Classification and lift-off height prediction of non-premixed MILD and autoignitive flames

Classification

and

lift-off

height

prediction

of

non-premixed

MILD

and

autoignitive

flames

M.J.

Evans

_,

_P.R.

_Medwell

_,

_H.

_Wu

_,

_A.

_Stagni

_,

_M.

_Ihme

b_{DepartmentofMechanicalEngineering,StanfordUniversity,California94305,USA}

c_{DipartimentodiChimica,MaterialiedIngegneriaChimica“G.Natta”,PolitecnicodiMilano,20133Milan,Italy}

Received4December2015;accepted1June2016

Abstract

Moderateorintenselowoxygendilution(MILD)combustionhasbeenthesubjectofnumerousstudiesin recentyears.Anissueremains,however,inthedefinitionoftheboundariesoftheMILDcombustionregime withrespecttonon-premixedconfigurationswithoutpredefinedreferencetemperatures.Aflameletdefinition isappliedtonon-premixedconfigurationstobetterunderstandtheMILDcombustionregimeandclassify previousexperimentalinvestigations.Throughasimplifiedanalysis,anewdefinitionforthenon-premixed MILDcombustionregimeisderived.Thisnewdefinitionisafunctionofinitialandfinaltemperatures,and theeffectiveactivationenergyofanequivalentone-stepchemicalreaction.Thisinherentlyagreeswiththe featuresofthepremixedflameletdefinitionandprovidesinsightintopreviousattemptstoreconcilepremixed andnon-premixedclassificationsof MILDcombustion.Previouslystudiedturbulentflamesareclassified usingthenewdefinitionof MILDcombustionandarecomparedtoexperimentalobservations.Thenew definitionof MILDcombustionissubsequentlycomparedtotheignitioncharacteristicsofopposed-flow ethyleneflames,showinggoodagreement.Finally,transientflameletsaresolvedforamodelledflow-field tosuccessfullyreproducenon-monotonictrendsinthelift-offthatisobservedexperimentallyinaseriesof MILDandautoignitive,turbulentethyleneflamesinhot,dilutedcoflows.

Keywords: MILDcombustion;Non-premixedflames;Liftedflames;Autoignition;Flamelettheory

∗_{Correspondingauthorat:SchoolofMechanical}

En-gineering,TheUniversityofAdelaide,SouthAustralia, 5005,Australia.Fax:+61883134367.

E-mail address: m.evans@adelaide.edu.au (M.J. Evans).

1. Introduction

Moderate or intense low oxygen dilution (MILD) combustion features reduced pollutant emissionsandefficiency improvements over con-ventionalcombustion[1].OperationintheMILD, or flameless, combustion regime is generally achieved byburning fuel in hot, low oxygen en-vironments.Thisreduceschemicalreaction rates,

Nomenclature

α Heatreleaseparameter

χ Scalardissipationrate

T Temperatureincrease

ω Reactionrate

ρ Density

τ Non-dimensionaltime

θ Non-dimensionaltemperature

D Jetexitdiameter

Da GlobalDamköhlernumber

Eeff Effectiveone-stepactivationenergy

R Universalgasconstant

r Radius (cylindrical polar coordi-nates)

Sct TurbulentSchmidtnumber

T Temperature

u0 Jetbulkvelocity relativeto coflow velocity

x Axialdistancefromjetexitplane

Subscripts

0 Referencevalue

b Fullyburntmixture

cofl Coflowconditions

ex Extinctioncondition

ign Steady-stateautoignitioncondition

in Initialcondition

mr Mostreactivemixture

si Self-ignitioncondition

st Stoichiometricmixture

u Unburnt(fresh)mixture

resultingindistributedreactionzonesasopposed to the high temperature peaks in conventional flames [1]. As a result, jet flames in the MILD regime featureaglobalDamköhler number(Da) nearunity,suchthatfinite-ratechemistrybecomes important [2,3]. Despite numerous investigations intotheuniquecharacteristicsof MILD combus-tion, the boundaries of the MILD regime have not been thoroughly defined in non-premixed configurations.

IgnitionandcombustionstabilityoftheMILD combustionregimehavebeeninvestigated experi-mentally[4]andnumerically[4–7]inpremixed re-actors[1].Theseanalyseshavebeenbasedoninitial temperature(Tin)andtemperatureincrease(T),

relativetoaself-ignitiontemperature(Tsi)[1].This

Tsi is defined as the minimum inlet temperature

requiredforignitioninaperfectly-stirredreactor (PSR)within one second[1]. This definitionhas sinceformedthebasisofpremixed[4–6]and non-premixed[8]analysesofMILDcombustion.

TheMILDcombustionregimeinapremixed re-actorhasbeendefined independentlytoTsi[1,5].

Bythisdefinition,MILDcombustionimpliesthat theS-shapedcurveoftemperatureasafunctionof thecharacteristictimeismonotonic,andwithout

ignitionorextinctionpoints[5,9–11].This defini-tionleadstoacriterionforpremixedMILD com-bustion,which,assumingconstantspecificheatat constantpressure,maybeapproximatedas[1]:

Ee f f/(RTin)≤ 4(1+Tin/T) (1)

whereRistheuniversal gasconstant andEeff is

theeffectiveactivationenergyofanequivalent one-stepreaction. This definitionseparates gradually ignitingMILDflamesfromconventional autoigni-tiveflames, whichfeatureignitionandextinction pointson the S-shaped curve. This is consistent withthe“flameless” descriptionofMILD combus-tion [1,5].The two alternatepremixed classifica-tionsof MILDcombustionbothproposedistinct definitionsoftheMILDregime,basedonacritical temperature,Tsi,[1]ortheglobalignitionprocess,

Eeff[5].

Thedefinitionof MILDcombustionbasedon theS-shapedcurvehaspreviouslybeenappliedin analytical[9]andnumerical[10,11]studies.A pre-viousanalyticalstudycombinedthemonotonic S-shapedcurvewithapre-definedquenching temper-ature,toenforce anextinctioncondition[9].The S-shapedcurveconcepthasadditionallybeenused toclassifyresultsinanumericalstudy,with extinc-tiondisappearingwithsufficientpreheatingand di-lution[11].

Experimental studies of non-premixed ethy-lene (C2H4) flames in a jet-in-hot-coflow (JHC) burnerindicatethatapparentlyattachedflames un-dergogradualignitioninlowoxygencoflows, cor-respondingtoMILDcombustion[12,13]. Increas-ingoxygenconcentrationleadstoatransitiontoa conventionalautoignitiveflamestructure[12–14]. Bothflame structureswere observedbyMedwell etal.[12]intwoflamesmeetingthePSRdefinition ofMILDcombustion,despitetheirdifferent igni-tioncharacteristics.

ThenumericalinvestigationofMILD combus-tioninaJHCconfigurationadded“quasi-MILD” and“MILD-like” regimes[8]tothePSRdefinition ofCavaliereanddeJoannon[1].Bothregimeskeep theconditionT < Tsi,however,theformer

de-scribescasesrequiringforcedignitionandthelatter doesnotmeettheimposed“lowoxygendilution” criterion[8].Neither[8],northesubsequent chemi-calkineticsanalysis[6]offerfurtherdistinctions be-tweenMILDcombustionandthesetwo regimes. These classifications expand the PSR definition, howeverareunabletodistinguishgradualMILD combustionfromconventionalautoignition.

The definitions of MILD combustion based on temperatures are not consistent between premixed and non-premixed configurations. The current work aims to use an idealised, one-dimensional flamelet analysis to define non-premixed MILD combustion without the requirementforcomposition-dependentreference temperatures, by including a fuel-specific Eeff.

concept [5,9] which is applied to non-premixed configurationsthroughanalysissimilartothatby Pitsch andFedotov [15].This newdefinition for non-premixed MILD combustion is quantified through an opposed-flow flamelet analysis, to produceacriterionfornon-premixedMILD com-bustion, which is compared to premixed regime classifications. This definition is subsequently used to classify previous experiments, and com-pare flamelet simulations to new experimental observationsinaJHCburner.

2. Numericalanalysis

2.1. Non-premixedflameletanalysis

The one-dimensional, opposed-flow flamelet equationsforanon-premixedsystemwithan irre-versible,one-stepreactionwereanalysedbyPitsch andFedotov[15].Thisanalysiscouplesthereaction rate(ω),scalar dissipationrate(χ), mixture frac-tion(Z)andnormalisedtime(τ).At stoichiomet-ricconditions(st),theflameletsolutionwasshown toyieldthefollowingequationrelatingnormalised temperature(θst)andχ alongtheS-shapedcurve

[15]: dθst dτ + (χst/χst,0)θst− ω(θst)=0 (2) withθ =(T− Tst,u)/Tand: ω=Da(1− θst)2 (1− α)exp(β0− β) 1− α(1− θst) ×exp  −αβ 1− θst 1− α(1− θst)  (3) whereα =Tst/Tst,bistheheatreleaseparameter,

β =Ee f f/(RTst,b)istheactivationtemperature

ra-tio,ureferstotheunburnt(fresh)mixture,b indi-catesfully-burnt,0indicatesareferencevalueand

Daisconstantforanygivenfuelandoxidant com-bination.DifferentiationofEq.(3)withrespectto

θst,atsteady-state,producestheconditionfor

turn-ingpointsintheS-shapedcurve(∂χst

∂θst =0),onthe interval0<θst<1:

ζ =(β2_{+6β +1)α}2_{− (6β − 2)α +1≥ 0 (4)} Satisfyingthisconditionimpliesturningpoints ex-istinthecurveχstversusθst,correspondingto

ig-nition(ig)andextinction(ex)givenby:

θst=1−

1+(3+β)α ± ζ1/2

2(α2_+(1+β)α) , θst,ex≥ θst,ign (5) Ifθst,ignandθst,exarereal,theS-shapedcurve

fea-turesautoignitionandextinction.Iftheseare com-plex,ζ < 0,thenχstversusθstismonotonic,

indi-catingMILDcombustion[5].Finally,negative val-uesindicatenophysicalsolution.

2.2. S-Shapedcurvegeneration

Sixty-threeS-shapedcurveswithC2H4fuelwere simulatedinFlameMaster[16].TheFlameMaster codeusesafinitedifferencemethodsolvedonan adaptivemeshwithasecond-order,implicit back-warddifferenceformula.TheseS-shapedcurve so-lutionswere usedtoform amapof θst,ex− θst,ign

(seeEq.(5)),withMILDcombustionidentifiedif

θst,ex− θst,ign was zero orcouldnot beevaluated.

Oxidisers rangedfrom 1000Kto 1600K,at in-tervalsof 100K,andcomposedof2–15%O2 by volume,atincrementsof1%from2–9%andthen every2%to15%.Theoxidisersconsistedof 10% H2Oand3%CO2,balancedbyN2[12].Thesewere solvedusingtheC1–C3sub-mechanismfromthe December 2014version of thedetailed POLIMI mechanismforhydrocarboncombustion[17].

2.3. Transientflameletanalysis

The ignition of MILD and conventional autoignitive flames was analysed using two-dimensionalprofilesforZandχ.Thisprocedure is similar to previous analyses of turbulent jet flames using transient, opposed-flow flamelets [18].Aconicalpotentialcorewasimposedforthe mixturefractionwith alengthof 7x/D.Further downstream (x/D ≥ 7), the Z profilewas taken fromtheself-similaranalysisby[19]:

x/D<7: Z=  1, R(x)<0  1+[γ Rη(x)]2/4−2Sct, R(x)≥ 0 x/D≥ 7: Z= 70 32 (1+2Sct)D (x+x0)(ρ0ρst)1/2  1+[γ η] 2 4 −2Sct (6) whereγ =[3× 702_/(64ρ st)]1/2 [19];η =rρD/(x+ x0) [19]; x0=[70/32(1+2Sct)ρst− 7]D; R(x)= [1− x/(7D)]/2and: Rη(x)= [rρ− R(x)]D x+[1− x/(7D)]x0 (7) rρ=D−1  2  r 0 ρ ρco f l rdr 1/2 (8) with Sct = 0.71 [19]. Values of D = 4.6 mm, ρ0 = 1.26 kg/m3, ρcofl = 0.31 kg/m3 and

ρst=0.20kg/m3andu0=15.2m/sweretakenfrom experimentalconditions.Densitywastakentobe thelinearmixtureofthefuelandoxidantstreams. Finally,theprofileofχ wastakenas[18,20]:

χ =u0/(35SctD)(ρ0/ρ)2 

_drdZ_ρ2 (9) Fuelandoxidiserstreamswerematchedtothe cur-rentexperimentalC2H4flamesin1250-Kcoflows of3%,6%and9%O2byvolumewithZst=0.01,

Premixed Flamelet Premixed Flamelet Non−Premixed Non−Premixed Non− − − PSR PSR T_in T/T in 5000 1000 1500 2000 2500 0.2 0.4 0.6 0.8 1 No Non−Premixed Solution Premixed F la Prem

Premixed Non Premixed Non Pre

Fig.1. CombinedregimemapforMILDcombustionaccordingtothreedifferentdefinitions:PSR[1](blue),premixed

flamelet[5](green),andnon-premixedflamelet(red).WithTsi=1000K,Eeff=1.67× 108J/kmol[1]andTin=Tst,u.(For

interpretationofthereferencestocolourinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle).

0.02and0.03,respectively.Flameswithhot oxidis-ersinitiallyigniteatthemost-reactivemixture frac-tion(Zmr) <Zst,withthemaximumreactionrate

[21].AlthoughZmr isnot strongly dependenton

χ,higherχ increaseignitiondelays[21].Changes inthereactantstreamsmayshift Zmr andthe

ig-nitionlocation,resulting insignificantlydifferent ignition delays. The flamelets were solved using the USC-II C1-C4 chemical kinetics mechanism [22].A stoichiometric flameletvelocity described thedownstreammotionof Zst intime[18],based

onaself-similarjetvelocityprofile[19].Higher val-uesofZstareclosertothefasterfueljet,andhence

havehigherflameletvelocities.Thestoichiometric flameletvelocitywassubsequentlyusedtoremap timestocorrespondingx/Dforanalysis.

3. Experimentaldetails

ChemiluminescenceimagesweretakenofC2H4 flames in a previously studied JHC burner [12]. Chemiluminescence of OH∗ is spontaneous UV emissionfromexcitedOH.Thepeakintensityof OH∗concentrationhasbeenshowntocorrespond topeakflametemperaturesinlaminarflames[11]. ImagingofOH∗chemiluminescencemaybe there-foreusedtoqualitativelyidentifythehighest tem-peratureregionsofaflame.

Fuelissuesfroma4.6-mmdiametercentraljet at a Reynolds number near 10,000 into 2.8 m/s coflowswithmeasuredcoflowtemperatures(Tcofl)

of 1250Kand3–11%O2.These coflowsalso in-clude10.7%H2O and3.6%CO2 byvolume, bal-ancedwithN2.Thesecompositionsaresimilarto previousexperiments[12],whichareusedforthe C2H4 regime map.This configurationprovidesa controlledenvironmentforapproximately100mm

downstreamof thecoflowexitplane.Flamesare imagedusingapco.pixelflycamerawithaLambert Instrumentsintensifier.Anf-number3.5,UV trans-missivelensisfittedwitha310nmopticalfilterwith abandwidthof 10nm.Meanimagesareformed fromaseriesof 50images,eachtakenwithagate timeof1msandcorrectedforbackground.

4. Resultsanddiscussion

4.1. MILDcombustiondefinitions

DifferentdefinitionsofMILDcombustionare shownoverlaidinFig.1.ThevaluesofTsi=1000K

andEeff = 1.67× 108 J/kmol (40kcal/mol) are

chosen from reference [1]. The blue region indi-catesthePSRdefinitionofCavaliereandde Joan-non [1],bounded by T≤ Tsi;the premixed

S-shapedcurvedefinitionofOberlacketal.[5],where Eq. (1) holds, is in green; and the current non-premixedstudy,wheretheconditioninEq.(4)is notmet,isshowninred.Theoverlapbetweenthe domainsindicatesthatbothgradualignitionand conventional autoignition flame structures exist withintheboundariesof thePSRdefinedregime. ThisindicatesthatthePSRregimeincludesflames featuringinstabilitiesduetolocalautoignitionand extinction, and those which are devoid of local extinction or sharp peaks in flame temperature, whichareconsistentwiththephysicaldescription of MILDcombustion[1].Thisisconsistentwith previous experimental investigations of ethylene 3%O2 and9%O2 oxidantswhichexhibit signifi-cantdifferencesinstructure[12],despiteboth con-ditionsmeetingthePSRdefinitionofMILD com-bustion[1].ThePSRdefinition simplylimitsthe maximumflametemperaturetoTin + Tsi,whereas

the definitions basedon theS-shaped curves in-dicatetheshiftfromgradualignitionto autoigni-tion.The maximum flametemperature of the S-shaped curve-based MILDregimes, however, in-creasewithTin,highlightinginconsistencybetween

T= Tst,b− Tst,u ≤ Tsi andtheflame ignition

characteristics. Thissupports theuseof the new MILDcombustiondefinition forpredicting igni-tionbehaviourofnon-premixedflames.

Combustion is apparent well below the pre-defined Tin = 1000 K PSR threshold [1] shown

in Fig. 1.This region exhibits whatWang et al. [6,8] term“quasi-MILD” combustion, which re-quiresan externalignition source. Thisindicates MILDcombustionoccurringunderforcedignition [6,8],in contrasttotheTin ≥ Tsi requirementof

thePSRdefinition[1].Inthissense,thenewMILD definitionpredicts“quasi-MILD” behaviour sug-gestedbyWangetal.[6,8].Theregionof “MILD-like” combustion[6,8] cannot,however,be deter-minedfromthisgeneralisedfigurewhichmakesno referencetooxygenlevels.

Of the flamelet regimes in Fig. 1, the non-premixedMILDregimeallowsforgreaterT com-paredtothepremixedcaseformostTin.Athigher

Tin,however,thenon-premixedlimitbeginsto

ap-proachalimitingvaluewhilstthemaximumT/Tin

for thepremixed MILD regime continues to in-crease.Additionally,theanalysisfeaturesaregion oflowT/Tinwhereanon-premixedsolutiondoes

notexist.Theseeffectsdemonstratethedifferences between premixed and non-premixedflames, de-spitequalitativelysimilartrends anddescriptions ofMILDcombustion.Thesedifferenttrendsshow thatforagivenfuelofsomeEeff,thereisalimiting

value of T/Tin fornon-premixedMILDflames

whichdoesnotexistinpremixedconfigurations.

4.2. Non-premixedregimemaps

The MILDregime mapin Fig. 1may be ex-pandedtoarbitraryfuelandoxidantcombinations ontheα andβ axes.TheregimediagraminFig.2 showsshadedcontoursofθst,ign,definedbyEq.(5),

inthethreedistinctregionsfordifferentfuelswith specificEeff.

Aselectionof experimentalcasesareincluded in Fig. 2 to classify flames as either MILD or autoignitive flames. Eeff is taken to be 2.51 ×

108 _{J/kmol (60 kcal/mol)[23] forall cases using} CH4-basedfuels. TheseareHM1-3casesusing a CH4-H2 blend[24],theDelftJHC(DJHC)using Dutch naturalgas[25],theF1, F4andF7cases usingpureCH4 [26]andCH4-airflameofCabra et al. [27].One set of data for pure C2H4 fuels is included [12] with Eeff = 1.26 × 108 J/kmol

(30kcal/mol)[28].Theclassificationofthe HM1-3flamesagreeswithpreviouslysimulatedS-shaped curves,whichindicateautoignitioninthetwocases withthegreatest%O2 coflows[10].Thecasesfor oxidants with 3% O2 in the studies from

Med-Fig.2.Normalisedautoignitiontemperature,_θst,ign,for

arangeofα andβ andshowingexperimentalcaseswith

coflowO2concentrationsaspercentageofvolume.

welletal.[12]andDallyetal.[24]arewithinthe MILDregime,whereastheremainingflameswith oxidantO2∼ 7–10%,areautoignitive.Thisis con-sistentwiththeexperimentallyobservedstructures oftheseflames[12,24–27].Thisisinspiteofsome oftheseflames[12,25]meetingthePSRconditions ofMILDcombustion[1].

TheregimediagraminFig.2separatesMILD andautoignitiveflamesandmaybeusedtopredict thestructureofflamesfromevaluationofthe ini-tialmixingtemperatureTst,u,adiabaticflame

tem-peratureTst,bandEeffforagivenfuel.Thisregime

mapshowsthelimitedachievablerangeof α with almostconstantβ usingCH4/air coflows[25,26]. BoththeHM1-3andC2H4setsofflames,igniteat almostconstantTst,uwithvaryingconcentrations

ofO2.Thishighlightsthenecessityofstudying ig-nitionincoflowswithdifferentfuelsanddiluents whichcanaccessawiderrangeofoperating condi-tions[12,24].

The regimediagram inFig. 2showsaregion ofsignificanttemperatureincreasefollowedby au-toignition(θst,ign>10%),whichmaybeindicative

ofthe“transitional” flamesdescribedbyMedwell etal.[12].Thewidthofthisregionincreaseswithβ, implyingprecursorreactionswithsignificantheat releasearemoreprominentforhighβ,orlowTst,b.

Additionally,increasingTst,uwithconstantT

re-sultsinlowerβ.ThisshowsthatMILDcombustion ismostreadilyachievableforhighTst,u,however

maybeachievedatanyTst,u withsufficientlylow

T,consistentwiththepremixeddefinition[5]and theregimesofWangetal.[6,8].

Figure 3 presents regimes of stoichiometric ethylene combustion as a function of oxidant O2 molar concentrationandinitial mixture tem-perature. This figure showsa pair of previously studied flames [12], and flame conditions to be

Fig.3.Contoursofθst,ex− θst,ignforC2H4flameletson TcoflandO2axes,withtheboundarybetweenMILDand

autoignitionregimes(ζ =0)fromEq.(4).

examinedin thenext section.The lineof ζ = 0 (seeEq.(4))withEeff =1.26× 108 J/kmol[28]is

plottedoverthesecontours,andshowsverygood agreementinthelocationoftheMILDcombustion regime boundary. Discrepanciesin the lower-left cornerofthefigureareduetosmallθst,ex− θst,ign <

100K.Theseignitioneventsaretheresultof two-stageignitionprocessesnotcapturedbythecubic S-shapedcurveof theanalytical model.Inthese flames,autoignitionoccursaftersignificant, grad-ualincreasesintemperature,whicharereminiscent ofgradualMILDignition.Additionally,thismay beindicativeofnon-unityLewisnumbereffectsin theflameletanalyses,neglectedinderivingζ .

The good agreement between regime bound-ariesinFig.3implies thatbothautoignition and MILDcombustionmay be analysedwith single-step reactions. Insuch analyses, different condi-tionsandchemicalpathwayscouldbe accounted forwithratecoefficientswhicharefunctionsofthe fuelandoxidantcompositions,andthelocal mix-turefraction.Thisisincontrasttoprevious mod-ellingofsimilarflameswhichstressedthe impor-tanceofmulti-stepkinetics[2].Theseresults sug-gestthepotentialeffectivenessofone-stepreaction models,usingfunctionsasratecoefficients,nearthe limitsofautoignition.

4.3. Chemiluminescenceofjetflames

Chemiluminescenceofexcitedhydroxylfroma seriesofturbulentC2H4jetflamesissuingintohot anddilutedcoflowsareshowninFig.4.Theregime diagraminFig.3indicatesthattheflamesissuing intothe9%and11%O2coflowsshouldbe autoigni-tive,withtheremainderintheMILDregime.These imagesshowstrongOH∗emissionsnearthebaseof theautoignitiveflameswhicharenotapparentin theMILDflames.TheOH∗signalmaybeusedas aqualitativeindicatorofregionsofpeak tempera-tures[11].Well-definedlift-offheightsof8mmand

Fig.4.Imagesof OH∗emissionsfromturbulentC2H4

flamesin1250-Kcoflowswithdifferent%O2(byvol.)

av-eragedover50_{× 1}msimages.Theheightisgivenin mil-limetres,withtheloweredgeoftheimagesatthejetexit plane.Imagesare16mm_{× 60}mmandcorrectedfor back-ground.

Fig.5.Tvs.Z/Zstprofilesoftransientflameletsat

differ-enttimesforC2H4fuelin1250-Kcoflows.

11mm(x/D=1.7and2.4)areseenfortheflames in11%and9%O2 coflows,withlessdistinct lift-off heightsof approximately 14mm (x/D = 3.0) in5%and6%O2coflows.NoOH∗ chemilumines-cenceisdetectablebelowthesepointsforany cam-eraandintensifierexposuretimes. Chemilumines-centemissionsarediscernibleinthe3%and4%O2 casesfrom11mmdownstreamofthejetexit, fol-lowingadjustmentsofthecolour-scale(notshown forbrevity).Belowtheselocations,anyOH∗ emis-sionis below the measurement threshold of the equipment. This trendin lift-off heights demon-strategradualignitioninMILDcombustioninlow O2coflows,andthetransitiontoconventional au-toignitionwithincreasingO2concentration.

4.4. Transientflameletanalyses

TransientflameletprofilesoftheMILDand au-toignitiveflamesfromFig.4arepresentedinFig.5. Theseresultsindicatethatallflamesbegintoignite atapproximately1.2ms.Thiscorrespondsto ini-tialignitionat1.6,1.8and2.0x/Dinthe3%,6% and9%O2 coflowsrespectively, afterthistimeis remappedtox/Dusingthestoichiometricflamelet

Fig.6. Tvs.Zprofilesoftransientflameletsatdifferent timesforC2H4fuelin1400-Kcoflows.

velocitiesfortherespectivevaluesof Zst [18].The

increasingheights with increasingO2 aredueto

Zstshiftingtowardsregionsof higherχ,delaying

ignition.Followinginitialignition,theflameletin the9%O2 coflow reachesitsmaximum tempera-ture by2 ms, which isremapped tox/D of 2.6. This isshorterthan the6%O2 casewhichtakes 2.6ms, correspondingtox/D of 2.7.The3%O2 casedoesnotreachasteadytemperatureuntil ap-proximately5ms,atx/Dof3.0,undergoinga sig-nificantlymoregradualignitionprocess.These re-sultsreplicate theexperimentallyobservedtrend, wherethemaximum chemiluminescenceof flame inthe6%O2coflowappearshigherthanthatinthe 9%O2coflowandtheflameinthe3%O2coflow ini-tiatesgradually,initiallyappearingclosesttothejet exitplane.ThisisrepresentativeoftheMILD com-bustionbehaviourinthe3%O2casetransitioning toautoignitivebehaviourinthe9%O2case.

TheeffectsofincreasedtemperatureonMILD flame stabilisation were assessed using transient flamelets with 1400-K oxidants. Fig. 3 indicates thatalloftheseflamesarewithintheMILD com-bustionregime.Temperatureprofilesfromthe tran-sient analyses areshown in Fig.6 with lines on each plotindicatingincrements of 0.10 ms from 0.25msto1.35ms.Theprofilesindicateignition initiating afterapproximately0.5 ms,0.4ms and 0.35msinthe3%,6%and9%O2oxidants, respec-tively.Flametemperaturesreachsteady-state val-uesby1.65ms,1.05msand0.65ms,at1.9,1.7and 1.3x/D,inthe3%,6%and9%O2oxidants, respec-tively.ThisshowsthatincreasesincoflowO2 de-creasetheheightsof boththeinitialignitionand thedistancetoreachasteadytemperatureanddo not indicate any non-monotonic trend inlift-off height.Incontrast,theflamesin1250-K coflows exhibitincreasingheightsbeforeinitialtemperature increaseswithincreasingO2concentration, demon-strating the effects of temperature, coupled with theimposedZandχ fields.Inthecooler1250-K coflow,ZmrshiftstowardsZstinregionsofhigher

χ andlowervelocity(describedintheanalysisof Fig. 5).Lower χ at Zmr allows the flame in3%

O2 coflow tostabilise closerto thejetexitplane thaninthe6%O2 case.Withtheincreaseto9% O2,theincreasedreactivityatZmrovercomeshigher

χ andtheflame-basemovesclosertothejetexit plane,asseenexperimentally.Thissuggeststhatthe non-monotonictrendinlift-offheightseen experi-mentallyindicatesZmrshiftsawayfromthecoflow,

intothehighshear mixinglayer,where autoigni-tiveflamesignitemorereadilythanMILDflames. Thisadditionallyexplainsthewiderreactionzones underMILDconditionsseeninpreviousworkat lower temperatures[12],as theburning mixtures areconfinedbythelowZflammabilitylimit and thehighχ turbulentmixinglayer.

5. Conclusions

Anewnon-premixeddefinitionforMILD com-bustion,basedonanequivalentactivationenergy rather thanprior assessmentof areference tem-perature,wasderivedandshowntobeconsistent withpreviousexperimentalobservationsof grad-ualignition.Thisdefinitionincorporates,and con-solidates,previousdefinitionsof theMILD com-bustionconditionsandthesuggestedcombustion regimeswhichexhibitsimilarignitionbehaviours. The new definition has shown good agreement withsteady-stateflameletsimulations, demonstrat-ingbetteragreementthanpreviousclassifications between the simulated andpredicted boundaries betweenthenon-premixedMILDandautoignitive regimes.Theseboundariesshowthatnon-premixed MILDcombustionisachievablebyminimisingthe overalltemperatureincrease, orincreasinginitial temperaturesandmaybeachievedfollowingforced ignition.

Time-averaged chemiluminescent images of a seriesofflamesshowedthatautoignitiveflames ex-hibitpeaktemperaturesattheflame-base,in con-trasttothegradualignitionpredictedandobserved inMILDjetflames.Transientflameletmodelling indicated thatthe shift inignition location from regionsof lowscalardissipationratetowardsthe jetshearlayerisresponsiblefortheobserved non-monotonictrendinflamelift-offheights.Thisshift towardsshearlayerisdrivenbydecreasing temper-atureandincreasingoxidant O2 levels. Thismay also explain the decreasing reaction zone width in the transition to conventional autoignition. These results provide a better understanding of theboundariesandstabilisationofnon-premixed flamesin,andnear,theMILDcombustionregime. Acknowledgements

The authors thank Ms Jingjing Ye for her assistance during experimental setup and flame imaging.The authorsacknowledgesupportfrom

The University of Adelaide, Stanford

Univer-sity and the Politecnico di Milano. M.J.E.

ac-knowledgesfinancialsupportfromtheEndeavour

Scholarships and Fellowship grant programme;

P.R.M.andM.J.E.acknowledgefinancialsupport

Australian Research Council (ARC) Discovery

(DPandDECRA)grantschemeandtheUnited

States Asian Office for Aerospace Research and

Development(AOARD);andH.W. andM.I.

ac-knowledgefinancialsupportthroughNASAwith

awardnumberNNX15AV04A.

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