JOURNALOFTHERMOPHYSICSANDHEATTRANSFER Vol.29,No.4,October–December2015 Numerical Analysis of Surface Chemistry in High-Enthalpy Flows AbhilashaAnna∗andIainD.Boyd† UniversityofMichigan,AnnArbor,Michigan48109 DOI:10.2514/1.T4530 Theeffectsofsurface-chemistryprocessesofagraphitesampleexposedtoasubsonichigh-enthalpynitrogenflow areinvestigatedusingacoupledcomputationalfluid-dynamics/surface-chemistrymodel.Theresultsobtainedare assessedfortheaccuracyofthemodelusingexperimentaldatafromtestsconductedina30kWinductivelycoupled plasmatorchfacilityattheUniversityofVermont.Significantdiscrepanciesareobservedbetweenthecomputational andexperimentalresults.Therefore,astudyisperformedtodeterminesensitivitiesofflowandsurfaceparametersto variationsintestinginputconditions,aswellasphysicalmodelingparameters.Measurementsoftheabsolutenumber 0 densityarerequiredtodrawfirmconclusionsaboutthesurface-chemistrymodels,aswellasthesurfacereactions 53 involved. 4 T 1. 14/ Nomenclature ν00 = productstoichiometriccoefficientforspecieskin 5 ki aa.org | DOI: 10.2 ECDEaEkkdR ==== Jcdee∕onnifmneefrrucoggeslyyinotbnrbaaactrrirooriieenefrrfoifcoffiorgeraandstEsosloepfryesp–cptiRieeocsindie,kes,Ja∕mlkm,romeolc∕l2om∕ms3bination, ww__kki == mrppmerraooooclldd∕∕tuuimmoccntt22ii∕∕ooissnn, rraattee ooffspspeceiceiseskkininallreraecatciotinonsi,, p://arc.ai hK == stopteaclinesumenbtehralopfys,pJe∕ckiges γYΓk === rimmeaapcsistniofgrneamcetfiefonicntieflnucxyofgasspeciesk,m2∕s 17 | htt KKgnb == tnoutmalbneurmobfesrpseocifegsaisnsbpuelckiepshasenb θns;k = fsruarcftaicoenpohfaascetinvsesitesoccupiedbyspecieskon 4, 20 Kns;na = pnhuamsbeenrsofspeciesinactivesitesetnaonsurface ρ = density,kg∕m3 er 1 k = Boltzmannconstant σ = Stefan–Boltzmannconstant,W∕m2∕K−4 cemb kBfi,kbi = forward and backward reaction rates for ΦΦns == accotnivceenstirtaetidoennsoiftyspoencsieusrfkacoenpshuarsfeacnes,pmhaosle∕mns2, er on De Mm_k == rmmeaoacslastirowbnleoiiwghintgofrsapteecideusek,tkog∕smurofalce reactions, χkns;k = mmoolle∕mfr2actionofspeciesk Cent b kg∕m2∕s χnb;k = molefractionofbulkspecieskinbulkphasenb dt N = totalnumberofphases a erst Nnb = numberofbulkspecies Subscripts ud N ,N ,N = numberofgas,surface,andbulkphases D g s b b = bulkphase n - Nns;a = numberofactivesitesetsinsurfacephasens e = emptysite chiga PNR == npuremssbuerreo,fPasurfacereactions g = gasphase University of Mi qqRqcduoifnfv ==== tcduoointfniafvuvlesehricsevtaaeivlthegfelahuasextac,ftolWunflxs∕u,txmaWn,2tW∕,mJ∕∕m2m2ol∕K nnnstrabs ===== nnnstruuuuarmmmnfsabbblcaeeeetrrripoooohnfffaaabsslucu-ertrliofkvateacptehsioiaptnseheasaslseensergymode d by ri;ns = rmeaocl∕timon2∕fslux ofreactionionsurfacephasens, ve = vibrational-electronicenergymode e w = wallvalue oad S,S0 = stickingcoefficient ∞ = referencefreestreamconditions nl T = translational-rotationaltemperature,K w Do νki = net stoichiometric coefficient for species k in reactioni ν = sum of the stoichiometric coefficients of all I. Introduction s surfacereactants HYPERSONICvehiclesexperienceheatingduringhigh-speed ν(cid:2) = thermalspeedofgas-phasespeciesk,m∕s k flightthroughtheatmospherethatcauseveryhightemperatures ν0 = reactant stoichiometriccoefficientfor speciesk ki ontheirsurface.Whenavehicleorprobeenterstheatmosphereof inreactioni anyplanetathypersonicspeeds,abowshockisformedinitsfront. Thekineticenergyofthehypersonicflowisconvertedintointernal energyofthegasthatcreates veryhightemperatures intheshock Received 9 July 2014; revision received 4 March 2015; accepted for layer [1]. These temperatures are high enough to excite thevibra- publication6March2015;publishedonline24April2015.Copyright©2015 tionalenergymodewithinthemolecules,aswellascausedissocia- bytheAmericanInstituteofAeronauticsandAstronautics,Inc.Allrights tion chemistry. Therefore, such vehicles use a thermal protection reserved.Copiesofthispapermaybemadeforpersonalorinternaluse,on system(TPS)thatprovidesinsulationfromthesevereaerodynamic condition that the copier pay the $10.00 per-copy fee to the Copyright heating encountered during hypersonic flight through a planetary ClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923;include atmosphere. The TPS is a single point-of-failure system, as the thecode1533-6808/15and$10.00incorrespondencewiththeCCC. prolongedexposuretohightemperaturecancausethematerialsto *Postdoctoral Research Fellow, Department of Aerospace Engineering. fail[2,3].TheneedtodesignareliableTPSnecessitatesgoodunder- MemberAIAA. †JamesE.KnottProfessor,DepartmentofAerospaceEngineering.Fellow standingofthephysicalandchemicalprocessesthatdeterminethe AIAA. aerothermalheatingenvironment. 653 654 ANNAANDBOYD Dependingontheheatingencounteredduringhypersonicflight, II. TechnicalApproach an ablative or nonablative TPS may be used [3]. Nonablative or Computationalfluiddynamicmodelscanbeusedforsimulating reusablematerials(e.g.,ceramictilesusedonthespaceshuttlewitha environmentsthatcannotbestudiedinanexperimentaltestfacility. peakheating[4]of60W∕cm2)areusedwherethereentryconditions Thesemodelscanbeusedforaccuratelypredictingtheaerothermal arerelativelymild.Inadditiontotheentryvelocity,theheatingisalso environmentofthevehicleTPSduringentry,butthesemodelscanbe dependentonthe entry flight-path anglethat is determined bythe usedtoperformsuchanalysisonlyaftertheyhavebeenvalidatedfor trajectoryofthevehicle[5].AnablativeTPSisusedwhererelatively physicalaccuracybycomparisonwithexperimentalmeasurements. highheatingratesaregeneratedduringreentry(e.g.,theheatshield Bothcomputationalandexperimentalmethodscanbeusedcollec- for the Stardust mission with a peak heating [6] of 942W∕cm2). tivelytounderstandthephysicalandchemicalprocessesthatdeter- Ablative TPS materials accommodate high heating rates and heat mine the aerodynamic heating of a probe or hypersonic vehicle loads through phase change and mass loss. The ablative material duringitsentryintoaplanetaryatmosphere. absorbstheheatandleavesthehypersonicvehicleasthematerialis Thissectiondescribestheexperimentalandcomputationaltech- consumed and ablates away. It is designed to slowly recess in a niquesthatareusedtostudythegas–surfaceinteractionsthatoccur controlledmanner.AnablativeTPShasbeenusedformostplanetary onavehiclesurfaceduringitsentryintoaplanetaryatmosphere.The entry probes and high-velocity Earth atmosphere reentry vehicles, sectionfirstprovidesabriefdescriptionoftheexperimentalfacilityat includingStardust,theMarsScienceLaboratory,Apollo,etc.Abla- theUniversityofVermont,followedbyanoverviewoftheCFDcode 0 tive TPS materials are usually of two types, viz., pyrolyzing and usedinthisworkalong,withthedescriptionofgas–surfaceinterac- 3 45 nonpyrolyzing ablators. Pyrolyzing ablators (also referred to as tionmodelsimplementedinthecode. T 1. charringablators)arereinforcedcompositesthathavepolymerresins 4/ 1 as binders. An example of a charring TPS material is phenolic- 5 A. ExperimentalFacility 2 10. impregnatedcarbonablator. Experimental tests were conducted by Professor Doug Fletcher OI: Nonpyrolyzingablators(alsoreferredtoasnoncharringablators) and his graduate students in a 30 kWinductively coupled plasma D arethosethatwithstandheatbylosingmassonlybysurfaceablation g | and mechanical erosion [7,8]. Examples of noncharring TPS torchfacilityattheUniversityofVermont[9,10].Laserdiagnostic a.or materialsarecarbon–carbonandsilica.Veryhightemperaturesinthe instrumentation that employs a laser-induced fluorescence (LIF) http://arc.aia smshuaortfceakrcieala,lyrceearcnomamcabtyiancsaaautisocenattaholefymsdtiosaslneodcc,uiailfaterddsispbseooccuiienasdtetaodryda-tilosasmyoescridasitpfefe.ucTsieehsetomTtPhaSye tvndeauecrsmhiconrbuiiebqsreufdsleoetwnhissepiitfaniaerscastimalalitleteytddeiarfsnfaetdsruettchenhecthalfosnacitcqraiaultniietosysnl.astthLiiaonItFntaahirlesetefcumlaospepwdaefbritaeloetludoro.befTtaahmniindseassespexuceprtceiiionreings- 17 | occur,whichincreasestheconvectiveheatingtothesurface.Thus,a mentaldatathatwillbecomparedtothenumericalresults. 0 lesscatalyticsurfaceisdesirabletominimizethisadditionalheating. 4, 2 Also,whenthevehiclesurfaceisheated,thesurfacematerialmay TheICPtorchfacilityisdesignedtotestscaledmaterialsamplesin 1 high-enthalpygasflowsforsimulationofplanetaryentryandEarth ber chemicallyreactwiththeboundary-layergases,leadingtosurface atmospherereentrytrajectoryheatingconditions.Itisconfiguredfor m recessionasaresultofsurfacematerialconsumption.Thesechemical ce operation with subsonic flow to simulate postshock conditions of De reactionscanbeendothermic(vaporization,sublimation)orexother- high-enthalpyflightforastagnationpointgeometry.Thefacilitytest er on mCaicta(loyxciidtyatioofn,annitraabtiloatniv)eanTdPwSillmafafteecrtiathleannedthseuartfiancget-opathrteicsiuprafaticneg. conditionscanbeextrapolatedtoflightconditionsbymatchingthree nt parameters at the edge of the boundary layer, i.e., the flight total dt Ce rheeaacttiinognsotfhtahtelevaedhtioclseursfuarcfeacree.ceTshseiorenfaorree,kedyetfaaicletodrssttuhdaiteismopfacthtethsee enthalpy, the stagnation pressure, and the velocity gradient. The dersta interactionsthatoccurbetweenthesurfaceandtheatmospheregas mpeertfhoormdoeldoguyndiesrkthneowasnsumasptlioocnalofhleoactaltrtahnesrfmerocshimemuilcaatiloenquainlidbriis- Du arerequiredfortheaccuratepredictionofaerothermalheatingofthe um.Itisdiscussedindetailin[11–13].Thestagnationpointheatflux n - vehicleTPSandincharacterizingTPSmaterials. intheflightisequaltothatingroundtestsiftheseparametersare higa The major objective of this work is to investigate surface- matched[14]. Mic chemistryprocessesusingacoupledcomputationalfluid-dynamics/ Thefacilityprimarilycomprisesthepowersupplyunit,gasinjec- of surface-chemistrymodelandassesstheaccuracyofthemodelusing tion system, and plasma test chamber. The gas-injection system versity ethxepecroimmpenuttaaltiodnataal.aSnidgneixfipcearnimtdenistcarlerpeasnucltise.sTahreeroefbosreer,vaendobtheetwreoebn- pqruoavrtizdecsotnhfeinneimtreongtentugbaeswatheroreomhottemniptreorgaetunrepltahsamt eanitsergseinnetorattehde Uni jectiveistounderstandthesensitivitiesofflowandsurfaceparam- throughaninducedRFmagneticfieldcreatedbyahelicalloadcoil. by eterstovariationsintestinginputconditions.Asensitivitystudyis Thehotnitrogenplasmathenflowsoutofthequartztubefromthe ed performed to understand the effects of various inputs, as well as topintothetestchamberoftheICPfacilitywherethesampleistested. d oa physicalmodelingparametersonthesubsonichigh-enthalpynitro- Thetestchamberisconstructedfromstainlesssteel,andthetorch wnl genflowintheboundarylayerinfrontofagraphitesampleandits locations with the highest heat loads are actively cooled with a o D surfaceproperties. closed-loop water system. The test sample is installed in a brass The layout of this paper is as follows. The paper comprises six sampleholder,andthebackspacesideofthesampleiswatercooled. sections,withtheIntroductionbeingSec.I.SectionIIoutlinesthe For this investigation, experimental results from graphite samples technicalapproachusedinthiswork.Itdescribestheexperimental testedinthenitrogenplasmastreamareused.Thetestsamplesare andcomputationaltechniquesthatareusedtostudythegas–surface constructedfromDFP2-gradegraphite,fabricatedbyPocoGraphite, interactions that occur on a vehicle surface during its entry into a Inc.[15].Mostablativeheatshieldsaredesignedfromcarbon-based planetary atmosphere. Section III presents a description of the matrix materials impregnated with low-temperature phase change numericalboundaryconditionsusedinthecode.SectionIVpresents polymerresinsthatpyrolyze,leavingacarbon-richcharlayer.Since adescriptionofthenumericalsetupusedinthisstudy. thecarbonlayercontinuestointeractwiththeboundary-layergases, SectionVpresentstheresultsobtainedfromthenumericalsimu- reactionsbetweenthislayerandthegas-phaseparticlesareofim- lations of the experimental configuration performed using the menseinterest,andthereforegraphiteisusedforthisstudy.Graphite computationalfluiddynamics(CFD)codeLeMANSandtheircom- is noncharring, and therefore pyrolysis gases are not produced. parison with the experimental data. The results obtained from the Figure1showsaphotographofthegraphitesampleduringexposure analysisperformedforsensitivityofboundary-layerflowparameters tothenitrogenplasmainthetestchamberoftheICPtorchfacility. andsurfacepropertiestodifferentchemicalcompositionsattheinlet The test sample is a 25-mm-diam graphite sample mounted at a oftheinductivelycoupledplasma(ICP)torchexitarealsopresented, distanceof90mmfromthequartztubeexit. in addition to the effects of including the conduction within the Thequantitiesmeasuredarethesurfaceheatflux,surfacetemper- sample wall in the calculations. The paper ends with conclusions ature,relativenitrogenatomnumberdensity,andtranslationaltem- inSec.VI. peratureinthereactingboundarylayerabovethegraphitesurface. ANNAANDBOYD 655 of all species are described by a single temperature T [20]. The ve production and consumption rates of species are modeled using a finite rate chemistry model developed by Martin and Boyd [21], alongwithPark’stwo-temperaturemodel[22],toaccountforthermal nonequilibriumeffectsonthereactionrates. The set of partial differential equations is solved using a finite volumemethodonunstructuredgrids.Theinviscidfluxesacrosscell facesarediscretizedusingamodifiedformoftheSteger–Warmingflux vector splitting scheme[23], which islessdissipative and produces betterresultsinboundarylayersthantheiroriginalscheme.Theviscous terms are calculated using a centered scheme. Time integration is performedusingapointimplicitoralineimplicitmethod.LeMANSis parallelizedusingMETIS[24],whichpartitionsthecomputationalgrid betweentheprocessorsandthemessagepassageinterfaceprotocolto communicateinformationbetweenprocessors.Turbulentflowscould be simulated for simplegeometries using a zero equation algebraic Baldwin–Lomax turbulence model [25] implemented in LeMANS. 0 53 Themodelisnotusedfornumericalsimulationinthiswork,asthe 4 T flowfield studied has laminar behavior. The freestream Reynolds 1. 4/ numberfortheflowfieldanalyzedinthisworkis295,indicatingthatthe 1 25 flowislaminar.Themixturetransportproperties(i.e.,thecoefficientsof 0. 1 viscosity,thermalconductivity,andmassdiffusion)canbecomputed OI: usingtwomodels.ThefirstmodelusesWilke’ssemiempiricalmixing D g | rule [26], with species viscosities calculated using Blottner et al.’s or model [27]; and the species thermal conductivities are determined aiaa. using Eucken’s relation [28]. The other model uses Gupta et al.’s arc. mixingrule[29],withspeciesviscositiesandthermalconductivities p:// calculatedusingcollisioncross-sectiondata.Detailsonthemodelingof 017 | htt cFoigd.e1LeMExApNerSi)m.entalsetup‡(sectioninboxissimulatedusingtheCFD tdhiemseenesqiounaatlio/anxsiscyamnmbeetrficoufnlodwisnu[s3i0n]g. aLneyMmAiNxtSurceaonfsqimuaudlraitleatetwraols- 2 andtriangles,aswellasthree-dimensionalflowsusinganymixtureof 4, 1 hexahedrals,tetrahedrals, prisms,and pyramids.The code has been ber Thestagnationregionheattransferismeasuredwithacopperslug extensivelyvalidatedforhypersonicflows[30–33]. m ce calorimeter[16].Thecopperslugisidenticalinsizeandshapetothe e D graphitetestsample.Itisexposedtoidenticalfreestreamconditions n III. NumericalBoundaryConditions nter o asasmthpelegsruaprfhaicteesteammppelerawtuhreenisthmeemaseuarseudreumsienngtsaatrweom-caodloe.rTinhferatreesdt A. InletandOutletBoundaryConditions e dt C opticalpyrometerwithatemperaturerangefrom1273to3273K.The InLeMANS,befoerthiswork,theinflowandoutflowboundary dersta enxitproergiemneanttoaml tneustmsbmeredaesunrseitythaendgtarsa-npshlaatsieonfallowtemppreorpaeturtriee)sin(it.he.e, cfloonwdsi,tioanllstwheerveasripaebcliefsiesdhoonullydfboerhspyepceirfsieodnicatfltohwesi.nFfloorwhyapnedrsnoonniec u D reacting boundary layer above the graphite surface using a two- shouldbespecifiedattheoutflowwhentheexitisalsoatsupersonic an - photon laser-induced fluorescence technique. Unfortunately, the speeds.TheflowinthecaseofanICPtorchtestfacilityissubsonicin hig calibratedabsoluteatomnumberdensityvaluesarenotyetavailable. nature. For a subsonic flow, the disturbances propagate upstream c Mi Therefore, the relative nitrogen atom number density is used for againsttheflowdirection,andthisneedstobeaccountedfor.There- of assessingthecomputationalsimulations.Therelativenitrogenatom fore,newinflowandoutflowboundaryconditionsareimplementedfor versity nICumPtbeesrtdcehnasmitbyeirsathnedrtahtieomofictrhoewspavecetdrailslcyhianrtgeegrfalotewdrLeIaFctsoigrn(MalDfoFrRth)e. sfruebessotrneiacmflostwatecoisndfuitliloynssp[e3c4if]i.eFdo.rInthtehissucbosnodniitcioinn,leatllbtohuenvdaarriya,btlhees Uni A MDFR is used to establish absolute species concentration and (i.e.,velocity,density,andtemperature)arespecifiedasinput. ded by terxapnlsalnataitoionnalotefmthpeetreacthunreiqiunethfeorfltohweqinuathnetiItCiePsmtesetacshuaremdbiesrp.Arovdiedteadileidn boFunodratrhye scuobnsdoitniiocnouistleimt bpoleumndeanrtyedcoinndiwtihoinc,hasctoantisctapnrtepssreusrseuries nloa [9,17,18]. The graphite sample mass loss (ablation) rate is also specifiedattheoutlet.Thevelocityanddensityvariablesaresolved w using zeroth-order extrapolation. The specified outlet pressure is o quantifiedfrompre-andposttestmassmeasurements. D usedtocomputethetemperaturevariableusingtheequationofstate. B. NumericalMethod B. WallBoundaryConditions Thenumericalsimulationsinthisworkareconductedusingthe Navier–StokescomputationalfluiddynamicscodeLeMANS[19], Inthesimplestapproach,wallcatalycityeffectsareaccountedfor inLeMANSbychoosinganoncatalyticorasupercatalyticsurfaceas developed at the University of Michigan. It is a general-purpose parallel three-dimensional code that solves the laminar Navier– thespeciesboundarycondition.Thecatalycityofasurfaceingeneral canbeaccountedforbyfourtypesofconditionsatthewallboundary, Stokes equations, including chemical and thermal nonequilibrium as described in Table 1. A supercatalytic boundary condition is effects on unstructured computational grids. The flow is modeled assuming the continuum approximation is valid. The translational androtationalenergymodesofallspeciescanbedescribedbytheir Table1 Speciesboundaryconditions respectivetemperatures,TandT ,inthecode.However,inthiswork, r thetranslationalandrotationalmodesareassumedtobeequilibrated, Boundarycondition Description as these modes usually require relatively few collisions to reach Noncatalytic Norecombinationofatomsonthesurface equilibrium.Therefore,thesemodesforallspeciesaredescribedbya Supercatalytic Atomsthatstrikethesurfacerecombine tothefreestreamgascomposition singletemperatureT .Thevibrationalandelectronicenergymodes tr Fullycatalytic Allatomsthatstrikethesurfacerecombine toformmolecules ¶PersonalconversationwithA.J.Lutz,UniversityofVermont,Mechanical Partiallycatalytic Someatomsreflectandsomerecombine Engineering,Burlington,VT,March2013. 656 ANNAANDBOYD inappropriatefortheflowsthatcomprisedissociatedspeciesatthe XNs NXns;a XNb freestream, as this condition will lead to the same composition K(cid:2)K (cid:3) K (cid:3) K (2) g ns;na nb throughdissociation/recombinationatthewallasinthefreestream, ns(cid:2)1na(cid:2)1 nb(cid:2)1 whichisundesirableforconditionswheretheeffectofrecombination ontheheattransferistobestudied.Inadditiontosurfacecatalysis, ForasystemwithKspeciesandNRsurfacereactions,thegeneral surface participating reactions are required to be included in the formofthesurfacereactionicanbeexpressedas analysis for a thorough understanding of gas–surface interactions. Therefore, a simple binary catalytic recombination model and a XK XK ν0A ⇌ ν00A (3) complex finite rate surface-chemistry model are implemented in ki k ki k LeMANS. k(cid:2)1 k(cid:2)1 where ν0 and ν00 are the respective reactant and product stoi- 1. BinaryCatalyticRecombinationModel chiometrkiiccoeffickiientsforspeciesA .Thenetproductionratew_ of k k Forthesimulationofthefullrangeofcatalycityregimes,froma speciesA isthesumoftheproductionratesfromallsurfacereactions k noncatalyticwalltoafullycatalyticwall,asimplifiedcatalyticatom givenbyEq.(4).Itappliestospeciesinanyphaseatthegas/surface recombination model (i.e., a binary interaction model with full interface: energy accommodation [35]) is implemented in LeMANS. It is a 530 simple model applied to a binary gaseous mixture of atoms and XNR 4/1.T4 mmoaslescfululexsooffththeereslaemvaenstpsepceiceise.sIattitsheimwpallelm.Ietnisteadppblyiebdaalasnacsinpgectihees w_k(cid:2) i(cid:2)1w_ki (4) 51 boundaryconditionbyconsideringafirst-orderrecombinationreac- 2 10. tion for a binary gas at the wall. It only accounts for catalytic wherethereaction-specificproductionratew_kiistheproductofnet OI: homogeneousrecombinationatthesurface. stoichiometriccoefficientνkiandreactionfluxri;nsforreactionion D phasensgivenbytheexpressioninEq.(5): g | or 2. FiniteRateSurface-ChemistryModel aiaa. Thefiniteratesurface-chemistry(FRSC)modelisageneralgas– w_ki(cid:2)νkiri;ns p://arc. seuffrefcatcseoifnsteurrafcatcieoncamtaolydseils[a3s6w–3e8ll].asItscuarnfacbeepuasretdicitpoaitninvgesrteigaactteiotnhse. νki(cid:2)(cid:4)νk0i0−νk0i(cid:5) 17 | htt TMhaecLFeRaSnCetmalo.d[3e7l]dwevaesliomppeldembyenMteadrisnchLaelMl aAnNdSMbaycALelkaann[d3r6y]eatnald. ri;ns(cid:2)kfiYK Xνkk0i−kbiYK Xνkk0i0 (5) 4, 20 [38]. The model can simulate the chemical reactions between the k(cid:2)1 k(cid:2)1 mber 1 hsiymppelrisfoiendicbginasarayndcastualryfaticceaotfomtherevceohmicbleindautiroinngmpoladneeltacrayneonntlryy.bAe wrehacetrieonkfii,arensdpekcbtiivaerely.thXefoisrwthaerdcoanncdenbtarcaktiwonarodfrsepaecctiioesnArateasttfhoer ece usedtostudytheeffectsofsurfacecatalysisforaconstantcatalytic surfaceand,foreachphaske,itcanbedescribedas k D n efficiencyappliedtoabinarygaseousmixtureofatomsandmole- Gasphase: o er cules.TheFRSCmodelcanbeappliedtomultiplegaseousspecies Cent and can account for different surface reactions, such as particle X (cid:2)C (cid:2)χ P (6a) dt adsorption/desorption,therecombinationofanatomofthegaswith k k kRT dersta abninaattoiomnaodfstworobeaddsoonrbtehdeawtoamlls[Ealtetyh–eRwidalela(lL(aEn-gRm)ureira–cHtioinns]h,erlewcoomod- Surfacephase: u an - D rneiatrcidtiaotnio),naannddroexaicdtaiotinosn)l.eTadhienFgRtoSCsumrfoadceelriescbeassseiodnon(et.hge.,ccoanrcbeopnt Xk(cid:2)Φns;k(cid:2)θns;kΦns (6b) g chi of simulating surface chemical reactions by competing finite rate Bulkphase: Mi processes.Itaccountsforcatalyticheterogeneousrecombinationat niversity of tehnevItisrcuoornfmamcpeerni.stes.sEtharceheeennvviirroonnmmeennttsc,avniczo.,ngsaiss,tsoufrofanceeo,ramndobreu“lkph(saosleids”) The forward reaction rateXfkor(cid:2)eaχcnhb;ksurface reaction type can(6bce) y U thatcorrespondtoadistinctphysicalregionoftherespectiveenviron- specifiedbyanArrheniusfunctionorusingakinetic-basedformula- ed b ment.Thegasenvironmentisasinglephase(Ng(cid:2)1)thatcontains tionforspecificprocesseslikeadsorption,Eley–Ridealrecombina- ad gas-phasespecies. tion,andLangmuir–Hinshelwoodrecombination.TheFRSCmodel o wnl The surface environment can consist of multiple phases repre- canaccountforcompetingfiniterateprocessesunderagivensetof Do sentedbynsrangingfromonetothetotalnumberofsurfacephases experimentalconditionsandprovidesaneffectivereactionefficiency Ns.EachsurfacephaseoccupiesafractionΩnsofthetotalsurface. for a gas-phase reactant consumed in a surface reaction process. Eachsurfacephasecancomprisemultiplesetsofactivesitesrepre- For this study, the FRSC model is used to simulate a constant sentedbynarangingfromonetothetotalnumberofactivesitesfor reaction efficiency by using the appropriate choice of reaction eachphaseNns;a.EachactivesitesethasasitedensityΦns;na.Allthe typesandparameters.Thegas–surfaceinteractionprocessesstudied surfacereactionstakeplaceatactivesites.Similarly,thebulkenvi- aretherecombinationofnitrogenatomstomoleculesatthesurface ronmentcanconsistofmultiplephases(nb(cid:2)1; :::;Nb),wherenb duetocatalysisandthecarbonnitridationreactionwherenitrogen isthenumberofbulkphases.Eachphaseoccupiesavolumefraction atoms react with the surface carbon to form gaseous CN. The vnb ofthebulkandcontainsauniquesetofspeciesKnb.Thetotal surface reaction types considered are adsorption and Eley–Rideal numberofphasesNis recombination to emulate a constant reaction efficiency for these processes.TheE-Rmechanisminvolvesthereactionofagas-phase specieswithanadsorbedspeciestoformagas-phaseproduct.The N(cid:2)1(cid:3)N (cid:3)N (1) s b surface reaction for an adsorption process for a particle A can be representedby Thetotalnumberofspeciesisthesummationofgas,surface,and bulkphasespeciesgivenbyEq.(2).Inthisformulation,aparticular A(cid:3)(cid:4)s(cid:5)→A(cid:4)s(cid:5) speciesisconsideredadifferentspeciesifitisingasphaseorina particular active site in a surface phase or in a bulk phase. The where(s)isanemptyactivesite,andA(cid:4)s(cid:5)isanadsorbedparticle.The descriptionofallthevariablesisprovidedinthenomenclature: forwardreactionfluxforanadsorptionprocessistheproductofthe ANNAANDBOYD 657 stickingcoefficientS ,theimpingementfluxΓ ofspeciesAonthe AB(cid:3)(cid:4)s(cid:5)→A(cid:3)B(cid:4)s(cid:5) (12b) 0 A surface,andthefractionθ ofavailableactivesitesthatareempty: s;e TheE-Rreactioncanalsobeusedtorepresentaprocesswherea rf (cid:2)SΓAθs;e (7) gas-phasespeciesimpingesonthesurfaceandreactswiththesurface. An example is shown in Eq. (13), where the gas-phase species A wherethestickingcoefficientis impingesonthesurfaceandreactswiththebulkphasespeciesB on b thesurface: (cid:2)−E (cid:3) S(cid:2)S0 exp RTad A(cid:3)(cid:4)s(cid:5)(cid:3)Bb →AB(cid:3)(cid:4)s(cid:5) (13) ThestickingoradsorptioncoefficientS isthefractionofthegas- Thisequationisusedtoemulatethecarbonnitridationreaction. 0 phasespeciesthathitsthesurfaceandbecomesadsorbed. Thespeciesmassfractionatthewalliscalculatedbybalancingthe Theimpingementfluxisgivenby mass flux of the relevant species, taking the consumption and productionatthewallintoaccountasshowninEq.(14): ν(cid:2) 0 ΓA(cid:2) 4ACA (8) −ρwDk∂∂Ynk(cid:7)(cid:7)(cid:7)(cid:7) (cid:3)ρwvwYk;w (cid:2)Mkw_k (14) 3 w 45 wherethethermalvelocityofspeciesAis T 1. Here,thefirstterm 4/ s(cid:4)(cid:4)(cid:4)(cid:4)(cid:4)(cid:4)(cid:4)(cid:4)(cid:4)(cid:4)(cid:4)(cid:4) 51 8RuT DOI: 10.2 ν(cid:2)A(cid:2) πMA −ρwDk∂∂Ynk(cid:7)(cid:7)(cid:7)(cid:7)w g | andthefractionofavailableemptyactivesitesis or represents diffusion of the gas-phase species, the second term aa. Φ ρ v Y representsthemassfluxofspeciesblownfromthesurface p://arc.ai θs;e(cid:2) Φss;e oinwrtcoowgnassku;pwmhpatsieo,naonfdstpheectieersmfroomntshuerrfiagchetrMeakcwt_ioknrse.pIrnesthenetssepcroonddutcetrimon, 7 | htt Theforwardreactionrateforanadsorptionprocessisexpressedby ρrewavcwtioinsst(hee.gm.,oasxsidbaltoiowni,nngitrriadtaetimo_nb,aantdthseubsluimrfaatcieond)u.Tehteovseulorfcaictye 1 thefollowing: 4, 20 oftheblowingmassisvw.Itisgivenbythefollowingexpression: cember 1 kf (cid:2)(cid:5)4νΦ(cid:2)Aνss(cid:6)S0 exp(cid:2)−REuaTd(cid:3) (9) m_b (cid:2)ρwvw(cid:2)−XNnb XKnb Mkw_k (15) e D nb(cid:2)1k(cid:2)1 n The surface reaction for an Eley–Rideal recombination of a o er particleAwithanadsorbedparticleB(cid:4)s(cid:5)canberepresentedby nt e C C. HeatFluxattheWall adt A(cid:3)B(cid:4)s(cid:5)→AB(cid:3)(cid:4)s(cid:5) Heattransfertothesurfaceiscomposedofconvectiveheatfluxand Michigan - Duderst iopmfroTpacvihenaesgisleafimobsrletewhneaatcrfpdltruivoxredeΓusaAcicttteoiosoffnsthtphaefetlcuaiEexrlseeAyfoo–corRcnuiatdpnheieeaEdslulrbeeryyfaa–cactRdieois,dnoaenreabdfleftidhcreeisecpfnorecamcycibteγisioEnnBRa,tθ:itsoh;Bne hhrtdioeeivftaaefattutihsffolieluonuaxnaxtldfhmilsueuoaexcdtoteofimslsu,dpmxaiofesofsswudesadeeirlloeelondafmsoacodfcoducsneepovletreeodcdciittnehiuosgesnitvntooidgbtuhrFaaeeotmiutsooruoniredatfhrlai’fecmsieetold.radaTwfenoh,.sreTlamanchtiodeooncfnsvoapFenlecivcctaeikinvec’dess- ersity of rf (cid:2)γERΓAθs;B lisawuAs[er3ad9d]fi.oartivtheeebqausielilbinrieumresbuoltusnadnadrypcaortnodfititohne,saesnsshitoivwitnyinstuEdqy..(1T6h)e, Univ wheretheEley–Ridealreactionefficiencyis walltemperatureTwissetbythisboundaryconditionwithemissivity oaded by γER (cid:2)γ0 exp(cid:2)−RETER(cid:3) ϵforgraphitesetto0.83q[15](cid:3): q (cid:2)σεT4 (16) nl conv diff w w o D andthefractionofavailableactivesitesis Thecontributionofconductiveheattransferisalsoevaluatedby usingthematerialresponsecodeMOPARdevelopedattheUniver- Φ θ (cid:2) s;B (10) sityofMichigan[40,41].MOPARiscoupledtoLeMANSandcan s;B Φ s modelheatconductionwithinthematerial.Theenergybalanceatthe surfaceiscalculatedusingtheboundaryconditionshowninEq.(17): The forward reaction rate for an Eley–Rideal recombination processisexpressedbythefollowing: q (cid:2)q (cid:3)q −ϵσ(cid:4)T4 −T4 (cid:5) (17) cond conv diff w res kf (cid:2)(cid:5)4νΦ(cid:2)Aνss(cid:6)γ0 exp(cid:2)−REuETR(cid:3) (11) wsimheurleatiTorness bisegtihnewciothnstthaentcornesveerrvgoeidr ftleomwpfieerladtusroel.utTiohneocbotuaipnleedd fromLeMANS.LeMANSfirstcallsMOPAR,andaninitialq is cond Thebackwardreactionrateforbothprocessesiszero,asboththe calculatedbasedonthetotalheatfluxfromLeMANS(i.e.,initialheat thermaldesorptionanddissociationwithapartialadsorptionprocess flux)fromEq.(17).MOPARthenrunsforauser-definedtime,and [shownbyEq.(12)]arenotconsideredinthiswork: thewalltemperatureiscalculated.MOPARpassesthiswalltemper- Thermaldesorption: aturevaluetoLeMANS,andthenthefluidequationsaresolvedfora user-defined number of iterations. The temperature along thewall A(cid:4)s(cid:5)→A(cid:3)(cid:4)s(cid:5) (12a) remains constant during this computation. MOPAR is then called again,andtheupdatedvaluealongwiththeinitialvalueofconductive Dissociationwithpartialadsorption: heatfluxareusedastemporalboundaryconditionstosolvethetime- 658 ANNAANDBOYD Table2 Freestreamandwallboundary Adsorption(E (cid:2)0 J∕mol) ad conditions Parameter Value N(cid:3)(cid:4)s(cid:5)!kf1N(cid:4)s(cid:5) (18a) Massflowrate,kg∕s 0.82×10−3 Velocity,m∕s 136 Eley–Ridealrecombination(E (cid:2)0 J∕mol) TemperatureT∞,K 7000 ER Pressure,kPa 21.3 WalltemperatureTwall,K 1598 N(cid:3)N(cid:4)s(cid:5)!kf2N (cid:3)(cid:4)s(cid:5) (18b) 2 Thesecondsetofsurfacereactions[showninEq.(19)]takesinto accurateenergyequation.Theprocessisrepeateduntilaconverged accountthenitrogenatomrecombinationonthewallduetosurface steady-state solution is obtained. In this study, the criterion for catalysisalongwiththecarbonnitridationreactionwherethecarbon convergence is when the wall temperature values are the same fromthesurfacereactswiththeimpingingnitrogenatoms.TheEley– betweenfinalandpreviouscallsofMOPAR. Rideal recombination reaction is used to represent the process of carbon nitridation. In these reactions, k , k , and k are the f1 f2 f3 respectiveforwardreactionrates: 4530 IV. NumericalSetup Adsorption(Ead (cid:2)0 J∕mol) T 1. Thetestconditions[i.e.,facilityinlet(ICPtorchexit)conditions] 514/ andthegraphitesamplewalltemperaturesimulatedbyLeMANSare N(cid:3)(cid:4)s(cid:5)!kf1N(cid:4)s(cid:5) (19a) 2 0. basedontheexperimentsconductedattheUniversityofVermontin 1 OI: order to compare the computational results with the experimental Eley–Ridelrecombination(E (cid:2)0 J∕mol) D measurements.Thesimulationsareperformedfortheexperimental ad g | conditions that are shown in Table 2. The boundary conditions c.aiaa.or acsosnifgingeudraftoiornthiseussiemdufloartiaolnlssiamreulsahtioownns.iTnhFeitge.st2c.hAanmabxeirswymalmliestsriect N(cid:3)N(cid:4)s(cid:5)!kf2N2(cid:3)(cid:4)s(cid:5) (19b) http://ar aTshaenteosntcsaatmalpylteicwwalallilswseitthtoanairsaodtihaetirvmeaelqwuaillilbtreimumpebroatuunrdeaorfy3c0o0ndKi-. Eley–Ridelrecombination(Ead (cid:2)0 J∕mol) 017 | tsitoang,naantidonthepoFiRntSiCsmalosodeslhioswapnpwliehderoenltyhetohtehaitswfluaxll.aInndadthdeitisounr,fathcee N(cid:3)(cid:4)s(cid:5)(cid:3)C !kf3CN(cid:3)(cid:4)s(cid:5) (19c) 2 b 4, temperaturearemeasured.Thegridisgeneratedusingthecommer- 1 er cialmeshgenerationsoftwarePointwise[42].Gridindependenceis b m achievedforaflowinthermalequilibriumusingagridwith22,000 e ec quadrilateralcells.ApictureofthegridisshowninFig.3. D n The gas–surface interaction processes studied are the recombi- o er nationofnitrogenatomstomoleculesatthesurfaceduetocatalysis ent andcarbonnitridationwherenitrogenatomsreactwiththesurface C dt carbontoformgaseousCN.Carbonnitridationisstudiedassample a erst masslossisobservedintheexperiment,andresultsforthesurface ud recessionarereportedintheworkbyLutzetal.[9,43]Therefore,two D an - smeotsdeolf.Tsuhrefafcirestrseeatctiisotnhseasruerftaackeerneaicnttioonac[schoouwntnuinsinEgq.th(1e8F)]RtShaCt g chi accountsonlyforthenitrogenatomrecombinationonthewalldueto Mi surfacecatalysis.Here,agaseousnitrogenatomisadsorbedontoan y of availableactivesiteonthesurfacethroughanadsorptionreaction. ersit Then,anothernitrogenatomfromthegasphaserecombineswiththe niv adsorbed nitrogen atom to form a gaseous nitrogen molecule and U leavestheactivesite.Inthesereactions,k andk aretherespective d by forwardreactionrates: f1 f2 Fig.3 Computationalgrid. e d a o nl w o D Fig.2 Boundaryconditions. ANNAANDBOYD 659 Allthetestcasesareinvestigatedusingaconstantreactionefficien- Table3 Testcases cyγ.Theeffectivereactionefficiencyforagas-phasereactantcon- Catalytic Carbonnitridation Effectivereaction sumed in a surface reaction process is the net result of competing Case efficiencyγ efficiencyγ efficiencyγ finite rate processes. An analytic expression for constant reaction N CN efficiency γ is derived for both the surface reaction set shown in 2 0 0 0 2 0.07 0 0.07 Eq.(18)aswellasforEq.(19). 3 0.07 0.005 0.0725 The constant reaction efficiency γ for a gas-phase reactant k is 4 1 0 1 definedasthefractionofcollisionsthatitexperiences,withthesur- faceresultinginitslossfromthegas-phaseenvironment: −w_ Fortheanalysiswhereonlycatalyticnitrogenatomrecombination γ(cid:2) Γ k (20) atthesurfaceisconsidered,thegasmixtureiscomposedofatomic k andmolecularnitrogen,andonlyEq.(26)isused.Fortheanalysis wherew_ isgivenbyEq.(4),andΓ istheimpingementfluxgivenby where both catalytic nitrogen atom recombination and carbon ni- k k Eq.(8).Thenegativeproductionratew_ representstheconsumption tridation reaction at the surface is considered, the gas mixture is k ofthegas-phasereactantatthewall.Theconstantreactionefficiency composed of atomic nitrogen, molecular nitrogen, atomic carbon, γforthesurfacereactionsinEq.(18)canbecalculatedusingEq.(4), andtheCNmolecule,anditusesbothEqs.(26)and(27). 530 Eq.(6),andEq.(8)as Thetestcasesconsideredinthisstudytodeterminetheeffectsof T4 gas–surfaceinteractionprocessesareshowninTable3.Thecatalytic org | DOI: 10.2514/1. equTahteinsgurEfqac.γe(4(cid:2)c)otn−oΓcwze_NenNrtoraftioγorn(cid:2)stoekfaftd1hyCe-NsatdΦa(cid:4)stνs(cid:2)oe;Nercb∕(cid:3)oe4nd(cid:5)kdCNfit2NiCaotnNosmΦasss;Nisobtained(2b1y) acevγMnofCafaNldniuccdieiLisiset[enis4soaece4nntyt]te[ofoo4qoffo5urnγn]ap.iNelutIrtrft(cid:2)ooeoigsrc0e0aa.on0.r0bfb0au7to5atlonliibynm.saeTcssbdaheaγtedfasNrevlooydaimntsliuocsaaenewvtfcaoaatolonrlmulc.ezeapTexrdarhbperoeoietsefrnpooirmamnnrrietaitbinrnaeinetdltaoldwaylntlbeiyccoeyaanndttDaaeedlltrfyyaeiftvttiriiacmeccirfeiwwrnanonaaecmlldydll c.aiaa. w_N(cid:4)s(cid:5)(cid:2)0 kf1CNΦs;e−kf2CNΦs;N(cid:2)0 Φs(cid:2)Φs;e(cid:3)Φs;N (22) anrictrjoegtetnestasndperrefsourmltsedfrofomrcpohmenpoultiact-iiomnparlesginmauteladticoanrsb.oInt sahbolautlodrbine p://ar Substitutingfork andk fromEqs.(9)and(11), notedthatγCNisdependentonthetypeofcarbonusedaswellasthe htt f1 f2 experimentalconditions. 17 | Φ S Case1representsawallwherenosurfacechemistryisaccounted 20 ⇒Φ (cid:2) s 0 forandistreatedasnoncatalytic.Thesurfacechemistryforcases2 14, s;N S0(cid:3)γ0 and4isdefinedbythereactionsshowninEq.(18)and,forcase3,itis er definedbyEq.(19).Theeffectivereactionefficiencyγforcases2and emb SolvingEqs.(21)and(22),thenetconstantreactionefficiencyγis 4iscalculatedusingEq.(23)and,forcase3,Eq.(25)isused. ec givenby D n dt Center o γ(cid:2)S20S(cid:3)0γγ00 (23) The comparisons of coVm.putRatieosnualltsresults with the measured udersta EqT.(h1e9)cocnanstabnetcraelcauctliaotendeuffsiicnigenEcqy.(γ4)f,oErqt.h(e6)s,uarnfadceEqr.e(a8c)tiaosns in efoxrpearllimteesnttacladseastaiasrtehperremseonctheedmhiecrael.Tnohneefqlouwilipbhriyusmicsflmowod.eTlhcehromseon- Michigan - D γ(cid:2)kf1CNΦs;e(cid:3)kf2(cid:4)Cν(cid:2)NN∕Φ4s(cid:5);NCN(cid:3)kf3CNΦs;eχb1;c (24) cta[h1hne8ed]mfirtnohicitataaettlifronlaonotewanloeiqfmsuciohinldeitbemhsreiiuacrmrameloramceshlesaeuaxmnmastieictodahnlatnoatrobebnoecethoqenuqvsiuilibiidlbriearbriteruiaodmtn.eTadfloh.rreIetttlhraisaexnasfslhtolioaowwtnifonianenilanddl versity of phTashee.SboullvkipnhgaEsqess.u(r2f4a)ceancdon(2c2en),ttrhaetionnetχcbo1n;cstiasnotnreeafcotrioansienfgfilceiebnuclyk ctthiooenndfsa.itcTiiolhinteys.fliAonwleutan(tiif.teoh.re,mtihnveleeqtlouocafirttthyze,tttueebsmetpceehxraiatm)tuibrseesr,piasencndiofidneeudnnisinfitoytrhmepr.soTifmhilueerlaea--t ni γisgivenby U fore,astudyisperformedtoassesstheeffectsofdifferentinletpro- y d b 2S γ (cid:3)γ γ files(i.e.,uniformandnonuniform)onthespeciesconcentrationand de γ(cid:2) 0 0 CN 0 (25) temperaturegradientsnearthematerialsurface,aswellasontheheat nloa S0(cid:3)γ0 transfertothematerialsurface.Itisconcludedthatthenonuniform ow inletprofiledoesnotsignificantlyaffectthesolution.Theresultsfor D Thereactionefficiencyγ0forsurfacecatalysis,alsoreferredtoas thestudyarediscussedin[18,46].Anassumptionofchemicalequi- catalyticefficiencyofnitrogenatoms,isdenotedbyγN.Itisdefined libriumofthenitrogengasmixtureattheICPtorchexitisusedto astheratioofthefluxofnitrogenatomsthatrecombineonthesurface calculateitscompositioninthesesimulations,asexperimentaldataat toformnitrogenmoleculestothetotalfluxofnitrogenatomsthat theexitarenotavailable.Theequilibriumcompositionofthenitro- impingeonthesurface.Aconstantcatalyticefficiencyisachievedby gengasmixtureatthequartztubeexitforthegiventemperatureand settingS0equaltoγ0.Thereactionefficiencyforcarbonnitridation, pressure [9] is calculated using the NASA program Chemical alsoreferredtoascarbonnitridationefficiency,isdenotedbyγCN.Itis EquilibriumwithApplications(CEA)[47]. defined as the ratio of nitrogen atoms reaching the surface and Themaincalculatedparametersanalyzedaretranslationaltemper- combiningwithsurfacecarbonatomstotheratioofthetotalfluxof ature,normalizednitrogenatomdensity,surfaceheatflux,andmass nitrogen atoms that impinge on the surface. It is assumed in this removalrate.Thenormalizednitrogenatomdensityiscalculatedby investigationthatallthecarbonmasslossoccursduetothecarbon scalingthenitrogenatomdensityvalueforeachcasewiththerespec- nitridationreaction. tivevalueatthelocationoftheexperimentallymeasureddataatthe The following dissociation–recombination reactions are consid- largestdistancefromthestagnationpointofthetestsamplealongthe eredintheanalysis: stagnation line. The experimental temperature and normalized nitrogenatomdensityvalueshaveuncertaintiesofabout(cid:6)500Kand N (cid:3)M⇌2N(cid:3)M (26) (cid:6)25%, respectively [48]. The simulation runtime for each case is 2 approximately6husing32processors. InSec.V.A,thebaselineresultsforthecomparisonsofcompu- CN(cid:3)M⇌C(cid:3)N(cid:3)M M(cid:2)N;N2;C;CN (27) tationalresultswiththemeasuredexperimentaldataarepresented.It 660 ANNAANDBOYD 0 3 5 4 T 1. 4/ 1 5 2 0. 1 OI: Fig.4 ComparisonoftranslationaltemperatureandnormalizedN-atomdensityalongthestagnationline. D g | or a. a ai c. ar p:// htt 7 | 1 0 2 4, 1 er b m e c e D n o er nt e C dt a erst d u D n - a g hi c Mi of y ersit Fig.5 Comparisonofwallheatfluxbetweenthecomputationalresults. v ni U y b d isseeninthebaselineresultsthattherearesignificantdiscrepancies chemistryprocesses.Thereisanincreaseinnitrogenatomdensity e ad between the computational and experimentally measured values, (Fig.4b)intheboundarylayerforcase1,whereasitisconsumedfor o wnl which could be explained by a combined effect of various allothercasesduetosurfacechemicalreactions.Thenitrogenatom Do mechanismsthatareaddressedinthisstudy.SectionV.Bpresentsthe loss is due to surface catalysis, i.e., catalytic recombination of results of the sensitivity analysis performed on the ICP torch exit nitrogenatomstomoleculesforcases2and4.Thenitrogenatomloss chemicalcompositiontoevaluateitseffectsontheflowparametersin seenforcase3isthecombinedeffectofsurfacecatalysisaswellas theboundarylayerandthesurfacepropertiesandtheircomparison carbonnitridation.Thenitrogenatomdensityforallcasesexceptcase with the measured experimental data. The results of the study 1showalossofnitrogenatomsintheboundarylayer,asisobserved performedtodeterminetheeffectsofconductionwithinthegraphite intheexperimentalmeasurements. sampleonthesurfacepropertiesarealsopresentedinSec.V.C. Theeffectofsurfacechemistryonthesurfacepropertiesisalso evaluated.Thepropertiesanalyzedarethesurfaceheatfluxandwall A. BaselineResults temperature.ThetotalheatfluxisplottedinFig.5aalongwiththe Thecomparisonsbetweenthenumericalresultsandexperimental diffusiveheatfluxinFig.5b.Anincreaseisseeninthetotalheatflux LIF measurements are presented for translational temperature and forallthecaseswithsurfacereactionsascomparedtothenoncatalytic normalizednitrogenatomdensityinthetestsampleboundarylayer wall.Thisincreaseisexplainedbythecontributionfromdiffusive alongthestagnationstreamline.Thestagnationlineboundary-layer heat flux for the cases with surface reactions, which is zero for a resultsareshownforthetranslationaltemperatureinFig.4aandthe noncatalyticwall. normalized nitrogen atom density in Fig. 4b. There is a rise in Thewalltemperatureforresultsfromdifferentsurface-chemistry temperature(Fig.4a)intheboundarylayerforcaseswheresurface modelsisshowninFig.6a.Case4withafullycatalyticwallhasthe chemistryisincludedascomparedtocase1foranoncatalyticwall. highest,andcase1withnosurfacechemistryhasthelowesttemper- Thecomparisonsbetweencases2,3,and4showthattemperaturein atureatthesurface.Thecarbonmassremovalfluxm_ asaresultof b theboundarylayerarenotsignificantlyaffectedfordifferentsurface- the carbon nitridation reaction for case 3 is also computed and is ANNAANDBOYD 661 0 3 5 4 T 1. 4/ 1 5 2 10. Fig.6 Comparisonoftemperaturefordifferentcasesandmassremovalfluxforcase3. OI: D g | aa.or showninFig.6b.Thetotalmasslossrateiscalculatedfromm_b,as B. SensitivitytoInletChemicalComposition c.ai showninEq.(28): 1. ComparisonBetweenEquilibriumandPowerEqualto13.8Kilowatts http://ar Z resTuhltissosbetacitnioendupsriensgenthtseitnhleetcgoamscpoamrispoonsitpioernfocramlceudlatbeedtwaseseunmitnhge 17 | mass lossrate(cid:2) m_bdA (28) chemicalequilibriumandthatobtainedforaICPtorchflowpower. 0 ThepowerabsorbedbytheflowintheICPtorchisusedtodetermine 2 4, thecompositionofthegasatthetestchamberinlet,i.e.,theICPtorch 1 ember weahcehresumr_fbaciesetlheemmenats,sanredmdoAviasltfhleuxsu[rcfaalcceualareteadofuesiancghEelqe.m(e1n5t).]Tfhoer eaxniet.ffTichieenpcoywfearcitnortheestfilmowateidstthoebper0o.d5u6c.t§oTfhtehevovlotaltgaegeis,1cu0r.3reknVt,aanndd c De stagnationpointheatfluxismeasuredexperimentallyusingaslug thecurrentis2.4Acurrent.Thecalculatedpoweris13.8kW.The nter on cmaeloarsiumreedtefrofrotrhteesctasceonodfiatio0n.8s4sigm∕islamratossthflioswcarsaet.eTahnedhpereastsfulurexoisf falnodwsppoewciefircisenatlhsaolpgyivhengbivyetnhebyprEoqd.u(c2t9o)f.tThheemsapsesciffliocwenrathtealmp_yfloiws Ce 21.3 kPa. A comparison between the experimental and computed dependent on the composition of the mixture given by the mass erstadt vfoarluceassefo3rsistapgrnoavtiidoendpioninTtahbeleat4f.lux,temperature,andmasslossrate fflroawctiTon:ofthegasmixturespeciesYiandtheinlettemperatureofthe d u D Itcanbeseenthatthecomputationalvaluesaremuchhigherthan n - the experimentally measured values. The higher computed values Power(cid:2)m_ Δh a flow Michig csuorufladcebienathttericbaultceudlattoioansh.iAghnearsdsuegmrpeetioonfonfitcrhoegmenicaatloemqufilluibxrituomthoef Δh(cid:2) X YiZ T CpidT(cid:3) X YiΔhfi (29) y of thenitrogengasmixtureattheICPtorchexitisusedinthebaseline i(cid:2)N;N2 298 i(cid:2)N;N2 versit saitmomuliactinointrso.gTehnewspitehcimesoplerefsreancttiionntsheogfa0s.1m5ixatnudre0a.r8e5m,roelsepceucltairvaenlyd. where ni U Theequilibriumgasmixturecompositionisprobablymoredissoci- y nloaded b arnatietterdocgthheaennmatithsotemrycs.oaTmvhapeiolraesbiftolieoremn,iftgohhretafblcuehxleetmsosittchhaaelnlyteursseteadscaitmnintpghleeflsooewfsidmwisuistlohactfiiiaontnietsde. Yi(cid:2)MMavigXi; Mavg(cid:2)i(cid:2)XN;N2XiMi Dow Alowernitrogenatomfluxtothesurfacewouldresultinalower Cpi(cid:2)Cvi(cid:3)Ri mass removal rate. A sensitivity analysis is performed on the ICP C (cid:2)C (cid:3)C (cid:3)C (cid:3)C torchexitchemicalcompositiontoevaluateitseffectsontheflow vi vi;t vi;r vi;vib vi;el parameters in the boundary layer and the surface properties. The C (cid:2)1.5R vi;t i analysisisperformedforcase3toincludetheeffectsoftheinletgas compositiononcarbonmassremoval.Theresultsofthesensitivity Fori(cid:2)N analysisperformedontheICPtorchexitchemicalcompositionare 2 presentedSec.V.B.Aradiativeequilibrium boundaryconditionis (cid:4)θ ∕T (cid:5)2exp(cid:4)θ ∕T (cid:5) used in these simulations where the heat conduction within the C (cid:2)R; C (cid:2)R vib;i vib;i vib;i vib sampleisnotincludedthat,ifaccountedfor,mayaffectthesurface vi;r i vi;vib i (cid:7)exp(cid:4)θvib;i∕Tvib(cid:5)−1(cid:8)2 properties.SectionV.Cpresentstheresultsofthestudyperformedto determinetheeffectsofconductionwithinthesample. Fori(cid:2)N C (cid:2)0; C (cid:2)0 vi;r vi;vib Table4 Stagnationpointvaluesandmasslossrates Fori(cid:2)N,N , q ,W∕cm2 T ,K Masslossrate,mg∕s 2 stag stag CEA 270 2757 2.2 Experiment 40–80 ∼1600 0.2–0.6 §PersonalconversationwithW.Owens,UniversityofVermont,Mechanical Engineering,Burlington,VT,January2013. 662 ANNAANDBOYD (P∞ g (cid:4)θ ∕T (cid:5)2exp(cid:4)−θ ∕T (cid:5) (cid:7)P∞ g θ exp(cid:4)−θ ∕T (cid:5)(cid:8)(cid:7)P∞ g (cid:4)θ ∕T2(cid:5)exp(cid:4)−θ ∕T (cid:5)(cid:8)) Cvi;el (cid:2)Ri j(cid:2)1Pj;∞i egl;j;iexepl(cid:4)−θ ∕Tel;j(cid:5);i el − j(cid:2)1 j;i el;j;i (cid:7)Pel;∞j;i gel exp(cid:4)j−(cid:2)0θ j;i∕Tel;j;(cid:5)i(cid:8)2 el el;j;i el j(cid:2)0 j;i el;j;i el j(cid:2)0 j;i el;j;i el where X is the species mole fraction; and M and M are the along with the constant power of 30 kWin the flow for chemical i i avg individualspeciesandaveragegasmixturemolecularweight,respe- equilibriumcompositionattheinlet.Itcanbeseenthatthepowerin ctively.C isthespecies-specificheatatconstantpressure,R isthe theflowisminimumforthezeronitrogenatommolefraction,i.e.,the pi i speciesgasconstant,andh isthespeciesheatofformation.C is flowisnotdissociated.Theflowpowerincreaseswiththelevelof fi vi thespecies-specificheatatconstantvolume.ThesubscriptsinC , dissociationintheflowandismaximumforfullydissociatedflow vi;t Cvi;r,Cvi;vib,andCvi;el representthetranslational,rotational,vibra- (XN(cid:2)1). The higher the degree of dissociation, the higher the tional,andelectronicspecificheatsatconstantvolume,respectively. power. θ isthespeciescharacteristicvibrationaltemperature.θ and Based on the chemical equilibrium and 13.8 kW inlet compo- vib;i el;j;i g arethecharacteristicelectronictemperatureandthedegeneracy sitions,thetranslationaltemperatureandnormalizednitrogenatom j;i ofthejthenergylevel,respectively[30]. number density profiles along the stagnation line in the boundary The composition of the gas mixture is calculated for 13.8 kW layer areshownin Figs.8aand8b,respectively.Thetranslational 0 powerusingthemassflowrateandinlettemperaturegiveninTable2. temperature in the boundary layer for 13.8 kW power is lower in 53 Thepowerintheflowforchemicalequilibriumcompositionatinlet comparisontotheequilibriuminletcomposition.Thereasonforthis 4 1.T and7000Kinlettemperaturecorrespondsto30kW,whichis100% is that the temperature in the flow decreases with a decrease in 14/ higherthanthecalculatedpower. enthalpy. Enthalpy is directly related to power [Eq. (29)]. Lower OI: 10.25 FigT.h7e,wrehlaetrieonpoowfpeorwiseprlwotittehdtahgeagiansstmthixetnuirterocgoemnpaotsoimtiomnoisleshfroawctnioinn ptShoeewcesef.frIeIicnatntohdfevIfIalIro.ywTinhgleetaredomsoptt-oemrlaoetawunree-rsaqtneudmarppeoepwraeetrurcrienen.tthFageuefrlteohrwerroidrsibpsecretuwssesenieotnendtohinne g | D XNforaconstanttemperatureof7000K[calculatedusingEq.(29)] translationaltemperatureforthechemicalequilibriuminletcomposi- or tion and the experimental values is 16.1%. The root-mean-square a. aia percentageerrorbetweenthetranslationaltemperaturefor13.8kW arc. powerandtheexperimentalvaluesis16.3%. p:// Theequilibriuminletcompositionhasahighernormalizednitro- htt genatomnumberdensityintheboundarylayerincomparisontothe 7 | inletcompositioncalculatedusing13.8kWpower.Theroot-mean- 1 0 2 square percentage error between the normalized nitrogen atom 14, numberdensityforthechemicalequilibriuminletcompositionand ber theexperimentalvaluesis15.2%.Theroot-mean-squarepercentage m e error between the normalized nitrogen atom number density for c e D 13.8kWpowerandtheexperimentalvaluesis10.9%.Thelevelof n o dissociationishigherforchemicalequilibriuminletcompositionas nter compared tothe 13.8kWpowerinlet composition. Therefore,the e C nitrogenatomdensityishigherforthechemicalequilibriumcaseas adt comparedtothe13.8kWpowercase. erst Thetotalheatfluxandtemperatureatthewallforthesecasesare d Du shown in Figs. 9a and 9b, respectively. The mass removal flux is n - showninFig.10. a hig Ascanbeseen,thereisasignificantreductioninheatflux,thewall Mic temperature,andmasslossfor13.8kWpowerincomparisontothe of results of equilibrium inlet composition. The comparison between ersity Fig.7 Plotofpoweragainstnitrogenatommolefraction. tmheensttaalgdnaattaioisnsphooiwnntvinalTuaebslefo5r.tThheetrweoiscaa5s2e%sarleodnugcwtioitnhinthheeeaxtpfleurxi-, v ni U y b d e d a o nl w o D Fig.8 ComparisonoftranslationaltemperatureandnormalizedN-atomdensityalongthestagnationlinefordifferentinletcompositions.