FLUENT中NOX模型的主要內(nèi)容

17.1.1OverviewandLimitations

NOxemissionconsistsofmostlynitricoxide(NO).Lesssignificantarenitrogenoxide(NO2)andnitrousoxide(N2O).NOxisaprecursorforphotochemicalsmog,contributestoacidrain,andcausesozonedepletion.Thus,NOxisapollutant.TheFLUENTNOxmodelprovidesatooltounderstandthesourcesofNOxproductionandtoaidinthedesignofNOxcontrolmeasures.

NOxModelinginFLUENT

TheFLUENTNOxmodelprovidesthecapabilitytomodelthermal,prompt,andfuelNOxformationaswellasNOxconsumptionduetoreburningincombustionsystems.ItusesratemodelsdevelopedattheDepartmentofFuelandEnergy,TheUniversityofLeeds,Englandaswellasfromtheopenliterature.

TopredictNOxemission,FLUENTsolvesatransportequationfornitricoxide(NO)concentration.WithfuelNOxsources,FLUENTsolvesanadditionaltransportequationforanintermediatespecies(HCNorNH3).TheNOxtransportequationsaresolvedbasedonagivenflowfieldandcombustionsolution.Inotherwords,NOxispostprocessedfromacombustionsimulation.ItisthusevidentthatanaccuratecombustionsolutionbecomesaprerequisiteofNOxprediction.Forexample,thermalNOxproductiondoublesforevery90

Ktemperatureincreasewhentheflametemperatureisabout2200

K.Greatcaremustbeexercisedtoprovideaccuratethermophysicaldataandboundaryconditioninputsforthecombustionmodel.Appropriateturbulence,chemistry,radiationandothersubmodelsmustbeapplied.

Toberealistic,onecanonlyexpectresultstobeasaccurateastheinputdataandtheselectedphysicalmodels.Undermostcircumstances,NOxvariationtrendscanbeaccuratelypredictedbuttheNOxquantityitselfcannotbepinpointed.AccuratepredictionofNOxparametrictrendscancutdownonthenumberoflaboratorytests,allowmoredesignvariationstobestudied,shortenthedesigncycle,andreduceproductdevelopmentcost.ThatistrulythepoweroftheFLUENTNOxmodeland,infact,thepowerofCFDingeneral.

TheFormationofNOxinFlames

Inlaminarflames,andatthemolecularlevelwithinturbulentflames,theformationofNOxcanbeattributedtofourdistinctchemicalkineticprocesses:thermalNOxformation,promptNOxformation,fuelNOxformation,andreburning.ThermalNOxisformedbytheoxidationofatmosphericnitrogenpresentinthecombustionair.PromptNOxisproducedbyhigh-speedreactionsattheflamefront,andfuelNOxisproducedbyoxidationofnitrogencontainedinthefuel.ThereburningmechanismreducesthetotalNOxformationbyaccountingforthereactionofNOwithhydrocarbons.TheFLUENTNOxmodelisabletosimulateallfouroftheseprocesses.

RestrictionsonNOxModeling

Youmustusethesegregatedsolver.TheNOxmodelsarenotavailablewitheitherofthecoupledsolvers.

TheNOxmodelscannotbeusedinconjunctionwiththepremixedcombustionmodel.

17.1.2GoverningEquationsforNOxTransport

FLUENTsolvesthemasstransportequationfortheNOspecies,takingintoaccountconvection,diffusion,productionandconsumptionofNOandrelatedspecies.Thisapproachiscompletelygeneral,beingderivedfromthefundamentalprincipleofmassconservation.TheeffectofresidencetimeinNOxmechanisms,aLagrangianreferenceframeconcept,isincludedthroughtheconvectiontermsinthegoverningequationswrittenintheEulerianreferenceframe.ForthermalandpromptNOxmechanisms,onlytheNOspeciestransportequationisneeded:

(17.1.1)

AsdiscussedinSection

17.1.5

,thefuelNOxmechanismsaremoreinvolved.Thetrackingofnitrogen-containingintermediatespeciesisimportant.FLUENTsolvesatransportequationfortheHCNorNH3speciesinadditiontotheNOspecies:

(17.1.10)

(17.1.11)

(17.1.12)

Intheaboveexpressions,k1,k2,andk3aretherateconstantsfortheforwardreactions

17.1-4

-

17.1-6

,respectively,andk-1,k-2,andk-3arethecorrespondingreverserates.

ThenetrateofformationofNOviaReactions

17.1-4

-

17.1-6

isgivenby

=

-

(17.1.13)

whereallconcentrationshaveunitsofgmol/m3.

InordertocalculatetheformationratesofNOandN,theconcentrationsofO,H,andOHarerequired.

TheQuasi-SteadyAssumptionfor[N]

TherateofformationofNOxissignificantonlyathightemperatures(greaterthan1800

K)becausefixationofnitrogenrequiresthebreakingofthestrongN2triplebond(dissociationenergyof941kJ/gmol).ThiseffectisrepresentedbythehighactivationenergyofReaction

17.1-4

,whichmakesittherate-limitingstepoftheextendedZeldovichmechanism.However,theactivationenergyforoxidationofNatomsissmall.Whenthereissufficientoxygen,asinafuel-leanflame,therateofconsumptionoffreenitrogenatomsbecomesequaltotherateofitsformationandthereforeaquasi-steadystatecanbeestablished.Thisassumptionisvalidformostcombustioncasesexceptinextremelyfuel-richcombustionconditions.HencetheNOformationratebecomes

(17.1.14)

SensitivityofThermalNOxtoTemperature

FromEquation

17.1-14

itisclearthattherateofformationofNOwillincreasewithincreasingoxygenconcentration.ItalsoappearsthatthermalNOformationshouldbehighlydependentontemperaturebutindependentoffueltype.Infact,basedonthelimitingratedescribedinEquation

17.1-7

,thermalNOxproductionratedoublesforevery90

Ktemperatureincreasebeyond2200

K.

DecouplingNOxandFlameCalculations

InordertosolveEquation

17.1-14

,concentrationofOatomsandthefreeradicalOHwillberequiredinadditiontoconcentrationofstablespecies(i.e.,O2,N2).FollowingthesuggestionbyZeldovich,thethermalNOxformationmechanismcanbedecoupledfromthemaincombustionprocess,byassumingequilibriumvaluesoftemperature,stablespecies,Oatoms,andOHradicals.However,radicalconcentrations,Oatomsinparticular,areobservedtobemoreabundantthantheirequilibriumlevels.TheeffectofpartialequilibriumOatomsonNOxformationratehasbeeninvestigated

[

159

]duringlaminarmethane-aircombustion.TheresultsoftheseinvestigationsindicatethatthelevelofNOxemissioncanbeunderpredictedbyasmuchas28%intheflamezone,whenassumingequilibriumO-atomconcentrations.

DeterminingORadicalConcentration

Therehasbeenlittledetailedstudyofradicalconcentrationinindustrialturbulentflames,butwork

[

56

]hasdemonstratedtheexistenceofthisphenomenoninturbulentdiffusionflames.Presently,thereisnodefinitiveconclusionastotheeffectofpartialequilibriumonNOxformationratesinturbulentflames.PetersandDonnerhack

[

178

]suggestthatpartialequilibriumradicalscanaccountfornomorethana25%increaseinthermalNOxandthatfluiddynamicshasthedominanteffectonNOxformationrate.Bilgeretal.

[

18

]suggestthatinturbulentdiffusionflames,theeffectofOatomovershootonNOxformationrateisveryimportant.

Inordertoovercomethispossibleinaccuracy,oneapproachwouldbetocoupletheextendedZeldovichmechanismwithadetailedhydrocarboncombustionmechanisminvolvingmanyreactions,species,andsteps.Thisapproachhasbeenusedpreviouslyforresearchpurposes

[

156

].However,longcomputerprocessingtimehasmadethemethodeconomicallyunattractiveanditsextensiontoturbulentflowsdifficult.

TodeterminetheOradicalconcentration,FLUENTusesoneofthreeapproaches--theequilibriumapproach,thepartialequilibriumapproach,andthepredictedconcentrationapproach--inrecognitionoftheongoingcontroversydiscussedabove.

Method1:EquilibriumApproach

ThekineticsofthethermalNOxformationrateismuchslowerthanthemainhydrocarbonoxidationrate,andsomostofthethermalNOxisformedaftercompletionofcombustion.Therefore,thethermalNOxformationprocesscanoftenbedecoupledfromthemaincombustionreactionmechanismandtheNOxformationratecanbecalculatedbyassumingequilibrationofthecombustionreactions.Usingthisapproach,thecalculationofthethermalNOxformationrateisconsiderablysimplified.Theassumptionofequilibriumcanbejustifiedbyareductionintheimportanceofradicalovershootsathigherflametemperature

[

55

].AccordingtoWestenberg

[

265

],theequilibriumO-atomconcentrationcanbeobtainedfromtheexpression

(17.1.15)

Withkpincluded,thisexpressionbecomes

(17.1.16)

whereTisinKelvin.

Method2:PartialEquilibriumApproach

Animprovementtomethod1canbemadebyaccountingforthird-bodyreactionsintheO2dissociation-recombinationprocess:

(17.1.17)

Equation

17.1-16

isthenreplacedbythefollowingexpression

[

255

]:

(17.1.18)

whichgenerallyleadstoahigherpartialO-atomconcentration.

Method3:PredictedOApproach

WhentheO-atomconcentrationiswell-predictedusinganadvancedchemistrymodel(suchastheflameletsubmodelofthenon-premixedmodel),[O]canbetakensimplyfromthelocalO-speciesmassfraction.

DeterminingOHRadicalConcentration

FLUENTusesoneofthreeapproachestodeterminetheOHradicalconcentration:theexclusionofOHfromthethermalNOxcalculationapproach,thepartialequilibriumapproach,andtheuseofthepredictedOHconcentrationapproach.

Method1:ExclusionofOHApproach

Inthisapproach,thethirdreactionintheextendedZeldovichmechanism(Equation

17.1-6

)isassumedtobenegligiblethroughthefollowingobservation:

Thisassumptionisjustifiedforleanfuelconditionsandisareasonableassumptionformostcases.

Method2:PartialEquilibriumApproach

Inthisapproach,theconcentrationofOHinthethirdreactionintheextendedZeldovichmechanism(Equation

17.1-6

)isgivenby

[

12

,

264

]

(17.1.19)

Method3:PredictedOHApproach

AsinthepredictedOapproach,whentheOHradicalconcentrationiswell-predictedusinganadvancedchemistrymodelsuchastheflameletmodel,[OH]canbetakendirectlyfromthelocalOHspeciesmassfraction.

Summary

Tosummarize,thermalNOxformationrateispredictedbyEquation

17.1-14

.TheO-atomconcentrationneededinEquation

17.1-14

iscomputedusingEquation

17.1-16

fortheequilibriumassumption,usingEquation

17.1-18

forapartialequilibriumassumption,orusingthelocalO-speciesmassfraction.Youwillmakethechoiceduringproblemsetup.IntermsofthetransportequationforNO(Equation

17.1-1

),theNOsourcetermduetothermalNOxmechanismsis

(17.1.20)

whereisthemolecularweightofNO,andiscomputedfromEquation

17.1-14

.

17.1.4PromptNOxFormation

Itisknownthatduringcombustionofhydrocarbonfuels,theNOxformationratecanexceedthatproducedfromdirectoxidationofnitrogenmolecules(i.e.,thermalNOx).

WhereandWhenPromptNOxOccurs

ThepresenceofasecondmechanismleadingtoNOxformationwasfirstidentifiedbyFenimore

[

63

]andwastermed``promptNOx''.ThereisgoodevidencethatpromptNOxcanbeformedinasignificantquantityinsomecombustionenvironments,suchasinlow-temperature,fuel-richconditionsandwhereresidencetimesareshort.Surfaceburners,stagedcombustionsystems,andgasturbinescancreatesuchconditions

[

6

].

AtpresentthepromptNOxcontributiontototalNOxfromstationarycombustorsissmall.However,asNOxemissionsarereducedtoverylowlevelsbyemployingnewstrategies(burnerdesignorfurnacegeometrymodification),therelativeimportanceofthepromptNOxcanbeexpectedtoincrease.

PromptNOxMechanism

PromptNOxismostprevalentinrichflames.Theactualformationinvolvesacomplexseriesofreactionsandmanypossibleintermediatespecies.Theroutenowacceptedisasfollows:

(17.1.21)

(17.1.22)

(17.1.23)

(17.1.24)

AnumberofspeciesresultingfromfuelfragmentationhavebeensuggestedasthesourceofpromptNOxinhydrocarbonflames(e.g.,CH,CH2,C,C2H),butthemajorcontributionisfromCH(Equation

17.1-21

)andCH2,via

(17.1.25)

TheproductsofthesereactionscouldleadtoformationofaminesandcyanocompoundsthatsubsequentlyreacttoformNObyreactionssimilartothoseoccurringinoxidationoffuelnitrogen,forexample:

(17.1.26)

FactorsofPromptNOxFormation

PromptNOxformationisproportionaltothenumberofcarbonatomspresentperunitvolumeandisindependentoftheparenthydrocarbonidentity.ThequantityofHCNformedincreaseswiththeconcentrationofhydrocarbonradicals,whichinturnincreaseswithequivalenceratio.Astheequivalenceratioincreases,promptNOxproductionincreasesatfirst,thenpassesapeak,andfinallydecreasesduetoadeficiencyinoxygen.

PrimaryReaction

Reaction

17.1-21

isofprimaryimportance.Inrecentstudies

[

201

],comparisonofprobabilitydensitydistributionsforthelocationofthepeakNOxwiththoseobtainedforthepeakCHhaveshownclosecorrespondence,indicatingthatthemajorityoftheNOxattheflamebaseispromptNOxformedbytheCHreaction.AssumingthatReaction

17.1-21

controlsthepromptNOxformationrate,

(17.1.27)

ModelingStrategy

Thereare,however,uncertaintiesabouttheratedatafortheabovereaction.FromReactions

17.1-21

-

17.1-25

,itcanbeconcludedthatthepredictionofpromptNOxformationwithintheflamerequirescouplingoftheNOxkineticstoanactualhydrocarboncombustionmechanism.Hydrocarboncombustionmechanismsinvolvemanystepsand,asmentionedpreviously,areextremelycomplexandcostlytocompute.InthepresentNOxmodel,aglobalkineticparameterderivedbyDe

Soete

[

223

]isused.De

SoetecomparedtheexperimentalvaluesoftotalNOxformationratewiththerateofformationcalculatedbynumericalintegrationoftheempiricaloverallreactionratesofNOxandN2formation.Heshowedthatoverallpromptformationratecanbepredictedfromtheexpression

=

(17.1.28)

Intheearlystagesoftheflame,wherepromptNOxisformedunderfuel-richconditions,theOconcentrationishighandtheNradicalalmostexclusivelyformsNOxratherthannitrogen.Therefore,thepromptNOxformationratewillbeapproximatelyequaltotheoverallpromptNOxformationrate:

(17.1.29)

ForC2H4(ethylene)-airflames,

kpr

=

Ea

=

60kcal/gmol

whereaistheoxygenreactionorder,Ristheuniversalgasconstant,andpispressure(allinSIunits).TherateofpromptNOxformationisfoundtobeofthefirstorderwithrespecttonitrogenandfuelconcentration,buttheoxygenreactionorder,a,dependsonexperimentalconditions.

RateforMostHydrocarbonFuels

Equation

17.1-29

wastestedagainsttheexperimentaldataobtainedbyBackmieretal.

[

4

]fordifferentmixturestrengthsandfueltypes.Thepredictedresultsindicatedthatthemodelperformancedeclinedsignificantlyunderfuel-richconditionsandforhigherhydrocarbonfuels.ToreducethiserrorandpredictthepromptNOxadequatelyinallconditions,theDe

Soetemodelwasmodifiedusingtheavailableexperimentaldata.Acorrectionfactor,f,wasdeveloped,whichincorporatestheeffectoffueltype,i.e.,numberofcarbonatoms,andair-to-fuelratioforgaseousaliphatichydrocarbons.Equation

17.1-29

nowbecomes

(17.1.30)

sothatthesourcetermduetopromptNOxmechanismis

(17.1.31)

Intheaboveequations,

(17.1.32)

nisthenumberofcarbonatomspermoleculeforthehydrocarbonfuel,andistheequivalenceratio.Thecorrectionfactorisacurvefitforexperimentaldata,validforaliphaticalkanehydrocarbonfuels(CnH2n+2)andforequivalenceratiosbetween0.6and1.6.Forvaluesoutsidetherange,theappropriatelimitshouldbeused.Valuesofk'prandE'aareselectedinaccordancewithreference

[

58

].

Heretheconceptofequivalenceratioreferstoanoverallequivalenceratiofortheflame,ratherthananyspatiallyvaryingquantityintheflowdomain.Incomplexgeometrieswithmultipleburnersthismayleadtosomeuncertaintyinthespecificationof.However,sincethecontributionofpromptNOxtothetotalNOxemissionisoftenverysmall,resultsarenotlikelytobebiasedsignificantly.

OxygenReactionOrder

Oxygenreactionorderdependsonflameconditions.AccordingtoDeSoete

[

223

],oxygenreactionorderisuniquelyrelatedtooxygenmolefractionintheflame:

(17.1.33)

17.1.5FuelNOxFormation

Fuel-BoundN2

Itiswellknownthatnitrogen-containingorganiccompoundspresentinliquidorsolidfossilfuelcancontributetothetotalNOxformedduringthecombustionprocess.Thisfuelnitrogenisaparticularlyimportantsourceofnitrogenoxideemissionsforresidualfueloilandcoal,whichtypicallycontain0.3-2%nitrogenbyweight.Studieshaveshownthatmostofthenitrogeninheavyfueloilsisintheformofheterocyclesanditisthoughtthatthenitrogencomponentsofcoalaresimilar

[

107

].Itisbelievedthatpyridine,quinoline,andaminetypeheterocyclicringstructuresareofimportance.

ReactionPathways

TheextentofconversionoffuelnitrogentoNOxisdependentonthelocalcombustioncharacteristicsandtheinitialconcentrationofnitrogen-boundcompounds.Fuel-boundnitrogen-containingcompoundsarereleasedintothegasphasewhenthefueldropletsorparticlesareheatedduringthedevolatilizationstage.Fromthethermaldecompositionofthesecompounds,(aniline,pyridine,pyrroles,etc.)inthereactionzone,radicalssuchasHCN,NH3,N,CN,andNHcanbeformedandconvertedtoNOx.Theabovefreeradicals(i.e.,secondaryintermediatenitrogencompounds)aresubjecttoadoublecompetitivereactionpath.Thischemicalmechanismhasbeensubjecttoseveraldetailedinvestigations

[

157

].AlthoughtherouteleadingtofuelNOxformationanddestructionisstillnotcompletelyunderstood,differentinvestigatorsseemtoagreeonasimplifiedmodel:

Recentinvestigations

[

94

]haveshownthathydrogencyanideappearstobetheprincipalproductiffuelnitrogenispresentinaromaticorcyclicform.However,whenfuelnitrogenispresentintheformofaliphaticamines,ammoniabecomestheprincipalproductoffuelnitrogenconversion.

IntheFLUENTNOxmodel,sourcesofNOxemissionforgaseous,liquidandcoalfuelsareconsideredseparately.Thenitrogen-containingintermediatesaregroupedtobeHCNorNH3only.Twotransportequations(

17.1-1

and

17.1-2

or

17.1-3

)aresolved.Thesourceterms,,andaretobedeterminednextfordifferentfueltypes.DiscussionstofollowreferonlytofuelNOxsourcesfor.Contributionsfromthermalandpromptmechanismshavebeendiscussedinprevioussections.

FuelNOxfromGaseousandLiquidFuels

ThefuelNOxmechanismsforgaseousandliquidfuelsarebasedondifferentphysicsbutthesamechemicalreactionpathways.

FuelNOxfromIntermediateHydrogenCyanide(HCN)

WhenHCNisusedastheintermediatespecies:

Thesourcetermsinthetransportequationscanbewrittenasfollows:

(17.1.34)

(17.1.35)

HCNProductioninaGaseousFuel

TherateofHCNproductionisequivalenttotherateofcombustionofthefuel:

(17.1.36)

where

=

sourceofHCN(kg/m3-s)

=

meanlimitingreactionrateoffuel(kg/m3-s)

=

massfractionofnitrogeninthefuel

Themeanlimitingreactionrateoffuel,,iscalculatedfromtheMagnussencombustionmodel,sothegaseousfuelNOxoptionisavailableonlywhenthegeneralizedfinite-ratemodelisused.

HCNProductioninaLiquidFuel

TherateofHCNproductionisequivalenttotherateoffuelreleaseintothegasphasethroughdropletevaporation:

(17.1.37)

where

=

sourceofHCN(kg/m3-s)

=

rateoffuelreleasefromthe

liquiddropletstothegas(kg/s)

=

massfractionofnitrogeninthefuel

V

=

cellvolume(m3)

HCNConsumption

TheHCNdepletionratesfromreactions(1)and(2)intheabovemechanismarethesameforbothgaseousandliquidfuels,andaregivenbyDeSoete

[

223

]as

(17.1.38)

(17.1.39)

where

,

=

conversionratesofHCN(s-1)

T

=

instantaneoustemperature(K)

X

=

molefractions

A1

=

3.5s-1

A2

=

3.0s-1

E1

=

67kcal/gmol

E2

=

60kcal/gmol

Theoxygenreactionorder,a,iscalculatedfromEquation

17.1-33

.

Sincemolefractionisrelatedtomassfractionthroughmolecularweightsofthespecies(Mw,i)andthemixture(Mw,m),

(17.1.40)

HCNSourcesintheTransportEquation

ThemassconsumptionratesofHCNwhichappearinEquation

17.1-34

arecalculatedas

(17.1.41)

(17.1.42)

where

=

consumptionratesofHCNin

reactions1and2respectively(kg/m3-s)

p

=

pressure(Pa)

=

meantemperature(K)

R

=

universalgasconstant

NOxSourcesintheTransportEquation

NOxisproducedinreaction1butdestroyedinreaction2.ThesourcesforEquation

17.1-35

arethesameforagaseousasforaliquidfuel,andareevaluatedasfollows:

(17.1.43)

(17.1.44)

FuelNOxfromIntermediateAmmonia(NH3)

WhenNH3isusedastheintermediatespecies:

Thesourcetermsinthetransportequationscanbewrittenasfollows:

(17.1.45)

(17.1.46)