北航工程流体力学课件(王洪伟).pdf
- 文档编号:30859265
- 上传时间:2024-04-18
- 格式:PDF
- 页数:142
- 大小:10.06MB
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》由会员分享,可在线阅读,更多相关《北航工程流体力学课件(王洪伟).pdf(142页珍藏版)》请在冰豆网上搜索。
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
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 北航 工程 流体力学 课件 王洪伟