2008--Rannou G--Lattice-Boltzmann method and immiscible two-phase flow.pdf

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1、LATTICEBOLTZMANNMETHODANDIMMISCIBLETWO-PHASEFLOWAThesisPresentedtoTheAcademicFacultybyGuillaumeRannouInPartialFulfillmentoftheRequirementsfortheDegreeMasterofScienceintheSchoolofSchoolofMechanicalEngineering/PaperScienceandEngineeringGeorgiaInstituteof

2、TechnologyDecember2008LATTICEBOLTZMANNMETHODANDIMMISCIBLETWO-PHASEFLOWApprovedby:Dr.CyrusK.Aidun,AdvisorSchoolofMechanicalEngineeringGeorgiaInstituteofTechnologyDr.S.MostafaGhiaasiaanSchoolofMechanicalEngineeringGeorgiaInstituteofTechnologyDr.MarcK.Smi

3、thSchoolofMechanicalEngineeringGeorgiaInstituteofTechnologyDateApproved:November13,2008ACKNOWLEDGEMENTSIwanttothankmyadvisor,Dr.CyrusAidun.Iamgratefulforhissupportandguidance,whichhashelpedmeateverystepofmyMaster'sthesis.Ithasbeenanhonortoworkunderhim.

4、IwanttothankDr.M.K.SmithandDr.S.M.Ghiaasiaanforacceptingtoserveonmythesiscommitteeandfortheirinsightfulcomments.Finally,Iwouldliketothankmyfamily,forbelievinginmeandsupportingme.iiiTABLEOFCONTENTSPageACKNOWLEDGEMENTSiiiLISTOFTABLESviLISTOFFIGURESviiLIS

5、TOFSYMBOLSixLISTOFABBREVIATIONSxiSUMMARYxiiCHAPTER1INTRODUCTION12LATTICE-BOLTZMANNMODELSFORIMMISCIBLETWOPHASEFLOW5Single-phaselattice-Boltzmannmodel(D2Q9)5Colorfluidmodel6Interparticle-potentialmodel10Free-energymodel13OriginalFree-energymodel14Free-en

6、ergymethodforlargedensityratios16Mean-fieldtheorymodel183POISEUILLETWO-PHASEFLOWANDCONTINUITYISSUEATTHEINTERFACE21Testcase:two-phasePoiseuilleflow21Resultsobtainedwiththecolor-fluidmodel22Resultsobtainedwiththeinterparticle-potentialmodel31Resultsobtai

7、nedwiththefreeenergymodel38ivResultsobtainedwiththemean-fieldtheorymodel44Conclusion4843DIMPLEMENTATIONOFTHECOLOR-FLUIDMODEL49Introduction49Validationofthecode493Dimplementation49Coalescenceoftwosphericalbubbles,freedeformationofacubicbubble50Laplacebu

8、bbletest51Freeriseofabubbleinaquiescentviscousfluid53Conclusion565GENERALCONCLUSION57APPENDIXA:EXPLANATIONOFTHEDISCONTINUITYFORTHECASEρα≠159ρβREFERENCES61vLISTOFTABLESPageTable1:simulationswiththecolor-fluidmodel(BGKcollisionoperator)22