第五节 动力传递与流动阻力导论

1.5流体流动的阻力(ResistanceofFluidFlow)1.5.1流动阻力与能量损失的概念(ConceptofflowresistanceandEnergyLoss)1.5.1.1动量传递与流动阻力产生的机理(mechanismofmomentumtransferandflowresistance)【动量传递机理】流体分子或质点之间的动量传递引起内摩擦。不同流型的动量传递机理不同。层流：分子之间的动量传递(molecularmomentumtransfer)湍流：质点之间的动量传递(momentumtransferofmasspoints)层流中的分子动量传递引起的内摩擦力遵循牛顿黏性定律：dy)ud(dy)ud(dyduxxxρρρμμτνInternalfrictioncausesbyeddytransfer（涡流传递）:dyuρdετxr)(dyuρdεντττxrt)()(时间面积动量smm/skgmm/skgmN][2222τmomentumflux(动量通量)theoverallinternalfrictioninturbulentflowinvestigatingthedimensionsofvariousphysicalquantitiesintheequationabove体积动量33mm/skgm/s][kg/m][ρu（动量浓度）距离动量浓度dyρud)(所以（动量浓度梯度）传递阻力动量浓度梯度νdyρuddyρudντ1)()(传递阻力动量传递推动力动量通量dy)ud(ρετxr在涡流动量通量里dy)d(ρντxu动量通量=动量扩散系数×动量浓度梯度ε称为涡流黏度，是湍动程度和管路形状、位置等的函数。【流动阻力产生的机理】流动阻力产生的原因在于：流体具有黏性，流动时存在内摩擦现象，这是流动阻力产生的根本原因（内因）；流体与其相接触的固体壁面之间的作用，促使流体内部发生相对运动，提供阻力产生的条件（外因）。因而，流动阻力产生的大小与流体的性质、流动类型、流过距离、壁面形状等有关。【VelocityDistributioninPipe(流体在圆管内的速度分布)】Whetherlayerfloworturbulentflow,thevelocityoffluidmassponitflowinginapipechangeswithdistancebetweenthemasspointandthepipecenterline—velocitydistribution(速度分布).Generally,thevelocityofmassponitatpipewallisdeemedtobezero.Thenearerthemasspointtothepipecenterline,thefasteritmoves.ForLayerFlowThedistributionofvelocityisparabolicintheradialdirection.Thevelocityhasthelargestvalueatthepipecenter.Meanvelocityishalfthemaximumvelocity,thatmaxb21uuForTurbulentFlowmasspointsvigorouslymixandcollideeachother,whichallowvelocitydistributiontobecomeuniformThegreaterthevalueofRe,theflatterthecurvetop.Owingtothevigorousmixingandcollisionbetweenmassponits,theflowresistanceinturbulentflowismuchlargerthanthatinlayerflow.Thevelocitynearthewalldropssuddenly.maxb0.82)~(0.8uu1.5.1.2管内流动阻力的分类直管阻力:resistancelosscausedbyinternalfrictionwhenfluidflowsthroughastraightpipe,denotedbyhf.gowiththewholeflowprocess,alsocalledon-wayresistancejffhhΣhtotalresistanceSometimes,theresistancelosscouldbeexpressedaspressuredrop（压强降）,jsffΔpΔpΔpDifferingfromΔp,Δpfisnotinvolvedinenergyconversion.Localresistance(局部阻力):resistancelosscausedbywhenfluidflowsthroughpipefitting,valves,sectiononsuddenlyshrunkenandexpandedandotherlocalplaces,denotedbyhj.1.5.1.3计算直管阻力的通式Whensteady-stateflowingthedrivingforce=thefrictionalresistancerLπτrπpp2212)(rLΔpτ2thatTheequationaboveshowsthatinternalfrictionchangeslinearlyintheradiusdirectionwhenfluidflowsinapipe.foranarbitraryfluiddifferentialunitwithlengthLandradiusr,itsforceanalysisthesamedirectiondrivingforce:22121)(rπppPPrLπτF2frictionalresistance:oppositedirectionWhenfluidflowsinahorizontalandequal-diameterstraightpipe,ΔpisnumericallyequaltotheresistancelossΔpfcausedbyinternalfriction(内摩擦力).f2222121122hpugzWpugzeef22WhpuzgAtthewall,r=ri=d/2,theequationabovecanbeconvertedtoffphprLp2dLΔprLΔpτis42τs—fluidshearingstrengthatthewalldLp4sfdLph4sffsoTheequationaboveisrelationexpressionsbetweentheresistancelossandfrictionstress.τisrelatedtotheflowpattern.kineticenergyu2/2hasthesameunitashf,sohfcanbeexpressedascertainmultiplesofu2/2.2822442222fudLuudLudLhsss28us22fudLhlet22sfudLporgeneralformulaofcalculationofstraightpiperesistance,calledFanningequation(范宁公式)λ—frictioncoefficient,dimensionless,it’srelatedtotheflowpatternandroughnessofpipewall.22fudLh22sfudLpand1.5.2圆管内的稳态层流1.5.2.1速度分布rdrduLSr2drdurNewton'slawofviscositySApsfCrLpu2sf4rLpdrdu2sfonintegrating0urri2isf4rLpCrdrduLrpsr2f2稳态流动rdrLpdu2sf)(422isfrrLpuvelocitydistributioninlayerflowletr=0)(422isfrrLpu2isfmax4rLpu2i2max1rruuanotherformofvelocitydistributioninlayerflowforanannularfluiddifferentialunitwiththicknessdr1.5.2.2层流时的摩擦系数annularsectionareardrdA2totalflowinpipeis0r0ss2rVrdrudVVvolumeflowrateofthedifferentialunitrdrudVrs22isf0422isf2i022isf2i8)42(42)(42iirLprrrLprrdrrrLprurr＝2i0ri2rrdruAVsurmeanvelocityatacross-section2sf32dLupsoHagon-Poiseuilleequation(哈根-泊谡叶方程)264223232222sfudLduuudLddLupsoRedu6464Ref164Fanningfrictionfactor(范宁摩擦因子)22sfudLpcomparedwithFanningequation1.5.3圆管内的湍流1.5.3.1管内粗糙度对摩擦系数的影响pipewallconditionisrepresentedinroughness.dabsoluteroughness(绝对粗糙度e),averageheightofwallbulgerelativeroughness(相对粗糙度e/d),ratioofabsoluteroughnesstopipediameterⅠ.ForlayerflowλisindependentofevalueroughnessdoesnotaffectflowresistanceⅡ.Forturbulentflowlaminarbottom(层流内层)δb①eδbλisalsoindependentofevaluehydraulicsmooth(水力光滑)②eδbThelargerthevalueofReandthesmallerthevalueofδb,themoresignificanttheeffectofeonλ.1.5.3.2湍流时的摩擦系数Dimensionalanalysismethod(因次分析法)—serveralphysicalquantitiesarecombinedintooneormoredimensionlessgroups(无因次数群)bydimensionlesstreatment(无因次化),thentherelationbetweendimensionlessgroupsaresetupwithhelpofexperiments.Buckinghamstheorem(白金汉定理)0)(n21x,,x,xr0N21),,,(fWhereN=n–m,m—numbersofthefundamentaldimensionExample)(sfe,,,u,L,drpdimensionofvariousphysicalquantities