race car aerodynamics designing for speed 空气动力学.docx
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racecaraerodynamicsdesigningforspeed空气动力学
Racecaraerodynamics,designingforspeed
Fig.1-7.Trendsshowingtheincreaseofthemaximumcorneringaccelerationoverthepastyearsforracecarswithandwithoutaerodynamicdownforce.
Fig.1-11Schematicdescriptionofthe“groundeffect”thatincreasestheaerodynamicliftofwingswhenplacedneartheground.
Fig.2-1.Streamlinesinasteady-stateflowoveranairfoil.
Byobservingseveralstreamlinetracesintheflow(asinFig.2-2),itispossibletoseeiftheflowfollowsthevehicle’sbodyshapeclosetoitssurface.Whenthestreamlinesnearthesolidsurfacefollowexactlytheshapeofthebody(asintheupperportionofFig.2-3)theflowisconsideredtobeattached.Iftheflowdoesnotfollowtheshapeofthesurface(asseenbehindthevehicleinFig.2-2andinthelowerpartofFig.2-3)thentheflowisconsidereddetachedorseparated.Usuallysuchseparatedflowsbehindthevehiclewillresultinanunsteadywakeflow,whichcanbefeltuptolargedistancesbehindthevehicle.Asweshallseelater,havingattachedflowfieldsisextremelyimportantinreducingaerodynamicdragand/orincreasingdownforce.
Fig.2-2.Visualizationofstreamlines(bysmokeinjection)duringawind-tunneltest.CourtesyofVolkswagenAG.
Fig.2-3.Attachedflowoverastreamlinedcar(A),andthelocallyseparatedflowbehindamorerealisticautomobileshape(B).
Fig.2-4.Sideviewofthevelocitydistributionnearaflatplateinafreestream,V∞(velocityprofileontheuppersurfaceisdescribedbytheVvszgraph)
Now,leavingmomentarilythediscussionaboutthebasicdefinitions,wecanobserveacoupleofinterestingfeaturesinFig.2-4.First,theairvelocitynearthesurfacecomestoahalt!
Thisisknownasthe“no-slip-condition.”Thefluidparticlestouchingthebodywillsticktothesurface;theyhavenorelativevelocity.Fartherawayfromthesolidbodythevelocityincreases,untilitequalsthelocalfree-streamvalue.Thisthinboundaryistermedtheboundarylayerandwillbediscussedwithmoredetaillater.
Fig.2-5.Fluidparticletracesinlaminarandinturbulentflow.
FluidProperties:
e.g.,temperature,pressure,density,viscosity.,etc.
Viscosityis,inaverygenericsense,ameasureoffluidresistancetomotion(similartofriction),andisdesignatedbytheGreeksymbolμ.
TheeffectofviscosityinafluidcanbedemonstratedbythesimpleexampleshowninFig.2-6(followingtheanalogytodryfriction)whereaviscousfluidisplacedbetweentwoparallel,solidsurfaces.Thelowersurfaceisstationary,whiletheupperoneismovingtotherightataconstantspeed.Thefluidparticlesnearthetwowallstendtosticktothesolidsurfaceandmaintainazerorelativevelocity(thisisthepreviouslymentionedno-slipcondition).
Fig.2-6.Velocitydistributionbetweentwoparallelplates,causedbythemotionoftheupperplate.Thelowerplateisstationary,andtheupperoneismovedbytheforceFataconstantspeedV∞.
ThemagnitudeoftheshearforceFcanbeconnectedtothespeedoftheupperplateandtotheviscosityofthefluidbytherelation:
Asanexample,assumethattheupperplatewithanareaofA=1m2isbeingpulledataspeedof5m/s.Thefluidbetweenthetwosurfaceiswater,andtheseparationdistanceis0.02m.TakingthevalueoftheviscositycoefficientμfromTable2.1wecancalculatetheforceFrequiredtopulltheplateas:
TheReynoldsnumber:
TheRenumberrepresentstheratiobetweeninertialandviscous(friction)forcescreatedintheairandisdefinedbythefollowingformula:
Hereρ(pronouncedrho)isthefluiddensity,μistheviscosity,Vrepresentsthevelocity,andLissomecharacteristiclength(ofthevelocity,forexample).
Animportantfeatureofthisnumberisthatitisnondimensional,thatis,theunitscancelout(evenifweuseBritish,USA,orEuropeanunits).ForatypicalnumericalvalueoftheReynoldsnumberwecanassumeacarlengthof4mandaspeedof30m/sec,andusethepropertiesofairfromTable2.1,thus;
Forexample,forReynoldsnumbervalues(baseonthecarlength)oflessthan105theflowoverwingswillbelaminarandthedragandtheliftobtainedatthisrangmaybeconsiderablydifferentthanatthehighervaluesoftheReynoldsnumber.Returningtothecaseofaracecarpiercingitswaythroughair(withverysmallviscosity)wefindthattheReynoldsnumberwillbeontheorderofseveralmillions.ButifthesamevehiclemovesthroughahighlyviscousfluidsuchasmotoroilthentheReynoldsnumberwillbefarless.
雷诺数代表流场中物体所受的惯性力与粘性力的比。
因此,Re数越小的流动,粘性作用越大(相对于惯性力来说);Re数越大的流动,粘性作用越小。
AnotherinterestingfeatureoftheReynoldsnumberisthattwodifferentflowscanbeconsideredsimilariftheirReynoldsnumberarethesame.Apossibleimplementationofthisprinciplemayapplywhenexchangingwatertunnelforwindtunneltesting,orviceversa.Typicalgainsareinreducedmodelsize,orinlowertestspeeds.Foeexample,theratioofviscosity/densityinairisabout15timeslargerthaninwater;therefore,inawatertowtankmuchslowerspeedscanbeusedtotestthemodelatthesameReynoldsnumber(andthishasbeendonebutseemsnotbeverypracticalforautomobiletesting).Amorepracticalapplicationofthisprinciplewouldbetotesta1/15-scalesubmarinemodelinawindtunnelattruewater-speedcondition.Usuallyitisbettertoincreasethespeedinthewindtunnelandthenevenasmallerscalemodelcanbetested.
Boundarylayer:
Theconceptofaboundarylayercanbedescribedbyconsideringtheflowpastatwo-dimensionalflatplatesubmergedinauniformstream,similartotheoneshowninFig.2-4.
Thislayerofrapidchangeinthetangentialvelocity(shownschematicallybythevelocityprofileinFig.2-4)iscalledtheboundarylayer,anditsthicknessδ(delta)increaseswiththedistancealongtheplate.Theboundarylayerexistsonmorecomplicatedshapes,aswell,(e.g.,theautomobileshowninFig.2-7).Atypicalvelocityprofilewithinthislayerisdescribedbytheinsetonthisfigure.
Thethicknessofthisboundarylayerisonlyseveralmmatthefrontofacartravelingat100km/hr,andcanbeseveralcmthicktowardthebackofastreamlinedcar.Asyouwillsee,athickerboundarylayercreatesmoreviscousfrictiondrag.Furthermore,atoosteepincreaseinthisthicknesscanleadtoflowseparation,resultinginadditionaldragandalossinthedownforcecreatedbyaracecar’swings.
Fig.2-7.Boundarylayernearavehicle’ssurface,andtypicalvelocitydistributionwithinthislayer
Fig.2-8.Variationoftheboundarylayerthicknessalongaflatplate.Notethevelocitydistributioninsidetheboundarylayeranditsincreaseinthicknessduringthetransitionfromlaminartoturbulentflow.
TheSkin-FrictionCoefficient:
Theskin-FrictioncoefficientCfisanondimensionalnumber(independentofunits)indicatingtheleveloffrictionbetweenthevehiclesurfaceandtheair.Itisdefinedas:
Whereτisthesurfaceshearforceperunitsurface(frictionresistance)anditisnondimensionalizedbythequantity
(calledthedynamicpressure)sothatthenumericalvalueof
willbe(almost)independentofspeed.
Forexample,ifthefrictioncoefficientisCf=0.002(fromFig.2.9)andtheairmovesovertheplateataspeedof30m/sec(108km/hr)thentheshearforceperunitarea(1m2)is:
AndthedensityofairwastakenfromTable2.1.
Nowintermsoftheeffectofspeedonfriction,notethattheboundarylayerthicknessdecreasesasairspeedincreases.Thisisduetothelargermomentum(theproductofmasstimesvelocity)ofthefreestreamcomparedtothelossofmomentumcausedbytheviscositynearthesolidsurface.Therefore,thefrictioncoefficient(thatcontributestothevehicle’sdrag)willbereducedwithincreasedflowspeed.
Fig.2-9.Skin-frictioncoefficientCfvaluesonaflatplate,placedparalleltotheflow,forlaminarandturbulentboundarylayers,versustheReynoldsnumber.
Theinterestingobservationsonthisfigurearethattherearetwoseparatecurves:
oneforlaminarandoneforturbulentflow,andthatbothdecreasewithincreasedReynoldsnumber.Furthermore,foralargerangeoftheReynoldsnumber,bothturbulentandlaminarflows(sometimes4to5timesless)whichmeansthatforthepurposeofdragreduction,laminarflowispreferred.
Wecandrawafewimportantconclusionsabouttheboundarylayer:
1、Boundarylayerthicknessislargerforturbulentthanforlaminarboundarylayers.
2、TheskinfrictioncoefficientbecomessmallerwithincreasedReynoldsnumber(mainlyforlaminarflow)
3、AtacertainReynoldsnumberrangebothlaminarandturbulentboundarylayersarepossible.Thenatureoftheactualboundarylayerforaparticularcasedependsonflowdisturbances,surfaceroughness,etc.
4、Theskinfrictioncoefficientisconsiderablylargerfortheturbulentboundarylayer(largerskinfrictionresultsinlargerfrictiondrag).
5、Becauseofthemomentumtransfernormal(perpendicular)tothedirectionoftheaveragespeed,inthecaseofaturbulentboundarylayer,flowseparationswillbedelayedsomewhatcomparedtoalaminarboundarylayer.Thisisanimportantandindirectconclusion,butinmanyautomotiveapplicationsitforcesustopreferturbulentboundarylayersinordertodelayflowseparation.
Fig.2-10.Schematicdescriptionofthelaminarbubbleandthetransitionfromlaminartoturbulentboundarylayer
AtypicalcaseisdemonstratedinFig.2-10,wheretheboundarylayeronastreamlinedhoodisinitiallylaminar.However,duetothelargecurvatureoftheuppersurfacethelaminarboundarylayerseparatesinitially,thenreattached