Impact of swirl and bluff-body on the transfer function of premixed flames

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Gatti, Marco and Gaudron, Renaud and Mirat, Clément and Zimmer, Laurent and Schuller,

Thierry

Impact of swirl and bluff-body on the transfer function of premixed flames. (2019)

Proceedings of the Combustion Institute, 37 (4). 5197-5204. ISSN 1540-7489

Impact

of

swirl

and

bluff-body

on

the

transfer

function

of

premixed

flames

M.

Gatti

, R. Gaudron

,

,

,

a_{LaboratoireEM2C,CNRS,CentraleSupélec,Université Paris-Saclay,3,rueJoliotCurie,Gif-sur-Yvettecedex91192,}

France

b_{CNRS,InstitutdeMécaniquedesFluidesdeToulouse,IMFT,Université deToulouse,Toulouse,France}

Abstract

Thefrequencyresponseofthreeleanmethane/airflamessubmittedtoflowrateperturbations isanalyzed forflames featuringthesameequivalenceratioandthermalpower, butadifferent stabilizationmechanism. Thefirstflameisstabilizedbyacentralbluffbodywithoutswirl,thesecondonebythesamebluffbody withtheadditionof swirlandthelastoneonlybyswirlwithoutcentralinsert.Inthetwolastcases,the swirllevelisroughlythesame.Thesethreeflamesfeaturedifferent shapesandheatreleasedistributions, but theirFlameTransferFunction(FTF)featureaboutthesamephaselagatlowfrequencies.Thegainofthe FTFalsoshowsthesamebehaviorfortheflamestabilizedbythecentralinsertwithoutswirlandtheone fullyaerodynamicallystabilizedbyswirl.Sheddingofvorticalstructuresfromtheinjectornozzlethatgrow androlluptheflametipcontrolstheFTFoftheseflames.Theflamestabilizedbytheswirler-plus-bluff-body systemfeaturesapeculiarresponsewithalargedropoftheFTFgainaroundafrequencyatwhichlargeswirl numberoscillationsareobserved.Velocitymeasurementsincoldflow conditionsrevealastrongreduction ofthesizeofthevorticalstructuresshedfromtheinjectorlipatthisforcingcondition.Theflame stabilized aerodynamicallyonlybyswirlandtheonestabilizedbythebluffbodywithoutswirldonotexhibitanyFTF gaindropatlowfrequencies.Intheformercase,largeswirlnumberoscillationsarestillidentified,butlarge vorticalstructuresshedfromthenozzlealsopersistatthesameforcingfrequencyinthecoldflowresponse. Thesedifferentflameresponsesarefoundtobeintimatelyrelatedtothedynamicsoftheinternal recirculation region,whichresponsestronglydiffersdependingupontheinjectorusedtostabilizetheflame.

Keywords: Flamedynamics;Transferfunction;Swirlnumberfluctuations

∗_{Correspondingauthor.}

E-mailaddress:[email protected]

(M.Gatti).

1. Introduction

The frequency response of premixed swirling flames submitted to flow rate modulations is a topicof highscientific andtechnicalinterestdue to the problems raised by combustion instabili-ties in gas turbines[1–3].This response is often https://doi.org/10.1016/j.proci.2018.06.148

characterizedbyaFlameTransferFunction(FTF) ormorerecentlybyaFlameDescribingFunction (FDF)whenthelevelofflowdisturbancesis con-sidered[4].

ChangingtheshapeoftheFTF/FDFby mod-ifyingtheinjectordesignisawaytoaugmentthe stabilitymarginsofacombustor.However,thereis stillnosystematicwaytomakethesechanges, be-causethedynamicsof swirlingflamesisnotfully understood[4,5].Improvedcombustorstabilityis thusgainedbyacostlytrialanderroriterative pro-cessandthereisaneedforbetterknowledgeofthe fundamentalmechanismscontrollingtheshapeof theFTFofswirlingflames.

TheFTFofpremixedswirlingflamescanbe de-termined analytically insimplified configurations [6–8] or by numerical flow simulations in more complex geometries [9–11]. Most often this re-sponseisdeterminedexperimentallybyusingwell proven opticaltechniques [12–15]evenin engine likeconditions[16].

Since shear layers are highly responsive to acousticforcing,theFTFofpremixedflames sta-bilizedbyabluffbodyismainlycontrolledbythe shedding of large coherent structures, which are thenconvected bythemean flowandroll-upthe flame.Thisflameroll-upprocessarounda coher-entvortical structureconstitutesthemain contri-butioncontrollingtheFTFphaselagofpremixed laminar[17]andturbulentnon-swirlingjetflames [18].Italsoconstitutesoneofthefundamental pro-cesscontrollingthedynamicsofpremixedswirling flames[19–21].

Ithasbeendemonstratedthattheresponseof theswirlingvaneneedstobetakenintoaccountin thedynamicsof swirlingflames[20,22,23]. Vorti-caltransverseperturbationstriggeredbytheaxial flowdisturbancesattheswirleroutletleadto oscil-lationsoftheswirllevelattheburneroutlet.This inturnleadstooscillationsoftheflameangleatthe anchoringpointlocation[19].Thisswirloscillation mechanismanditsimpactontheFTFhavebeen identifiedinseveralsetupsinwhichtheflameis sta-bilizedbyacentralbluffbody[20,22,23].Thesame dynamicsisobservedwhentheacousticpulsationis introducedfromtheupstreamordownstreamside oftheswirler[24].

In high power systems, the flame is most often fully aerodynamically stabilized without the help of any solid central insert. Giuliani et al. [25] also report large swirl number oscil-lations in the response of an aeronautical in-jector powered by kerosene when it is submit-tedtoflow ratemodulations.They however pro-vide no FTF data. Biagioli et al. [10] analyzed theFTFofaerodynamicallyswirl-stabilizedflames andfoundthatthepositionof theInternal Recir-culation Zone(IRZ) andtheflame leading edge respondtotheacousticforcingbyalargeaxial mo-tion,butthetangentialflowcomponentisnot

con-sideredintheiranalysisandonecannotconclude abouttheroleofswirloscillations.

There is yet no detailed investigation on the impact of swirlnumber oscillations onthe FTF ofswirlingflamesaerodynamicallystabilizedaway fromallsolid components.This response is ana-lyzedhereforflamesstabilizedeitheronlybyabluff body,onlybyswirlorbybothswirlandbluffbody. Thepremixedflamesinvestigatedfeaturethesame equivalenceratioandthesamethermalpower.

Theexperimentalsetupanddiagnosticsare pre-sentedin Section 2,followed by adescriptionin Section3 of theirflame structurein theabsence offorcing.Theirfrequencyresponseisanalyzedin Section4forthedifferentinjectorstested.Theflow andflamedynamicsatselectedfrequenciesare in-vestigatedinSection 5to infertheswirlnumber fluctuations and the mechanisms controlling the response of these flames. Conclusionsare finally drawninSection6.

2. Experimentalsetup

The experimentalsetup is sketched in Fig. 1. Theburnerispoweredbyamethane/airmixture. Experimentsareconductedatafixedequivalence ratio φ =0.82 and bulk velocity Ub=5.44 m/s (T =20o_{Candp=1atm)intheD=22mm}

di-ametersectionbeforetheswirlerunit.These con-ditions correspond to a constant thermal power

P=5.44kWassumingtotalcombustion. Twodifferentradialswirlerscanbefixedinthe injectionunit.Theybothfeaturesixradial injec-tionchannelsof dc=6mmdiameter.Thedesign ofswirlersS0 andS2onlydifferbythedistancex

indicatedinFig.1.Inthefirstdevice,designatedas

S0,thechannelsarealignedwiththeradial

direc-tion(x=0mm).Inthesecondone,designatedas

S2,thechannelsareshiftedfromtheradial

direc-tionbyx=6mm,toimpartastrongrotationto theflow.

Theflowleavestheswirlerthroughaninjector thatcantaketwodifferentdesigns.Itisastraight tubeof diameter D=22 mm with acentral rod of diameter d=6mm, toppedby aconeof di-ameterC=14mmand10mmlength,tostabilize flamesS0-bbandS2-bbshowninFig.1.Thecone

protrudes2.5mminsidethecombustionchamber fromtheinjectorbackplane.Thedistancebetween theswirlerback-planeandthechamberback-plane isL=56 mm.Forflame S2-as atthebottom in

Fig.1,thecentralrodisremovedandtheflameis fullystabilizedaerodynamically.Thecentral injec-tiontubeisinthiscaseslightlymodifiedand com-prisesatubewithdiameterD=22mmoverafirst sectionoflengthL1=22mm,followedbya

noz-zleof lengthL2=34mm,whichisterminatedby

adivergingcupwithanangleβ =15◦.Thenozzle throatdiameterisinthiscaseD0=12mminFig.1.

Fig.1.Experimentalsetup.S0-bb:non-swirlingflame an-choredbyabluff-body,D0=22mm,C=14mm.S2-bb: Flame stabilized by swirl S₌0_.8 and the bluff-body,

D0=22mm,C=14mm.S2-as:swirlingflameS=0.75 stabilizedaerodynamically,D0=12mm,β =15◦. The maindimensionsareindicatedinmillimeters.

Thecombustionchamberhasan82mmsquare cross-section and a length of 150 mm, and is equippedwithfourquartzwindows.Atthebaseof theburner,aloudspeaker(MonacorSP-6/108PRO, 100WRMS)ismountedtopulsatetheflow.The velocity is measured with a hot wire anemome-terprobe(DantecDynamics– Probe55P16with amini-CTA 54T30)belowtheswirlerunitwhere the velocity has a top hat profile. A photomul-tiplier(Hamamatsu, H5784-04),equippedwith a narrowbandfilter(AsahiSpectra,ZBPA310) cen-teredaround310nmandwitha10nmbandwidth, isusedtorecordtheOH∗chemiluminescence sig-nal.

A2D-2CParticleImageVelocimetry(PIV) sys-tem isalso usedto analyzetheflow structure at theinjectoroutletundercoldflowoperation.Small oildropletsof diameter1–3μmare,inthiscase, seeded in the flow. The PIV system consists of 2× 400mJNd:YAGlaserdoubledat532nm op-eratedat10Hzanda2048× 2048px2_CCD

cam-era(DantecDynamics,FlowSenseEO 4M).Two different optical setupsare usedfor longitudinal andtransversemeasurements,withatimedelay

be-tweenthetwolaserpulsest=10μsandapixel pitchof27.9px/mminthefirstcaseandt=25μs with a pixel pitch of 40.1 px/mm in the second one. Eight hundred images are taken to obtain converged mean and rms values of the velocity field,whichisdeducedfromthecross-correlation ofthePIVimagesbyathreepasseswindow defor-mationtechnique(from64× 64px2_{to16× 16px}2

interrogationareas),withanuncertaintyof0.1px onthecalculateddisplacement.

AnintensifiedCCDcamera(Princeton Instru-ments, PI-MAX 4, 1024× 1024 px2_{), mounted}

withanUVobjective(Nikkor105mmf/4.5)and equippedwith thesamefilterasthe photomulti-plier,isalsousedtoanalyzetheflamestructure un-dersteadyandforcedconditions.Phasedaveraged imagesoftheOH∗ signalsandthePIVfieldsare synchronizedbythesignaldrivingtheloudspeaker.

3. Steadyinjectionconditions

ThePIVdatagatheredintheaxialplaneanda transverseplane2mmabovethetopconeofthe centralbluff-body(flamesS0-bb,S2-bb)and2mm

abovetheinjectoroutlet(flameS2-as)arefirstused

todetermine theswirlnumberS [4]atthe injec-toroutlet:S=0.20forS0-bb,S=0.80forS2-bband

S=0.75forS2-as,witharelativeprecision ± 3%.

The swirllevel forflameS0-bb slightlydiffers

fromzeroduetosmallimperfectionsintheswirler manufacturing. Several PIV measurements were madeto checkthisfeaturethatwas foundtobe reproducible,withthesamevelocityprofile,from tests to tests by mounting and demounting the swirlerandtherod.Nonetheless,theswirlnumber

S=0.2remainsinthiscasesmallandthe config-urationS0-bbwillbereferredinthefollowingasa

non-swirlingflame.

Effects of the swirl number S on the shape takenbytheflamesareshowninFig.1.Theflame

S0-bb is anchored on the bluff body at the top

in Fig. 1 with a relatively narrow reaction layer spreadingoveralongdistanceinthewakeofthe central bluff-body.The flameS2-bbproducedby

thesameinjectorbutwithahigherswirlS=0.8is morecompactinFig.1.Whenthecentralrodis re-moved,Fig.1showsthattheliftedflameS2-ashas

aboutthesameaxialextentasflameS0-bbbutwith

anemissionintensitypeakinginthecentralregion.

4. Flametransferfunctions

TheFTFofthethreeprecedingflamesis deter-minedfromthevelocitysignalmeasuredbythehot wireanemometerandtheOH∗chemiluminescence intensityImeasuredbythephotomultiplier gath-eringlightfromthewholecombustionregion.This signalisassumedtobeagoodtracerof theheat releaserate.Flamesareexcitedbytheloudspeaker

Fig.3.OH∗intensityphaseaveragedimagesataforcing levelu/u=0.30RMS. +:flamerootposition.♦:flame tipposition.H:flameheight._αb:flamebaseangle.(For interpretationofthereferencestocolorinthisfigure,the readerisreferredtothewebversionofthisarticle.)

closetof∼ f0.At higherforcingfrequencies, the

data for the FTF phase lag of flame S2-bb are

foundtobeparalleltotheFTFphaselagplotof thenon-swirlingflameS0-bboffsetbyaconstant

value of ϕ0−1.3 rad. The FTF phase lag of

theaerodynamicallystabilizedswirledflameS2-as

regularlyincreaseswithadifferentslopethanflame

S0-bbanddoesnotexhibitanyinflectionpoint.

5. Flamedynamics

PhaseaveragedimagesoftheOH∗ chemilumi-nescence conditioned bytheharmonic excitation areexaminedinFig.3toelucidatesomeofthe pre-vious observations. The forcing level u/u=0.30 RMSisthesameasinFig.2showingtheFTF re-sults.TheintensifiedCCDcameraissynchronized withthesignaldrivingtheloudspeakeratthe bot-tomoftheburner.Imagesaretakenforeach con-figurationatthesamephasesseparatedbya con-stantintervalof30o_{.Thephaseanglesareindicated}

inFig.3withrespecttothehot-wiresignalbelow theradialswirlerandaphaseshiftarisesbetween flamesforcedat96Hzand170Hz.AnAbel decon-volutionrevealsthetraceof theflameluminosity inanaxialplanecrossingtheburneraxisforflames

S0-bbandS2-bb.Thispost-processingwasnot

pos-sibleforflameS2-asduetothetoohighintensity

valuesclosetothesymmetryaxis(seeFig.1).The same colorscale is usedfor allimages to better highlightboththeflamemotionandchangesofthe flameluminosityduringtheforcingcycle.

ThefirstsequenceinFig.3highlightsthelarge motion undergone bythe non-swirling flameS0

-bb attheforcingfrequency f =96 Hzwhenthe FTFgainismaximuminFig.2.Largeroll-upof theflametipisseenat195° and255°.Theflameis stretchedintheverticaldirectionduringthe forc-ingcyclewithrelativelyminorchangesoftheOH∗ luminosity.

ThesecondandthirdsequencesinFig.3show theresponsesofflameS2-bb,attheFTFgain

mini-mumatf0=96HzandattheFTFgainmaximum

at f =170 Hzin Fig.2.The motion undergone bytheflamedoesnotdiffersignificantlyatthese twoforcingfrequencies,butitismainlychangesof theflameluminositythatexplainthelarge differ-encesobservedfortheFTFgainatf0=96Hzand

f =170HzinFig.2.Atf0=96Hz,thereisa

rel-ativelyweakflameroll-upmotionaccompaniedby weakchangesoftheflameluminosityoverthe forc-ingcycleinFig.3.Atf =170Hz,theflameroll-up processisabitfurtherpronounced,buttheOH∗ lu-minosityundergoeslargechangesduringthe forc-ingcycle explaining the high valuetaken bythe FTFgainatthisfrequencyinFig.2.

ThelastsequenceinFig.3showsthe dynam-icsof theaerodynamically stabilizedflameS2-as

at f =96HzcorrespondingtoitspeakFTFgain valueinFig.2.Theflameisrolled-upbyvortex in-teraction(75◦–195◦)andisstretchedinthevertical direction,butalsoundergoeslargechangesof its luminosityasflameS2-bbatf =170Hz.The

posi-tionoftheleadingedgeofflameS2-asalsoexhibits

alargeverticaloscillationduringtheforcingcycle, ashighlightedbythewhitecrossesinthissequence, whileflamesS0-bbandS2-bbremainanchoredon

thebluffbodyinFig.3.

Further analysis is made at the forcing fre-quency f0=96 Hz by determining the average

flamepositionforeachimagesequences.This pro-fileisobtainedbyfindingthemaximumrow-wise intensityof thepixelluminosity,weightedbythe distancefromtheburneraxisasexpressedby:∫I(r, x)2πrdr.Athresholdof 25%isselectedto delin-eatethelower(crosssymbol)andupper(diamond symbol)flameboundaries.ForflameS2-as inthe

lastsequenceinFig.3,theflamecontourisusedin placeoftheaverageflamepositionfortheanalysis. Thispost-processingisusedtodeducetheflame heightHcorrespondingtotheverticaldistance be-tween theupper (diamondsign) andlower (plus sign)flameboundariesi.e.,thelengthof the ver-ticalwhitesegmentshownin Fig.3atthephase 195o_{.Thisprocessprovestobeefficientandrobust}

evenwhentheflameisstronglymodulatedby vor-texinteraction.Theflameangleαbwithrespectto

Fig.4. EvolutionsoftheswirlnumberSandaxialvelocityuz(r=0)attheburneroutletwithrespecttothephaseofthe

hot-wiresignal.TherelativeflameheightH_/Hrefandflamebaseangleαb/αboscillationsarealsoplotted.Twooscillation

cyclesarerepresentedforbetterreadability.(Forinterpretationofthereferencestocolorinthisfigure,thereaderisreferred tothewebversionofthisarticle.)

theverticaldirectionisalsodeterminedattheflame leading edgepositionasshowninthesecond se-quenceinFig.3at195o_{.EvolutionsofHandα}

b areplottedinFig.4overtwoperiodsforthethree flamesS0-bb,S2-bbandS2-asexcitedatf =96Hz.

Thesame referenceheightHref =25 mmisused

tonormalizetheresults.Thethreeflamesexhibit amodulation of theirheight Hduring the forc-ingcycle,buttheoscillationamplitudeHisabit lowerforS2-bbcomparedtoS0-bbandS2-as.The

swirlingflameS2-bbstabilizedbythebluff body

alsofeaturesalargeoscillationoftheflameangle

αbatitsbaseatf0=96Hz.Theseflameangle

oscil-lationsarenotobservedforthenon-swirlingflame

S0-bb andcouldnot be determinedforthe fully

aerodynamicallystabilizedflameS2-as.

Figure4alsoshowstheevolutionof theswirl number S atthe injector outlet,determined, for eachselectedphaseinthecycle,byPIV measure-ments conducted incold flow conditions, witha relativeprecisionof ± 5%.Oneclearlyidentifiesa largemodulationoftheswirllevelatf =96Hzfor theswirlingflames S2-bbwithandS2-as without

bluff body,whileatthesamefrequencythereare noswirloscillationsfortheflameS0-bb.This

anal-ysisconfirmsthatbothflames,S2-bbandS2-as,

un-dergolargeswirlnumberoscillationsatf =96Hz, buttheirFTFlargelydiffereventhoughtheyshare aboutthesameswirllevelS∼ 0.8.

Finally,theaxialvelocitysignaluzonthe sym-metryaxisr=0isexaminedinFig.4.Thissignal measured2mmabovethetopconeisbarelyaltered bytheflowmodulation at f0=96Hzforflames

S0-bbandS2-bbanchoredinthewakeofthe

cen-tralbluffbody.Thiscontrastswiththelarge oscil-lationinFig.4observedforthesamesignal mea-sured2mmabovetheinjectoroutletfortheswirling flameS2-aswithoutbluffbody.Thislarge

modula-tionisresponsibleforthedisplacementofthe lead-ingedgepositionoftheaerodynamicallystabilized flameS2-asinthebottomimagesequencesinFig.3.

Furtheranalysisisnowcarriedoutundercold flowconditionsbyexaminingthedynamicsof co-herent vortical disturbances synchronized bythe

acousticpulsation.ResultsarepresentedinFig.5. Toidentifyvorticalstructures,theQcriterion[29]is selected:

Q= 1

2(||

2_{− |}

S|2) (3)

where S and  are the symmetric and anti-symmetric components of the velocity gradient respectively.Iso-contoursof Q areinferredfrom PIVmeasurementsintheaxialplane.Onlypositive valuesofQareretained.Negativevalues, indicat-ingregionswhereshearispresentbutnoswirling motion,areforcedtoazerovalue.

Inthefirst,thirdandlastsequencesinFig.5, correspondingtoFTFgainmaximainFig.2,large vorticalstructuresgeneratedattherimofthe injec-torareproducedbytheacousticforcingand con-vecteddownstreaminthechamber.Inthesecond sequenceinFig.5correspondingtotheFTFgain minimuminFig.2forflameS2-bbat f0=96Hz,

vorticalstructuresaremuchweakerasemphasized bythemuchlowervaluestakenbytheQcriterion. Asaconsequence,theflameresponseremainslow atthisforcingfrequency.

Isolines of axial velocity are also shown in Fig.5,tohighlightthedifferentdynamicsofthe in-ternalrecirculationzonedependingupontheflame stabilization mechanism. Flame S0-bb feature a

smallrecirculationregioninthewakeofthe bluff-body. Flame S2-bb feature a larger IRZ,

under-goingaflappingmotionduringtheforcingcycle, whichis more evident at f0=96 Hz. Whenthe

flame is stabilizedwithout bluff-body, S2-as, the

IRZismuchthinnerandoscillatesverticallyinand outoftheinjector.

Theseobservationsareconfrontedwithcurrent interpretationsof theresponseof swirlingflames associatedwiththecombinedeffectsofswirl num-ber oscillations and flame vortex roll-up. Palies et al. [19] explained that atthe FTF gain mini-mum,largeswirlnumberoscillationsmodulatethe strengthof theIRZ.Thisoscillationweakensthe formationof eddiesandalsoleadstoflamebase angleoscillations.Whentheflameanglefluctuates,

Fig.5. QcriterioncontourobtainedfromPIVmeasurementsincoldflowconditions,foraforcinglevelu/u=0.30RMS. Isolinesofaxialvelocityaresuperimposed.Blackcontour:uz=0m/s.Graycontour:uz=−2.5m/s.Thepositionwhere

theaxialvelocityuzfortheanalysisofFig.4ismeasured,isshownasagreencrossatthephase15o.(Forinterpretation

ofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthisarticle.)

vortex growth is rapidly hindered by the flame flapping motion and the flame response is low. When the flame angle oscillation weakens, the responseishighbecausevorticescanfullydevelop before interacting with theflame. Interaction of vortexsheddingandflameangle fluctuationshas beenfurtheranalyzedin[20].Theseauthorsargue thatastheflamemovesclosertotheshear layer, the vorticity of the flow isdissipated due to its interactionwiththeflameandtheflameresponse islow.Incontrast,whenthemeanflamepositionis stationary,thevorticityoftheflowisnotdissipated beforeinteractingwiththeflame,whichleadstoa largeflameresponse.

Theobservationsmadeinthisworkareforsome aspectsconsistentwiththeseconclusions,butalso reveal new mechanisms. Figure 4 confirms that swirlnumberandflamebaseangleoscillationsare largeforflameS2-bbstabilizedbyabluff bodyat

f0=96HzwheretheFTFgainisataminimum.

Itishoweverfoundthattheformationoflarge vor-ticalstructuresaredampedevenwithout combus-tion.Thisphenomenonisherenotrelatedtothe flappingmotionoftheflame,butisfoundtobe re-latedtothegeometryoftheinjector.Atthesame excitation frequency,large vortical structures are shed fromthe injector withoutbluff-body, while largeswirlleveloscillationsarealsoobserved.In

thiscase,theresponseofflameS2-asremainshigh.

Thisflamealsoexhibitsalargeverticaloscillation of itsleading edgeandapeakvalueof theFTF gainat f =96Hz.Thisanalysis revealsthatthe mechanismscontrollingthefrequencyresponseof swirledflameslargelydifferwhentheyarestabilized byabluffbodyorwhentheyarestabilized aerody-namically,themaindifferencesbeingrelatedtothe dynamicsoftheIRZ.

6. Conclusion

Transferfunctionsofflamesstabilizedwith dif-ferent injectordesigns havebeeninvestigated for differentswirllevels,withandwithoutacentral in-sertintheinjector.Dependingontheflame stabi-lizationmechanismabovetheinjector,flame vor-texroll-up,oscillationsoftheflamebaseangle in-ducedbyswirlleveloscillationsandvertical oscil-lationsoftheflameleadingedge,arefoundtobe thecompeting mechanisms controlling the flame response. WhentheFTF gainisat amaximum, the threeflames investigated arestrongly modu-latedbytheirinteractionwithlargevortical struc-turesconvectedintheexternalshearlayerof the flow,regardlessof changesof theswirllevel and the way the flame is stabilized. In contrast, the formationoflargevorticalstructuresishindered,

evenincoldflowconditions,atthefrequency cor-respondingtoaminimumintheFTFgaincurve,a propertywhichisfoundinthepresentstudyonly fortheswirlingflame stabilizedby abluff body. Atthisfrequency,largeswirlnumberoscillations leadtoamodulationof theflamebaseangleand weakvortexformation.Atthesamefrequency,but forthe aerodynamically stabilizedflame without centralinsert,thesamelevelofswirlnumber oscil-lationisobserved,butthegainoftheFTFremains high.Inthiscase,theflamedynamicsiscontrolled bylargevorticalstructuresshedfromtheinjector lipsandlargeverticaloscillationsoftheflame lead-ingedge.Theoriginofthelowresponseofswirling flamesatspecificfrequenciesisfoundtonotonly berelatedtolargeoscillationsoftheswirllevel,but alsototheflamestabilizationmechanismandmore specificallytothedynamicsoftheinternal recircu-lationregion.

Acknowledgments

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 643134. ThisworkissupportedbyAgenceNationaledela Recherche,NOISEDYNproject ( ANR-14-CE35-0025-01).

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