空气动力学电子教案Chapter-01

PARTIFUNDAMENTALPRINCIPLES（基本原理）InpartI,wecoversomeofthebasicprinciplesthatapplytoaerodynamicsingeneral.ThesearethepillarsonwhichallofaerodynamicsisbasedChapter1Aerodynamics:SomeIntroductoryThoughtsTheterm“aerodynamics”isgenerallyusedforproblemsarisingfromflightandothertopicsinvolvingtheflowofair.LudwigPrandtl,1949Aerodynamics:Thedynamicsofgases,especiallyofatmosphericinteractionswithmovingobjects.TheAmericanHeritageDictionaryofEnglishLanguage,19691.1ImportanceofAerodynamics:

HistoricalExamplesSeabattlebetweenEnglishfleetandSpanishfleet,Englishchannel,8-8-1588(英国与西班牙海战，英吉利海峡）FirstflightofWrightbrothers,12-27-1903(怀特兄弟首次飞行）MinimizingofaerodynamicheatingofICBMs(洲际弹道导弹气动热降低问题）Impetustothestudyoffluidmechnics（流体力学研究的推动力）1.Newton’ssine-squarelaw2.ExperimentscarriedoutbyD’Alembert3.Euler’sdescriptionoftheflowmodel1.Newton’ssine-squarelawa)Newtonconsideredafluidflowasauniform,rectilinearstreamofparticles,muchlikeacloudofpelletsfromashotgunblast.b)Newtonassumedthatuponstrikingasurfaceinclinedataangletothestream,theparticleswouldtransfertheirnormalmomentumtothesurfacebuttheirtangentialmomentumwouldbepreserved.Hence,aftercollisionwiththesurface,theparticleswouldthenmovealongthesurface.Thisledtoanexpressionforthehydrodynamicsforceonthesurfacewhichvariesas2.D’Alembert

Theexperimentresultsshow:therulethatforobliqueresistancevarieswiththesinesquareoftheangleoftheincidenceholdsgoodonlyforanglebetween50and90degandmustbeabandonedforlesserangles3.Eulernoted

Thefluidmovingtowardabody“beforereachingthelatter,bendsitsdirectionanditsvelocitysothatwhenitreachesthebodyitflowspassitalongthesurface,andexercisenootherforceonthebodyexceptthepressurecorrespondingtothesinglepointsofthecontact.”4.Realcaseforfluidapproachingabody

Allthefluidparticlesareinrandommotion,andhasaaveragevelocity.Duringtheirmotion,theycollidewitheachother.

Themoleculesstrikeontothesolidsurfacewillberebounded,andthesereboundedmoleculeswillmakecollisiontoothermolecules.

Thisprocesstransfersthemessageoftheexistenceofthebody,andmostoftheparticleswillgootherround.Afterthecollisionbetweenfluidparticlesandsolidsurface,the

momentumchangeoftheparticlesisintheperpendiculardirectionofthesurface.FirstflightofWrightbrothersDec.17,1903WilburandOrvilleWright'sWrightFlyerwasthefirstsuccessfulairplane.OnDecember17,1903,atKittyHawk,NorthCarolina,OrvilleWrightflewthefirstheavier-than-airmachineinapowered,controlled,andsustainedflight.TheFlyer,constructedofwood,wire,andmuslin,wentadistanceof120feetin12seconds.Itwasatremendoussuccess,comingfromalongseriesofaeronauticsexperimentsthattheWrightBrothersstartedin1899withakite.Attherearofthe1903WrightFlyeronefindsapairofpusherpropellers.Thepropellersarelong,thin,twistedpiecesofwoodwhicharespunathighspeed.Controlofroll:WINGWARPOverviewofWrightBrothersDiscoveriesAerodynamicheatingofthereentryvehicle

ICBMsreentrytheatmosphereatthespeedsoffrom6to6.7km/s.Theaerodynamicheatingofthereentryvehiclesbecomessevere,thecoverofthewarheadwillbeheatedupto10,000K.Bluntreentrybodydesigncanminimizetheaerodynamicheatingproblem.1.2Aerodynamics:ClassificationandPracticalObjectives

(空气动力学：分类和应用目标）Distinctionofsolids,liquids,andgasesPracticalapplicationsinengineeringSolids,liquids,andgasesinacontainerThesolidobjectwillnotchange:itsshapeandboundarieswillremindthesame.Theliquidwillchangeitsshapetoconformtothatofthecontainerandwilltaketakeonthesameboundariesasthecontaineruptothemaximumdepthoftheliquid.Thegaswillcompletelyfillthecontainer,takingonthesameboundariesasthecontainer.Solidand“fluid”(aliquidoragas)underatangentialforce==deformation固体和流体在受到剪应力时，各自形状所发生的变化方式截然不同。Underaforceappliedtangentiallytothesurfaceofasolidbody,thesolidbodywillundergoafinitedeformation,andthetangentialforceperunitarea—theshearstress—willusuallybeproportionaltotheamountofdeformation.Ifthecasehappensforafluid,then,thefluidwillexperienceacontinuouslyincreasingdeformationandtheshearstresswillusuallybeproportionaltotherateofthedeformation.Solid:fluid:Shearstress剪应力Deformation变形Rateofdeformation变形率Mechanicsdistinctionofsolids,liquids,andgasesDistinctionofsolids,liquids,andgasesrespectstotheintermolecularforcesFluiddynamicsissubdividedintothreeareas:

Hydrodynamics---flowofliquidsGasdynamics---flowofgases

Aerodynamics---flowofairPracticalobjectivesofAerodynamics1.Thepredictionofforcesandmomentsonandheattransferto,bodiesmovingthroughafluid.2.Determinationofflowsmovinginternallythroughducts3.Externalaerodynamics4.Internalaerodynamics1.3RoadMapofthischapterWhat’stheusageoftheroadmapAtthebeginningofeachchapter,roadmapgiveyouthesenseforyougettoknowwhereyouare,whereyouaregoing,andhowcanyougetthereShowtheinterrelationshipofthematerialsinthechapterAttheendofthechapter,afteryoulookbackovertheroadmap,youwillseewhereyoustarted,whereyouarenow,andwhatyoulearnedinbetween.1.4SomefundamentalAerodynamicVariablesAerodynamicvariablesaresomethingliketechnicalvocabularyforthephysicalscienceandengineeringunderstandingFirstintroducedaerodynamicvariables:

pressure,density,temperature,andflowvelocityThevelocitydescriptionofafluidisquitedifferenttothatofasolidbody.VelocityofaflowinggasatanyfixedpointBinspaceisthevelocityofasmallfluidelementasitsweepsthroughB.1.5AerodynamicforcesandmomentsAerodynamicforcesandmomentsonamovingbodyareduetoonlytwobasicsources:1.Pressuredistributionoverthebodysurface2.ShearstressdistributionoverthebodysurfaceBothpressureandshearstresshavedimensionsofforceperunitarea.

pressureactsnormaltothebodysurface.shearstressactstangentialtothesurface.TheneteffectofthepressureandshearstressdistributionresultsinaaerodynamicforceRandmomentMonthebody.TheresultantforceRcanbesplitintocomponentsL=lift:componentofRperpendiculartoD=drag:componentsofRparallelto(windsystem)N=normalforce:componentofRperpendiculartoc

A=axialforce:componentsofRparalleltoc

(bodysystem)Afterthe

pressureandshearstress

distributionsbeingdefined,andthegeometryshapeofthebodybeingknown,theresultantaerodynamicforcecanbeobtainedbytheintegrationofthepressureandshearstress

distributionsalongthesurfaceofthebody.FromEqs.(1.7),(1.8)and(1.11),wecanseeclearly,thatthesourcesoftheaerodynamiclift,drag,andmomentsonabodyarethepressureandshearstressdistributionintegratedoverthebody.Thebasictaskoftheoreticalaerodynamicsistocalculatep(s)andτ(s)foragivenbodyshapeandfreestreamconditions,andthenobtaintheaerodynamicforcesandmomentswiththeuseofEqs.(1.7),(1.8)and(1.11)Dimensionlessaerodynamicforceandmomentcoefficientsareevenmoreimportantthantheaerodynamicforcesandmoments.Definitionofanddensityandvelocityinthefreestream,whichisfaraheadofthebody.Definitionofdynamicpressure

ThedynamicpressurehastheunitofpressureDefinitionofdimensionlessforceandmomentcoefficientsLiftcoefficient:

Dragcoefficient:

Normalforcecoefficient:

Axialforcecoefficient:Momentcoefficient:

:reference

area:reference

length

Definitionofandmaybedifferentfordifferentshapesofthebodybeingconcerned.Thesymbolsincapitalletters,suchasrepresentstheforceandmomentcoefficientsforathree-dimensionalbody.Thesymbolsinlowercaselettersdenotetheforceandmomentcoefficientsforatwo-dimensionalbody

areforceandmomentsperunitspanTwoadditionaldimensionlessquantitiesofimmediateusearePressurecoefficientSkinfrictioncoefficientWhereisthe

freestreampressure1.6Centerofpressure（压力中心）Thecenterofthepressureisapointonthebodyaboutwhichtheaerodynamicmomentcontributedbythepressureandshearstressdistributionsisequaltozero.Ifisdefinedasthemomentgeneratedbythedistributedloads,andisthecomponentoftheresultantforce,thenthepressurecentermustbelocateddownstreamoftheleadingedgeIftheangleofattackissmall,,thusItiscleartoseethatasliftapproachestozero,thecenterofpressuremovestoinfinity.So,thecenterofpressureisnotalwaysaconvenientconceptinaerodynamics.Thereareotherwaystodefinetheforce-and-momentsystemonanairfoil1.7Dimensionalanalysis:TheBuchinghamPItheorem（量纲分析：PI定理）※Whatphysicalquantitiesdeterminethevariationoftheaerodynamicforcesandmoments?Onaphysical,intuitivebasis,weexpectRisdependon:1.Freestreamvelocity2.Freestreamdensity3.Viscosityofthefluid4.Thesizeofthebody5.Thecompressibilityofthefluid※

Howtofindaprecisefunctionalrelationfortheequationabove?Executehugeamountofwindtunnelexperimentmightbeoneway.Isthereanyotherwaycandomoreeffectively?Methodofdimensionalanalysis※AnobviousfactforthedimensionalanalysisAllthetermsinthisphysicalrelationmusthavethesamedimensions※BuckinghamPItheorem1.LetKtobethenumberoffundamentaldimensionsrequiredtodescribethephysicalvariables2.LetrepresentNphysicalvariablesinthephysicalrelation3.Thenthephysicalrelationcanbereexpressedasarelationof(N-K)dimensionlessproducts.4.EveryproductisadimensionlessproductofasetofK

physicalvariablesplusoneotherphysicalvariable.5.iscalledrepeatingvariables.Thesevariablesshouldincludeall

theKdimensionsusedintheproblem.※Aerodynamicforceonagivenbodyatagivenangleofattack.1.Eq.(1.23)canbeexpressedas2.FollowingBuckinghamtheoremandourphysicalintuition,thefundamentaldimensionsarem,landt.Hence,

K=33.Thephysicalvariablesandtheirdimensionsareand

N=64.AsexplainedbyBuckinghamtheorem,Eq.(1.27)canbereexpressedintermsofN-K=3

dimensionlessproducts,thatis5.Now,wechoseasrepeatingvariables,fromEq.(1.26),theseproductsare5.Assume

indimensionalform6.Asisdimensionless,then7.TheaboveEquationsgived=-1,b=-2,ande=-2,thenwehaveor

whereS

isdefinedasreferencearea8.Inthesameway,wecanobtaintheremainingproductsasfollowsReynoldsNumber雷诺数

isaforcecoefficient,definedasMachNumber马赫数9.InsertingalltheproductsintoEq.(1.28)

oror10.Importantconclusion:Inthegeneralfunctionform,RisexpressedwithfiveindependentphysicalvariablesAfterourdimensionalanalysis,Rcanbeexpressedwithonly

twoindependentvariables

RcanbeexpressedintermsofadimensionlessforcecoefficientisafunctionofonlyReand11.ImportantapplicationsofReand.

similarityparameters

12.Asliftanddragarecomponentsoftheresultantforce,thentheliftanddragcoefficientsarealsofunctionsofonlyRe

and.Moreover,arelationsimilartoaerodynamicforcesholdsforaerodynamicmoments,anddimensionanalysisyields13.Iftheangleofattackisallowedtovary,then,thelift,dragandmomentcoefficientswillingeneraldependonthevalueof.14.Othersimilarityparametersassociatedwiththermodynamicsandheattransfer.Physicalvariablesshouldbeaddedtemperature,specificheat,thermalconductivity,temperatureofthebodysurfaceFundamentaldimensionshouldbeaddedunitofthetemperature(K)Similarityparameterscreated1.8Flowsimilarity（流动相似）※DefinitionofflowsimilarityDifferentflowsaredynamicallysimilarif:Thestreamlinepatternsaregeometricallysimilar2.Thedistributionsofetc.,throughouttheflowfieldarethesamewhenplottedagainstcommonnondimensionalcoordinates.3.Theforcecoefficientsarethesame※CriteriatoensureflowsimilarityThebodiesandanyothersolidboundariesaregeometricallysimilarforbothflows.2.Thesimilarityparametersareidenticalforbothflows.3.ReynoldsandMachnumberarethemostdominantsimilarityparametersformanyaerodynamicproblems.※Examples1.4and1.51.9FluidStatics：BuoyancyForce

(流体静力学：浮力）Skippedover1.10TypesofFlow（流动类型）1.Thepurposeforcategorizingdifferenttypesofflow.2.Thestrategytosimplifytheflowproblems.3.Itemizationandcomparisonofdifferenttypesofflow,andbriefdescriptionoftheirmostimportantphysicalphenomena.1.10.1Continuumversusfreemoleculeflow1.Definitionofmean-free

path.2.Continuumflow.3.Freemoleculeflow4.Inmostaerodynamicproblems,wewillalwaystreatthefluidascontinuumflow.1.10.2Inviscidversusviscousflow1.Therandommotionofthemoleculewilltransporttheirmass,momentum,andenergyfromonelocationtoanotherinthefluid.Thistransportonamoleculescalegivesrisetothephenomenaofmassdiffusion,viscosity,andthermalconduction.Allrealflowsexhibittheeffectofthesetransportphenomena;suchflowsarecallviscousflows.2.Aflowthatisassumedfreewithallthesephenomenaaboveiscalledinviscidflow.3.InviscidflowisapproachedinthelimitastheReynoldsnumbergoestoinfinity.4.TheflowwithhighReynoldsnumber,canbeassumedtobeinviscid.Andtheinfluenceof

friction,thermalconduction,anddiffusionislimitedintheboundarylayer.5.Theinviscidtheorycanbeusedtopredictsthepressuredistributionandlift.However,itcannotpredictstotaldrag.6.Flowsdominatedbyviscouseffects.

FlowaroundairfoilathighangleofattackFlowaroundbluntbody7.Noinviscidtheorycanindependentlypredicttheaerodynamicsofsuchflows.

1.10.3IncompressibleversuscompressibleFlowsAflowinwhichthedensityisconstantiscalledincompressible.Incontrast,aflowwherethedensityisvariableiscalledcompressible.

2.Alltheflowsarecompressible,moreorless3.Thereareanumberofaerodynamicproblemsthatcanbemodeled

asbeingincompressible

withoutanydetrimentallossofaccuracy.4.Inmanycases,whetherthecompressibilityshouldbeconsideredornot,ismanlybasedon

theMachnumberoftheflow.1.10.4MachnumberregimesLocaldefinitionSubsonicifSonicif

Supersonicif

WhereisthelocalMachnumberatanarbitrarypointinaflowfield.2.Definitionforwholeflowfield3.Blockdiagramcategorizingthetypesofaerodynamicflows1.11Appliedaerodynamics:Theaerodynamiccoefficients—TheirmagnitudeandvariationsDifferencebetweenthefundamentals

andapplicationsofaerodynamics.

2.Aerodynamiccoefficients,suchaslift,drag,andmomentcoefficients,aretheprimarylanguageofapplicationexternalaerodynamics.3.Typicalvaluesfortheaerodynamiccoefficientsforsomecommonaerodynamicshapesandit’svariationwithMachnumberandReynoldsnumber.4.Sometypicaldragcoefficientsforvariousaerodynamicconfigurationsinlowspeedflows.

Comparisonthroughcaseatoc:

theReynoldsnumbersforallthesethreecasesarethesamebasedond(diameter).thewakesaregettingsmallerinsizefromatoc

alsobecomessmallerfromcase

atoc

Comparisonbetweencasebandd:

theReynoldsnumberincaseb:theReynoldsnumberincased

:isthesameforcasebtod

foracircularcylinderisrelativelyindependentofReynoldsnumberbetweenRe=andComparisonbetweencasebtoe:

theReynoldsnumberincaseb:theReynoldsnumberincasee:incaseeis0.6

smallerwakebehindthecylinderincasee

comparedtothatincase

b.Note:Withbasedonthefrontalprojectedarea(S=d(1)perunitspan),thevalueofrangefromamaximum2tonumbersaslowas0.12.MagnitudeofReynoldsnumberofaflowaroundacircularcylinderatstandardsealevel,where,

Th