Curvature effects on NO formation in wrinkled laminar ammonia/hydrogen/nitrogen-air premixed flames

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ContentslistsavailableatScienceDirect

Combustion and Flame

journalhomepage:www.elsevier.com/locate/combustflame

Curvature effects on NO formation in wrinkled laminar ammonia/hydrogen/nitrogen-air premixed ﬂames

Corinna Netzer

^a^,^∗

, Ahfaz Ahmed

^a

, Andrea Gruber

^a^,^b

, Terese Løvås

^a

aDepartment of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim, Norway

bSINTEF Energy Research, Trondheim, Norway

a rt i c l e i nf o

Article history:

Received 29 June 2020 Revised 20 May 2021 Accepted 20 May 2021

Keywords:

Premixed ﬂames Wrinkled ﬂames Flame curvature NO formation

Hydrogen-nitrogen-ammonia fuel blending

a b s t r a c t

Theformationofnitrogenoxide(NO)inwrinkledlaminarNH₃/H₂/N₂-airpremixedflamesisinvestigated utilizingtwo-dimensionalDirectNumericalSimulation(DNS)withdetailedchemicalkineticsaswellas one-dimensionalfreelypropagatingflamecalculations.ThespatialpatternofNOformationisobserved tobecloselylinkedtoflamecurvatureandaffectedbythermo-diffusiveeffectsactingonkeychemical species.PreferentialdiffusionofH2 intoconvex-shapedportionsoftheflamefrontleadstoalocalin- creaseinequivalenceratio.ThischangeinlocalequivalenceratioisfoundtoprominentlyaffecttheNO formation.Ifthefuel-oxidantmixtureisgloballylean,alocalincreaseinequivalenceratiostrengthensthe NOformation(locally);inagloballyrichfuel-oxidantmixture,conversely,theNOconcentrationwillbe reducedincorrespondenceoflocalincrementsoftheequivalenceratio.Asensitivityanalysiswithrespect toNOformationrevealsthatdecompositionofNH2isgovernedbytwocompetingpathways:thedecom- positionviaNHandNtoN2 ontheonehandandtheoxidationviaHNOtoNOontheotherhand.The localradicalpool,whichisaffectedbypreferentialdiffusionofH₂anddepletionofO₂,andthelocalfuel- oxidantmixtureratiojointlystrengthenfurtherlocaldifferencesbetweenH2-depleted(concave-shaped) portionsoftheflamefrontandH2-enriched(convex-shaped)ones.Thisisconfirmedacrossawiderange ofequivalenceratiosfromleantorichconditions.

ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/)

1. Introduction

Hydrogen (H₂) represents the simplest and one of the clean- estenergycarrierforlargescalethermalenergyconversionandits widespreaddeploymentintheenergysector,ifrealized,represents oneofthemostpromisingstrategiestoreducethedependenceon fossilfuelsandsimultaneouslyreduce atmosphericpollution.This applies bothtopowergenerationwithpre-combustioncarbonse- questration, where hydrogen isproduced e.g. at large scale from naturalgasinconjunctionwithcarbondioxidecaptureandstorage [1],andtolarge-scale energy-storageschemes,wherehydrogenis produced fromwaterelectrolysisusingintermittentexcesspower from non-dispatchablerenewable energy sources (wind, sun) [2]. Inthecontextoflarge-scaleandlong-term(seasonal)energytrans- port andstorage,reﬁning hydrogento ammonia(NH₃), asa convenient carbon-free energy carrier, constitutes a viable and eco- nomicalternativetoliqueﬁedorhighlycompressedhydrogen.This is due to the fact that, at moderate pressure, the higher boil-

∗Corresponding author.

E-mail address: [email protected] (C. Netzer).

ing temperature ofammonia compared to hydrogen greatly sim- pliﬁes its transportation and storage in liquid phase. While the energypenalty of ammonia synthesis fromH₂ andnitrogen(N₂) [3]compares with that of the hydrogen liquefaction process, the energydensityofammoniaexceedsthatofliquidhydrogenby57%

(3.724MWh/m³versus2.368MWh/m³,respectively).Furthermore, duetothewidespreadutilisationofammoniainagricultureandas refrigerant,commercialtechnologiesare alreadyin placeforpro- duction,transportationandstorageofammoniawithanexcellent safetyrecorddespiteitscharacteristictoxicity.

The presence of a considerable differences betweenthe combustion propertiesofammonia andmethane(conservatively con- sideredhereasalower-reactivityrepresentativeofnaturalgas)im- pliesthatburnerdesignnecessarilybecomesrathersub-optimalin respecttotheexplorationoffuelﬂexibilityingasturbines.While earlystudieshaveindicatedanobviousinadequacyofneatammo- nia as a gas turbine fuel due to its poor reactivity compared to conventionalhydrocarbons[4],asigniﬁcantnumberofstudieshas beenpublishedoncombustionofhydrogen/ammoniawithair(e.g.

[5]) or hydrogen/ammonia/methane withair (e.g. [6]in order to mitigate the low reactivity of neat ammonia. Also, a number of

https://doi.org/10.1016/j.combustﬂame.2021.111520

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C. Netzer, A. Ahmed, A. Gruber et al. Combustion and Flame 232 (2021) 111520

more recent studies based on rich-lean fuel staging have shown encouraging results [7,8].Combustion tests withfuel blends consisting of mixtures of ammonia and hydrogen are indeed under investigation within industrial demonstration framework¹ In this context,it isinterestingtonote thatpartialcracking ofammonia, toformopportunelyselectedfuelmixturesofammonia,hydrogen andnitrogen, hasagoodpotential toimprovetheoverallreactiv- ityofthefuel anditscombustionperformance renderingitmore suitable to gas turbines originally designed for use with natural gas. Production ofnitrogen oxide(NO) through fuel chemistry in the combustionofammonia andammonia-containingfuel blends oftenis,however,adetrimentrequiringadetailedstudyofitsfor- mation mechanismwiththeultimateobjectiveofobtaining com- bustordesignguidelinesforitsmitigation.

Recentstudiesfromtheopenliteraturealsofoundthat,inam- moniacombustion,amoreprominentimpactontheformationof NOiscausedbytheequivalenceratioinrespecttothermaleffects, howeverall oftheseearlierstudies discussglobalrather thanlo- caldifferencesintheequivalenceratio.Sabiaetal.[9]investigated the NO formation in NH₃/air-mixtures as function of inlet temperature and equivalence ratioin a jet stirred ﬂow reactor. They concluded that NO formation is strongly affected by the equivalence ratio with increasing dependency on higher temperatures.

Sorrentino et al. [10], from their cyclonic burner measurements ofammoniaconversioninthemildcombustionregime,concluded that amajorimpactofthestoichiometryonNOformationatvar- ious inlet temperatures and nominal thermal powers is present.

Likewise, the papers by Somarathne et al.[11] andOkafor et al.

[12],suggest that,duetothestrongdependencyofNOformation onequivalenceratioforgasturbines,atwo-stagerich-leanconcept isfavourabletocontroltheNOformationinNH₃/air-mixtures.

The present work deploys the recently updated nitrogen- chemistrysubset oftheSanDiegomechanism[13]inconjunction with two-dimensional (2-D) Direct Numerical Simulation (DNS) performed withthe S3D code [14]. The fundamentalcharacteris- tics ofwrinkledlaminarNH₃/H₂/N₂-airpremixedflames isinves- tigatedtoquantifyandexplainNOconcentrationtrendsacrossthe relevant range of fuel-oxidantratios for gas turbine combustion, spanning fromfuel-lean to fuel-rich conditions.2-D DNS, featur- ing detailedchemical reaction kinetics,isa well-established(and now relativelyaffordable) numericalmodellingapproach thathas been widely usedin pastfundamentalcombustion studies to ac- curatelyquantifythelocaleffectsofcurvature,stretch,Lewisnum- ber, pocket formation and consumption, and non-homogeneous distribution of temperature and/or species on the propagation andspontaneous ignitioncharacteristics ofwrinkledlaminarpre- mixedflames [15–23]. Althoughthepresentwork doesnotclaim to closely(and ratherambitiously) reproducethe turbulent combustion process takingplace inrealistic burner geometriesatgas turbine conditions, DNS of 2-D geometrically simple flames pro- videsneverthelessusefulinsightintokey,rate-limitingfundamen- talmechanismsthatalsotakeplaceinmorecomplexflameconfig- urations. Thesecalculationsare,assuch, relevanttotheimproved understanding andthefurtherdevelopmentofindustrialcombus- tion applications. In our investigation, adopting the same fundamental methodologicalapproachasinearlierstudies, weprovide a detailedinsight into the spatial patterns of NO formation that take place in wrinkled laminar flames characterized by different global stoichiometric conditions andsubjectto various degree of strain and curvature, locally in the reaction layer. This is to im- prove our understanding of the chemical pathways and of their

1BIGH2/Phase III - ”Enabling safe, clean and eﬃcient utilization of hydrogen and ammonia as the carbon-free fuels of the future” - CLIMIT-Demo Project Num- ber 617137 performed by SINTEF, NTNU, Siemens Industrial Turbomachinery and Equinor ASA.

interactionwiththecharacteristicthermo-diffusive instabilitiesof hydrogenflames,thatultimatelyleadtodifferentlevelsofNOfor- mationfromcombustionofNH₃/H₂/N₂-airmixtures.Thepaperis organized as follows: Section 2 describes the numerical method andtheflameconfigurationssimulated,Section3presentstheDNS resultsandprovidesan interpretationbasedonchemical reaction kinetics considerations, while Section 4 summarizes the present findingsandsuggeststopicsforfurtherwork.

2. Numericalimplementationandsimulationdetails

TheS3Dcode,developedatSandiaNationalLaboratories[14],is employedto performtheDNSofNH₃/H₂/N₂-airpremixedﬂames.

The solver discretizes the Navier-Stokes equations for a reactive, multi-component, compressible ﬂuid on a 1024 x 512 Cartesian mesh that coversa rectangular domain of2 cmx 1cm, thereby providing a spatial resolution of approximately 20

μ

^m^. ^Spatial

derivativesare computedwithan eighth-order, explicit,centered, finite-difference scheme (third-order one-sided stencils are used atthedomainboundariesinthe non-homogeneousdirections) in conjunction with a tenth-order, explicit, spatial filter to remove high frequency noise and reduce aliasing error [24]. A fourth- order-accurate, six-stages-explicit, Runge-Kutta algorithm [25] is employed fortime integration andthetime step isfixed to 5ns throughoutthesimulations.Thespatialresolutionadopted,jointly withthe spatialandtemporaldiscretizationmethods,issufficient to accurately resolve the flame structure and all diffusive, reactive, and dissipative scales of the target reacting flows, even at the most severe level of stretch applied to the wrinkled flames.

The abilityof the DNScode to correctlyresolve the ﬂamestruc- tureresults fromthe combination ofthe formal numerical order of accuracyof the spatialdiscretization scheme andof the resolution adopted in the simulations (20

μ

^m^), ^this ^was^veriﬁed ⁱⁿ

a seriesofone-dimensional unstrained andstrainedlaminar pre- mixedflameDNScalculations(notshown).Amixture-averagedap- proximationisemployedforthediffusioncoefficientsthatarefor- mulatedintermsofthebinarydiffusioncoefficientsandthemix- turecomposition,wherethebinarycoefficientmatrixissymmetric and the diagonal elements are zero. Furthermore, thermal diffusion(theSoreteffect)isincludedinthemodelformulationforthe speciesdiffusion velocities becauseof its prominentrole in mix- turescontaining hydrogen.Boundary conditions(BC) are periodic (cyclic) inthe y-direction,perpendicular tothe meanflow ofthe freshreactantsthatenterthedomainfromtheinletpositionedat x=0cm.Thesimulationsareinitializedfromafreelypropagating planarlaminarflamesolutionthroughaprogressvariable(C)map- pingthat,atthebeginningofthetime stepping,placesareaction layerofappropriate thicknessatx =1 cm(the reactionprogress variableCisaparametrizationoftheflamestructurethatisequal to0inthefreshreactantsand1intheburntproducts).Wedefine theprogress variableCusing theequilibrium(subscript eq) mass fractionofwaterforeachglobalequivalenceratioinvestigated,respectively:

C= YH2O

YH2O,eq. (1)

Thecombustion products exitthecomputational domainfrom an outlet placed at x = 2 cm. Notably, for the domain inlet andoutlet, acousticallynon-reflective inflow andoutflow boundary conditions are adopted according to the Navier-Stokes char- acteristic boundary conditions (NSCBC) methodology. The NSCBC implementation in S3D is largely based on the formulation first described by Poinsot and Lele [26] and includes some modifica- tionslater suggestedforthe S3Dcodespecifically [27].Arandom 2-D flowfield witha prescribed Passot-Pouquetenergyspectrum (quantitativelycharacterizedby arms velocityfluctuation ofu =

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Fig. 1. Illustration of the 2-D computational domain with text labels marking the boundary conditions and color patterns highlighting the instantaneous shape of the wrinkled ﬂame. The lines represent isovalues of z-vorticity (dashed for negative values).

1m/sandanintegrallengthscaleofL_T =0.8cm)issuperimposed ontothemeanflowthatentersthedomainandinduceswrinkling ofthepremixedflamefront.TheturbulentReynoldsnumberrepre- sentativeofthepatternofvelocityfluctuationsthatisimposedon theflowfieldisestimatedtobeapproximatelyRet∼144.However, itisimportanttonotethatthepresentDNSstudyisnotintended toprovideanaccuraterepresentationofturbulentflames,whereas the syntheticturbulence israther usedasa mean ofachievinga well-characterized wrinkling of the flame front. For the full du- ration of the time stepping, the mean flow velocity at the inlet boundary isadjusted,ateachtime step,sothat thetotalamount offuelthatinstantaneouslyentersthedomainmatchesexactlythe fuel instantaneously consumed by the combustion process (inte- gratedthroughoutthecomputationaldomain).Thisprocedurewar- rants that the mean flow velocity is approximately equal to the propagation speed of the wrinkled flame front thereby ensuring that the latter remains within the central portionof the computational domain (approximately). A sketch of the computational setupisprovidedinFig.1specifyingtheboundaryconditionsim- posedandhighlightingtheinteractionoftheflamefrontwiththe 2-Dflowfield.Allofthecomputationsreportedherepertaintoat- mospheric pressureconditions andtoa reactants’temperature of 750K.

The fuel blend mixedwith air andintroduced atthe domain inlet consists of40% NH₃,45% H₂ and15% N₂ (byvolume). This specificfuelblendisselectedforthepresentinvestigationbecause its combustion in airresults inadiabatic flame temperatures T_ad, (unstrained)laminarflamethicknesses

δ

LandvelocitiesS_L thatare very close to typical valuesobserved forcombustion of methane (conventional gas turbine fuel) in air [13] (more prominently so at fuel-lean conditions). Accordingly, dueto its combustion sim- ilarities with methane at relevant conditions, this is considered a good candidate fuel mixture in a targeted search for potential carbon-free drop-in fuels substituting hydrocarbonfuels across a wide range of combustion devices. The presentchoice, however, doesnotnecessarilyimplythatthisspeciﬁcmixturerepresentsthe mostsuitable fuelforactualdeployment ingasturbinesandgas- ﬁred reciprocatingengines applications but, inthe authors’ view, itisrathertobe consideredasagoodstartingpoint.Additionally, inordertocomplementresultsfromcombustionofthetargetfuel blend, a different fuel blend consisting of72% NH₃, 21% H₂ and 7% N₂ (byvolume) is also included in the presentanalysis. This is meantasarepresentative casefortheprocess ofpartialcrack- ing of ammonia that is conductedto a lower extent,thereby re- quiringa smalleramountofwaste heatfromthethermodynamic cycle (gas turbineorinternal combustion engine). Extensive vali- dation ofall candidatefuelblends willhavetoincludestaticand

dynamicﬂame stabilization (ﬂashback and combustion dynamics control)andcontrol of pollutants(NOx, N₂Oand NH₃ emissions) andisbeyondtheobjectiveofthepresentinvestigation.

Sixdifferentvaluesoftheequivalenceratio^for^the^burnable fuel-oxidantmixtures are investigatedin the presentstudy, = 0.3, 0.45, 0,8, 0.9, 1.0 and1.1, spanning fromultra-lean to mod- eratelyfuel-richconditionsinordertoexplore NOformationpat- ternsthroughout thestoichiometric rangerelevantto gasturbine combustors with advanced fuel staging (e.g. Siemens’ Rich-Pilot- Lean,orRPL,stageintegratedwithasecondpilotandamainstage [28]).Laminarﬂamepropertiesforthefuelblendsinvestigatedare giveninTable1.

3. Results

3.1. Qualitativefeaturesoftheﬂamefront

Inordertoprovideaqualitativeoverviewofthespatialpatterns observedfor keyradical species,Figure 2illustrates theinstanta- neousflame front, subjected towrinkling withconvex(center of curvatureon theproducts’ sideofthe flame,inthe followingre- ferredas“convex” or“cx” inlater figures)andconcave(centerof curvatureonthereactants’ sideofthe flame,inthefollowingre- ferredas“concave” or“cc” inlaterfigures)characteristicshapes.A considerablevarianceinthespatialpatternofmassfractionNOis observedin thevicinity of thereaction zone.In thecaseof very lean mixtures,for = 0.3and0.45, theconvex-shaped portions oftheflame frontexhibit higher NOconcentration than thecon- cave ones; this trend is reversed upon crossing the threshold of 0.9equivalenceratioandforstoichiometricandrichconditions(

= 1.0, 1.1). At = 0.8, NO is more uniformly distributed along theﬂamefrontalthoughaslightdecreaseinitsmassfractioncan be observedatthecusp pointingtowardsthe burntproducts,i.e.

concave.Pleasenote that,forbetterandmoreimmediatecompar- ison,while at the higherequivalence ratios (= 0.9, 1.0, 1.1) it waspossibletoobtainnearlyidenticalwrinkledflamefronts (due to similar flamevelocities), atthe lower equivalence ratios ( = 0.3, 0.45, 0.8) the same convenient visualization was not possi- ble because of largely different temporal evolution of the flame fronts(duetodifferentflamevelocities).Figure3quantifiesthelo- cal changein OH andNO massfractions andtemperaturedown- stream of the flame reaction layer. In the course of the present analysis, we define the reaction layer for values of the progress variable between 0.6≤C≤0.8 (corresponding to the vicinity of thepeakheatreleaserate)whilehighervaluesC>0.8aredefined as”downstream of the flame reaction layer”. The NO mass fraction andother propertiesare analyzed along lines normalto the flamereaction layerdefined usingisolinescorresponding topeak heatreleaserate(this methodologyisdescribedinmoredetailin Section3.2).InFig.3theabsolutemaximumandminimumvalues ofthe NOmass fraction,foreachvalue ofthe globalequivalence ratio,isselectedoverthesimulationtime.Thesearerelatedtothe averageincrease,ordecrease,inNOmassfractiondownstreamof the reaction layer forconcave andconvex portions of the flame front,respectively.ForthechosenvaluesoftheNOmassfraction, OH andtemperature’s corresponding values are selected and re- lated to their mean. The observed local changes in OH and NO massfractionsaremorepronouncedatverylean conditions,with 70%and40%respectively,andatrichconditionswithchanges up to50%and30%respectively,whereas closetostoichiometry(= 0.8and=0.9),thelocalchanges inOH andNOmassfractions aresignificantlylower.Theobservedchangesinthelocaltempera- tureare,however,smallerwithamaximumvariationof7%anddo notshowthesamedistinctivetrendasNOandOH.

Theportionsoftheﬂamefrontthatarecharacterizedbyhigher NO concentrationsare always spatially correlatedwithregions of

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Fig. 2. Premixed wrinkled ﬂame fronts at 1 ms simulation time for all equivalence ratios studied. Contours of NO, OH and H mass fractions are shown from left to right.

Fig. 3. Relative change in OH and NO mass fractions and local temperature downstream of the wrinkled reaction layer in concave- and convex-shaped portions of the ﬂame front.

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Table 1

Laminar ﬂame properties for the fuel blends investigated in the DNS.

Equivalence ratio (-) 0.3 0.45 0.8 0.9 1.0 1.1

Laminar ﬂame speed (cm/s) 30.9 87.0 208.2 233.3 250.6 258.5

Laminar ﬂame thickness (mm) 1.545 0.857 1.163 1.183 1.185 0.941

Laminar ﬂame time (ms) 5.0 0.98 0.56 0.50 0.47 0.36

Inner layer temperature (K) 1358.9 1484.3 1691.8 1727.3 1750.9 1757.8 Temperature at maximal radical production (K) 1417.8 1603.3 1915.5 1976.3 2023.3 2053.4 Adiabatic ﬂame temperature (K) 1492.2 1772.6 2254.6 2347.2 2405.0 2405.4

Fig. 4. Sketch of the streamlines pattern as they approach the ﬂame front according to [29] and the resulting change in local equivalence ratio (DNS data is shown for comparison). Black dashed lines represent the ﬂow streamlines.

increased OH concentrations. These regions are accompanied, at lean conditions, by local enhancement of the heat release rate in convex-shapedportions ofthe flamefront (see Appendix) and their spatialpattern.Thisobservationinthepresentstudyiscon- sistent withearlierobservationsfoundintheopen literature[17]. At the higher equivalence ratios considered here, on the other hand, highNO concentrationsare present atthe concave-shaped portions oftheflamefront andcorrelatedwithlowvaluesofthe heat release rate(compared toelsewhere along the flame front).

This observationseems to suggest that NO formation patterns in these NH₃/H₂/N₂-air ﬂames are not necessarily correlated with high valuesofthe heat releaserateand, consequently, of thelo- caltemperature(duetotheZel’dovichmechanism).

The occurrence of high values of the H radical concentration intheconvex-shapedportions oftheflamefront isrelatedtothe fastdiffusionofhydrogenspecies(H₂andH).Whilemolecularhy- drogen (H₂) migratesfasterthantheother speciesfromthefresh reactants’sidetowardsthereactionlayer[29],atomichydrogen(H radical)isproducedinlargerquantitiestherein.NotethatH₂,dif- fusingtowardsthereactionzone,concentrateinconvexportionsof theflamefrontwhiletheydiffuseawayfromitinconcaveportions (”open tip” phenomenon), this is qualitatively illustrated in the sketchofFig.4[29].TheSoreteffect,i.e.thermaldiffusion,leadsto additionalH₂diffusiontowardsrelativelyhotterregionsincreasing localenrichmentorfall-off intheequivalenceratio,whichwede- finedusingtheelementalmassfractionsofhydrogenZ_H andoxy- genZ_Orelatedtotheirstoichiometric(subscriptst)ratiointheun- reacted(subscriptu)mixture:

local= ZH/ZO

(

^Z^H,u/ZO,u

)

st

(2) and

Z_i= S

j=1

μ

i jY_j (3)

where,iistheconsideredelement,S thetotalnumberofspecies, jthe speciesand

μ

i j themass proportionofiinj.Consequently,

Fig. 5. Temporal evolution of the NO mass fraction in concave and convex shaped portions of the ﬂame front for the richest ( = 1 . 1 ) and the leanest ( = 0 . 3 ) analyzed mixture.

thelocallaminarflamespeedsalsoincreasesordecreases,depend- ingonthelocalequivalenceratio,resultingindifferentialaccelera- tionofdifferentportionsoftheflamefrontthat,inturn,increases flamewrinklingandthegenerationofadditionalflamesurface.The impactofthermaldiffusionontheformationofNOisquantifiedin Section3.6.

TheobservedNOformationpatternisestablishedafter1msof simulationtime andremains unchangedoverthe transientsimu- lationperiod. The reactionfront spatialmotion andits curvature donotreachsteady-statesincetheﬂameiscontinuouslywrinkled duetothevorticitypresentintheapproachingreactants’ﬂowand alsobecauseoftheresultinglocalvariationsintheaccelerationof thereactionfrontitself.However,Figure5clearlyindicatesthatNO massfractionvaluestendtoa statisticallysteadyvalue.Thecom- parisonbetweenthe2DDNSdataandthe1Dsteady-statesimula-

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Fig. 6. Exemplary spatial evolution of NO mass fraction and temperature along lines normal to the reaction layer in convex and concave portions of the ﬂame front. Symbols mark the maximum values.

tions,discussedinSection3.3andindicatingsimilarNOmassfrac- tion values,conﬁrmsthat theNO massfractionscan be assumed tobestatisticallysteady-state.

3.2. Quantitativeanalysisoftheﬂamefront

In ordertounderstand theinter-dependencybetweenfasthy- drogen species diffusion, local concentrations of radical species along the wrinkled flame front and, ultimately, the production rates of NO, we conduct a detailed, quantitative analysis of the chemical reactionkinetics foropportunely selectedrepresentative portions of the wrinkled flame front. For this analysis, temperature,concentrationsandreactionratesforallspeciesareextracted along lines perpendicular to the flame front, in correspondence of concave”cusps” towardsthe products andconvex”bulges” towards thereactants,forallequivalenceratiosconsidered.Inorder to meaningfully compare the quantities extracted from the DNS database, the line-data is normalized with respect to the flame front usingthemaximumrateofO₂ consumption,asproposed in [16].Theselectedvaluesofspeciesconcentrationsandtemperature

aresampledimmediatelydownstreamofthereactionlayer(asde- ﬁnedearlier).ThisbehaviorisillustratedinFig.6.

InordertoidentifyanyeventualmajordependencyofNOmass fractionontheflame characteristics,firstordercorrelation coeffi- cients(Rvalues)are calculatedoverseveraltime steps(1–3.5ms in 0.5 ms steps) for all equivalence ratios considered. A linear weighted regression is calculated where the weighting is imple- mented according to the mean value of the NO mass fraction.

The curvature K is calculated from isolines extracted atC=0.6 marking the upstream limit of the reaction layer in our defini- tion.Second-orderpolynomialsarefittedtotheextractedisolines in order to obtain their parametric representation expressed as L(x)=(a(x),b(x)). Conveniently, this polynomial representation al- lows the calculation of the flame front curvature using first and secondderivatives:

K

(

^x

)

=a

(

^x

)

^b

(

^x

)

−b

(

^x

)

^a

(

^x

)

(

^a²

(

^x

)

+b²

(

^x

))

⁽³^/²⁾ ⁽⁴⁾

For a more convenient comparison,the instantaneous values are normalizedbythe maximumvalueofthe curvatureoveralltime

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Fig. 7. Local maxima in NO mass fraction, for convex (black, open symbols) and concave (gray, filled symbols) portions of the flame front, versus corresponding normalized flame front curvature, local temperatures and OH mass fraction.

steps considered. Here,thenormalized ﬂamecurvaturek, deﬁnes convexregionsbyk<0andconcaveonesbyk>0.

The correlationsshowninFigs.7and8illustratethe relation- ship betweenNOmassfractionandselectedﬂamecharacteristics, such as local curvature, local temperatures, combustion progress andOH, O₂,N₂ massfractions.Theirinspection suggeststhat NO mass fractioncorrelateswell withthelocalequivalence ratioand thecorrespondingoxygenlevel.Thesecorrelationsgainweightto- wardsleanandrichconditionswheretheincreaseanddecreaseof NOandOHformationismostpronounced(compareFig.3).Forall globalequivalenceratios,acorrelationwiththenormalizedcurva- tureisfound.Nevertheless,thiscorrelationisweakercomparedto

the one associatedto local equivalence ratio.Due tothe dispari- tiesin globalequivalence ratio(indicatedin thefigure), however, theunsteadyflamesurfacesevolvedifferentlyintheDNScalcula- tions and, ultimately, this resultsin flame shapesand a reaction front curvature that maynot be directly comparable at homolo- goussimulationtimes(Fig.2).Thepresentmethodologytakesinto account theNO massfractionvaluesbutdonot directlyconsider thesizeoftheareauponwhichNOisdistributed.Thisissueisfur- therdiscussed inSection3.6,anditis supportedby Figs.A1and A2intheAppendix(withincreasingcurvaturetheaffectedportion ofthe postflamebecomeslarger). In general, thepresentresults suggest that trends in local NO formation largely depend on the

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Fig. 8. Local maxima in NO mass fraction, for convex (black, open symbols) and concave (gray, ﬁlled symbols) portions of the ﬂame front, versus O 2, N 2mass fractions and local equivalence ratio.

signoftheﬂamecurvaturebutnotnecessarily(toaﬁrstorderap- proximation)onitsstrength.

The leanertheglobalmixture,thestrongerNO correlateswith the local temperature and combustion progress.With decreasing global equivalence ratio, the combustion progress at which the local maximum and minimum NO mass fraction are located increases. For very lean conditions (≤0.45) superadiabatic con-

ditionsare observed.At moderatelylean conditions(=0.8and =0.45),NOformationisenhancedinconvexshapedportionsof theﬂame front whilethelocal temperatureiscomparableto the one observed inconcave ones. At rich conditions (≥0.9), conversely,thetemperaturesobservedinconcaveandconvexportions oftheﬂamefrontaresimilarbutNOformationislargerinconcave ones.Forincreasinglylean conditions,thetemperatureimpactin-

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creases,sothatat=0.3,thehigherNOvaluesarecorrelatedto thehighertemperatures.

The reason forthisdistinct trendis twofold.Firstly, the char- acteristicspatialpatternofmaximumNOconcentrationdiffersbe- tweenrichandleanconditions.InregionswithincreasedOHactiv- ity,localpeaksinNO concentrationareobservedtobe veryclose to the reaction zone ofthe flame whilethe temperaturestill in- creasesfurtherdownstreamtowardsthecombustionproductsand the post-flamezone (Fig. 6). Conversely, inregions with reduced OHactivity,localpeaksinNOconcentrationarefounddownstream of thereaction zoneandare co-locatedwiththemaximum temperature.Thistrendismoredistinctiveatleanconditions,forrich conditions (> 0.9), peak NO mass fractions occur shortly after the flame reaction layer and it remains at this level further downstream.Secondly,butnotleastimportantly,theNOchemistry seemstobeaffectedbypreferentialdiffusionofH₂andbythere- sultinglocalradicalpool,availableoxygenO₂andthelocalchange in equivalenceratio,as theseareclosely correlated.The previous statementwillbeclarifiedinthediscussionabouttheroleofther- maldiffusion(theSoreteffect)presentedinSection3.6.

3.3. Roleofthelocalequivalenceratio

It has been discussed earlier how the preferential diffusion characteristics of hydrogen species (H radical andmolecular hydrogen)leadtochangesinthelocalequivalenceratioofthereact- ing mixture [29]. The local changein equivalence ratio is shown in Fig. 9 and along lines extracted perpendicularly to the flame frontinFig.10,forall globalequivalenceratiosconsideredinthis work. Note Fig. 10 is split in two plots for improved clarity. In all convex-shapedportions of the flame front (solidline) the local equivalence ratio, after an initial reduction, increases beyond its initial (global) value within the reaction zone, while, for the concave-shapedportionsoftheflamefront,itdecreasestoavalue below its initial (global) value. In these concave-shaped portions of the flame front the local equivalence ratio reaches again the global valuefurther downstream ofthe reactionzone (except for =1.1,wherethelocalvalueoftheequivalenceratioalways re- main belowthe globalvalue).Forincreasingly highglobal equivalence ratios, the absolute change in equivalence ratio increases from=0.3 =0.02to=1.1 =0.15forconvex-shapedportions oftheflamefront,withreductionsofthesameorderinconcave- shaped ones. However, therelative changein equivalenceratiois similar, overthe wholerangeinvestigatedandvariesbetween5%

and15%,whichissmallerthantheincrease/decreaseinOHandNO massfractions(Fig.3).Figure10onlyshowsaportionoftheflame- normal,one-dimensional region verycloseto theflame front.All local equivalence ratiosconverge tothe initial globalequivalence ratio further downstream(Fig.9). Local differencesin the supply offueltothereactionzoneisthusaffectingthecombustionkinet- ics of thisregion of the flame,including the NO production and consumption chemistry. The dependency onlocal equivalenceratio can be studied more conveniently by using one-dimensional (1-D) premixed flames (here: freely propagating flames obtained by the module available within LOGEresearch 1.10 [30]) to anal- yse the local chemistry for comparison with the 2-D DNS data.

Thelocalequivalenceratiosaftertheﬂamefront,atx=0.025cm, are extractedandimposedinto1-D premixedﬂamescalculations.

Theequivalenceratioobtainedfromthe2-DDNSdataisenforced in the 1-D calculations by mixing the unreacted fuel blend with air.Thismeansthat noother speciesare includedexceptthesta- ble species,in order to isolate andinvestigate the impact ofthe local equivalence ratio. In these 1-D simulations, the trends in NO formationpredictedby the2-DDNScalculationsbetweenthe convex versus the concave regions of the ﬂame front are repli- cated,asillustratedinFig.11.Thepresentanalysissuggestsindeed

thatlocalequivalenceratiovariationsduetoﬂamecurvatureplay a signiﬁcant role on the formation of NO in ammonia/hydrogen combustion.

Note that other recently updated chemical kinetic schemes availableintheopenliterature[31–33] havebeentestedandpre- dict similar trends, thereby conﬁrming that the presentobserva- tions are independentofthe speciﬁc reactionscheme adoptedin theDNScalculations, althoughabsolutevaluesofNO differsome- whatbetweenthedifferentkineticschemes(Fig.12).

3.4. AnalysisoftheNOchemistry

Inorder tounderstand how NOformation is affectedby local equivalence ratio changes that are caused, in turn, by wrinkling of the flame front, the mass fraction of selected species is first plotted against the mixture’s equivalence ratio and presented in Fig.13 basedon datafrom1-D numericalsimulations oflaminar premixedflames.Atgloballyleanconditions,anincreaseinequiv- alenceratioenhancestheproductionofNOduetotheavailability ofadditionalfuelandtheresultingincreaseintheadiabaticflame temperature. This trendis reversed at = 0.8where, upon fur- therincreaseoftheequivalenceratio,adecreaseinNOisobserved, duetotheincreasingscarcityofO₂.Thetrendclearlyillustratedby theanalysisof1-Ddatawellreflectsthehomologouspeakinmass fractionNOata global=0.8observedfromthe2-D DNSdata.

NotethatthepeakinmassfractionNOat(^NO^max)=0.8isspa- tiallyclosertothepeaksinmassfractionOandOHratherthanto thepeakinadiabaticflametemperaturewhichis,forthismixture, at(^Tad,max) = 1.06. In the2-D wrinkledflames, convex-shaped portionsofthe flamefrontprotruding intothereactantsare sub- jecttolocalenrichment,thuswhethertheglobalequivalenceratio is smalleror higherthan = 0.8will determine an increase or decreaseofNOconcentration. Thisfindingissupportedby the1- Danalysisandthecomparisonofthe1-Dwiththe2-DDNSdata inFig.13(b).Furthermore,sincetheNO massfractionpeaksat

=0.8,smallchangesinthelocalequivalenceratio,eithertowards lean orrich conditions,lead toa decreasein NO formation.Ulti- mately,thisimpliesasomewhat weakerdependency onthelocal equivalenceratiobuttheNOsensitivitytolocaltemperatureisin- creased,asindicatedbytheﬁrstordercorrelations(Figs.7and8).

NotethatpreferentialdiffusionofH₂leadsnotonlytoachangein localequivalenceratiobutalsoinlocalhydrogen/ammoniaratioas wellasdepletionofO₂,asdiscussedbelow.

AreactionsensitivityanalysistowardsNO formationiscarried out in order to identify the nature of the driving NO chemistry.

Note that, inthe following, reactions are numbered according to the original mechanism for consistency (allelementary reactions discussedhereareprintedinTable2).AtleanconditionsNOpro- ductionis highlysensitiveto fuelNO pathwayssuch asR32, R35 andR44in[13],whereasthermalNO production(R50, R58,R59) becomes more dominant under rich conditions as the adiabatic ﬂame temperatureincreases. Thisaligns withthe strong correla- tionof NO tomass fractionN₂ atrich conditions,withreference toFig.8.Figure14showsthecharacteristicofthereactionsystem:

twocompetingpathwaysofNH₃consumptionthroughtheforma- tion ofNH₂ leading, in turn,tocompeting routesforN₂ and NO formation. At rich conditions, the N₂ formation pathway via NH andNisdominant,whileinleanermixtures,theNOformationvia HNOgetsincreasinglyimportant.Thiscompetitionofthepathways isalsopresentintheotherinvestigatedmechanismspresentedin Fig.12.NOisadditionallyformedtoacertain amountby theoxi- dationofNHandNandthepathwayviaR39ispresentunderlean conditionsonly.TheimportantroleofNH₂ decompositionandNO formationviaHNOisalsoobservedin[9]formanydifferentreac- tionmechanisms,whereastheauthorsdiscusspathwaysfordiffer- enttemperaturesandequivalenceratios.

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Fig. 9. Spatial variation in the reacting mixtures’ local equivalence ratio. Dashed lines denote the preheat layer (C = 0.1), solid black lines the combustion zone (0.6 < C <

0.8).

Table 2

Selected reactions, from the mechanism by Jiang et al. [13] , that affect directly or indirectly the NO chemistry.

Reaction number Reaction

R1 H 2+O = OH+H

R2 H+O 2= OH+O R9 H+O 2= HO 2

R32 NH 2+N = N 2+H+H

R33 NH 2+O = HNO+H

R35 NH 2+NO = N 2+H 2O

R39 NH + O = NO+H

R44 NH+NO = N 2+OH

R50 N 2+O = N+NO

R52 HNO ( + M) = NO+H (+M)

R56 HNO+OH = NO+H 2O

R58 N+O 2 = NO+O

R59 N + OH = NO+H

3.4.1. Leanconditions

Lean conditions ( = 0.45) favor the decomposition pathway of NH₂ via HNO. Moreover, H₂ diffusing into the convex-shaped ﬂame portion will lead to an increased production of H, O and

OHradicalsviathehighlysensitivereactionsR1andR2.Thisrad- ical pool enhancesthe pathway via HNO further (R33) and lead toan increase inreactionrateofreactionR56.IncreasedO₂ consumption, via reactionsR1 andR9, drives theequilibriumof R52 towards higher production of NO. The shift is visible in Fig. 15, wherereactionR52isexothermicinconvex-shapedportionsofthe flamefront,whileitisendothermicinconcaveones.Theincreased O₂ consumption inconvex-shapedsectionsofthe flamefront results in theclearly distinguishable region of lower mass fraction O₂ showninFig.16andleadingtostrongcorrelationswiththelo- cal massfractionO₂,inreferencetoFig. 8. Overall,theincreased equivalence ratio, the increased H₂ concentration and the avail- abilityofO₂ causehigherNOformationinconvexportionsofthe flamefrontcomparedtoconcaveones.

TheimpactonNOformationoftheavailableradicalpoolisalso discussed by Okafor et al. [12]. The authors, in their study on a low-NO_x ammoniacombustorforamicrogasturbine,foundacor- relation between OH and local equivalence ratio proﬁles in 3-D LargeEddySimulation (LES).Theyconcluded that controlling the globalequivalenceratio(throughstaging)mayprovidesome level ofcontrol onO, Hand OH radicals availability and consequently theNOxemission.

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Fig. 10. Spatial variation in the reacting mixtures’ local equivalence ratio along lines extracted perpendicularly to the ﬂame front for the different global equivalence ratios considered in this study.

3.4.2. Roleofthehydrogen/ammoniaratio

ThepreferentialdiffusionofH₂affectsthelocalequivalencera- tio, but also the local composition of the NH₃/H₂/N₂ fuel blend since H₂ concentration is increasedordecreased. Inorderto un- derstandhowimportantistheimpactofthechangeinthehydro- gen/ammoniaratiointhefuelblendonthereactionsystem,three differentmixturesarecompared.The2-DDNSsimulationsarecar- ried outforafuelblend of40%NH₃,45%H₂ and15%N₂ byvolume.Inthementionedfuelblend,thehydrogen/ammoniaratio(on massbasis)isH₂/NH₃=11.6%/88.4%.Thisratioiscomparedtothe homologous ratioobserved atthe location ofmaximum NO concentrations (Fig. 6) forconvexandconcave portions oftheﬂame front.Forexample,at=1.1,moleculardiffusionchangesthisra- tioinconcaveportionsoftheﬂamefronttoH₂/NH₃=9.6%/90.4%

andinconvexonestoH₂/NH₃ =12.7%/87.3%,relativelytotheun-

Fig. 11. Maximum NO mass fraction in concave versus convex regions. Compari- son between the 2-D DNS data and 1-D laminar ﬂame predictions. Gray symbols:

DNS data as in Fig. 7 . Black symbols: predicted trends using 1-D laminar premixed ﬂames.

Fig. 12. Maximum NO mass fraction in concave versus convex regions. Comparison between different chemical kinetics mechanisms. Solid line: Jiang et al. [13] , used in the present DNS calculations. Dashed line: Shrestha et al. [31] . Dotted line: Otomo et al. [32] . Dash-dotted line: Glarborg et al. [33] .

burnedmixture.ForeachoftheH₂/NH₃ratioslisted,aflowanaly- sisiscarriedoutandresultsareshowninFig.17.Theconsumption percentagesshowthat theincrease ofH₂ inrespectto NH₃ leads to an additional enhancement of the dominant pathway of NH₂ consumption via NH andthe directformation of N₂. The further decompositionof NHtoN is,inthe caseofconcave-shaped por- tionsoftheflame,withadecreaseofH₂ intheH₂/NH₃ ratio,lim- ited to58.4%consumption,whereas withhigherlocalH₂ amount itisincreasedtoalmost69%.ThedecreaseofH₂ inthelocalfuel blend further leadsto an augmentation ofthe NO formation via HNO. However, thefurther conversion ofNO to N₂ islimited, as consequence moreof theformed NO remains. Togetherwith the increase inOH radicalconcentration andhigher heatreleaserate intheconcave-shapedflamefronts,aspreviouslydiscussed,more NO is formed. The trend observed inthe 1-D simulations agrees wellwiththe2-DDNSresultswhereareaswithlowerH₂concen- trationhavehigherNOlevels(Fig.16).

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Fig. 13. Mass fractions of selected species over equivalence ratio in 1-D premixed laminar ﬂames (N 2goes with right y-axis) and comparison to the DNS results.

3.4.3. Depletionofoxygen

AnothereffectofthefastH₂diffusionintotheconvexportions of the flame front is the depletion of O₂. By analysing O₂ con- centrationprofilesalongthelinesextractednormallytotheflame front, it is found that H₂ diffusioninto the convex-shapedflame leadstodepletionoftheoxidizerandasignificant decreaseinlo- cal O₂ concentration. WhereasO₂ depletion doesnot play a key rate-limiting roleatthe leanerconditionsinvestigatedduetothe considerablesurplusofO₂ thatispresent,itdefinitivelydrivesthe local equivalenceratiofurthertowards stoichiometry for= 0.9 andtowardsricherconditionsfor>1.0and,consequently,leads to lowerproductionofNO.Asdiscussedearlier,theturningpoint forthisequivalenceratioscalingoftheNOformationisat=0.8 (Fig.13). Thisis wherethe highestNO formation andthe small- estdifferencebetweenconcaveandconvex-shapedportionsofthe flamearefound.

3.5. Impactofthespeciﬁcfuelblend

Asecondfuelblend,nominallyaresultoflowerdegreeofam- moniacracking,isanalyzed inorderto understandthesensitivity

Fig. 14. Flow analysis of the main fuel nitrogen pathways. Percentages give the consumption ﬂuxes at different equivalence ratios.

Fig. 15. Heat release rate for reactions R1, R9 and R52 along lines extracted perpendicularly to the ﬂame front in concave and convex ﬂame portions at = 0.45.

Labels for R52 on the right y-axis.

of the NO formation process to the fuel blend. This second fuel blend is set to 21% H₂, 72% NH₃ and 7% N₂ by volume and its combustioninairsimulatedwithina2-Dconﬁgurationthatisoth- erwiseidenticaltothatusedfortheﬁrstblend,aspreviouslydiscussed.Fuellean(=0.45)andfuelrich(=1.1)conditionsare investigated.

InspectionofFig.18showsthat forthissecondfuel blendthe characteristicspatialpatternofNOconcentrationissimilar tothe

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Fig. 16. Contours of O 2mass fraction at 1 ms for = 0.45 and H 2mass fraction at 1 ms for = 1.1. Black lines indicate the NO islands in Fig. 2 .

oneindicatedpreviouslyforthefirstfuelblend:atrichconditions, NO formationisenforcedinconcaveshapedportionsoftheflame and, atlean conditions,inthe convexones. Overall,thepeak NO mass fractions are lower comparedto the firstfuel blend witha maximummassfractionofY_NOmax(blend2)= 0.013(Y_NOmax(blend 1) = 0.02).Thelocation ofthismaximum isshiftedto =0.85.

Theregressionlinesshowthat,forblend2,theimpactoftheflame frontcurvatureandlocaltemperatureincreasecomparedtoblend 1, howeverthe strong dependencyon the local equivalence ratio remains (Fig.19). Theincreasedsensitivityto curvatureandtem- peraturecanbe relatedtothelowerhydrogencontent,wherehy- drogen diffusion becomesthe limiting factor. It affects the local equivalence ratio, dependingon the localgeometrical features of theflame,aswellasthelocaltemperatures(seeFig.7).Ultimately, the lowered hydrogen content in the fuel blend leads to lower NO formation, even though local temperatures are higher and a nitrogen-containing fuelis still present.This findingconfirmsthe dominantrole ofpreferential diffusionofH₂ onthelocal equiva- lenceratioandtherewithOHandNOformation.

3.6. Impactofthermaldiffusion(Soreteffect)

The ﬂuid temperatureisnot onlyimpacting thereactionrates of the chemical kinetics, butit also represents the main driving force behindthermal diffusion(Soreteffect). Inorder toquantify theimpact oftheSoreteffectontheobservedNO formationpat- terns,otherwiseidentical2-DDNScalculationsarerepeatedwith- out accountingforthermaldiffusionwithin themixture-averaged diffusionmodel(itisincludedinall calculationsconsideredupto thispoint).Figure20illustrates,foranequivalenceratio=0.45, acomparisonoftheNOmassfractionspatialdistributionthrough- out the computational domain from calculationsperformed with (top) andwithout(bottom) takingintoaccount thermaldiffusion.

Minor differencesin the curvature ofthe flame front are visible, thesearecausedbydifferencesinlocalequivalenceratio(impacted bythermaldiffusion)that,inturn,affectlocalflamespeed.Asthe simulations advances in time thesecurvature differencesbecome more evident.Here, arelatively earlytime (t = 1.1ms)ischosen inordertomoreconvenientlycomparehomologousfeaturesofthe flamefront:intheabsenceofthermaldiffusiontheregionsofhigh NOmassfractionappearsmaller.

Fig. 17. Flow analysis of the main fuel nitrogen pathways. Percentages indicate the consumption of the initial fuel species ratio (H 2/NH 3= 11.6%/88.4%) and their ratio in concave (H 2/NH 3= 9.6%/90.4%) and convex (H 2/NH 3= 12.7%/87.3%) portions of the ﬂame front for = 1.1.

Fig. 18. Contours of NO mass fractions at 4 ms for = 0 . 45 and = 1 . 1 . The fuel blend is 21% H 2, 72% NH 3and 7% N 2by volume.

The analysisconductedalong linesperpendicular tothe ﬂame front, asinFig. 7,is alsocarried out toanalyse the role ofther- maldiffusionandpresented inFig.21.TheDNS calculationsthat eitherincludeordonottakeintoaccountthermaldiffusionshow similartrendsandNOlevelsandsimilarcorrelationstolocaltem- perature, mass fraction OH and equivalence ratio. This indicates

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Fig. 19. Local maxima in NO mass fractions, for convex and concave portions of the ﬂame front, versus the corresponding ﬂame curvature, local temperature and equivalence ratio.

Fig. 20. Contours of NO mass fractions at 1.1 ms for = 0 . 45 . In the upper ﬁgure, the Soret effect is included in the numerical model while, in the lower ﬁgure, it is not considered.

that theformationofNO,inthevicinityofcurvedflameportions anditsmaximumconcentration,isimpactedbypreferentialdiffu- sion,asdiscussed above,buttheoccurrenceof thermaldiffusion, actinginaddition tothat, expandsthesediffusive effectstowards lesscurvedpartsoftheflame,andfurtherdownstream,bydriving additionalhydrogenintothecriticalflameregions.Theseobserva- tions support thefindings discussed earlier;that fastdiffusion of hydrogen species,enhanced by flamecurvature andtheresulting enrichmentorfall-off inlocalequivalenceratiodominatethelevel andthelocationofNOformation,whilethermaleffectsasthermal diffusionandthermalNOformation,reinforcetheseeffects.

4. Conclusions

Two-dimensionalDNSwithdetailedchemicalkineticshasbeen employed to understand the fundamental reaction-diffusion pro- cesses leading to the formation of NO in NH₃/H₂/N₂-air wrinkled laminar premixed flames. The fast diffusion of H₂ (preferential comparedto other species) intoconvex-shapedportions of theflamefrontleadstoa localincreaseinequivalenceratio.This changeinlocalequivalenceratioisfoundtoprominentlyaffectthe NOformation.Ifthefuel-airmixtureisgloballylean,thelocalin- crease in equivalence ratio strengthens the formation of the NO species;ifthe fuel-airmixtureisgloballyrich itwill weakenthe NO formationprocess. The decomposition ofNH₂ is governed by twocompetingpathways:thedecompositionvia NHandNtoN₂ on theone hand andthe oxidationvia HNO to NO on theother hand.Thelocalradicalpool,whichisaffectedbypreferentialdiffu- sionofH2 anddepletionofO2,andthelocalfuel-airmixtureratio jointly strengthen further local differences between H₂-depleted (concave) portions of the flame front and H₂-enriched (convex) ones.

Leanconditions havebeen found to be moresensitive to fuel NO.Themorefuelisavailableandthehigheristheadiabaticﬂame temperature,the moreNO forms.Atrich conditions,theavailable oxidizeristhelimitingfactorinrespecttheNOformation.Thelo- caldegradation inequivalenceratioinconcave-shaped ﬂamepor- tions,towards stoichometric conditions,leadsto ahigherNO formation,andH₂presencefavoursthedirectN₂formationpathways.

Slightly lean conditions ( = 0.9) is found to follow the same trend asrich mixture since the maximum NO formation isat

=0.8andduetodepletionofO2 inconvex-shapedsectionsofthe ﬂamefront.

Alltheseconsideration areuseful, atthedesignstage ofcom- bustion systems, in order to selectthe optimal equivalence ratio orthe optimal sequence of equivalence ratios instaged systems, as well as to minimizes NO emissions from equipment burning NH₃/H₂fuelblends.Althoughchemicalreactionsinpracticalcom- bustion devices(gas turbines andreciprocatingengines) typically take placeatpressurized conditions,the presentresultsobtained atatmosphericpressureconditionsareindicativeofanalogouslo- caltrendsandspatialpatternsalsoobservedathigherpressuresin preliminaryinvestigations (notshownhere).Furtherresearch will

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Fig. 21. Local maxima in NO mass fractions, for convex and concave portions of the ﬂame front, versus local temperature, OH mass fraction and equivalence ratio. Squares:

Soret effect included. Crosses: Soret effect not included.

systematically address the pressure scaling effecton the NO for- mationpatternsdescribedinthepresentworkandinvestigatethe roleofturbulence-chemistryinteraction.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgments

The present research is funded by the CLIMIT-Demo pro- gram of theResearch Council of Norway, Project Number 617137 (BIGH2/Phase III), Siemens Energy AG, Equinor ASA. Computa- tionalresourcesareprovidedbyUNINETTSigma2Project Number nn9527k and Norstore Project Number ns9121k. Furthermorewe kindlyacknowledgetheﬁnancial andcollaborative supportofthe CCRC,KAUST.

AppendixA

Fig. A1. Temporal of the predicted ﬂame using DNS for =0 . 45 . Contours of temperatures,heat release, local equivalence ratio, mass fractions H 2, H, OH and NO are shown from left to right. Dashed lines denote the preheated layer (C = 0.1), solid black lines the combustion zone (0.6 < C < 0.8).