comsol等离子体放电一维模型

SolvedwithCOMSOLMultiphysics5.21|ATMOSPHERICPRESSURECORONADISCHARGEAtmosphericPressureCoronaDischargeIntroductionThismodelsimulatesacoronadischargeoccurringbetweentwoco-axiallyfashionedconductors.Thenegativeelectricpotentialisappliedtotheinnerconductorandtheexteriorconductorisgrounded.Thedischargegassimulatedisargonatatmosphericpressure.ModelDefinitionFigure1showsacrosssectionofthemodel.Byconsideringalonganduniformcoaxialconductorconfiguration,themodelcanbeviewedasaxisymmetricandthussimplifiedtoa1Dproblem.Themodelpresentedinthefollowingsectionisusedtosimulatetheionizationoftheneutralgas(Ar)aswellasthefluxofchargedparticles(Ar+andelectrons)whenthenegativeelectricpotentialisappliedattheinnerconductor(cathode).Thehighelectricfieldgeneratedbythecombinationofhighpotentialandsmallconductorcurvatureradius(innerconductor,ri)causeselectrondriftandionizationoftheneutralgassurroundingthecathode.Theresultingionsgeneratemoreelectronsthroughsecondaryemissionatthecathodesurface.Theseelectronsareacceleratedthroughasmallregionawayfromthecathode,wheretheycanacquiresignificantenergy.Thiscanleadtoionizationwhichcreatesnewelectron-ionpairs.Thesecondaryionsmigratetowardsthecathodewheretheyejectmoresecondaryelectrons.Thisprocessisresponsibleforsustainingthedischarge.ThemodelisbasedonthefluidequationsforelectronsandionsaswellasonPoisson’sequation.Secondaryelectronsgeneratedbyionbombardmentofthecathodesurfacearetakenintoaccount.ThemodelusesaScharfetter-Gummelupwindschemetoeliminatenumericalinstabilitiesinthenumberdensityofthechargedparticlesassociatedwiththefiniteelementmethod.Thisisneeded,inparticularclosetothecathode,wheretheionfluxisparticularlyhigh.SolvedwithCOMSOLMultiphysics5.12|ATMOSPHERICPRESSURECORONADISCHARGEFigure1:Not-to-scalecrosssectionoftheco-axialconfiguration.Thenegativepotential(-Vin)isappliedattheinnerconductor(cathode)andtheouterelectrodeisgrounded(anode).Theshadedarearepresentstheionizationregioncreatedbythepositivespacechargedistributiongeneratedinthevicinityofthecathode.DOMAINEQUATIONSt∂∂ne()∇neμeE•()–Dene∇•–[]⋅+Re=Theelectrondensityandmeanelectronenergyarecomputedbysolvingthedrift-diffusionequationsfortheelectrondensityandmeanelectronenergy.Convectionofelectronsduetofluidmotionisneglected.FormoredetailedinformationonelectrontransportseethesectionTheoryfortheDriftDiffusionInterfaceinthePlasmaModuleUser’sGuide.TheelectronsourceReandtheenergylossduetoinelasticcollisionsRεaredefinedlater.Theelectrondiffusivity,energymobility,andenergydiffusivityarecomputedfromtheelectronmobilityusingtherelationsriroanodecathode(-Vin)simulateddomain(1D)t∂∂nε()∇nεμεE•()–Dε∇nε•–[]EΓe⋅+⋅+Rε=DeμeTe=με,53---μe=Dε,μεTe=SolvedwithCOMSOLMultiphysics5.23|ATMOSPHERICPRESSURECORONADISCHARGEThesourcecoefficientsintheaboveequationsaredeterminedbytheplasmachemistryusingratecoefficients.SupposethatthereareMreactionsthatcontributetothegrowthordecayofelectrondensityandPinelasticelectron-neutralcollisions.Ingeneral.Inthecaseofratecoefficients,theelectronsourcetermisgivenbywherexjisthemolefractionofthetargetspeciesforreactionj,kjistheratecoefficientforreactionj(SIunit:m3/s),andNnisthetotalneutralnumberdensity(SIunit:1/m3).Theelectronenergylossisobtainedbysummingthecollisionalenergylossoverallreactions:HereΔεjistheenergylossfromreactionj(SIunit:V).Theratecoefficientscanbecomputedfromcross-sectiondataastheintegralswhereγ=(2q/me)1/2(SIunit:C1/2/kg1/2),meistheelectronmass(SIunit:kg),εistheenergy(SIunit:V),σkisthecollisioncrosssection(SIunit:m2),andfistheelectronenergydistributionfunction.Inthiscase,aMaxwellianEEDFisassumed.Fornon-electronspecies,thefollowingequationissolvedforthemassfractionofeachspecies:Fordetailedinformationonthetransportofthenon-electronspeciesseethesectionTheoryfortheHeavySpeciesTransportInterfaceinthePlasmaModuleUser’sGuide.TheelectrostaticfieldiscomputedusingtheequationPM»RexjkjNnnej1=M=RεxjkjNnneΔεjj1=P=kkγεσkε()fε()εd0∞=ρt∂∂wk()ρu∇⋅()wk+∇jk⋅Rk+=∇–ε0εrV∇⋅ρ=SolvedwithCOMSOLMultiphysics5.14|ATMOSPHERICPRESSURECORONADISCHARGEThespacechargedensityρisautomaticallycomputedbasedontheplasmachemistryspecifiedinthemodelusingtheformulaFordetailedinformationaboutelectrostaticsseeTheoryfortheElectrostaticsInterfaceinthePlasmaModuleUser’sGuide.BoundaryConditionsElectronsarelosttothewallduetorandommotionwithinafewmeanfreepathsofthewallandgainedduetosecondaryemissioneffects,resultingintheboundarycondition(1)fortheelectronfluxand(2)fortheelectronenergyflux.Thesecondtermontheright-handsideofEquation1isthegainofelectronsduetosecondaryemissioneffects,γpbeingthesecondaryemissioncoefficient.ThesecondterminEquation2isthesecondaryemissionenergyflux,εpbeingthemeanenergyofthesecondaryelectrons.Fortheheavyspecies,ionsarelosttothewallduetosurfacereactionsandthefactthattheelectricfieldisdirectedtowardsthewall:Thedischargeisdrivenbytheelectricpotentialappliedtotheinnerconductorofthecoaxialgeometry(atcoordinater=ri).wherethefunctiontanh(t/τ)isusedtogeneratethevoltagestepfunction(−1000V).Theotherboundary(atcoordinater=ro)isgrounded.ρqZknkk1=Nne–=n–