计算流体力学（传热传质）patankar01

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1、NumericalTransferProcessesE4386MethodsofpredictionExperimentalinvestigation:fullscaleexpensiveandoftenimpossiblemeasurementerrorsonasmallscalemodelsimplifieddifficulttoextrapolateresultsmeasurementerrorsTheoreticalcalculation:analyticalsolutionsexistonlyforafewcasessometimescomplexnumericalsolu

2、tionsforalmostanyproblemModelingvs.experimentationAdvantagesofmodeling:cheapermorecompleteinformationcanhandleanydegreeofcomplexityaslongas…Disadvantagesofmodeling:dealswithamathematicaldescriptionnotwithrealitymathematicaldescriptioncanbeinadequatemultiplesolutionscanexist…andthewinneris…Conse

3、rvationprincipleleadstoageneraldifferentialequation:MathematicaldescriptionoftransferprocessesNatureofcoordinateswithrespecttoxj:1D,2D,3Dwithrespecttot:steadyunsteady(transient,timedependent)one-waycoordinates=>parabolicproblemtwo-waycoordinates=>ellipticproblemDiscretizationmethodsanalytical

4、solutiongivesafunction(continuous)numericalsolutiongivesasetofnumbers(discrete)TxExample:steady1DheatconductionxSIntegrationPWExweDx(dx)w(dx)eDiscretizationTxPWEweTpTwTEDiscretizationequationconductancesheatgenerationSourcetermlinearizationGuidingprinciplesSolutionshouldalwaysbephysicallyrealis

5、ticOverallbalanceoffluxesmustbemaintainedxTexactapproximate,butphysicallyrealisticunrealisticFourbasicrulesRule1.Fluxconsistencyatcontrolvolumefaces“whenafaceiscommontotwoadjacentcontrolvolumes,thefluxacrossitmustberepresentedbythesameexpressioninthediscretizationequationsforthetwocontrolvolume

6、s”Rule2.Positivecoefficients“allcoefficientsamustalwaysbepositive”FourbasicrulesRule3.Negativeslopelinearizationofthesourceterm“WhenthesourcetermislinearizedasS=SC+SPTP,thecoefficientSPmustalwaysbelessthanorequaltozero.”Rule4.Sumoftheneighbourcoefficients“itisrequiredthataP=anbforsituationswhe

7、rethedifferentialequationcontinuestoremainsatisfiedafteraconstantisaddedtothedependentvariable”exampleBackto:steady1Dheatconduction