Boyd Review 2003

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1、PredictingBreakdownoftheContinuumEquationsUnderRarefiedFlowConditionsIainD.BoydDepartmentofAerospaceEngineering,UniversityofMichigan,AnnArbor,MI48109Abstract.Thebreakdownofthecontinuumequationsofgasdynamicsunderconditionsofrarefiedflowisconsidered.Theconditionsofbreakdownareofinterestinassessin

2、gthephysicalaccuracyofcontinuumsolutions,inunderstandingthemathematicalrelationsbetweendifferentsetsofcontinuumtransportequations,andplayasignificantroleinthedevelopmentofhybridmethodsthatusebothcontinuumandkineticsimulationtechniques.Anumberofpreviousbreakdownparametersarereviewed.Anewmethod,b

3、asedonkinetictheoryanalysis,isintroducedfordetectingconditionswherethecontinuumapproachisvalid.Continuumbreakdownisdiscussedindetailforgasexpansionsandshockwavesbyconsideringthebasicphysicalphenomenainvolvedineachcase.Successofthebreakdownparametersfortheseflowsisassessed.Itisshownthatcontinuum

4、breakdowningasexpansionsandshockwavesproceedsthroughdifferentphysicalmechanismsthatarebestpredictedbydifferenttypesofbreakdownparameters.Thenewmethodfordetectingcontinuumonsetisappliedtoshockwavesandshowntoofferpromisingresults.INTRODUCTIONThefailureofthecontinuumequationsofgasdynamicsundercert

5、ainphysicalconditionsisthereasonwhythereisafieldofrarefiedgasdynamics.Ingeneral,itiswidelyrecognizedthatacontinuumapproachisinvalidwhentheKnudsennumberislargeandthisoccursforflowswithlowdensityand/orsmallcharacteristiclengthscales.Inaglobalsense,alargeKnudsennumbermeansthatthereisnotenoughphysi

6、calspacetoallowthegastoundergoasufficientnumberofcollisionstomaintainequilibriumvelocitydistributionfunctions.AtsufficientlylargeglobalKnudsennumbers,anentiregasflowsystemmustbemodeledusingnon-continuum,kineticmethods.However,inmanygasflowsofinterest,theglobalKnudsennumbermaybesmallandyettherea

7、relocalizedregionswherethecontinuumapproachmayfail.Thisarticleismotivatedbytheneedforpredictionofthefailureofthecontinuumequationsinthesetypesofflowswithamixtureofcontinuumandkineticflowregions.Themostfundamentalmodelofdilutegasdy