ANSYS-FLUENT-14.5-Population-Balance-Module-Manual

ANSYSFLUENTPopulationBalanceModuleManualRelease14.5ANSYS,Inc.October2012Southpointe275TechnologyDriveCanonsburg,PA15317ANSYS,Inc.iscertifiedtoISO9001:[e-mail](T)724-746-3304(F)724-514-9494CopyrightandTrademarkInformation©2012SASIP,Inc.Allrightsreserved.Unauthorizeduse,distributionorduplicationisprohibited.ANSYS,ANSYSWorkbench,Ansoft,AUTODYN,EKM,EngineeringKnowledgeManager,CFX,FLUENT,HFSSandanyandallANSYS,Inc.brand,product,serviceandfeaturenames,logosandslogansareregisteredtrademarksortrademarksofANSYS,Inc.oritssubsidiariesintheUnitedStatesorothercountries.ICEMCFDisatrademarkusedbyANSYS,Inc.underlicense.CFXisatrademarkofSonyCorporationinJapan.Allotherbrand,product,serviceandfeaturenamesortrademarksarethepropertyoftheirrespectiveowners.DisclaimerNoticeTHISANSYSSOFTWAREPRODUCTANDPROGRAMDOCUMENTATIONINCLUDETRADESECRETSANDARECONFID-ENTIALANDPROPRIETARYPRODUCTSOFANSYS,INC.,ITSSUBSIDIARIES,ORLICENSORS.ThesoftwareproductsanddocumentationarefurnishedbyANSYS,Inc.,itssubsidiaries,oraffiliatesunderasoftwarelicenseagreementthatcontainsprovisionsconcerningnon-disclosure,copying,lengthandnatureofuse,compliancewithexportinglaws,warranties,disclaimers,limitationsofliability,andremedies,andotherprovisions.Thesoftwareproductsanddocumentationmaybeused,disclosed,transferred,orcopiedonlyinaccordancewiththetermsandconditionsofthatsoftwarelicenseagreement.ANSYS,Inc.iscertifiedtoISO9001:2008.U.S.GovernmentRightsForU.S.Governmentusers,exceptasspecificallygrantedbytheANSYS,Inc.softwarelicenseagreement,theuse,duplication,ordisclosurebytheUnitedStatesGovernmentissubjecttorestrictionsstatedintheANSYS,Inc.softwarelicenseagreementandFAR12.212(fornon-DODlicenses).Third-PartySoftwareSeethelegalinformationintheproducthelpfilesforthecompleteLegalNoticeforANSYSproprietarysoftwareandthird-partysoftware.IfyouareunabletoaccesstheLegalNotice,pleasecontactANSYS,Inc.PublishedintheU.S.A.TableofContentsUsingThisManual........................................................................................................................................v1.TheContentsofThisManual................................................................................................................v2.TheContentsoftheFLUENTManuals...................................................................................................v3.TypographicalConventions.................................................................................................................vi4.MathematicalConventions................................................................................................................vii5.TechnicalSupport.............................................................................................................................viii1.Introduction............................................................................................................................................11.1.TheDiscreteMethod.........................................................................................................................11.2.TheInhomogeneousDiscreteMethod...............................................................................................11.3.TheStandardMethodofMoments....................................................................................................31.4.TheQuadratureMethodofMoments................................................................................................42.PopulationBalanceModelTheory..........................................................................................................52.1.TheParticleStateVector....................................................................................................................52.2.ThePopulationBalanceEquation(PBE).............................................................................................52.2.1.ParticleGrowthandDissolution...............................................................................................62.2.2.ParticleBirthandDeathDuetoBreakageandAggregation.......................................................72.2.2.1.Breakage.........................................................................................................................72.2.2.2.LuoandLehrBreakageKernels........................................................................................82.2.2.3.GhadiriBreakageKernels.................................................................................................92.2.2.4.LaakkonenBreakageKernels...........................................................................................92.2.2.5.ParabolicPDF................................................................................................................102.2.2.6.GeneralizedPDF............................................................................................................102.2.2.7.Aggregation........................................................................................