ComputationalfluiddynamicswithheatandmasstransferE4465FundamentalsoftransferprocessesConservationofmassConservationofmomentumConservationofenergyConservationofchargep-v-trelationsturbulenceboundarylayerapproximationsNumericaltechniquesfortransferprocessesDiscretizationmethodsfor:conductionconvectivediffusionBasicequationsGridNonlinearityBoundaryconditionsTransientsRelaxationCalculationofthe:flowfieldtemperaturedistributionconcentrationfieldVehicle-CFDComputationalFluidDynamics(CFD)isadisciplinethatsolvesasetofequationsgoverningthefluidflowoveranygeometricalconfiguration.Theequationscanrepresentsteadyorunsteady,compressibleorincompressible,andinviscidorviscousflows,includingnonidealandreactingfluidbehavior.Theparticularformchosendependsontheintendedapplication.Thestateoftheartischaracterizedbythecomplexityofthegeometry,theflowphysics,andthecomputertimerequiredtoobtainasolution.ApplicationsinPowerIndustryHeatfluxdistributioninaboilerHeattransferandpressurelossinaheatexchangerFlow,heattransferanderosioninacondenserPerformanceofagasturbinecombustionchamberandflowthroughagasturbinetestcellFlowthroughahighpressuresteamturbinevalveHazardanalysisVariousapplicationsAnimationshowingtheeffectsofbicycledrafting.,datacourtesyFluentInc.Hypervelocityimpactstudyforthespaceshuttle.DatacourtesyNASAJohnson.Animationofamodelofsubmarine.CourtesyFLUENT/UNSfromFluent,Inc.Simulationofaracingyachtkeeldesign.CourtesySiliconGraphics.CarsFourviewsofcylinderintakeflow.DatacourtesyFordMotorCo.Sideandtopviewsoffuelsprayinadieselengine.Sequencefromacarinawindtunnelanimation.DatacourtesyFluent,Inc.Animationofflowoveracarinawindtunnel.DatacourtesyFordMotorCo.Twoviewsofacarcrash.CivilandEnvironmentalEnvironmentalImpactAssessment

FloodAnalysisandDamBreachSimulationHydro-PowerSystemsWind

Interaction

with

Structures

PollutantDispersalandAirQuality

FireandSmokeSpread

HeatingandAirConditioning

WasteWaterTreatmentandWaterQuality

OilandGasFluidsloshingintankers

DrillingoperationsandequipmentsimulationFluidflowaroundplatforms

WindandwaveloadingonstructuresFireriskandhazardanalysis

Industrialseparationprocesses

TransportationAerodynamicsofAirplanesandtrainsCarsandtrucksMotorcyclesHydrodynamicsofshipsandsubmarinesDesignofcarcomponentsexhaustvalveModelingofsupersonic/hypersonicflowPassengersafetyanalysis

FuelsloshinganalysisOtherapplicationsFlowthroughporousmediaMixingvesseldesignCyclonedesignMetalcastingTurbinebladedesignPolymerizationreactorvesseldesignCoatingprocessesInkjetdesignCoolingofelectroniccomponentsNumericalTransferProcessesE4386MethodsofpredictionExperimentalinvestigation:fullscaleexpensiveandoftenimpossiblemeasurementerrorsonasmallscalemodelsimplifieddifficulttoextrapolateresultsmeasurementerrorsTheoreticalcalculation:analyticalsolutionsexistonlyforafewcasessometimescomplexnumericalsolutionsforalmostanyproblemModelingvs.experimentationAdvantagesofmodeling:cheapermorecompleteinformationcanhandleanydegreeofcomplexityaslongas…Disadvantagesofmodeling:dealswithamathematicaldescriptionnotwithrealitymathematicaldescriptioncanbeinadequatemultiplesolutionscanexist…andthewinneris…Conservationprincipleleadstoageneraldifferentialequation:MathematicaldescriptionoftransferprocessesNatureofcoordinateswithrespecttoxj:1D,2D,3Dwithrespecttot:steadyunsteady

(transient,timedependent)one-waycoordinates=>parabolicproblemtwo-waycoordinates=>

ellipticproblemDiscretizationmethodsanalyticalsolutiongivesafunction(continuous)numericalsolutiongivesasetofnumbers(discrete)TxExample:steady1DheatconductionxSIntegrationPWExweDx(dx)w(dx)eDiscretizationTxPWEweTpTwTEDiscretizationequationconductancesheatgenerationSourcetermlinearizationGuidingprinciplesSolutionshouldalwaysbephysicallyrealisticOverallbalanceoffluxesmustbemaintainedxTexactapproximate,butphysicallyrealisticunrealisticFourbasicrulesRule1.Fluxconsistencyat controlvolumefaces“whenafaceiscommontotwoadjacentcontrolvolumes,thefluxacrossitmustberepresentedbythesameexpressioninthediscretizationequationsforthetwocontrolvolumes”Rule2.Positivecoefficients“allcoefficientsamustalwaysbepositive”FourbasicrulesRule3.Negativeslope linearizationofthe sourceterm“WhenthesourcetermislinearizedasS=SC+SPTP,thecoefficientSPmustalwaysbelessthanorequaltozero.”Rule4.Sumoftheneighbour coefficients“itisrequiredthataP=

anb

forsituationswherethedifferentialequationcontinuestoremainsatisfiedafteraconstantisaddedtothedependentvariable”exampleBackto:steady

1DheatconductionBackto:steady

1DheatconductionPWExweDx(dx)w(dx)eDiscretizationTxPWEweTpTwTEDiscretizationequationconductancesheatgenerationSourcetermlinearizationforexamplewhenS=f(T)Nonlinearityforexamplewhenk=f(T)theanswerisiterationInterpolationof

interfacialconductivityPExwe(dx)e(dx)e+(dx)e-Firstguess:Interpolationof

interfacialconductivityrememberallweneedisthefluxInterpolationof

interfacialconductivityrememberthefirstguess:for:whichoneiscorrect?GridspacingUniformeasytoset-upcomputationallyexpensiveNon-uniformhardertoset-upneedsiterationcomputationallyeconomicalBlockgrids?Multi-grids?Boundaryconditions1.Givenboundarytemperaturesimple2.Givenboundaryheatflux a)asaconstantb)specifiedviaa

heattransfercoefficientandthetemperatureofthesurroundingfluidBoundaryconditionsPWEIBiIBDx(dx)iiqBqiSBoundaryconditionsIBDx(dx)iiqBqiSBoundaryconditionsifqBspecifiedasaconstantthen:BoundaryconditionsifqBspecifiedviaa

heattransferhcoefficientandthetemperatureofthesurroundingfluidTf:SolutionofthelinearalgebraicequationsPossibilitiesIterationGaussianeliminationTri-Diagonal-Matrix-AlgorithmTDMAPWE1i-1ii+1NchangeofnotationTDMAPWE1i-1ii+1Nwhathappenswhenaboundarytemperatureisgiven?TDMAPWE1i-1ii+1NTDMAPWE1i-1ii+1NTDMAalgorithmCalculate:

P1=b1/a1andQ1=d1/a1

UserecurrencerelationstogetPiandQifori=2,3…N.SetTN=QNUserecurrencerelationstoget

Ti=PiTi+1+Qifori=N-1,N-2…3,2,1

toobtain TN-1,TN-2,…T3,T2,T1.Unsteady1Dheatconductionsteady:unsteady:(transient)PWExweDx(dx)w(dx)etIntegrationTxPWEweTpTwTEintegratewithrespecttox:integratewithrespecttot:TimeintegrationrepeatforpointsEandW:tTExplicitvsimplicitf=0 explicitschemef=0.5 semi-implicit(Crank- Nicolson)schemef=1 fullyimplicitschemeTpoldtTpnewt+Dtf=0f=1f=0.5Explicitschemefor:inordertogiverealisticsolutionsCrank-NicolsonschemecangiveunrealisticsolutionsImplicitschemealwaysgivesrealisticsolutionsUnsteady2-Dheatconductionxyz=1PWEweDxNSnsDyDiscretizedunsteady2-DheatconductionequationUnsteady3-DheatconductionequationDiscretizedunsteady3-DheatconductionequationSolutionoftheequationsdirectmethodGauss-Seidelmethodline-by-linemethodalternating-directionimplicitstronglyimplicitprocedureRelaxationoverrelaxationunderrelaxationRelaxationrelaxationthroughinertia:Convectionanddiffusionassumeaknownflowfieldgeneralize Tandkas

FandGcontinuityandmomentumequations: