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1、DIFFERENTIALANALYSISOFFLUIDFLOWA:MathematicalFormulation(4.1.1,4.2,6.1-6.4)B:InviscidFlow:EulerEquation/SomeBasicPlanePotentialFlowsBasic,PlanePotentialFlows(65(6.5-67)6.7)C:ViscousFlow:NavierViscousFlow:Navier-StokesEquationStokesEquation(6.8-6.10)Introduc
2、tionDifferentialAnalysisòThereTherearesituationsinwhichthedetailsoftheflowaresituationsinwhichthedetailsoftheflowareimportant,e.g.,pressureandshearstressvariationalhilongthewing….òTherefore,,pweneedtodeveloprelationshippthatapppplyyatapointoratleastinaverys
3、mallregion(infinitesimalvolume)withagivenflowfield(infinitesimalvolume)withagivenflowfield.òThisapproachiscommonlyreferredtoasdifferentialanalilysis.òTheesouososolutionsoftheequoseeequationsareratheerddcifficuult.òComputationalFluidDynamic(CFD)canbeappliedt
4、ltocomplexflflbowprobllems.PARTAPARTAMathematicalFormulationMathematicalFormulation(Sti(Sections44114261.1.1,4.2,6.1-64)6.4)FluidKinematics(41142)FluidKinematics(4.1.1,4.2)òKinematicsinvolvesposition,velocityandaccelileration,notfforces.òkineeatcsoteoto:mat
5、icsofthemotion:velocityandaccelerationofthefluid,andthedescriptionandvisualizationofitsmotiondescriptionandvisualizationofitsmotion.òTheanalysisofthespecificforcenecessarytoprodtducethhtemotiion-thdthedynamicsoffththemotion.4.1TheVelocityFieldAfieldrepresen
6、tation–representationsoffluidppparametersasfunctionsofspatialcoordinateòthevelocityfieldV=u()x,y,z,ti+v(x,y,z,t)j+w(x,y,z,t)krdruurA=VAdtV=V(x,y,z,t)1(222)2V=V=u+v+wAchangeinvelocityresultsinanaccelerationwhichAchangeinvelocityresultsinanaccelerationwhichma
7、ybeduetoachangeinspeedand/ordirection.4.1.1EulerianandLagggrangianFlowDescriptionsòEulerianmethod:thefluidmotionisgivenbycompletelyprescribingthenecessarypropertiesasfunctionsofspaceandtime.òFromthismethod,weobtaininformationabouttheflowintermsinformationab
8、outtheflowintermsofwhathappensatfixedpointsinspppaceasthefluidflowspastthosepoints.òLagrangianmethodLagrangianmethod:folloingfollowingindividualfluidparticlesastheymoveaboutanddetermininghowthefluidabo
