Numerical Analysis of Surface Chemistry in High-Enthalpy Flows

19 Pages·2015·1.17 MB·English

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.