北航工程流体力学课件(王洪伟).pdf

北航工程流体力学课件(王洪伟).pdf

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1EngineeringFluidMechanicsSchoolofEnergyandPowerEngineering20142Textbook:

气体动力学基础王新月，陆利蓬等“FluidMechanics”FrankM.WhiteReferences:

气体动力学基础潘锦珊，单鹏等Grades:

Assignments:

20%Inclassdiscusses&quizs:

10%Midtermexam:

30%（Openbooks）Finalexam:

40%（Closebooks）3Chapter1Introduction（5hours）Chapter2PressureDistributioninaStaticFluid（3hours）Chapter3IntegralRelationsforaControlVolume（12hours）Chapter4DifferentialRelationsforaFluidParticle（8hours）Chapter5FlowPastImmersedBodies（6hours）Chapter6ViscousFlowinDucts（2hours）Schedule4Chapter1Introduction1.1PreliminaryRemarksAlmosteverythingonthisplaneteitherisaFLUIDormoveswithinornearaFLUID.SoccerSoccerPlumePlumeJupiterJupiterTacomaTacomaOceanOceanFrankM.WhiteSmokeSmoke5Howdoesanaircraftfly?

Aircrafts&EnginesFluidMechanicsisthestudyoffluidandeffectsofthefluidupontheboundaries.Thrust?

6Asolidcanresistastressbyastaticdeformation.Forliquidorgas?

Whatisafluid?

CompressionCompressionTensionTensionShearShearAfluidcannotresistashearstressbyastaticdeformation.Afluidisasubstancethatcontinuallydeforms（flows）undershearstressesappliedtoit.7Isitasolidoraliquid?

Canafluidinmotionresistashearstress?

Howaboutthis?

SurfacetensionSurfacetension81.2SomePropertiesofFluidsWhenafluidissheared,itbeginstomove.Subsequently,apairofforcesappearontheshearsurface,whichresiststheshearmotionofthefluid.Thisiscalledviscosity.

（1）Viscosity（粘性）VelocitygradientVelocitygradientNewtonianlawofviscosity（Newtonianlawofviscosity（牛顿粘性定律，牛顿内摩擦定律）ShearstressShearstressThiskindoffluidiscalledlinearfluidorNewtonianfluid.（牛顿流体）:

Coefficientofviscosity:

CoefficientofviscosityMovingwallMovingwallStaticwallStaticwalluyContinuousdeformation（Flow）Continuousdeformation（Flow）9ThenatureofviscosityConnectedlooselyConnectedtightlyNotconnectedConnectedlooselyConnectedtightlyNotconnectedIceWaterVaporIceWaterVaporAllofthethreegeneratesshearstressinmotion.Forsolid,theshearstressiscalledfriction.FN101

（1）Forgases:

Transportofmomentum（Transportofmomentum（动量输运）Forliquids:

Cohesion（Cohesion（结合力）Doesviscosityvarywithpressureortemperature?

Similar（butnotsame）tothefrictionforcebetweentwosolids.Molecularscollidewitheachother.TwhenTwhen11Mostliquidflowsaretreatedasincompressible.ErnstMach（1838-1916）ErnstMach（1838-1916）（3）Compressibility（压缩性）RTp

（2）StateRelationsforGasesR=287.06forairPerfectgasLaw（完全气体状态方程）InaflowIfkeepsconstantTheflowisincompressible.IfchangesTheflowiscompressible.MachnumberMachnumberGasflowscanalsobetreatedasincompressiblewhenMa0.3.121.3ForcesonaFluidPerunitarea（单位面积）stress（N/m2）Perunitmass（单位质量）g（m/s2）Actsthroughoutthevolumeofabody.Theforcesonthisduckling?

GravityBuoyancyDrivingforceResistanceBodyforcePressureFrictionSurfaceforceActsonthesidesurfacesofabody.InertiaElectromagnetic131.4TheFluidasaContinuum（连续介质）DensityLargeenoughinmicroscope;Smallenoughinmacroscope.Sodifferentialcalculuscanbeusedtoanalyzethesubstance.ContinuumContinuumMolecularMolecularV0VElementalvolume（Elementalvolume（流体微团/质点）0VVmVVlim039mm10airat1atmcontainsmolecules.7103141.5TwoDifferentPointsofViewinMechanicsLagrangianview（拉格朗日法）Followsanindividualparticle,appropriatetosolidmechanics.Concerningwiththefieldofflow,appropriatetofluidmechanics.TheEulerianview（欧拉法）Findingforces15Flowclassification（流动分类）InEulerianviewpoint,anypropertyisfunctionofspaceandtime.InCartesiansystem（直角坐标系），itcanbeexpressedas:

Functionofspace:

1D,2D,3D）,（tzyxEulerianvariablecomponent（欧拉变量）tzyx,:

Functionoftime:

0t0tSteady（定常）Unsteady（非定常）16Apathlineisthepathtraversedbyagivenfluidparticles.Whatisapathline?

1.6Pathline（迹线）,Streamline（流线）&Flowfield（流场）17Whatisastreamline?

Astreamlineisthelineeverywheretangenttothevelocityvectoratagiveninstant.Streamline=PathlineInsteadyflowInunsteadyflowStreamlinewillnotintersect,Exceptforsingularitypoint（奇点）,whereV=0.2

（2）18Streamsurface（流面）andStreamtube（流管）Streamsurface:

Streamtube:

Noflowpassthroughastreamsurfaceorthewallofastreamtube.Noflowpassthroughastreamsurfaceorthewallofastreamtube.Flowfield（流场）Acollectionofstreamlinespassingthroughacurvewhichisnotastreamline.Aclosedcollectionofstreamlines.Aflowfieldreferstothespacetimedistributionsoffluid.19Streamlineequation（流线方程）Findstreamlinefromthegivenvelocity.dtVdsvdyudxwdzvdyudxdtdsV（2D）（3D）atinstantt）（xfy）,（yxfzor?

dtdxudtdyv）,（yxfV）（xfy?

20Example1.1Givensteady2Dvelocityu=kx,v=-ky,wherekisapositiveconstant.Computeandplotthestreamlinesoftheflow,includingdirection.IntegratingHyperbolasHyperbolas（双曲线）CyxlnlnSolution:

vdyudxkydykxdxydyxdxCxyAtthepointo:

0,0yx0,0vuxyoDirection?

Singularitypoint（saddleSingularitypoint（saddle鞍点）0vuA12.5（2.5）1Chapter2PressureDistributioninaStaticFluid2.1IntroductionBlaisePascal（1623-1662）Archimedes（285-212BC）BlaisePascal（1623-1662）Archimedes（285-212BC）2Pressureistheonlysurfaceforce,andisbalancedbybodyforce.FluidMechanicsFluidStaticsFluidDynamicsAerodynamicsWhenfluidisatrest2mNPa2cmkgatmPSImmHgOmmH2barAtanypoint,pressureisindependentoforientation.AFpAlim03Pressureisindependentoforientation.Verification0zWhenppppnzxnpzxzxzpxp（up）gInxdirection:

sin）sin/（zpzpnxnxppPressureisbalancedbybodyforcezgppnz21WhenfluidisatrestNoshearstressPressureisbalancedbyitselfPressureisindependentoforientationatapoint4Consideracubicfluidelementinastaticfluid,pressureatthecenterisp,bodyforcesarekZjYiXR2.2EquilibriumofaFluidElementX,Y,Zarebodyforcesperunitmass（m/s2）2dxxpp2dxxpppdxdydzXdydzdxxpp2dxdydzdydzdxxpp20XdxdydzXxpxFxyz5XxpYypEulerEquilibriumEquations（1775）Pressureincreasesinthedirectionofbodyforce.Rp）（ZdzYdyXdxdpSurfacesinfluidwithsamepressure,verticaltobodyforceeverywhere.Equipressuresurface（等压面）0dpZzpLeonhardEuler（1707-1783）LeonhardEuler（1707-1783）3（0.5）62.3PressureDistributionUnderGravity）（ZdzYdyXdxdpZdzdpgdz）（gZCgzp0zz0pp00gzpC）（00zzgppghpp0hp0BoundaryCondition:

EulerEquilibriumEquations:

z0zhxzPascalsbarrelPascalsbarrel77ghpp0PressureatfreesurfacePressureduetoweightontopPressureatfreesurfacePressureduetoweightontophp0pghppA0Absolutepressure（绝对压力）ghpppG0Gaugepressure（表压力）Relativepressure（相对压力）21pppAtmosphereAtmosphereatmpkm7.03atmpkm3.09atmpkm05.0208AAghdAApdFF0sinyhdAghppdAdF）（0AydAgApFsin0AydAyAxdAxAcAc,Centerofform（形心）Centerofform（形心）AygApcsin02.4HydrostaticForceonFlatandCurvedSurfacehB0pAghpFc）（0AtpointBpressureattheplatecenterpressureattheplatecenterIstheactingpointofforceFatcenterofform?

DhDhcC92.5.1UniformLinearAcceleration（恒加速直线运动）x2.5FluidinrigidbodymotionTheshapeoffreesurface?

aX=-ag10gdzdxaxBoundarycondition:

0,0ppzx）（0gzxappxAtfreesurfacexgazxEquipressuresurfaceCxgazxEulerEquilibriumEquations）（ZdzXdxdpazgxaxxa0ppThefreesurfaceisflatverticaltototalbodyforce.11Acupofbeeris7cmdeepatrest,willitspilloutwhileax=7m/s2?

Example2.1cmDz14.2tan2gaxtanSolution:

AAghp）1010（3mkgPa906）0214.007.0（8.91010Itwillnotspillout!

Acm6cm7cm3g27smaxxazPressureofpointA?

12Discussion:

DrawthefreesurfacewhenthepressureatpointBisatmosphere.BB

（1）

（2）xa13xX2yY2gZ）（ZdzYdyXdxdpyx2.5.2RigidBodyRotation（恒速旋转）（22gdzydyxdxdpCgzyxp）2121（2222Cgzr222100gzpC00:

0ppzzrTheshapeofthesurface?

220021）（rzzgpp0z1402221zrgzFreesurface：

0ppPressureatpointA?

220021Rgzpp0,zRr220021Rgzpp0zyx220021）（rzzgppParaboloid（Paraboloid（抛物面）orAZRA24（1.5）1SomeflowproblemsMostflowproblemsinthenatureisthreedimensional.Alotofthemcanberegardedasonedimensional.BlowBlowNaturewaterNaturewaterShuttlelaunchingShuttlelaunchingSuctionSuctionChapter3IntegralRelationsforaControlVolume3.1PreliminaryRemarks1Dor3D?

2Aerodynamicdrag?

surfaceAFFdAtVmVmF21）（）（IntegralapproachDifferentialapproachIntegralapproachDifferentialapproach1Dintegralapproachisveryusefulforengineeringproblems.1V2V3tVmVmF21）（）（1V2VinoutWhatisthemassandtime?

System:

Anarbitraryquantityofmass.（LagrangeViewLagrangeView）3.2System（体系）vsControlVolumes（控制体）Followseveryfluidparticleandaddsalltheimpactsup.ControlVolume（CV）:

Aspecificregionwithopenboundaries.（EulerianviewEulerianview）SelectacontrolvolumeandfindnetforceusingNewtonssecondlaw.4BasicLawsforaSystemBasicLawsforaControlVolumeTheReynoldsTransportTheorem（雷诺输运定理）TheboundaryoftheControlVolume（CV）iscalledControlSurface（CS）Mass,momentumandenergyareallowedtocrosstheCS.FixedCVmovingCVdeformingCVFixedCVmovingCVdeformingCV53.3TheReynoldsTransportTheorem（雷诺输运定理）tt+dtInflowInflowOutflowOutflowControlVolumeControlVolumeSystemSystemFlowoutoftheCVFlowoutoftheCVFlowintotheCVFlowintotheCV6Lettobeanypropertyoffluiddtdcvdttdttcvcv）（）（）（）（ttscvinoutscvdddttdtt）（）（）（）（dttdddttdtdsinoutscv）（）（）（）（dtdddttdttinoutss）（）（）（）（dtdddtdinouts）（）（canbemass,momentum,orenergyCVSystemCVSystemInflowInflowOutflowOutflow7dtdddtddtdinoutcvs）（）（Forsteadyflow:

0dtdcvdtdddtdinouts）（）（dmdTheamountofperunitmass1Dflow）（xoutoutdmd）（）（outAdx）（outAVdt）（xdxAVRTTforsteadyflowReynoldsTransportTheoremRTTforsteadyflowReynoldsTransportTheoremInflowInflowOutflowOutflow8Steady,1Datinletsandoutlets,nomatterhowtheflowiswithintheCV.dtdddtdinouts）（）（inoutsAVAVdtd）（）（Multiinletsandoutlets:

iniiiioutiiiisVAVAdtd）（）（1DRTT1DRTTxdxAVRequireVverticaltoAatinletandoutlet.ininAVdtdm）（）（outoutAVdtdm）（）（）（）outoutdAVdt93.4ContinuityEquation（连续方程）AVmmdtdmdmdtdminouts）（）（inoutAVAV）（）（RTTRTTdtdddtdinouts）（）（0dtdmsinoutmmdtdmmoutoutMassflux（Massflux（质量流量）1-DRTT1-DRTTinoutsAVAVdtd）（）（1dmdMassflowout=MassflowinsteadyinCVMassflowoutofCVperunittime.5

（1）10Forincompressibleflow:

Multiinletsandoutletsconst黄河Volumeflux（Volumeflux（体积流量）AVQinoutAVAV）（）（iniioutiiVAVALeonardodaVinci（1452-1519）LeonardodaVinci（1452-1519）A311Discussion1V2V21VVA.21VVB.21VVC.Airgoesinorout?

123.5TheLinearMomentumEquation（动量方程）1-DRTT1-DRTTinoutsAVAVdtd）（）（Linear-momentumLinear-momentumVmVdmdinoutsVAVVAVdtVmd）（）（）（inoutVmVm）（）（Newtons2ndlaw：

dtVmdFs）（inoutVmVmF）（）（:

Momentumflux（:

Momentumflux（动量流量）Vm:

NetforceonsystemorCV（:

NetforceonsystemorCV（体系或控制体受到的合外力）FAforceresultsinmomentumflowinoroutfromaCV14Example3.112Solution:

xySelectcoordinateandCV）（12VVmF）（12xxxVVmF2Vm222V