Influence of flame-holder temperature on the acoustic flame transfer functions of a laminar flame

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Influence of flame-holder temperature on the acoustic

flame transfer functions of a laminar flame

Daniel Mejia, Maxence Brebion, Abdulla Ghani, Thomas Kaiser, Florent

Duchaine, Laurent Selle, Thierry Poinsot

To cite this version:

Daniel Mejia, Maxence Brebion, Abdulla Ghani, Thomas Kaiser, Florent Duchaine, et al.. Influence

of flame-holder temperature on the acoustic flame transfer functions of a laminar flame. Combustion

and Flame, Elsevier, 2018, 188, pp.5-12. �10.1016/j.combustflame.2017.09.016�. �hal-01730352�

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pen

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rchive

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To link to this article : DOI:10.1016/j.combustflame.2017.09.016

URL :

http://dx.doi.org/10.1016/j.combustflame.2017.09.016

To cite this version : Mejia, Daniel and Brebion, Maxence and

Ghani, Abdulla and Kaiser, Thomas and Duchaine, Florent and

Selle, Laurent and Poinsot, Thierry Influence of flame-holder

temperature on the acoustic flame transfer functions of a laminar

flame. (2018) Combustion and Flame, vol. 188. pp. 5-12. ISSN

0010-2180

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Influence

of

flame-holder

temperature

on

the

acoustic

flame

transfer

functions

of

a

laminar

flame

Daniel

Mejia

a

_,

_Maxence

_{Miguel-Brebion}

a

_,

_Abdulla

_Ghani

a

_,

_Thomas

_Kaiser

a

_,

Florent

Duchaine

b

_,

_Laurent

_Selle

a,∗

_,

_Thierry

_Poinsot

a,b

a Institut de Mécanique des Fluides de Toulouse (IMFT), Université de Toulouse, CNRS, INPT, UPS, Toulouse, France b CERFACS, CFD team, 42 avenue G. Coriolis, Toulouse, France

Keywords: DNS

Conjugate heat transfer Analytically reduced chemistry Flame transfer function Premixed flame Laminar flame

a

b

s

t

r

a

c

t

Theoccurrence ofcombustion instabilitiesin high-performanceengines suchas gas turbines is often affectedbythethermalstateoftheengine.Forexample,strongburstsofpressurefluctuationsmayoccur atcoldstartforoperatingconditionsthatarestableoncetheenginereachesthermalequilibrium.This observationraises thequestionoftheinfluence ofmaterial temperatureontheresponse offlamesto acousticperturbations.Inthisstudy,weassesstheinfluenceofthetemperatureoftheflameholderfora laminarflame.BothexperimentsandnumericalsimulationsshowthattheFlameTransferFunction(FTF) isstronglyaffectedbytheflame-holdertemperature.ThekeyfactorsdrivingtheevolutionoftheFTFare theflame-rootlocationaswellasthemodificationoftheflow,whichaffectsitsstability.Inthecaseof thecooledflame-holder,theformationofarecirculationzoneisidentifiedasthemainimpactontheFTF.

1. Introduction

Experimentalists are aware that the wall temperatures of a combustion chamberaffectthe thermoacousticcombustion insta-bilitieswhichcandevelopinthecombustor[1–4]:achamberdoes not exhibit the same noise and unstable modes when it starts (and walls are cold)or when it has run for a few minutes (and wallshavereachedahighersteadytemperature).Fromthe model-ing pointofview,however,mostmodelsassume adiabaticflames anddonotincludeanyinteractionbetweenwallsandflames.This is clearlya weak aspectofmostLargeEddySimulation (LES) ap-proaches for turbulent burners. Among all the walls found in a combustionchamber,flameholdersplayaveryspecificrole:thisis whereflamesareanchoredandwheretheyarethemostsensitive toheattransfer.Anytemperaturechangeofthesolidintheregion where flames are stabilized can change not only its stabilization point (the placewhere it is anchored)but alsoits dynamics(its responsetoacousticwavesaswellasitsblow-off limits).TheMIT group usedDNSto studythestabilizationofpremixedflames on square flame holders [5–7] and showed that the location of the flameroots andtheblow-off limitswere stronglyaffectedby the temperature of the flameholder. Kaess etal. [8] proved that the temperature of a laminar flame stabilized in a dump combustor controlled the flame response to acoustic waves. Duchaine etal.

∗ _{Corresponding author.}

E-mail addresses: laurent.selle@imft.fr , selle@imft.fr (L. Selle).

[9] used sensitivity analysis on a DNS to show that the acous-tic response of flames stabilized by a backward facing step de-pendedstronglyonthewalltemperatures.Mejiaetal.[3] demon-strated experimentally that controlling the wall temperature of a 2D triangular laminar flame was sufficient to bring it in and out ofthermoacousticoscillations.Theseconclusions,obtainedfor laminar flames,havebeenconfirmedforturbulent flames[10,11].

[10] showed that the thermal conductivity of the backward step blocks used tostabilize aturbulent flame,controlled the level of self-sustainedinstability.

The present work focusesonlaminar flames andanalyzesthe acoustic response of V-flames stabilized on a two-dimensional cylinder which can be water cooled to fullycontrol its tempera-ture between 300 and700 K. The setup corresponds to the one usedbyMiguel-Brebionetal.[12]:alaminarmethane/airflameis stabilized onacylinderwherethe temperatureofthiscylinderis controlled by water cooling. Miguel-Brebion etal. [12] described thedifferentflametopologiesandstabilizationpositionsobserved when theflame-holdertemperaturewas changed.Whenitcomes todescribingthecapacityoftheseflamestocreateself-excited in-stability modes,themostusefulquantitytoconsideristheFlame TransferFunction(FTF)F

(

ω

)

whichmeasuresthenormalized vari-ations ofthe globalreaction rate(q′_{/¯q) induced by a normalized}

inletacousticvelocitypulsation(u′_/u

b)[2,13,14]: F

(

ω

)

= q ′_/¯q u′_/u b https://doi.org/10.1016/j.combustflame.2017.09.016

FTF’s can be obtainedexperimentally ornumerically: both meth-odswillbeusedhere.Thepresentstudyfocusesonmeasurements ofFTFinthesetupofMiguel-Brebionetal.[12]andshowsthatthe FTFareextremelysensitivetotheflameholdertemperaturewhich appears tobeafirst-orderparametercontrollingtheFTFinterms ofgainandphase.Oneofthenewresultsobtainedhereisthatthis effectsoftheflameholdertemperatureisduenotonlytoa mod-ificationoftheflamerootdynamics,closetotheflameholderbut also to a drastic change ofthe mean flow itself,far downstream asseenin[15],butinthiscaseinducedbythecreationofalarge recirculationzonewhentheflameholderiscooled.

Thepapercombinesexperimentalmeasurementsanddirect nu-mericalsimulation(DNS)resultstoanalyzetheFTF’sofalean pre-mixed laminar methane/air flame. Simulations are performed in dualmode: theflowiscomputedwithDNSusinga19species ki-neticschemeforCH₄ /airflames[16]whilethetemperatureinthe solid iscomputedwithaheattransfersolver,coupledtotheflow solver.Theexperimentusesamulti-microphonetechniqueandhot wiremeasurementstoquantifyu′_{aswell asunsteadyCH}∗

chemi-luminescenceandhighspeedimaginarytoevaluateq˙′_.

The paper isorganized asfollows: the configurationis briefly described in Section 2.The experimentalset-up used tomeasure theFTF’sisdescribedinSection3.TheDNStoolsusedtocompute the FTFofthe flamesaredescribed inSection4.Finallya discus-sionoftheresultsobtainedexperimentallyandnumericallyis pre-sentedinSection5.

2. Configuration

The experimental bench consist of alean premixed methane– airV-flamestabilizedinthewakeofasteelcylindricalbluff body (diameter d=8 mm). The burner has a constant cross section of h=34 mm by l=94 mm so that the flame remains two-dimensional, allowing fasterDNS(Section 4). TheReynolds num-ber based on the bluff-body diameterRecyl≈ 500 is low enough

toensurelaminarflow.Thereactantsarepremixedinaone-meter long injectiontubeandequallydistributedtosixinjectorsplaced at the bottom ofthe injectionchamber. The flow is laminarized by an array of small glass balls and one honeycomb panel and passesthroughthecooledplenumtoensureaconstantfresh-gases temperature. Finally,itentersthecombustionchamberwherethe bluff-bodyislocated.Thelateralsidesofthecombustionchamber arewatercooledtoimposethewalltemperature.Theplenumhas three pressure plugsand one loudspeaker plug ateach side. The combustion chamber has three optical accesses: one atthe front toallowadirectviewoftheflameandone3mmslotoneachfor thelasersheet.

Twodifferent bluff-bodiesareused tostabilizethe flame.The first,calledCBB(CooledBluff-Body),isasteelwater-cooled cylin-der (Fig.2,left).Drilledholesattheendofthefeedinglineallow the waterto flowto the6 mmouter line, whereit isevacuated. The cooling system isdesignedto maintaintemperatures around 285Kinthebluff-bodywalls.Thesecondflameholder,calledUBB (UncooledBluff-Body)isafull,solid,steelcylinder,withthesame externaldiameterasthecooledone(Fig.2,right).Itstemperature isnotcontrolledanddependsontheflameshape.Itcanreachup to700K.

The operatingcondition isthesameforallcases(Table 1).For this regime and thisgeometry ofthe chamber, there is no com-bustion instabilities (CI) so that the flame is steady. The burner power is 7kW foran equivalence ratio

8

=0.75 anda bulk ve-locity ub=1.07ms−1 . Theflame holdertemperatureismeasured

witha K-type thermocouple:TUBB

cyl =670±40K.In theCBBcase,

the temperature elevationof the waterused for cooling isequal to

1

T=0.15±0.05K sothat thecooling watertemperaturecan be assumedtobeconstant.The totalfluxtakenfromtheflameis

CH4+Air

Tranquilization

Plenum

Combustion

Chamber

138 200 200 37 Glass Balls Honeycomb Flame Holder 34 Flame 68

Injection

Loudspeakers Cooled Walls Windows H2O In H2O Out CH4+Air CH4+Air

Fig. 1. Transverse cut ( left ) and isometric view ( right ) of the Intrig burner.

Cooled Bluff-Body (CBB)

Water inlet _{Water outlet}

Uncooled Bluff-Body (UBB)

Fig. 2. Cooled bluff-body, CBB T w ≈ 285 K ( left ) and uncooled bluff-body, UBB

Tw ≈ 700 K ( right ).

Table 1

Operating conditions.

Name Quantity Value

8 Equivalence ratio 0.75 ub Bulk velocity 1.07 ms −1

sl Laminar flame speed 0.24 ms −1

Tu Injection temperature 292 K

Tadia Adiabatic flame temperature 1920 K

Table 2

Thermal properties of the flame-holder steel. The emissivity ǫranges from 0.2 for polished surfaces to 0.9 for oxidized surfaces.

Material ρcp [K −1 m −3 ] λ[W/m/K] ǫ

35NCD16 3.5 10 6 _{32 0.9}

8

xp_{s→ w}=m˙C p

1

T=24W.The thermalpropertiesofthesteelused inboth UBB andCBBcases aregiven inTable 2.In this configu-ration,Miguel-Brebion etal.. haveshownthat radiationform the flameholderisakeyfactortopredictthetemperatureoftheUBB case.Inthepresent experiments,bluff-bodiesareoxidizedsothat anemissivityof

ǫ

=0.9isretained.

3. Experimentalstrategy

ThedeterminationoftheFTF(cf.Eq.2)requirestheknowledge oftheheatreleaseratefluctuations.Foraperfectlypremixed mix-tureatagivenequivalenceratio,theheatreleaserateq˙is propor-tionalto the flame surface, A, andto the light emission, I,from freeradicalsCH∗_{[17–19],anditispossibletodeterminethe}

trans-ferfunctionfromoneofthefollowingexpressions:

F

(

ω

)

= q˙ ′

₍

_t

₎

_/¯˙q u′

₍

_t

₎

_/u b =A ′

₍

_t

₎

_/A¯ u′

₍

_t

₎

_/u b = I ′

₍

_t

₎

_/¯I u′

₍

_t

₎

_/u b

H

2O In

H

2

t

u

O

O

PM

HW

PM line-of-sight

CH* Filter

x

z

y

Acoustic waves from Loudspeaker

Fig. 3. Iso-transverse cut of the experimental configuration used to measure the FTF (CBB configuration).

Toreducetheerrorduetoexperimentalnoisetheflame trans-ferfunctionmaybecalculatedby:

F

(

ω

)

= Suq

(

ω

)

Suu

(

ω

)

(3)

Where,Suqis the crosspower spectral density betweenthe u′(t)/ub

andI′

₍

_t

₎

_{/¯IsignalsandS}

uuisthepowerspectraldensityofthe

ve-locitysignal, u′_(t)/u

b.The flameis excited withapure sinusoidal

acousticsignal,andtheFouriertransformoftheinputandoutput signaliscalculatedatexactlytheforcingfrequency.Thegainis de-finedasthemagnitudeofF

(

ω

)

,G=

|

F

(

ω

)

|

whilethephaseisits argument,

ϕ

=arg[F

(

ω

)

].

3.1. Experimentalmeasurements

MeasuringthecomplexnumberF

(

ω

)

,requiresastable config-uration thatcan bepulsated overtherangeof frequencieswhere theflameissensitiveto acousticperturbations. Twoloudspeakers placedatthebottomoftheplenumareusedtosendphasedplanar harmonic acousticwaves towards theflame. Lightemission from CH∗ _{free radicals, I}′ _{and velocity fluctuations u}′ _{are recorded}

si-multaneouslybythephotomultiplier(PM)andthehot-wireprobe (HW) representedinFig.3,respectively.The HW isplacedatthe centeroftheplenumthroughapressurepluglocatedat

(

x,y,z

)

=

(

0,0,−61mm

)

anditisorientedtomeasurethevelocity compo-nent uz.The PM axisis alignedwiththe cylindercentreline axis

(x) anditcollects the 2D line-ofsight integratedflame CH∗ _light

emission.

Duroxetal.[20]showedthat fortheseflames,thegainofthe FTFstronglydependsontheamplitudeofthevelocityfluctuations, even forlowamplitudes(5–10% ofthebulk velocity).In orderto avoidnonlinear-effects,theamplitudeofthevelocityperturbation iskeptaslowaspossible,whilepreservingagoodsignaltonoise ratio(SNR).Withoutmodulation,thermsvelocityfluctuationsare lessthan 0.4% ofthe bulk velocity: a velocity modulation ampli-tudeof1%ofthebulkvelocityisenoughtohaveatleastaSNRof 2.Figure4isanexampleofthetimetraces,overthreeacoustic pe-riods,ofthenormalizedvelocityandheatreleaserate,foran exci-tationfrequencyof fex=100Hzandanamplitudeofu′/ub=0.01.

The FTF corresponds to the mean value of four runs at each frequency.ThegainandthephaseoftheFTFforthetwocasesCBB andUBBarepresentedinFig.5.InbothcasesthegainG

(

ω

)

starts from unityat low frequencies, reachesa maximum around fex=

100Hzand returnstozeroathighfrequenciesabovefex>250Hz. Theamplitudeofthepeaks,however,variesconsiderablyfromone caseto another. InUBB case, the peak amplitudeis closeto G≈ 2.5whileforthecooledcaseCBBitreachesvaluescloseto4.0.

Phases (

ϕ

=arg[F

(

ω

)

]) increase linearlyfor both cases. How-ever, the slope of

ϕ

(

ω

), which corresponds to the time delay

u'/ub ICH*'/ICH* amps. (relative)0.02 0 0.02 t [ms] 0 10 20 30

Fig. 4. Experimental results: time traces of normalized velocity ( ) and heat release rate ( ) for a frequency of f ex = 100 Hz and a modulation amplitude of

u′ /u = 0 . 01 in the UBB configuration.

Fig. 5. Experimental results: gain ( top ) and phase ( bottom ) of the FTF for both CBB ( ) and UBB ( ) cases, for excitation frequency of f ex = 100 Hz and an amplitude

of u ′ /u

b = 0 . 01 .

(

τ

=

ϕ

/

ω

)betweentheacousticperturbationandtheheatrelease rate response, is different. The time delay

τ

decreases with the flame holdertemperature, itgoesfrom45ms intheCBBcaseto 35msfortheUBBcase.

Figure5bringsuptwoimportantresults:

• Thechangeoftemperatureoftheflameholderhasamajor ef-fectonbothgainandphaseoftheFTF.

• The absolute values of gain are very large for these flames (from2.5to4).Suchvalueshavealreadybeenreportedfor con-ical ”V” flames [20,21].They are dueto the 2D nature ofthe flamesandareanalyzedinthenext sectionwheretheDNSof thesameflamesareperformed.

4. Numericalstrategy

TocapturetheeffectsofflameholdercoolingontheFTF,a cou-pledDNSoftheflowandofthetemperaturefieldwithintheflame holder isperformed. The choice ofa 2D configurationallows the useofhighorderschemesandcomplexchemistrytoproperly de-scribethenearwallchemistry.

4.1. Fluidandsolidsolver

The compressible NavierStokes equationsare solved withthe AVBPsolverusingathird-orderschemeforspatialdifferencingon a two-dimensional hybrid mesh combined withan explicit two-stepschemefortimeadvancement[22,23].TheNSCBCformulation

[2,24]isusedfortheboundarieswhilethemoleculartransport de-scriptionisbasedon theHirshfelderCurtisapproximation[25].A multistepanalyticalmechanism,referredtoasLU19isusedto de-scribethechemicalkineticsofthemethane–aircombustion[16].1

1 This chemical mechanism was used instead of the 13-species schemes used in

Miguel-Brebion et al. [12] because it provides better results for the flame position

The resolution ofthe heat transfer equation in thebluff-body reliesonanimplicit[27]first-orderforwardEulerschemefortime integration anda second-order Galerkin scheme [28]. Local heat fluxes

φ

s are imposed inthesolid solveratthe boundaryshared

between the solid and the fluid domains. The solid solver then sends skintemperatures back to the DNScode forthe next iter-ation.

4.2. Couplingstrategy

TheDNScode(aroundthecylinder)andtheheattransfersolver (in the cylinder) are coupled with a software called OpenPALM

[29] which exchanges heatfluxesandtemperatures onthe cylin-der skin. The local temperature obtained by the solid solver on thecylindersurfacesolverisappliedthroughanisothermalNSCBC boundary condition [24] in AVBP whereas the local heat flux is given by AVBP to solid solver. The characteristic flow time

τ

f is

of theorderof 50ms whilethe solidcharacteristic time

τ

s is of

the order of100 s. The simulationof the flame forseveral

τ

s is

impractical butitisnot neededsincethebluff-body temperature changes very slowly and only the steady-state temperature field isrelevanthere. Therefore,thecouplingstrategy toacceleratethe convergence towards steady state isthat each domain (flow and solid)isadvancedatits owncharacteristictimeusingatimestep

α

f

τ

fforthefluidand

α

s

τ

sforthesolidwith

α

f=

α

s[9].Thisis

sufficienttoobtainsteadystatevaluesofthecylindertemperature. This temperatureisalmostconstant whenflames are acoustically forcedsothatonlytheflowsolverisrunningwhencomputingthe FTF’s.

Moreover, radiativeheatlossesfromtheflameholdermustbe accountedforwhenrelativelyhightemperaturesarereached.They are taken intoaccount inthe localflux condition imposed onin thesolidsolverbyaddingaradiativeflux

φ

rad:

φ

rad=

σ ǫ

(

T4 −Text4

)

(4)

where

σ

is the Boltzmann constant,

ǫ

is the emissivity coeffi-cient ofthebluff-body surface andT isits localtemperature. Ra-diation from the gas (H₂ O, CO₂ ) and from the hot walls down-stream of the combustion zone is neglected. Furthermore, walls at the same height of the flame holder are assumed to have a temperatureclosetothefreshgasandtobehaveasblackbodies:

Text=Tu=300 K.This simplecoupling strategy hasbeen already

usedinseveralstudieswithgoodresults[12,30].

4.3. Simulateddomainandmesh

The computation of realistic flame dynamics responses must takeintoaccounttheinteractionbetweentheflameandthe exter-nalwalls.Thus,thewholeflamemustbecalculated.Thesimulated domain used to calculateFTFs has beenspecifically adapted:the plenumhasbeenkeptasshortaspossiblewhilethechamberwas kept identical to the experimental one (Fig. 6). The mean veloc-ityprofilehasbeenmeasuredexperimentally 35mmupstreamof thecylinderandisimposedattheDNSinletwhilethecombustion chamberwallsarecooled.Coolingtheexternalwallssimplifiesthe set-upoftheDNSbecauseasimpleisothermalboundarycondition isimposedattheDNSsidewalls.

Anunstructuredhybridmesh,[12],isusedtoaccuratelycapture theconjugateheattransferbetweenthesolidandthereactiveflow

[31,32].Fivelayersofquadelementsareusedoutsideofthe cylin-der boundary(flowregion)andtenareusedinside(solidregion). The remaining partsofthegeometries are meshedwithtriangles (Fig.6).Themeshesforsolidandfluiddomainsarenotcoincident

reactions and predicts a more precise flame velocity. The 19-species scheme also provides a better description of low-temperature chemistry near the cylinder.

Fig. 6. Comparison between the experiment and computational domain. With a zoom on the mesh. The stream lines show that the recirculation zone is well cap- tured by the hybrid mesh.

Fig. 7. Comparison between the experimental and simulated flames for the CBB and UBB cases.

ontheflameholderskinandasecond-orderinspaceinterpolation isperformedtotransferinformationbetweenthetwosolvers.The meshisrefinedalongtheflamefrontandclosetothebluff-body. Aconvergencestudywasperformedinastationaryflame[12]and amesh resolutionof70

µ

misretained providingatleast8cells intheflameregion.

Inordertovalidate thechoicesmadeabove acomparison be-tween the experimental and the simulated stationary flame is showninFig.7,fortheCBBandUBBcases.Theexperimentalflame correspondstoalineofsightintegratedCH∗_field.

Inbothcases,theflameshapeandtheflameanchoringposition arewellreproducedbytheDNS.Tofirstorder,theFTFiscontrolled bythestationaryflameshape[33,34],determinedbytheflame an-gle

α

(Table7),forlongflames

α

≈tan−1 sl₀ /ub.Agoodagreement

isfoundbetweenexperimentsandDNS(Table3).Another impor-tantaspectcontrollingtheFTFistheflameanchoringmechanism. The flame stand-off distance,

ψ

0 , is defined as the distance

be-tweentheflameholderandtheflameroot(Fig.7).Recentstudies haveshownthatsmallchanges

ψ

0 canhavesignificantimpacton

theflame dynamics[3,14,35,36].Figure 7andTable3 show good agreementfor

ψ

0 betweenexperimentsandDNS.

Table 3

Comparison between the flame stationary parameters of the flame shape for CBB and UBB cases. ψ0 is the

flame stand off distance and αis the flame angle. Parameters CBB UBB

Exp. DNS Exp. DNS

α[rad] 0.09 π 0.07 π 0.08 π 0.07 π ψ0 [1/ D ] 0.95 0.94 0.64 0.52

Fig. 8. Flame Transfer Function (FTF) for the two configurations in DNS CBB ( ) and UBB ( ) along with the previous experimental results CBB ( ) and UBB ( ).

Thissteady-stateanalysisallowstoconcludethat theessential parameters,

α

and

ψ

0 ,controllingtheFTF,arewellreproducedby

theDNS.ThereforewecanproceedtocalculatethenumericalFTF.

4.4. Flametransferfunctioncalculation

There are twomain methods tomeasure Flametransfer func-tionsforalinearinvariantsystem.[37–40]:

• Forcingwith a singlefrequency to obtain both FTF [41,42] or FDF[39,43–45].

• ForcingwithabroadbandsignalandusingWiener-Hopfsystem inversion[40,46–48]toretrievetheFTF.

HarmonicforcingcanbeCPUintensivesinceonesimulationper frequencyisrequired.Nevertheless,itispossibletopulsateat dif-ferentamplitudes,allowingtoexplore theflameresponseinboth linear and non-linear regime. On the other hand, the broadband noiseforcingmethodcanbemorefrugalsinceonecanobtainthe FTFforthewholerangeoffrequenciesinonerun.However, broad-band is onlysuitable inthe linearregime when the heatrelease perturbation remains small.Here, we use thebroadband method

[48]to obtain the FTF’s in the linear regime for the two cases2_.

TheFTFwascalculatedfortheCBBandUBBconfigurations.The amplitudeofthevelocityfluctuationsiskeptunder1%ofthebulk velocity(u′_/u

b<0.01).

The gains andphasesof the FTFs fromexperiments and sim-ulations are presented in Fig.8 along withthe FTF experimental results. The agreement is very good for the phase andconfirms the influenceofthe flameholdertemperatureseen inthe exper-iments. In the UBB case, the agreement on the gain is also fair, however, pastthe peak that is around 80Hz, the gain decreases faster inthe experimentthan inthe DNS. Inthe CBBcase, how-ever,theagreementinthegainislesssatisfactory:Thevalueofthe maximumgainobtainedbytheDNSexceedsbyafactoroftwothe

2 The harmonic response method was used, to validate the results of the broad-

band noise, for a single excitation frequency of f ex = 100 Hz and a velocity fluctua-

tion amplitude of u ′ /u

b = 0 . 01 . No difference was found between the two methods.

one foundintheexperiments.Thisdiscrepancyisduetothefact that,unlike thestationaryflamethatfitsinthevisualization win-dow,thepulsatedflamesometimesleavesthefieldofviewofthe PM.Duringsomepartoftheacousticcycle,theflametipleavesthe domain,makingimpossibleforthePMtocapturethetotalheat re-leaseratefluctuation.ThisisnotthecaseintheUBBcase,because, asseeninFig.7,theflameisclosertothecylinderandthetipof the flame remains inside the field of view of thePM during the whole acousticcycle.Globally,experimentsandsimulations show the same trend anda simple conclusion arises: asthe tempera-ture ofthebluff-body decreases (UBB → CBB), thegain andthe delay ofthe FTF both increase. The changes of theFTF are large andthemaximumgainofF

(

ω

)

canchangebyafactoroftwo(in the simulations)whenthebluff-bodytemperaturegoesfrom300 to700K.

5. Discussion

5.1. Flamefrontfluctuations

We propose to investigate the discrepancy between the FTF gainsfortheCBBconfigurationbytrackingtheinstantaneousflame front fluctuations. Here the flame was pulsated at fex=100 Hz, in both experiments and DNS, and the acoustic velocity ampli-tudewassettoasufficientlyhighvalue(u′_/u

b=0.05)forthetwo

casesinordertomagnifytheflamesurfacedisplacement.Itiswell known that V-shape flames are very sensitive to non linearities, increasing the amplitudeofthe acousticperturbation usually de-creases thegain oftheFTF([20]).However, forthisflame,itwas checked that at100 Hz, the influence offlame-holder cooling is similar at1% and5%pulsation amplitude,thereforevalidatingthe increasefortheflamefrontstudy.

Intheexperimentstheflameimageswererecordedwitha1280 × 800pixelsPhantomV1210high-speedcameraequippedwitha 700nmlow-passinfraredfilter(toeliminatetheburntgases emis-sion, and increase the contrast) and a Nikkor lens (focal length 200 mm/aperture4).Lietal.[19]showedthatitisnotnecessary to operate with an interference filter (CH∗ _{or OH}∗ _{for example)}

in front of the camera to examine heat release rate fluctuations of laminarpremixedflames fromhydrocarbonfuels submitted to flowratedisturbanceswhentheequivalenceratio,

8

,islowerthan 1.2.Thecameraistriggeredbythevelocitysignal,itstarts record-ing ata rateof5000fps whenthevelocityfluctuationatthe ref-erencepoint reachesitsfirstmaximum(the amplitudeofthe ve-locity fluctuationis fixed to1% ofthe bulkvelocity). The camera recordsduring 4swhichgiveus20,000images.Then theimages are averaged to obtain one image, which is the average of 4000 images, every 1/50 of the period. In the DNS the flame front is trackedasanisocontourofheatreleaseratesetat20%ofthe max-imum reactionrateinthecorresponding freelypropagating lami-narflame.

Figures9and10showtheexperimental andnumerical instan-taneous flame fronts for four different excitation phases for the CBBandUBBcases,respectively.Inbothcases,wrinklesare prop-agated along the flame front at the convective speed ub. These

wrinkles are created in the vicinity of the flame holder, where the flame is attached. The agreement between experiments and simulations isvery goodforboth casesandtheamplitudeofthe wrinklesiswell reproducedby theDNS. Onecanalsonoticethat the flameisanchoredclosertotheflameholderintheUBBcase, whichisconsistentwiththeresultsof[12].Figures9and10show thatforthesameamplitude,thewrinklesaremorepronouncedin the cooledcase.ThisiscoherentwiththehigherFTFgain forthe CBBconfiguration(Fig.5).

A proper framework to analyse the wrinkles observed in

Fig. 9. Experimental and numerical instantaneous flame front during one acoustic period of excitation for the CBB case at a frequency of 100 Hz and an amplitude of 5% of the bulk velocity. The black arrow represents the instantaneous direction of the acoustic velocity fluctuation at the reference velocity location ( z = −61 and z = −20 mm upstream of the cylinder for the experiments and the DNS respectively).

Fig. 10. Experimental and numerical instantaneous flame front during one acoustic period of excitation for the CBB case at a frequency of 100 Hz and an amplitude of 5% of the bulk velocity. The black arrow represents the instantaneous direction of the acoustic velocity fluctuation at the reference velocity location ( z = −61 and z = −20 mm upstream of the cylinder for the experiments and the DNS respec- tively).

schematic representation of the perturbed flame front with the laboratory (z, y) andthe steady flame (Z, Y) reference frames,

α

correspondsthesteadyflameanglewithrespecttothemeanflow direction. The instantaneous flame front position relative to the steadyflame isgivenby

ξ

(Y,t). Theamplitudeoftheflamefront fluctuationnormaltothesteadyflamefront

ξ

˜ZisshowninFig.12

for both cases CBBand UBB. Experimentsand DNSprovide very consistentresults.Figure12showsthatflamewrinklesarelinearly amplified along the flame front as already described in [50]. In theCBBcasethegrowthrateoftheamplificationislargerthanin theUBBcase.Theflameholdertemperatureistheonlyparameter varying inthe two differentcases andall other parameters such as bulkvelocity, equivalence ratio,external wall temperatureand freshgasestemperatureremainconstant.

Additionalinformationcanbeobtainedbylookingattheflame roottrajectories(Fig.13).IntheUBBcasetheflamerootgoesback andforth along asingleline, induced bythe acousticforcing. On

Fig. 11. Schematic representation of the perturbed flame front in the G-equation framework.

Fig. 12. Experimental and numerical amplitude of the flame front fluctuation nor- mal to the steady flame front ˜ ξZ , for both cases CBB and UBB.

Fig. 13. DNS flame root trajectories in the ( y, z ) plane for the two configurations CBB ( ) and UBB ( ).

the other hand, the CBB flame root moves in a circular pattern suggestingthe presenceof avortex inthe stabilizationregion as discussedinthenextsection.

5.2.Meanflowfield

Figure12 showsthatthe growthrateoftheflame wrinklesis largerfortheCBBthanforUBB.Thissuggestsamodificationofthe meanvelocityfield downstreamthecylindercausedbythe flame holder temperature difference between the two cases. Figure 14

shows a comparison between the two mean DNS axial velocity fieldsforthe CBBand UBBflames. Upstream ofthe cylinder, the mean velocity field is not affected by the cylinder temperature.

Fig. 14. DNS mean axial velocity fields for CBB and UBB configurations. White lines represent iso-contours of mean axial velocity u .

Fig. 15. DNS mean axial velocity profiles for both configurations, CBB ( ) and UBB ( ) and four different axial positions z/D = 0, 1, 2 and 3.

However,downstreamofthecylinder,theCBBflowexhibitalarge recirculation zone withnegative axial velocity (Fig. 14 left). This negativevelocityzoneisnotpresentintheUBBcase(Fig.14right). Thisinformationisconfirmedbylookingatthemeanaxial ve-locityprofiles forboth configurationsandfourdifferent axial po-sitions z/D= 0,1, 2 and 3 (Fig. 15). The velocity profiles atthe centerofthecylinder(z/D=0)arethesamefortheCBBandUBB case. However, downstreamof thecylinder(z/D=1,2and3) the velocity profilesareverydifferent:theCBBcaseexhibitsnegative velocitiesatz/D=1andstilldiffers fromitsUBB counterpartfar downstream: obviously, thisalso induces differenthydrodynamic stabilitycurvesandperturbationswhicharemoreamplifiedforthe CBBcase.At z/D=1,forexampletheCBBflowfield stillexhibits

a backflowzone andtherefore,a higherhydrodynamic sensibility toperturbations.Thismayexplainswhyflameperturbationsgrow fasterfortheCBBthantheydofortheUBBcase(Fig.12).This re-sultconfirmsthattheinfluenceoftheflameholdertemperatureis notlimitedtoitsimmediatevicinity.Whentheflameholder tem-peratureisbroughtdownfrom700K(caseUBB)to300K(CBB),it affectstheflameresponseintwoways.First,theflameroot posi-tionispushedawayfromthebluff body(Fig.7).Eventhoughthis effect isthe mostobvious,itis not themostimportant one.The secondeffectisthatthewholeflowfielddownstreamofthe cylin-der ischanged:alargerecirculationzoneappearsintheCBBcase (Fig.15),leadingtoaflowwhichismorehydrodynamically unsta-ble and which amplifiesflame front perturbations more strongly as revealedby Fig. 12.This indicates a globaleffectof theflame holder temperatureon the whole flow field andnot only alocal effectontheflamerootlocationinthevicinityofthebluff body.

6. Conclusion

This paperdescribes a studyof theflame holder temperature influence ontheresponseoflaminarpremixedflamestoacoustic oscillations. ExperimentsandDNSare used tocalculate theFTF’s for two differentconfigurations, acooled flame holder, CBBcase, witha temperatureof285K,andan uncooledflameholder,UBB casewithatemperatureof700K.TheexperimentsandDNSshow consistent results: the flame holder temperaturehas a large im-pactontheFTF’softheseflames,forbothgainandphase.TheCBB configurationshowsastrongerresponseforthesameamplitudeof velocity fluctuations. Thiseffect isalsoseen inthe instantaneous flame front fluctuations (Fig. 9). Far downstream of the cylinder the flamewrinklesaremuch largerfortheCBBcasethan forthe UBBcase.

The amplitudeoftheflame wrinklescreatedinthe nearwake ofthecylinderareofthesameorderofmagnitudeforbothflames butthegrowthofthesewrinklesismuchlargerfortheCBBcase than it is forthe UBB case(Fig. 12). This growthis observed far downstream ofthecylinderandisdueto thefact thatthe mean velocity fieldsintheUBB andthe CCBcasesdiffernotonly close tothecylinderbutalsofardownstream.Theflamepresenceclose to thecylinderintheUBBcasecompletelydestroysthe recircula-tion zone observedintheCBBcasewherethe flameisstabilized furtherawayfromthecylinder(Fig.15).Thevelocityprofileinthe CBBcaseexhibitsnegativevelocitiesandstilldiffersfromitsUBB counterpart fardownstream:obviously,thisalsoinducesdifferent hydrodynamic stability curves andperturbations which are more amplified fortheCBBcase.Thisresultconfirmsthattheinfluence of the flame holder temperature is not limited to its immediate vicinity. It affectsboth the flame positionand themean velocity field sothat theflamewrinklesare affectedintwoways:(1)the flame rootpositionisshifted downstreamwhentheflameholder is coldand(2)themeanflowisalso changedeverywhere down-stream: the CBB case exhibits a strong recirculation zone and a strongergrowthrateforflameperturbations.

These results demonstrate that the temperature of the flame holderplayamajorroleontheflamepositionandthemeanflow as well as on the flame dynamicswhere it controls theFTF’s to alargeextent.Studingflamesstabilizedonbluff bodiesshould in-cludetheirflameholdertemperatureasamajorcontrolparameter.

Acknowledgment

This work was granted access to the high-performance com-puting resources of CINES under the allocation A0012B07036 made by Grand Equipement National de Calcul Intensif. The re-search leading to these results has received funding from the

Framework Programme (FP/2007-2013) / ERC Grant Agreement ERC-AdG319067-INTECOCIS.

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