A three-dimensional volume of fluid & level set (VOSET) method for incompressible two-phase flow

Athree-dimensionalvolumeof uid&levelset(VOSET)methodforincompressibletwo-phase

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KongLinga,Zhao-HuiLia,Dong-LiangSunb,Ya-LingHea,Wen-QuanTaoa,

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KeyLaboratoryofThermo-FluidScience&EngineeringofMOE,SchoolofEnergy&PowerEngineering,Xi’anJiaotongUniversity,ChinaSchoolofMechanicalEngineering,BeijingInstituteofPetrochemicalTechnology,China

articleinfoabstract

Thispaperpresentsathree-dimensionalVOSETmethod,whichcombinesbothadvantagesoftheVOFandlevelset.Thebasicideaisthesamewiththatin2DVOSET,butnewmethodsareproposedtodealwithnewgeometricproblemsinthreedimensions.Aniterativeroot- ndingmethodisusedforimplementingPiecewiseLinearInterfaceConstruction(PLIC)inthreedimensions.Aniterativegeometricmethodispresentedtocalculatethelevel-setfunction.Thefeasibilityandaccuracyofthismethodareanalyzedbysomeclassicaltestproblems.Combiningtheuseofprojectionmethodthatsolvesthe ow eld,the3DVOSETisadoptedtosimulatealiquiddambreakproblemandasingle-bubblerisingproblem.Ournumericalresultsarefoundtobeingoodaccordancewiththoseinpreviousstudies.

Ó2015ElsevierLtd.Allrightsreserved.

Articlehistory:

Received30September2014

Receivedinrevisedform2May2015Accepted13June2015

Availableonline18June2015Keywords:VOF

Levelset

DistancefunctionTwo-phase ow3DVOSET

1.Introduction

Flowwithmovinginterfacescanbewidelyfoundinthedailylifeandindustrialprocesses,suchasmovingofdropletsandbubblesingas–liquid ow,ashdepositionontubesingas–solid owsandphasechangeheattransfer.Inrecentyears,withthefastdevelopmentofcomputer’sperformance,directnumericalsimula-tionisbecominganincreasinglyimportanttoolforstudyingthesekindsofproblems.

Inthepastdecades,anumberofdifferentmethodsweredevel-opedfordealingwithmovinginterfaces.Amongthesemethods,vol-umeof uid(VOF)[1]andlevelset[2]wereprobablythemostwidelyusedones.VOFwasproposedbyHirtandNichols[1].Inthismethod,acolorfunctionCrangingfrom0to1,whichwecallVOFfunctionhere,isusedtoidentifythetwophasesdividedbytheinter-face.TheVOFfunctiondenotesthevolumeproportionofonephaseinacomputationalcell.C=1demonstratesthatthiscellis lledwithonephaseandC=0meansthatthecellis lledwiththeotherphase.IfCvaluesbetween0and1,thecellisregardedtocontainbothphases.ThemajoradvantageofVOFisthatthetotalmassconserva-tionofthetwophasescanbekeptverywell.However,theinterfacenormalandcurvaturecannotbesolvedaccuratelyinaconvolvedschemeduetothefactthattheVOFfunctionisastepfunction,anditwillproducelargenumericalerrorinsurfacetension.LevelsetmethodwasproposedbySethianandOsher[2].Inthismethod,Correspondingauthor.Tel.:+8602982669106.

E-mailaddress:wqtao@mail.xjtu.edu.cn(W.-Q.Tao).

doc.xuehai.net uid.2015.06.0180045-7930/Ó2015ElsevierLtd.Allrightsreserved.

acontinuousfunction/namedlevel-setfunctionisusedtoidentifytheinterfaceandthetwophases.Thewholecomputationaldomainisdividedintotwopartsaccordingtothesignofthelevel-setfunc-tion.The rstpartreferstotheareaoccupiedbythe rstphasewhereitsatis es/>0,and/<0representsthelocationintheotherphase.Theinterface,therefore,isdenotedbythezerocontouroflevel-setfunction.Inthelevelsetmethod,interfacenormalandcurvaturecanbecomputedmuchmoreaccuratelyduetotheuseofthecontinuousfunction.Ontheotherside,however,thelevelsetmethodsuffersfromtheweaknessofloss/gainofmass.

Ascanbeseenthat,bothVOFandlevelsethavedisadvantages,butindifferentaspects.Therefore,thecombinationofthetwomethodscouldbeagoodchoiceforimprovement.In2000,SussmanproposedacoupledlevelsetandVOF(CLSVOF)method[3],whichsuccessfullycombinesbothadvantagesofVOFandLS.However,theadvectionequationsfortheVOFandlevel-setfunctionsbothneedtobesolved,whichmakesthismethodmorecomplicated.Asasimplerapproach,acoupledmethodofvolume-of- uidandlevelset(VOSET),whichcombinestheadvantagesofVOFandlevel-setaswell,wasproposedbySunandTao[4].Inthismethod,onlytheadvectionequationoftheVOFfunctionissolved,andthelevel-setfunctioniscomputedfromtheVOFfunctionindepen-dently.However,SunandTao’smethodisdevelopedonlyintwodimensions.Recently,Sun[5]hasextendedVOSETtothreedimensions.However,Sun’smethodneedstousemuchmoreclassi cationsondifferentinterfaceshapes.OntheextensionofVOSETto3D,thepresentauthorstrysimplerapproaches.

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