteronparasitecurrents.Then,theoptimumarrangementoffilters
iscomparedwiths-CLSVOFmethodandinterFoam.Presentstudyshowsparasitecurrent
magnitudecanbereducedatleastupto50%inthemodiiedsolvers.Also,thecomparisonof
pressurejumpfromnumericalresultsandanalyticalresultwithYoung-Laplaceequationshows
modifiedsolverscanpredictpressurejumpbetterthanoriginalsolver.Thepressurejumperroris
reducedupto400%inthemodiiedsolvers.Thepresentstudyalsoshows iltershavebetter
performancethans-CLSVOFmethodandcanbeconsideredas  suitablealternativeforcoupled
methods.
Keywords:
VOFmethod
LevelSetMethod
ParasiteCurrent
interFoam
Filter

1- 

 
 .
 .
 
]1-5[ . 
 .
 :























244
139415 2


 
1


2
 .

 .) VOF(]1-3[
 
3
)LS (]4[ 
4
)PF(]5[   
  .
  .
5

 .


6
  . 
]6[. 1 -  
7
 :
8

 .CICSAM9
]2[ HRIC10
]7[  2 -  :
 .
 .
     : -
11
]3[ ) PLIC12
(]1[
   
         
]7-12[ .
 

]8,12[ .

) 1 (]13[:
)1(




(2 ) (2 )
lg lg
uu
pp nn
nn



 




n
 

u

p

    : 
13
)CSS (]11 , 14[
14
)CSF(]9[
15
)SSF(]15[ 
16
]16[  

  .   
 .

1-fixedgrid
2-movinggrid
3-LevelSet
4-PhaseField
5-transportequation
6-boundness
7-directmethod
8-highresolutionscheme
9-CompressiveInterfaceCapturingSchemeforArbitraryMesh
10-HighResolutionInterfaceCapturingScheme
11-donor-acceptor
12-Piece-wiseLinearInterfaceConstruction
13-ContinuousSurfaceStress
14-ContinuousSurfaceForce
15-SharpSurfaceForce
16-ghost


]8,13[ .
 () 
   ]13[ .
) 
Ca
U



 (

]15[ .
) 
1/2
Ca
Oh()
Re

 ( ]10[.
  
 .
]17 -19[  
17
)HF (]20,21[ 
 .
 .

]22[ .

18

 .

]11,15,23[.
]22[ 3  :
) ) PLIC (
 
PLIC 
 -

 .
19

 
20
 .
    .
) 
21
 ( 

 .
)CSF (   .]6[ 
      .
  
CSF 
 .
]17[ 

 .]23[ 

 .]15[

17-HeightFunction
18-SmoothingFunction
19-interFoam
20-OpenFOAM
21-surfacecompression























139415 2
245





         

 .


  . 

2-  2-1-) 

1

 .
 
   .
 .
1


 .
)2 (
)2(
1
1
( ,t)=
V
x
V



 -
)  .3 ( )3(
11 12
(1.0)
yyy

 


{,}
y


.
) 4( 
)4(
11
1 11
0 ( ) ()
U UU
tt

 

      

  

 )5 (
)5(
( ) ( ) 0  ( )=0
UU
t


   

 

        
) 6 (
)6(
1
1
( )0
U
t




 

1

 .  
  .
) 
1
1


 ( .  

6 ]6[ .
 .
CICSAM ]2[HRIC ]7[  . )7 (

1- OneFluidMethod
)7(
1
1 11
( ) ( (1 ))0
c
UU
t
 

   

  
c
U


 )8 (
)8(
1
1
min( ,max( ))
C
U CUU





   

C


.
04
C


]24,25[ 
0
C



 . - ) 9 . (
)9(
()
()
 ( (( ) ))
T
U
UUp
t
U UF



 

 

 
  
   .       
1
F



 .CSF 
) 10 (.
)10(
1
1
()
||



 
2-2- 

 .

]17[ .  .
 
 . ) 11 (

)11(
1
1
()
||








1



1

 -
]11,23[)  .12 (
)12(
1
1
1
1
n
ff
f
p
n
f
f
S
S







p

f

 .
f


1



S
f
 .

1

n  .

1


1
p



1


m 
]15[.
)13(
*
,1 11 11
,0
2(1)(12(1))()
sis
s
  





)14(
*
1
1
n
ff
f
s
n
f
f
S
S




























246
139415 2

     
1

  
c




F

c


) 15 (
)15(
1
[min(max(,),1)]
1 2 22
p pp
c
p
C CC
C


 

 
0
p
c

  CSF 
p
c
 
 
c


 
   
SSF            .
0.9 0.99
p
C

]15[ .

 . ) 1( 
 .
2-3-s-CLSVOF )
s-CLSVOF 

 .


 .
0



 .

 


) 16 ( )16(
01
(2 1)

  

 
x


0.75
x

 .
]26[]17[ 






1

 
 .
0



) 17 (
)17(
0
0
( )(1 | |)
(,0) ()
S
xx




 



1 ) 15 (
1




 .
x

0
()
S
 .

0.1
x


  .17 
      
) 18 (
)18(
corr







1.5
x



 .

F
) 9)  (19 (
 )19(
()()
F




()

) 20 (
)20(
()()
||

 

 
()

 )  .21 (
)21(

1

() (1 cos( ))| |
2


 











3-  3-1 - 
     
]12,17[ .m2
05/0 ×05/0 
m005/0 
 .  1  .

1


p



U
 .2
 .
 
 ()
) 1 (  .
) 1 (-
pa 2 
)22(
exact
lg
p pp
R


 
1  







) 

(

kg/m3
1000

1

) 

(

kg/ms

3
-
10

5
-
10

) 

(

N/m
01
/
0
























139415 2
247


2 
D/20

) 23 ( )23(

1
max(| |)
LV


   
     .


10.5



0



 . )24 (
)24(
exact
0
exact
||
pp
E
p
 


     
s-CLSVOF  .

) 25 (

{ ,,}
y mnc


)25(
max(| |)
max(| |)
ty
t
U dt
Ef
U dt









Ef
 (
2 
0
c

CSF 3 

c



0.98
c

 .4 5 
12 14  .
14 )1
m
 (2  
 .
12 2 3  .2  ) 2
n
 ( .
) 
0.98, 2, 1
c nm
 
(
 

s-CLSVOF 
2 ) 25(

0

c

5
/
0

c

98
/
0

c

Ef

1

1853
/
0

1764
/
0


1

m

2

m

3

m

Ef

4545
/
0

5637
/
0

4368
/
0


1

n

2

n

3

n

Ef

5821
/
0

4497
/
0

3832
/
0

3 ) 15 (
4 ) 14 (
5 ) 12 (
0
0.05
0.1
0.15
0
.
2
00.2 0.4 0.6 0.8
1
max(|
U
|)(m/s)
t(s)
c=0
c=
0
.
5
c=
0
.
98
0
0.05
0.1
0.15
0.2
00.2 0.4 0.6 0.8 1
max(|
U
|)(m/s)
t(s)
m=
1
m=2
m=
3
0
0.05
0.1
0.15
0
.
2
00.2 0.4 0.6 0.8 1
max(|
U
|)(m/s)
t(s)
n=
1
n=2
n=
3






















248
139415 2



D/10

D/20

D/40

D/80  .3 4 
) s-CLSVOF . (


  .3 

 .
 
  . )D/10 (100 %) D/80 (400 %
        .  
  8
5 
2  .6

 
  s-CLSVOF         

   .

3 )m/s (t=0.1sec


D/10D/20D/40D/80


0452
/
0

0997
/
0

1742
/
0

1971
/
0



0223
/
0

0346
/
0

04119
/
0

0478
/
0

s-CLSVOF
1220
/
0

1876
/
0

1343
/
0

1982
/
0

4  t=0.1sec


D/10D/20D/40D/80


32
/
24

94
/
19

46
/
15

76
/
12




17
/
9

67
/
6

29
/
6

53
/
5

s-CLSVOF
25
/
15

04
/
10

62
/
8

27
/
7

6 
D/10 1 
 )  - (
 .
s-CLSVOF 
 .4  
 50 %s-CLSVOF 
 .
   

s-CLSVOF  .
)   - (
 .

 .7 

 .s-CLSVOF 
      

.
8 

 .


 .9 ) 
s-CLSVOF (
 
   .10  


 

3-2-

 .]27[

 .
m 15/0 ) 75/0 5/0 (
m2
1×1    .
 .
]28,29[sec 8T=  . )26 (
)26(
2
2
sin(
)sin(2)cos(/ )
sin(
)sin(2)cos(/ )
u x y tT
v y x tT

 
  
T/2  .
0
0.1
0.2
0.3
00.5 1
max(|
U
|)(m/s)
t(s)


s
-
CLSVOF























139415 2
249

T  .
   ) 27 (  
A
  

I

F
 
)27(
2
1
||
N
IF
D jjj
j
A
 



32×3264×64 128×128 
5  .
5 

 .
 :


 :
s-CLSVOF


 :


7  t=0.1sec
11 
s-CLSVOF 

 5  
2D


32×3264×64128×128


1287
/
0

47
/
0

0929
/
0

87
/
0

0507
/
0



1319
/
0

62
/
0

0858
/
0

78
/
0

0499
/
0

s-CLSVOF
1310
/
0

58
/
0

08714
/
0

9
/
0

0464
/
0

 :


 :
s-CLSVOF


 :


8 t=0.1sec 























250
139415 2

9 ) 24 (t=0.1sec
10 ) 23 (t=0.1sec






s-CLSVOF
11 t=T/2 128×128

3-3 - 

 .
 . 6  .320×480 
12 .
m 031/0 .
6 







) 

(

kg/m3
998

2
/
1

) 

(

kg/ms

4
/
1

5
-
10
×
8
/
1

) 

(

N/m
062
/
0

13 
 .


 .14 
) s-CLSVOF (
 .
 4-  

  . () 

 
s-CLSVOF       

1 - 
 () 
)  (
1
0,0,0
U
p
nn








1
0
:slip
0
p
n
U
n








1
0,(0,0,0), 0
p
U
nn







12  
13 
0
0.1
0.2
0
.
3
0.01 0.1 1 10 100 1000
E%
LG

s
-
CLSVOF

0
0.2
0.4
0.6
0.01 0.1 1 10 100 1000
max(|
U
|)(m/s)
LG

s-CLSVOF

0
0.1
0.2
0.3
0.4
0 0.2 0.4 0.6 0.8 1
X(m)
t(s)
s-CLSVOF

























139415 2
251

 :
s-CLSVOF


 :


 :


14 
100 . %
2 - 
) s-CLSVOF

50 %
3 - 
) s-CLSVOF (
 4 - s-CLSVOF
s-CLSVOF  


 . 5 - 

5- 
[1] D.Youngs,Time-dependentmulti-materialflowwithlargefluid
distortion,Numericalmethodsforfluiddynamics,Vol.24,pp.273-285,
1982 .
[2] O.Ubbink,R.Issa, methodforcapturingsharpfluidinterfaceson
arbitrarymeshes,JournalofComputationalPhysics,Vol.153,No.1,pp.
26-50,1999 .
[3] C.W.Hirt,B.D.Nichols,Volumeoffluid(VOF)methodforthedynamics
offreeboundaries,JournalofComputationalPhysics,Vol.39,No.1,pp.
201-225,1981 .
[4] M.Sussman,P.Smereka,S.Osher ,levelsetapproachforcomputing
solutionstoincompressibletwo-phaseflow,JournalofComputational
Physics,Vol.114,No.1,pp.146-159,1994 .
[5] D.Jacqmin,Calculationoftwo-phaseNavier–Stokesflowsusingphase-
fieldmodeling,JournalofComputationalPhysics,Vol.155,No.1,pp.96-
127,1999 .
[6] J.Klostermann,K.Schaake,R.Schwarze,Numericalsimulationof single
risingbubblebyVOFwithsurfacecompression,InternationalJournalfor
NumericalMethodsinFluids,Vol.71,No.8,pp.960-982,2013 .
[7] S.Muzaferija,M.Peri´c,Computationoffree-surfaceflowsusingthe
finite-volumemethodandmovinggrids,NumericalHeatTransfer,Vol.
32,No.4,pp.369-384,1997 .
[8] M.Seifollahi,E.Shirani,N.Ashgriz,Animprovedmethodforcalculation
ofinterfacepressureforceinPLIC-VOFmethods,EuropeanJournalof
Mechanics-B/Fluids,Vol.27,No.1,pp.1-23,2008 .
[9] J.Brackbill,D.B.Kothe,C.Zemach,continuummethodformodeling
surfacetension,JournalofComputationalPhysics,Vol.100,No.2,pp.
335-354,1992 .
[10] Y.Renardy,M.Renardy,PROST:   parabolicreconstructionofsurface
tensionforthevolume-of-fluidmethod,JournalofComputationalPhysics,
Vol.183,No.2,pp.400-421,2002 .
[11] B.Lafaurie,C.Nardone,R.Scardovelli,S.Zaleski,G.Zanetti,Modelling
mergingandfragmentationinmultiphaseflowswithSURFER,Journalof
ComputationalPhysics,Vol.113,No.1,pp.134-147,1994 .
[12] D.Gerlach,G.Tomar,G.Biswas,F.Durst,Comparisonofvolume-of-fluid
methodsforsurfacetension-dominanttwo-phaseflows,International
JournalofHeatandMassTransfer,Vol.49,No.3,pp.740-754,2006 .
[13] Z.Wang,A.Y.Tong,sharpsurfacetensionmodelingmethodfor
two-phaseincompressibleinterfacialflows,InternationalJournalfor
NumericalMethodsinFluids,Vol.64,No.7,pp.709-732,2010 .
[14] D.Gueyffier,J.Li,A.Nadim,R.Scardovelli,S.Zaleski,Volume-of-fluid
interfacetrackingwithsmoothedsurfacestressmethodsforthree-
dimensionalflows,JournalofComputationalPhysics,Vol.152,No.2,pp.
423-456,1999 .
[15] A.Q.Raeini,M.J.Blunt,B.Bijeljic,Modellingtwo-phaseflowinporous
mediaattheporescaleusingthevolume-of-fluidmethod,Journalof
ComputationalPhysics,Vol.23 1 , No.17,pp.5653-5668,2012 .
[16] M.M.Francois,S.J.Cummins,E.D.Dendy,D.B.Kothe,J.M.Sicilian,M.W.
Williams,  balanced-forcealgorithmforcontinuousandsharp
interfacialsurfacetensionmodelswithin volumetrackingframework,
JournalofComputationalPhysics,Vol.213,No.1,pp.141-173,2006 .
[17] A.Albadawi,D.Donoghue,A.Robinson,D.Murray,Y.Delauré,Influence
ofsurfacetensionimplementationinVolumeofFluidandcoupled
VolumeofFluidwithLevelSetmethodsforbubblegrowthand
detachment,InternationalJournalofMultiphaseFlow,Vol.53,pp.11-28,
2013 .
[18] M.Sussman,E.G.Puckett,coupledlevelsetandvolume-of-fluid
methodforcomputing3Dandaxisymmetricincompressibletwo-phase
flows,JournalofComputationalPhysics,Vol.162,No.2,pp.301-337,
2000 .
[19] D.Sun,W.Tao,coupledvolume-of-fluidandlevelset(VOSET)method
forcomputingincompressibletwo-phaseflows,InternationalJournalof
HeatandMassTransfer,Vol.53,No.4,pp.645-655 ,2010 .
[20] S.J.Cummins,M.M.Francois,D.B.Kothe,Estimatingcurvaturefrom
volumefractions,Computers structures,Vol.83,No.6,pp.425-434,
2005 .
[21] S.Popinet,Anaccurateadaptivesolverforsurface-tension-driven
interfacialflows,JournalofComputationalPhysics,Vol.228,No.16,pp.
5838-5866,2009 .
[22] F.Denner,D.R.vanderHeul,G.T.Oud,M.M.Villar,A.d.SilveiraNeto,B.
G.vanWachem,Comparativestudyofmass-conservinginterface
capturingframeworksfortwo-phaseflowswithsurfacetension,
InternationalJournalofMultiphaseFlow,Vol.61,pp.37-47,2014 .
[23] D.A.Hoang,V.vanSteijn,L.M.Portela,M.T.Kreutzer,C.R.Kleijn,
Benchmarknumericalsimulationsofsegmentedtwo-phaseflowsin
microchannelsusingtheVolumeofFluidmethod,Computers Fluids,
Vol.86,pp.28-36,2013 .
[24] N.Samkhaniani,A.Gharehbaghi,Z.Ahmadi,Numericalsimulationof
reactioninjectionmoldingwithpolyurethanefoam,JournalofCellular
Plastics,Vol.49,No.5,pp.405-421,2013
[25] E.BerberoviN.P.v.Hinsberg,S.JakirliI.V.Roisman,C.Tropea,Drop
impactonto  liquidlayeroffinitethickness:Dynamicsofthecavity
evolution,TheAmericanPhysicalSociety,Vol.79,No.3,pp.036306(15),
2009 .
[26] M .Sussman,   secondordercoupledlevelsetandvolume-offluid






















252
139415 2

methodforcomputinggrowthandcollapseofvaporbubblesComputPhys
Vol.187,No.1,pp.110-136,2003 .
[27] W.J.Rider,D.B.Kothe,ReconstructingVolumeTracking,J.Comput.Phys,
Vol .141 ,No. pp.112-152,1998 .
[28] S.S.Deshpande,L.Anumolu,M.F.Trujillo,Evaluatingtheperformance
ofthetwo-phaseflowsolverinterFoam,ComputationalScience 
Discovery,Vol.5,No.1,pp.014016,2012 .
[29] F.Xiao,S.Ii,C.Chen,Revisit totheTHINCscheme:  simplealgebraic
VOFalgorithm,JournalofComputationalPhysics,Vol.230,No.19,pp.
7086-7092,2011 .