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1、J.FluidMech.(1970),vol.43,part4,pp.771-783771Printedin&eatBritainMeasurementsandcomputationsofflowinpipebendsByM.ROWEEngineeringDepartment,UniversityofCambridge(Received29December1969andinrevisedform9April1970)Measurementsaregivenofthetiotalpressureandyawrelativetothepipeaxisofflowinva
2、riouspipebendsattachedtotheendofalongstraightpipe,forapipeReynoldsnumberof2-36xlo5.Thebehaviouroftheinducedsecondaryflowsispresentedindetail.Ina180"benditisfoundthat,fromthestartofthobend,thesecondaryflowsincreasetoamaximumandthendecreasetoasteadyvalue.Thiseffectisexplainedbyrelatingth
3、elocaltotalpressuregradienttothepro-ductionofstreamwisevorticity.ThesameflowmechanismisusedtopredictqualitativelytheflowpatterninanS-bendinwhichitisfoundthatthesecondaryflowscauseacompleteinterchangeoftheslowmovingwallfluidandthefastercentralcore.Resultsofacomputerprogramforcalculating
4、thesecondaryflowfromaknowledgeoftheupstreamvelocityprofileareincluded.Althoughrealfluideffects,otherthanthosecausingtheupstreamvelocityprofile,areomittedfromthecomputations,themeasuredflowpatternisreasonablywellpredictedinalongbenduptoabendangleofabout75".IntroductionThegeneralcharacte
5、roffluidmotioninabendiswellknown(Goldstein1938;Schlichting1955).Whenthefluidentersabend,apressuregradientissetuptoprovidethenecessaryinwardacceleration.Iftheflowhasanon-uniformvelocity,thepressuregradientisinsufficientforthefastermovingparticlesandmorethansufficientfortheslowerones.Ase
6、condaryflowisthereforeformedwiththefasterfluidmovingtotheoutsideofthebendandtheslowerfluidtotheinside.Thus,inapipebendinthehorizontalplanewithavelocityprofilethatisinitiallyaxi-symmetric,theresultantflowishelicalintheupperandlowerhalvesofthepipe.Ifthebendhasaconstantradiusandthepipeaco
7、nstantcross-sectionandissufficientlylong,thecurvedfloweventuallybecomesfullydeveloped,i.e.thevelocitiesdonotvarywithdistancealongthepipeaxis.Considerableworkbymanyauthorshasbeendoneonfullydevelopedcurvedflow(e.g.Adler(1934),forlaminarflow,andIt6(1959),forturbulentflow).Themainobjecth
