LATTICE BOLTZMANN SIMULATION OF MELTING PHENOMENON

LATTICEBOLTZMANNSIMULATIONOFMELTINGPHENOMENONWITHNATURALCONVECTIONFROMANECCENTRICANNULUSbyMahmoudJOURABIAN,MousaFARHADI*,AhmadAliRABIENATAJDARZI,andAbbasABOUEIFacultyofMechanicalEngineering,BabolUniversityofTechnology,Babol,I.R.ofIranOriginalscientificpaperDOI:10.2298/TSCI110510012JInthepresentstudy,adouble-populationthermallatticeBoltzmannmethodwasappliedtosolvephasechangeproblemwithnaturalconvectioninaneccentrican-nulus.ThesimulationofmeltingprocessfromaconcentricallyandeccentricallyplacedinnerhotcylinderinsideanoutercoldcylinderwithPrandtlnumberof6.2,Stefannumberof1,andRayleighnumberof105wascarriedoutquantitatively.Itwasfoundthatthepositionoftheinnercylinderinsidetheoutercylindersignifi-cantlyinfluencetheflowpatternsincludingthesizeandshapeoftwoformedvor-texes.Itisalsoobservedthatthemaximumofliquidfractionsoccurswherethein-nercylinderismountedatthebottomofoutercylinder.Keywords:latticeBoltzmannmethod,melting,solid-liquidphasechange,Bhatangar-Gross-Krookcollision,naturalconvection,phasechangematerialIntroductionNumericalmodelingoftransportphenomenonassociatedwithphasechange(meltingandsolidification)hascontinuedtobeasignificantresearcharea,owingtothefactthatmeltingplaysanimportantroleinmanyindustrialapplications,suchaswelding,metalcasting,andther-malenergystorage(TES).Investigationofmeltingprocesswithnaturalconvectioninarectangularcavityhasbeenconductedexperimentally[1-3],theoretically[4-5],andnumerically[6-7].Similartothisstudy,manypapershaveconcentratedonthemeltingofphasechangematerials(PCM)thatareencapsulatedinanannulusasamoresophisticatedmodelforlatentheatthermalstoragesystems(LHTSS).Freeconvection-controlledmeltingofaPCMinsideacylindrical-horizontalannuluswassimulatednumericallybyNgetal.[8].ItwasconcludedthatbyincreasingtheRayleighnumberthemeltingratewasaugmented.Furthermore,meltingofPCMinthebottomhalfoftheannuluswasveryineffectivebecausemostofthechargedenergywastransferredtothetophalfoftheannulusbytheconvectiveflow.BetzelandBeer[9]investi-gatedmeltingandsolidificationprocessesofanunfixedPCMencapsulatedinahorizontalcon-centricannulusbyexperimentalmethodsandacombinedanalyticalandnumericaltechniques.Inthemeltingprocess,thinliquidfilmappearedbetweentheun-meltedPCMandtheheatedwallsandtheconductionplayedthemainmodeofheattransfer.Attheupperpositionsconvec-tionheattransfercausedmeltingalthoughthemeltingratesweresmall.ConvectionmeltingofapurePCMencapsulatedinaconcentrichorizontalannuluswithtwodifferentconfigurationswasinvestigatednumericallybyKhillarkaretal.[10].Liuetal.[11]examinedexperimentallyJourabian,M.,etal.:LatticeBoltzmannSimulationofMeltingPhenomenon...THERMALSCIENCE:Year2013,Vol.17,No.3,pp.877-890877*Correspondingauthor;e-mail:[e-mail]ricacidinanannulusenhancedbyinsertingfins.Experimentalandnu-mericalstudyofparaffinwaxmeltingintheannulusoftwocoaxialcylinderswascarriedoutbyDuttaetal.[12].Itwassaidtheconvectionheattransferdominatedinthemeltingphaseandtheeccentricityplayedakeyroleforthenetcirculationoftheliquidphase.TombarevicandVusanovic[13]performedthenumericalmodelingoficemeltinginhorizontalcylindricalannu-lususingmodifiedenthalpymethod.Theinfluenceofinnerpipetemperatureontheshapeofphasechangefront,meltingrateandflowandtemperaturefieldswasstudied.NumericalstudyofmeltingofN-eicosaneinsideahorizontalannuluswascarriedoutbyRabienatajetal.[14].Resultsshowedthattheconductionwasprevailingattheearlystagesofprocess.However,aftersomeelapsedtimes,convectiveheattransferdominatedattophalfofannuluswhileconductionheattransferremainedprevailinginthebottomofheatedcylinder.Inthesolid-liquidphasechangeproblem,thecomplexcouplingwhichexistsbetweenthefluidflowandthemovingboundarydeterminestheexactpositionofsolid-liquidinterface.Inordertoovercomethisdifficulty,differentschemeshavebeensuggestedintheliterature.Bertrandetal.[15]utilizedthefront-trackingmethodforaneasyproblemwherephasechangeisdrivenbylaminarthermalconvectioninthemelt.Theyfoundthatthismethodisbetteradaptedforaproblemoffusionofapuresubstance.Thelevelsetmethodisadifferentmethodtodealwithsolid-liquidinterfaceandtoavoidtheasymptoticanalysisusedinphasefieldmodels.Toexplicitlytracktheinterfacegrowth,TanandZabaras[16]appliedafronttrackingapproachbasedonthelevelsetmethod.Theadaptivegridmethodisanotherwaythathasbeensuccess-fullyexaminedforsimulationofviscousandinviscidflowsbyJinandXu[17].Theyfoundthatforunsteadyflowcomputation,theuseofadaptivemeshhasobviousadvantageintermsoftheaccuracyandefficiencyincomparisonwiththemethodswithstaticmeshpoints.Boettingeretal.[18]employedthephase-fieldmethodformodelingofsolidification.Thismethodappliesaphase-fieldvariableandacorrespondinggoverningequationwhichdescribe,respectively,loca-tionofaliquidorsolidnodeandstateinamaterialasafunctionofpositionandtime.Itissignifi-canttoknowthatgoverningequationsfortheheatandsolutecanbealsosolvedwithouttrack-ingtheliquid-solidinterface.Inrecentyears,methodsbasedonlatticeBoltzmannequation(LBE)hasrecentlybe-comeanalternativeforsimulatingfluidflowsinchannels[19],curvedbo