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1、Anenergypreservingformulationforthesimulationofmultiphaseturbulent?ows.AbstractInthismanuscriptweproposeanenergypreservingformulationforthesimulationofmultiphase?ows.Thenewformulationreducesthenumericaldi?usionwithrespecttopreviousformulationsdealingwithmultiplephases,whichma
2、kesthismethodtobeespeciallyappealingforturbulent?ows.Inthisworkwediscusstheaccuracyandconservationpropertiesofthemethodinvariousscenarioswithlargedensityandviscosityjumpsacrosstheinterfaceincludingsurfacetensione?ects.1IntroductionNowadaysthesimulationofturbulent?owsistheobje
3、ctofintenseresearch.Althoughnumericaltechniquesandmodelshavebeenalreadywidelyinvesti-gatedintheliteratureforsinglephase?ows,currentstudiesarestillfarfromacompleteunderstandingofrealprocessesencounteredinacountlessnumberofapplicationsinvolvingmultiplephases,suchasrocketengines
4、injectors,dieselenginesorchemicalprocess.Whentwoormoredi?erentphasesarepresentinthesystemwecandistinguishnotonlyarangeofcharacteristiclength-scalesrelatedtotheturbulentnatureofthe?ow,butalsoarangeofsizesandshapesofeachofthephasespresentinthesystem.Thisfactsigni?cantlyincrease
5、sthecomplexityofthesimulationsrequiredtoinvestigatesuchtypeofproblems,whichrequireacontinuousdevelopmentandoptimizationofthenumericaltech-niquesandmodels.Thescienti?ccommunityhasmadeanimportante?ortdevelopingmodelsformultiphase?owswhenoneofthephasescanbeconsid-eredasdisperse(
6、onlysomeexamplescanbefoundin[27,11,29]).However,theextensionandevaluationnumericalmodelstosituationswherethestruc-turesoftheinterfacesiswellcapturedislessproli?c.Thedevelopmentofthesemethodsisimportantinordertoevaluatetheimportanceofturbulenceinpro-cesswhereanyofthemultipleph
7、asespresentonitcanbeconsideredasdisperse.Numericaltechniquesusedforthesimulationofturbulent?owsandmulti-phase?owshavebeentraditionallydi?erent.Ononehand,numericalschemestypicallyusedforthesimulationofturbulent?owsmustpayanespecialatten-tiontotheconservationofglobalpropertiess
8、uchasenergy.Becauseweusuallywanttosolveforproblemswherethesmallestsc
