The effect of hydrogen addition on the amplitude and harmonic response of azimuthal instabilities in a pressurized annular combustor

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Combustion and Flame 228 (2021) 375–387

ContentslistsavailableatScienceDirect

Combustion and Flame

journalhomepage:www.elsevier.com/locate/combustflame

The effect of hydrogen addition on the amplitude and harmonic

response of azimuthal instabilities in a pressurized annular combustor

Thomas Indlekofer

^a^,^∗

, Byeonguk Ahn

^a

, Yi Hao Kwah

^a

, Samuel Wiseman

^a

, Marek Mazur

^b

, James R. Dawson

^a

, Nicholas A. Worth

^a

aDepartment of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim N-7491, Norway

bCORIA-UMR 6641 Normandie Universit, CNRS-Universit et INSA de Rouen, Campus Universitaire du Madrillet, Saint Etienne du Rouvray, France

a rt i c l e i nf o

Article history:

Received 19 September 2020 Revised 10 February 2021 Accepted 11 February 2021

Keywords:

Annular combustion chamber Combustion instabilities Hydrogen

Flame dynamics Pressurized combustor

a b s t r a c t

Thepresent work introducesan annularcombustion chamberoperatedatintermediatepressures.The combustor isoperated withCH₄-H₂ blendsleading to avarietyof azimuthalcombustion instabilities.

Theinfluenceofthehydrogencontent,theairmassflowrateandtheequivalenceratioontheinstabili- tiesisinvestigatedoverawiderangeofoperatingconditionswithmeanchamberpressuresfrom1.5to 3.3bar.Thisleadstoarangeofexitboundaryconditions,frompartiallytofully reflecting.Itisfound thatpuremethaneand methane-hydrogenmixtureswithlowhydrogencontentsresultinstable combustion.However, whenthehydrogencontentreaches25%by volumehigh-amplitude instabilitiesare excited,whichexhibithigher orderharmonics withsignificantpressureamplitude contributions.Such harmonicresponsewasnotpreviouslyobservedinatmosphericannularcombustors.Theamplitudesde- creaseslightlywhentheH2 contentisincreasedfurther.Theharmonicresponseisfoundtobeampli- tudedependentwithfewersignificantharmoniccontributionsoccurringatlow-amplitudesandacut-on amplitudeofthefundamentalmodeatwhichhigherharmonicsbecomesignificant.Theinteractionbe- tweentheharmoniccomponentsofthepressureamplitudesisshowntofollowaquadraticrelationship.

Themodalresponsewasanalyzedanditwasfoundthatallhigh-amplitudeinstabilitiesfeatureclockwise spinningmodeswhereaslower-amplitudeinstabilitiesfeaturecounterclockwisespinningmodes.Finally, alow-andhigh-amplitudecasewereinvestigatedindetailandphase-averagedimagesarediscussed.The low-amplitudeinstabilitiesresultinflamedynamicssimilartothoseobservedinatmosphericcombus- torspreviouslywhereasthehigh-amplitudeinstabilitiesexhibitlargeoscillationsintheflameheightand intensity.Acharacterizationoftheboundaryconditionsisalsoprovidedfornumericalsimulationswhich includestemperaturemeasurements,acousticcharacterizationandcoldflowvelocityprofiles.

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

1. Introduction

The shifttowardsrenewable energysources,suchaswindand solar power,is leadingto an increasing shareof intermittenten- ergy sources in the future energy mix. Gas turbines are seen as a vital enablingtechnology forrenewable energysources asthey are highlydispatchable,meaning theycan berapidlydeployedto stabilizethegrid[1].

Apromisingwaytoreducecarbonemissionsistoincreasethe use of hydrogen as a fuel. While the introduction of hydrogen intothefuel(usuallyCH₄)canincreasetheﬂammabilitylimitand power density, the high reactivity ofhydrogen can also promote

∗Corresponding author.

E-mail address: [email protected] (T. Indlekofer).

flashback[2].Evenamodestadditionofhydrogenleadstoanin- crease in the laminar flame speed and a reduction of the flame heightwhichcanhaveamajorimpactonthethermoacousticsta- bilityofacombustor[3,4].

Thermoacousticinstabilitiesresultfromaconstructivecoupling betweentheacousticfieldandfluctuationsintheheatreleaserate thatleadtolargepressureoscillations[5],therebylimitingtheop- erationalenvelopeandreducingthelifetimeofthecombustor.De- spitedecadesofinvestigation,self-excitedthermoacousticinstabil- ities still remain a serious problemandfurther understanding of the phenomenon in practically relevant configurations is needed [6,7].

Modern gas turbines and aeroengines often have annular combustion chambers. Azimuthal modes propagating in either direction around the annulus have been observed in industrial combustors [8–10], and have been reproduced in atmospheric

https://doi.org/10.1016/j.combustﬂame.2021.02.015

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pressure laboratory combustors [11–13], as well as high-ﬁdelity numericalsimulations[14,15].Azimuthalmodescantaketheform of standing modes, with a ﬁxed nodal line position, spinning modes with the nodal line spinning around the annulus at the speedofsound,oracombinationofbothleadingtomixedmodes.

These modes can undergo continuous transitions betweeneither modenature[11,12,14,16],aphenomenoncommonlyreferredtoas modal dynamics [9].Over the last decade, thedynamic nature of thesemodes hasreceived signiﬁcantattentionfromthe scientiﬁc community. Modal dynamics were shown to be dominated by the effects of symmetry breaking [11,17–20] and turbulent noise [9,21,22].

Even though several laboratory annular combustion chambers now exist[11,13,23],theyusually featurean exitboundarycondi- tion open to atmosphere. This complicates the transferability to industrial engines (gas turbines for power generation operate at around20bar[24])andtheabilitytoconducthighﬁdelitynumer- ical simulations duetocomplex boundaryconditions [6,25].Sub- sequently, thereis a need forchokedexperimental rigs, enabling the study of combustion instabilities with more realistic acous- ticboundaryconditionsathigherpressures,turbulencelevelsand powerdensities.

There has beena numberofstudies investigating thedynam- icsofswirlorbluff bodystabilizedflamesatelevatedpressure in single isolatedflames. Freitaget al.[26] measured flametransfer functions(FTFs) from1.1−5barto investigatetheeffectofpres- sure onthe FTF.Theyfound that pressure can introducea phase shift, which has an influence on the stabilityof a combustor. In termsofthegain,theeffectofpressureledtoahigherresponseat higherfrequencies andtheoppositeatlow frequencies.Thisfind- ingwassupportedbyCheungetal.[27].Sabatinoetal.[28]found thatelevatedpressuremodifiestheflame-vortexinteractionscaus- ing an increase in the gain. It was also found that the effect of pressure on flame interaction was fuel-dependent. While the lo- cal maxima of the FTF increasedmonotonically for methane, for propaneitincreaseduntil3barandthendropped.

Under well controlled laboratory conditions there are only a few pressurized experiments in annular combustion chambers.

Fanaca et al. [29,30] introduced a down-scaled model of an Al- stomgasturbine,whichwasoperatedatelevatedpressurebutdid not feature self-excitedazimuthal instabilities underfully choked exitconditions.Underforcedoperation,theyobservedadifference between FTFs of the single sector and annularcombustor which wasattributedtodifferencesintheresultingaerodynamics.Mazur etal.[31]reportedself-excitedlongitudinalandazimuthal modes inapressurizedannularcombustor.However,theoccurrenceofaz- imuthal modeswaslinkedtoaﬂashback phenomenonprecluding longruntimesbutstrongharmoniccontributionsappearedwhich werenotobservedinpreviousatmosphericstudies.

In addition to theeffect ofpressure on self-excitedazimuthal modes, information on the thermal state and acoustic boundary conditions ofthe combustor isalso neededforhigh-ﬁdelitysim- ulations. Progress dependson both simulations and experiments, andtherefore,partoftheaimofthisresearchistoprovideatest case that can replicate as manyof the important boundary conditions foundonarealengineaspossible,whilst maintainingthe well-controlledconditionsofanopticallyaccessiblelabsetup.

Thisworkconstitutestheﬁrstdetailedstudyofazimuthalcom- bustion instabilities atelevated pressures across a wide range of operating conditions in order to study the modal dynamics, the role ofpressurescaling ontheresponse,andtoexaminein more detail the behaviour of the harmonic contributions. In addition, a thorough characterization of the boundary conditionswas performed.

Thepaperisorganizedasfollows.First,thesetupandtheoper- atingconditionsareintroduced.Thenthegeneralsystemresponse

in terms of the amplitudes and nature of the modes is investigated andanalyzed fordifferent hydrogencontents, airﬂow rate andequivalenceratio.Wethenfocusourinvestigationontwopar- ticularcases,ahigh- andlow-pressureamplitudecase,byanalyz- ingtheirpressuretime-seriesandﬂamedynamics.

2. Experimentalmethods

2.1. Intermediatepressureannular(IPA)combustor

AschematicofthecombustorispresentedinFig. 1.Premixed fuel-air mixtures are fed into a cylindrical plenum that conditions the ﬂow (through a bed of glass beads in the expansion) beforeit passesthrough a22mm thick sinteredmetal plateand is dividedbetween twelveburners.The twelve burnersare com- prisedof tubes that holdthe bluff bodies andcounter clockwise swirlers(asviewedfromabove)whichare equallyspacedaround thecircumferenceoftheannularcombustor. Thelower sectionof the outer wall consists of a quartz glass window enabling opti- cal accessfor high-speed imaging. The combustion chamber has a length of168 mm andan inner/outerdiameter ofd_i=128mm anddo=212mmrespectively.Theouterandinnerwalls,aswellas thedump plane arecooled byseparate watercircuits.The cham- berendswithasymmetriccontraction(contractionratioCRc=7) beforetheﬂowispassedthroughachokingplate(CR_p=5),which furtherreducesthe outer diameter,leadingtoCR_total=35.A sec- ondchokingplatecanbemountedupstreamoftheplenumexpan- sion.

Furtherdetails anda limitedsetofdatawiththeupperchok- ingplatearepresentedinA.1forcomparison,anacousticcharac- terization ofthe glass beadsection, thesintered metal plateand theswirlerisfound inA.2andthesupplementalmaterial.Details aboutthe pressure drop acrossthe sintered metal plate are pre- sentedin A.3 andinformationabout thecooling heat transfer in AppendixD.Thecomplete3D CADmodelisavailableinthesup- plementalmaterial.

2.2. Experimentalmeasurements

Dynamic pressure measurements (Kulite XCE-093 sensors, 1.43×10⁻⁴mVPa⁻¹) were recorded at ﬁve azimuthal positions (0−4=0,30,60,120and240^◦) andtwolongitudinalpositionsin the injector tube at z₁=−81mm (upper microphone) and z₂=

−133mm.Thesignalswereacquiredatasamplingfrequency fs= 51.2kHzanddigitizedusinga24-bitDAQsystem(NImodel9174).

Additionallytwo DanfossMBS3000pressuresensorsmonitorthe meanpressureinthecombustionchamberandtheplenum.

A high-speed camera (Phantom V2012) with intensiﬁer and UV ﬁlter (

λ

=310nm, FWHM 10 nm) and a photo multiplier tube (PMT) with the same UV ﬁlter are used to capture OH^∗- chemiluminescenceat=30^◦.

To determine the temperature of the bluff body, dump plane andinner wall at certain locations, a pyrometer (Optris CTLaser 3MH)wasused.Anexplanationoftheprocedureandtemperatures fortwooperatingconditionsareprovidedinAppendixC.

2.3. Operatingconditionsandexperimentalprocedure

TheoperatingconditionsaredescribedinTable1.Airmassﬂow ratesrangedfrom61.25to122.5gs⁻¹ andthefuelwascomposed ofmethane(CH₄)withvaryingquantitiesofhydrogen(H₂).Airand fuelarecombinedinamixingchamberupstreamoftheplenum.A rangeofvolumefractions PV=V˙H2/(^V^˙CH4+V˙H2)^of⁰−0.5,where 0isno hydrogenand1is purehydrogen,were investigated.This ratio can be translated to the power fraction P_H, resulting in a

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T. Indlekofer, B. Ahn, Y.H. Kwah et al. Combustion and Flame 228 (2021) 375–387

Fig. 1. (a) Schematic of the Intermediate Pressure Annular (IPA) combustor with (b) top view showing the azimuthal position of microphones and the high-speed camera to acquire OH ^∗-chemiluminescence, (c) detailed view of the modiﬁed bluff body/swirler assembly (d) Photograph of the IPA combustor during operation and e) quasi- instantaneous image of the ﬂame dynamics.

Table 1

Operating conditions in terms of the air mass ﬂow rate m ˙ a, the hydrogen power fraction P H, the hydrogen volume fraction P V, the equivalence ratio , the laminar ﬂame speed at p = 2 bar and the resulting thermal power Pand exit bulk velocities u b.

Stable Presented data set Flashback

˙

m a[g/s ⁻¹] 61.25–122.5

P H 0-0.05 0.1 0.15 0.2 0.25

P V 0-0.14 0.25 0.35 0.43 0.5

0.65-1.0

s L[m/s ⁻¹] 0.17-0.35 0.19-0.39 0.2-0.43

P[kW] 170-350

u b[m/s ⁻¹] 28-22

range of 0−0.25, which was investigated in steps of 0.05. Al- though stabilitymapswereperformedforP_H=0and0.05,noneof the investigated cases featured self-excited instabilities. For P_H= 0.25itwasfoundthatthecombustorwaspronetoﬂashback.Sub- sequently, thiswork will focuson P_H=0.1−0.2with an equiva- lenceratio(⁾^range^of⁰.65−1withstepsof0.05.

Ignition and light-around was performed at m˙a=40.83gs⁻¹, =0.7 and initiated by a rich ethylene pilot flame at =0^◦. This differs from the usual method of ignition in laboratory annular combustion chambers, which typically use one ormultiple sparkignitors[32,33].Inthepresentprocedureacombustiblemix- tureisintroducedintothecombustionchamberonlyafterthepilot flamehasbeensuccessfullyignited.Assoonasacombustiblefuel- air mixturereaches thechamber, the pilot ignitesa flame kernel which is advected downstream towards the chokingplatewhere it ignitesa largerportionoffuel-airmixtureandinitiatesthefull light-around which eventually leadsto a stabilization ofthe single flames on thebluff bodies. After successfulignition,the pilot flameisswitchedoff andtheflowratesofairandfuelarelinearly (constant⁾încreasedôver¹⁰^s^beforeîsîncreasedôver⁵^s^to reachthetargetoperatingcondition.

2.4. Modedetermination

The investigated operating conditions feature self-excited azimuthal modes, which occasionally show signiﬁcant harmonic components.To separate the differentcomponents andharmonic contributions of the azimuthal modes (of order n), the pressure time seriesare bandpass-ﬁlteredwitha bandpasswidthof^f= 100Hzcenteredonthepeakfrequency fn.

Todetermine the nature ofthe azimuthal modes, the Quater- nionformalism,introduced by GhirardoandBothien[34] isused.

Theacousticpressureinanannuluscanberepresentedas

p

(

,t

)

=Acos

(

ⁿ

(

−

θ ) )

^cos

( χ )

^cos

( ω

^t+

ϕ )

+Asin

(

ⁿ

(

−

θ ) )

^sin

( χ )

^sin

( ω

^t+

ϕ )

, (1) withâs^theâzimuthal ^coordinateândⁿ^describing^theôrderôf themode.The ordersn=1−5areherein referredto asthefun- damentalandthefirsttofourthharmonicfrequencies.Adescribes theamplitude ofthe mode.The slowlyvarying real-valued angle

θ

(^t) ^describes ^the ângular ^location ôf ^the ânti-nodal ^line ând ît isboundedbetween−

π

^and

π

^.^However, îtîs împortant^to^note

that foranincreasing order oftheazimuthal modes, thenumber ofanti-nodallinesincreases.Forexampleforn=1,oneanti-nodal line exists, whose position is described by

θ

^or

θ

+

π

, while a mode of n=2features two anti-nodal lines whose positions are describedby

θ

^or

θ

+

π

/2.Subsequently,foranunambiguous de- scription,eachanti-nodallinepositionwillbedescribedinarange of[0,

π

/n].

Thenatureangleisdescribedbytheslowlyvaryingreal-valued angle

χ

(^t) ândîndicates ^whether ^the âzimuthal êigenmode îs â standing wave (

χ

=0), a pure clockwise (CW) or counterclock- wise (CCW)spinning wave (

χ

=∓

π

/4) ora mix ofboth for 0<

| χ |

<

π

/4. We adopt the reference frame where a CW spinning modewillrotateagainst^and^a^CCW^spinning^mode^with^(see

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Fig. 2. Mean ﬂame shape and corresponding streamwise distribution of the inte- grated heat release rate for stable operating conditions: m ˙ a= 91 . 87 gs ⁻¹, a) P H= 0.1, = 0 . 65 and b) P H= 0.2, = 0 . 65 .

Fig.1). Thefourthvariable

ϕ

^describes^the^temporal^phase^which

isrelatedtoslowandsmallchangesofthefrequency.

3. Experimentalresults

3.1. Generalsystemresponseandstability maps

Mean flame shapes for two stable operating conditions are showninFig.2withthestreamwisedistributionoftheintegrated heatreleaseratedepictedbygreyplotsonadjacentsides.Increas- inghydrogenenrichmentincreasestheflametemperature,laminar and turbulent flame speeds(see Table1) andchanges the Lewis number (as the diffusivity of hydrogen is high) which generally leadstoshorter,morecompactflamesforthesamepower[35,36]. In comparison to the previous configuration [31] the flames are morecompactandthemodifiedbluff bodyleadstoawiderflame angle with stronger flame-flame interactions at the end of the flamebrusheswhichcorrespondstothelocationofmaximumheat releaserate.

AlthoughtheflameisslightlymorecompactwhenP_H=0.2,the location ofmaximumheat releaserateremains attheendofthe flamebrush.Italsoreducesinteractionswithneighbouringflames.

This is shownby the much larger interactingregion for P_H=0.1 incomparisontoP_H=0.2.FortheP_H=0.1case,theflamebrushes fromadjacentflamescanbeseentomergeneartheside edgesof the image. Thiscreates a large vertically oriented region of high heatreleaseratebetweentheflamesfoundalongthesidesofthe image which extends downstream. This is not observed for the P_H=0.2flamealthoughthere issome evidenceofinteractions at theflametips.

Fig. 3 shows themean chamber pressure p, bulk velocity u_b, fundamentalazimuthalfrequency f andthethermalpowerovera rangeof^for^different^m^˙^a^for^PH=0.1.Forclarity,datapointsfor allmassﬂowsareonlydisplayedforP_H=0.1,whileP_H=0.15and 0.2areplottedform˙a=91.87gs⁻¹only.

With increasing m˙a and ^the ^chamber ^pressure ^p încreases from 1.5 to 3.3 bar. When p > 1.89bar the choked condition is reachedresultingina fullyreflectedcondition. Thereforecases with m˙_a>102.08gs⁻¹ always result in a choked exit condition, whileitdependson^for^lower^m^˙â^.În^contrast^to ^p,u_bdecreases withincreasing^due^to^theîncreasing^gastemperatureandpres- sure. Nonetheless, increasing m˙_a leads to a slight increase in u_b. The increasedflame temperaturewithhydrogenaddition alsoaf- fects the meangas temperaturein the chamber andthereby the oscillation frequency. The fundamental frequency f lies between 1450−1650Hzandincreaseswithâsêxpectedândîs^relatively insensitive to changes inm˙a exceptat the lowestflow rate. At a fixed operatingpointan increaseinPH resultsinanincrease ofP and fwhereas pandu_bremainalmostunaffectednotingthatonly smallhydrogenmassfractionswereinvestigated.

During the experiments the combustor exhibited both stable and unstable conditions, including a wide range of instabilities.

Figs.4andE.6displaytheamplitudesnormalizedbythechamber pressureandthenatureangleoftheazimuthal modes. Eachsub- plotcorrespondstoaspeciﬁcm˙aandP_H.Thecolordenotesthefre- quencyoftheazimuthalmode,e.g.lightyellowdenotesthefunda- mentalfrequency,while purpledenotes thefourthharmonic.The normalizedamplitudewascalculatedusingthemeanvalueofthe Quaternionamplitudeattheuppermicrophonenormalizedbythe chamber pressure. The bar markers show the standard deviation ofthetime-seriesforthreeseparateruns(separatetestdays)illus- tratingtherepeatabilityoftheexperiments.Amajordifference to previousexperimentsatatmosphericpressures[11,13]istheoccur- renceofsigniﬁcanthigherharmonicsforhigh-amplitudeinstabili- tieswhichwillbediscussedlaterinthepaper.

Focusingonthegeneralsystemresponsefirst,Fig.4showsthat thecombustorisunstableoverlargepartsofthestabilitymapand stableatlean valuesof âs^well âs^the^lowest ^valuesôf^m^˙â ^for P_H=0.1.Withsmallamountsofhydrogenadditionthenormalized amplitudes of the fundamental eigenmode reach values that are nearthepeak valuesorhigherthanthosefoundpreviously inat- mosphericannularcombustors[11–13].Peakoscillationamplitudes occurforP_H=0.1andthelargestm˙_a.Theyreach2%ofthecham- ber pressure which translatesto 6 kPa at the uppermicrophone and8.5kPa atthedump plane (evaluated fromthemultiplemi- crophonemethod).

Inallcasestheonsetoftheinstabilitiesoccursatleaneroper- atingconditionswithincreasingm˙a.Asimilar trendisalsofound forincreasingP_H.

ConsideringthecaseofP_H=0.1, Aincreasesslightlywithm˙a. Justaftertheonsetoftheinstability,the amplitudeofthefunda- mentalmodeinitially showsa weakbutnon-monotonicvariation with ^withâ ^consistent ^dip ⁱⁿ^the âmplitudeôccurring âround =0.85afterwhich furtherincreasesin ^resultⁱⁿân încrease inA.Overall,theamplitudevariationofthehigherharmonicsalso showssimilartrends.Theonlynotabledifferencebeingaslightde- creaseinAofthefirstharmonicforincreasing^.

For P_H=0.15, the onset of the instabilities occurs at leaner , however the overall trends are similar to those observed for P_H=0.1.Initiallythe amplitudeoftheexcited fundamentalmode isslightlylowercomparedtotheP_H=0.1casebuteventuallyin- creases to similar values.The amplitude variation with ^shows astrongernon-mononticresponseandanincreasinglypronounced dipinamplitudewhenm˙a>81.67gs⁻¹.Thelocationofthedipoc- cursatincreasing equivalenceratioasm˙a isincreasedandthere- foreexhibitsaStrouhalnumberdependence(which isnotshown directlyhereforbrevity).Theamplituderesponseoftheharmonics follows the fundamental component closely. The harmonics only reach a signiﬁcant amplitude when the amplitude of the funda- mentalmodeishigh.Thiscut-onbehaviourisdescribedlater.Itis alsoworthnotingthatatthishydrogenpowerfraction,self-excited instabilities appearfor the lowest m˙_a reducing thestability window.

When P_H is increased to 0.2, the amplitudes are signiﬁcantly lowercomparedtothepreviouscases.Onlyatstoichiometriccon- ditionsandlowermassﬂowratesdoestheamplitudeofthefun- damentalmodesurpass1%.

Whiletheresultsarenotpresented,atP_H=0.25theamplitudes oftheinstabilitiescontinuedto decrease.However,atthishydro- gen powerfraction occasional flashback events were observed at high ^. ^For ^low ^levels ôf ^hydrogen âddition, ^PH=0−0.05, the combustorwasstable.Basedonthelargedifferencesinamplitude fordifferingP_H one canseethat thestabilityofthecombustoris stronglyaffected by hydrogenenrichment andvarying trends are observedforeachdistinctsetofP_H cases.

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Fig. 3. Mean pressure p , bulk velocity u b, fundamental frequency of the azimuthal mode fand thermal power Pas functions of m ˙ a, and P H.

Fig. 4. Mean and standard deviation of the amplitude at the upper microphone for the azimuthal modes (order n = 1 −5 ) as functions of m ˙ a, and P H. Color denotes the frequency. Triangular markers correspond to p < 1 . 89 bar , circles to choked conditions at p > 1 . 89 bar .

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Fig. 5. Amplitude of the fundamental component A n=1versus amplitudes of the harmonic components A n=2−5. Color denotes the order n of the azimuthal component and the marker P H. Circular markers correspond to P H= 0 . 1 , triangles to P H= 0 . 15 and diamonds to P H= 0 . 2 . Dashed lines depict the best quadratic (a) and linear (b-e) ﬁts.

Interestingly, thegeneralsystemresponse seems notto be al- tered when thechoking conditionis fulﬁlled,forexample atap- proximately =0.9and m˙a=81.67gs⁻¹ for all P_H.A likely rea- son for this is that the exit nozzle is already strongly reﬂecting for chamber pressures >1.5bar[37], thereby whenthe chamber pressureof1.89barisapproachedthereisnotadrasticchangein termsoftheacousticboundarycondition.

3.2. Harmonicresponse

Thepresenceofhigherharmonicscanindicatethepresenceof nonlinear dynamics. However modelling approaches such as the ﬂame describing function (FDF) do not take them into account based on the assumption that harmonic contributions are small [38]. There are examples whereharmonics can contribute signif- icantlytotheoverallsoundpressurelevelandbeincludedwithin the FDF framework [39] and given the results presented so far are worth further investigation. The role of harmonics has been investigated previously for singleburnersunder both self-excited [40] andforced conditions[41].Untilnow,higherharmonics have not been observed in annular combustors at atmospheric conditions. Under pressurized conditions, their occurrence has been limitedtooperatingconditionswithstrongintermittentﬂashback events that were coupled to large-amplitudeoscillations [31]. As showninFig.4,inthepresentwork, harmonicscorrespondingto azimuthalmodesofordern=2−5areexcitedforawiderangeof operatingconditions.

Fig.5plotstherelativenormalizedamplitudesoftheharmon- ics versus thefundamental andshowsthat there isa correlation betweentheamplitudeofthefundamentalandtheamplitudesof the higher harmonics. A cut-on amplitudefor the first harmonic can be identifiedin Fig.5a), which showsthatthe amplitudeof A₂ only becomes significant when the normalized amplitude of A₁ surpasses ≈0.35%. Higher cut-on amplitudes were found for thehigherharmoniccontributions(notshownhere).However,this cut-on behaviour cannot be solely due to the large amplitudes as significant harmonics have not been observed in atmospheric experiments withsimilarlylarge amplitudeinstabilities [42].This strongly suggests that the chokedexit conditionsplay an impor- tantrolegiventhattheacousticreflectiondropssignificantlywith increasingfrequencyforanopenend[43]inanatmosphericcom- bustor. Similar to [40,41], we observe a quadratic dependence of the amplitudes of the first harmonic on the fundamental component. As showninFig. 5the amplitudeofthe higherharmon- icsshowsadependenceon thefundamentaltothen^th poweral- thoughthereisanotableincreaseinscatterwithincreasingorder.

3.3. Natureangleandmodalresponse

Thenatureanglesoftheself-excitedmodesareplottedinFig.6. Only data points exhibiting a normalized amplitude larger than

0.05% are included. In general, the system response near onset conditionsleadstoCCWspinningmodesalthoughtherearesome cases where standing modes occur. For conditions further away from the stability border the nature angle shows that most of the self-excitedmodesare stronglyspinning inthe CWdirection over the instability range with the exception of the case where P_H=0.15,m˙a=122.5gs⁻¹and=0.85whichrepeatedlyfeatures astrongCCWspinningmodewithanormalizedamplitudeof1.5%

(seeFig.4)andsigniﬁcantharmonics.ForcaseswhereP_H=0.2the nature angle shows that the predominantly CW spinning modes tendmoretowardsmixedmodesincomparisontotheothercases.

The dynamicsobserved in thesestability mapsdiffer strongly fromobservations madein the atmosphericversion of thiscom- bustor[11,12],whichhasthesamedimensionsexceptfortheout- letboundary conditionandthebluff bodies.In thepresentwork, the spinning modesapproach pure spinning modes which have, to date, not been typically found in noisy atmospheric annular combustors,whichhaveshowedapredominanttendencytowards standingmodesandmixedmodes.Afurtherdifferenceisthesup- pression of modal dynamics [9],which we deﬁne as the instan- taneoustransitionsbetweenstanding,spinningandmixedmodes.

In addition to the changein acoustic boundary conditions,these instabilities havecomparablyhighlimit-cycle amplitudesand are subsequentlyfurther away fromthe bifurcation point whichmay act to prevent instantaneousmode switching dueto alarger po- tentialbarrier[16]betweendifferentattractors.Subsequently, the largestdegreeofswitchingandthereforeanincreasedstandardde- viation,isobservedclosetothestabilityborders,whilethemode wasnot observedto changenature assoon astheCWstate was reached.

Ahandfuloftheoreticalpapershavetriedtoshed lightonthe modeselection inannularcombustors [9,20,21,44,45].Speciﬁcally, [45] showedthat the ratioofthe amplitudetobackground noise ofthecombustorisakeyparameterthatdeterminesthenatureof the mode. Therebyan increasing amplitude isexpected to excite purerspinningmodes. Tothebestoftheauthors’knowledgethis hasnotbeeninvestigatedexperimentally.Fig.7showstherelation ofAand

χ

^on^thefundamentalandtheharmoniccomponentsover the full range of operating conditions. Overall, Fig. 7 shows that asthe amplitudeincreases themodes tend towardsstrongly CW spinningmodesforallharmonics.Beginningwiththefundamental mode,standingmodesappearﬁrstatlowamplitudeswhich then quicklytransitiontowardsCCWmodesastheamplitudeincreases.

Athighamplitudesmixed/CWspinningmodesbecomedominant.

Theoccurrenceof CCWspinningmodesdecreaseswithmode order asalmost pure CWspinningstatesbecome dominant.Thisis relatedtothecut-onamplitudesobservedinFig.5.

Fig.7 alsoshows differentbehaviour to previous observations madein[31],where thehigherordermodescould havea different

χ

^and^showed^a ^higherprobability ofstandingmodes. How-

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Fig. 6. Mean and standard deviation of the nature angle for the azimuthal modes (order n = 1 −5 ) as functions of m ˙ a, and P H. Color denotes the frequency. Triangular markers correspond to p < 1 . 89 bar , circles to choked conditions at p > 1 . 89 bar .

Fig. 7. Nature angle in dependence of the amplitude for the fundamental and harmonic components. Circular markers correspond to P H= 0.1, triangles to P H= 0.15 and diamonds to P H = 0 . 2 .

ever, that could be attributed to the occurrence of states where not allburnersexhibitedﬂashback whichintroduced asigniﬁcant asymmetry intheheatreleaseresponseovertheannulus,thereby pushingthemodetowardsastandingmode[9,21].

Although not shown for brevity, it is worth mentioning that clearly preferred orientation angles for the pressure anti-nodes of the standingcomponent,

θ

, were observed foreach operating condition. While themodesaremostlystronglyspinningandthe standingcomponentofthemodethereforehadaminoramplitude,

apreferred

θ

îs^most^likelyânîndicatorôf^smallgeometricalasym- metriesthat leadtotheanti-nodal linelockingintoacertain position[18,20].Whentheharmoniccomponentsalsoshowedapre- ferred orientation,the preferrednodallineposition,

θ

ⁿ, were not alwayssame.Forthecasesstudieditwasoftenfoundthat

θ

1and

θ

2collapsed,butthatthehigherharmonicspreferreddifferentori- entations(seeforexampleFig.9).FortheP_H=0.1and0.15cases,

θ

1 and

θ

2 arecentered around20−30^◦ butforP_H=0.2 thepre-

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Fig. 8. Time-series, PDFs and phase space plots at m ˙ a= 91 . 87 gs ⁻¹for differing and P H.

ferredanti-nodallinepositiontransitionsquasi-linearlyfrom60to 30^◦ forincreasing^.

3.4. Timeseriesandphasespace

Fig.8aimstoprovidea morevisualrepresentationofhowthe harmonic contributions inﬂuence the time-series of the pressure ﬂuctuations p’. The plotted data corresponds to m˙a=91.87gs⁻¹ andcompares the time-series(with corresponding PDFs)andthe phase spaceplotsforP_H=0.1−0.2(shown inrows)fordifferent equivalence ratios, =0.7, 0.8, 0.9and 1.0(shown incolumns).

The time-series data are cropped to segment lengths of 10 ms while the data used to calculate the PDFs corresponds to a seg- mentof5s.

Focusing on the first row, the combustor is initially stable at =0.7,whichisvisualizedbyrandomtrajectoriesinphasespace and the flat response of p. At =0.8 the combustor features a strong limit-cycle that has significant harmonic contributions which manifests ina distortion ofthe phase spaceand a highly asymmetric PDF whichhas its mean probability in the region of negative fluctuations. Withincreasing ^thepeak-to-peak ampli- tudeincreasesalongwiththeharmoniccontribution,leadingtoa stronglydistortedphasespaceandanincreasing numberofpeaks inthePDFofp.

As previously discussed, when P_H is increased the amplitude and the degree of harmonic contributions decrease. At P_H=0.15 and=0.8−0.9thephasespaceisonlyslightlydistortedresult- ing ina moresinusoidalresponsebutstillfeatures anasymmetry in its PDF. For =1the signal is highlydistorted withthe PDF showing adifferentdistribution compared tothe lowerhydrogen content casealthoughthe amplitudeof thefundamentalmodeis comparable.Still,thereisahigherprobabilityofnegativepvalues, but two smaller peaksoccur in the PDF for positive values.The

reasonfor thisis that the amplitudes ofthe harmonics decrease withorder.Higher harmonicsaresuppressed whenP_H=0.2asis evident inthesinusoidal responsein thepressuretime-series. At =0.8−0.9thePDF issymmetricandthephasespaceshowsa uniformtoruswhichagainbecomesdistortedfor=1.

Interestingly,one observes that higherharmoniccontributions always leadto a deformationof theacoustic wave,such that the leadingedge hasa steeperslopethan thetrailingedge.Thisphe- nomenonisknownaswavesteepeningandconstitutesawelldoc- umentednon-linearphenomenon[46].

3.5. Investigationofahighandlow-amplitudeinstabilityoperating condition

In this section we analyze two speciﬁc operating conditions more closely: One that features a high-amplitude mode with signiﬁcant harmonics (P_H=0.1, m˙a=91.87gs⁻¹,=0.8) and one featuring a low-amplitude instability (PH=0.2, m˙a= 91.87gs⁻¹,=0.8)withweak harmonics.Thesecaseswere cho- senastheiroperatingconditionsleadtochamberpressureswhich arehighenoughtochoketheexitnozzle,whilethethermalstress isstillrelativelylow,enablingrun timesthatbringthecombustor closetothermalequilibrium.Extensivetemperaturemeasurements ofthesetwocasesarepresentedinAppendixC.

Fig.9showsthetime-series,thesoundpressurelevel(SPL)and PDFsofthethreeslowﬂowvariablesA,

χ

,and

θ

^of^the^resulting

modes.

The ramp procedure forboth cases is identical andthe onset oftheinstabilitiesoccursshortlybeforethetarget operatingcon- ditionis reached.Comparingthe SPLs,one can seedrastic differ- encesnotonlyintheSPLofthefundamentalcomponent,whichis morethan10dBhigherforP_H=0.1butalsointheharmoniccom- ponentswhichremainsigniﬁcantuptofrequenciesaround12kHz.

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Fig. 9. Pressure time-series, sound pressure level (SPL) and PDFs of the slow ﬂow variables for P H= 0 . 1 (a-e) and P H= 0 . 2 (f-j), m ˙ a= 91 . 87 gs ⁻¹, = 0 . 8 . The orientation angle θis displayed from [0, π/ 2 ] for viewing clarity as no occurrence of θn=1> π/ 2 was observed.

Fig. 10. Mean ﬂame shape and corresponding streamwise distribution of the integrated heat release rate for unstable operating conditions: m ˙ a = 91 . 87 gs ⁻¹, a) P H = 0 . 1 , = 0 . 8 and b) P H = 0 . 2 , = 0 . 8 .

WhilebothcasesfeaturestronglyCWspinningmodes,

χ

^is^closer

to astanding/mixed mode forP_H=0.2.No majorvariabilityin

χ

isobservedforthefundamentalandtheharmoniccomponentsat P_H=0.1,butthenatureangleofthefundamentalmodeissigniﬁ- cantlylowercomparedtothatoftheﬁrstharmonicforP_H=0.2.

For clarity,

θ

^is ^displayed ^from ^[0,

π

/2] as no occurrence of

θ

n=1>

π

/2wasobserved.Generally,preferredanti-nodal linepo- sitions were observed for every n. ForP_H=0.1, the preferred

θ

for n=1,2,5 lies at≈20^◦ whereas for n=3,4 it lies at≈ 0^◦ and45^◦ respectively.ForP_H=0.2,

θ

^is^only^shown^forⁿ=1, 2as theamplitudeswereverylowforthehigherharmonics.Whilethe preferredanti-nodal linelocation forbothordersisat≈55^◦,this locationdiffersfromthelocationsobservedforP_H=0.1.

ForcomparisontoFig.2,themeanﬂameshapesfortheinves- tigatedcasesareshowninFig.10.Onehastonotethatdespitethe

smalldifferencesinflamespeedandtemperatureduetothediffer- enthydrogenmassfractions,themaindifferencebetweenthetwo casesis theamplitude ofthe instability.Thereforeany difference observedintheflamedynamicsofthetwocasesismostlikelyre- latedtotheamplitudeoftheoscillation(andthereforeonlyindi- rectlytoP_H).Duringtheinstability,adrasticchangeinflameshape occursforboth casesleadingtomorecompact flames.While the stable flames exhibit a slight asymmetry, this asymmetry is increased forthe unstable flames leading to a stronger mean heat releaserate on theright side of theflame. This mayalso be re- latedtothe effectofthespinningdirectionoftheacoustic mode onthefluctuatingheatreleaserate[47].

To investigate the flame dynamics of both cases, the phase- averaged responses are shown in Fig. 11. For the low-amplitude case (bottomrow) flame shapes similar to the stableflames are

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Fig. 11. Phase averaged images for m ˙ a = 91 . 87 gs ⁻¹at = 0 . 8 and P H= 0 . 1 corresponding to a high amplitude case (top row) and 0.2 corresponding to a low amplitude case (bottom row). Large modulations to the flame height and intensity are observed compared to the low-amplitude flame dynamics in the bottom row which shows the flame deformed by structures but not affecting the flame height. To calculate the phase averages, the images were divided in 20 bins based on the phase of the fundamental frequency which resulted in more than 300 images per bin.

observed andthe flameheight showsminimal variation overthe cycle.Inresponsetothevelocityoscillationsattheinlet,theshear layers roll-upleadingtotheformationofvortex structureswhich are advected downstream along theflame ascan be seen bythe modulations along the flame.The presence of such vortex structures is inferred, as these structures roll-up the flame, resulting in observable wrinkles in the phase average distribution. In the caseofpurelylongitudinal velocityoscillations,distortions dueto vortex-flame interactions wouldbe axisymmetric. However, these azimuthalinstabiltiesresultinbothlongitudinalandazimuthalve- locityoscillations, resultinginan asymmetricresponse, asshown by the side-to-sideflappingmotion.This asymmetry canbe seen as a slight stagger between the wrinkles on either side of the flame. The flame roll up is also observed to be stronger on the righthand side(t/T=1/10−4/10) whichislikely thereasonfor theincreasedasymmetry inFig.10.Thissuppression oftheshear layerdisturbanceononesideoftheflamedependingonthespin- ningdirectionwaspreviouslyobserved atatmosphericconditions in[47].

Much stronger modulations to the flame shape including a more pronounced asymmetric response appear for the high- amplitudecase.Thisresultsinmuchstrongervariationofthefluc- tuating heat releaserate. The large pressure amplitudesmanifest instrongaxialandtransversemotionsoftheflamewhichstrongly distorttheflameshape.Thestrongertransverseflappingmotionat thebaseoftheflame,arean indicationofstrongerazimuthal velocityoscillations. Theresultingflamedynamics giverise toare- gionofpeakheat-releaserateontherightsideoftheflamewhere theinteractionwiththeneighboringflameoccurs.

4. Conclusion

The present work introduces an annularcombustion chamber operating at elevated pressures and exhibiting self-excited combustion instabilitiesfora widerangeofoperatingconditions.The largest amplitude self-excited response was found for a hydro- gencontentof25%byvolumewhiletheamplitudesdecreasedfor largerhydrogencontents.Theamplitudeoftheinstabilitiesshowed a non-monotonicdependencyon thechamber pressure (whichis controlled bytheairmassﬂowrate).Whiletheamplitudetended to increase slightlywithincreasing pressurefor25% and35%hydrogen,itdecreasedslightlyfor43%.Forallblendsamplitudedips were observedatintermediateequivalenceratios.Whenthecom- bustor featured a high-amplitude instability,signiﬁcant harmonic contributionsareobserved,distinguishingtheseinstabilitiesclearly from recentresults in atmosphericcombustors. Complex interactions between the fundamentaland harmonic components were observed anda quadratic dependence between the amplitude of

aharmoniccontributionandtherespectivelower ordercontribu- tionwasidentiﬁed.The investigationintotheharmoniccontribu- tionsalso revealedacut-onamplitudeatwhichharmoniccontri- butionsbecome signiﬁcant. Interms ofthe natureof themodes, thecombustorpreferentiallyexhibitedCCWspinningmodesclose tothestabilityborders,whileallother modeswerespinningCW.

Fundamental andharmoniccomponentswere showntohavedif- feringnatureangles.Thesedifferencesincreasedforlow-amplitude instabilities. For the first time a clear trend between the ampli- tudeandthenatureoftheazimuthalmodewasobserved,support- ingrecenttheoreticalstudies[45]whichpredictedhigh-amplitude modestobespinningwhiledecreasedamplitudespushthemodes towardsstandingstates.Time-seriesrevealedthedistortionofthe pressuresignalsduetoharmoniccomponentswhichresultsinthe leadingedgeofthepressuresignal havingaverysteep slopedur- ing high-amplitude instabilities. Analysis of the flame dynamics also demonstrated the presence of significant asymmetry in the response during both low andhigh-amplitude instabilities, again distinguishingtheresponsetotheseazimuthalmodes.Athorough characterizationofthesetupisprovided,givingadetaileddescrip- tionoftheboundaryconditionsandtherebypositioningthisstudy asapossiblebaselinecaseforfuturesimulationstudies.

DeclarationofCompetingInterest

Theauthorsdeclarethattheyhavenoknowncompetingﬁnan- cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgments

This project has received funding from the European Union’s Horizon2020researchandinnovationprogramunderGrantAgree- ment No 677931 (TAIAC) and 765998 (ANNULIGhT). We also ac- knowledgeCBOneforthedesignandmanufactureoftheIPAfacil- ityandwouldliketothankEirikÆeforhelpingwiththeacoustic characterizationofthecomponents.

AppendixA. Boundaryconditions

A1. Effectofanadditionalupstreamchokingplateintheplenum

Toevaluatetheinﬂuence oftheupstreamboundarycondition, achokingplate,resultinginafullyreﬂectingboundary condition, wasintroducedupstreamoftheglassbeadsectionintheplenum.

The chokingplate consistsof a 10 mm thick steelplate with25 holesofdiameter2.2mm.Theinvestigatedsetofoperatingcondi- tions islimitedtom˙a=71.46gs⁻¹.Amplitudesandnature angles

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Fig. A1. Comparison of three data sets at m ˙ a= 91 . 87 gs ⁻¹with (colored) and without (grey symbols) upstream choking plate.

are displayedinFig.A1andcomparedto theresultswithoutup- streamchokingplate(greysymbols).

Generally, few differencesbetweenthe two configurations are observed. For P_H=0.1 the normalized amplitudes collapsewhile A is slightly lower compared to cases without choking plate for P_H=0.15and0.2. Theonsets oftheinstabilitiesareidenticaland thenatureangles showgreatcomparability.Inconclusion,thein- troduction ofthe upperchokingplatedoesnot alterthe stability ofthecombustorintheinvestigatedsetofoperatingconditions.A likely reasonforthisis thelarge reflectioncoefficient ofthesin- teredmetalplatewhicheffectivelyisolates thecombustioncham- berfromtheplenum.

A2. Acousticcharacterization

Boundary conditions constitute crucial parameters for models aiming to predict the stabilityof a combustor. Subsequently the acoustic characterizationof certain elementsisessential andwill thereforebe presentedhereafter.Theframework ofthescattering matrix,whichthischaracterizationisbasedoniswellknownand constitutesaconvenientdescriptiontorelate theacousticinterac- tionbetweentwoducts.Fordetailsonthemethod,theinterested readerisreferredto[48].Inshort,thescatteringmatrix

p⁻_x p⁺_y

=

S₁₁ S₁₂ S21 S22

p⁺_x p⁻_y

(A.1)

which is used to characterize the element, relates the travelling waveamplitudes p⁺andp⁻oftwoductsxandy.

We use an impedance test rig based on two straight ducts which are equipped withmicrophones andconnected by the in- vestigatedelement.Speakersonbothoroneside actasanacous- ticsourceandwe useatotalofﬁveindependentstates.Thescat- tering matrices for the sintered metal plate, the swirler andthe glass beadsection aswellasa descriptionofthesetupare made available inthe supplemental material S1. Figure A2displaysthe S₁₁ and S₁₂ elements (for notation, refer to [48]) ofthe sintered metal plate’sscatteringmatrix.Forafrequencyrangeupto3kHz,

|

^S11

|

^lies^between⁰.7−0.8thereby describing a stronglyreﬂec- tive boundary whichislikely tobe thereasonthat the introduction ofan upper chokingplatedoesnot alter thestabilityofthe combustor.

Fig. A2. Scattering matrix of the sintered metal plate.

Fig. A3. Measured pressure drop over the sintered metal plate for P H= 0 . 1 , 0.2 and =0 . 8 .

A3. Pressuredropoverthesinteredmetalplate

The sintered metal plate (SIKA B-100 from GKN) is made of brass,hasathicknessof22mm andaporosity of0.12atamean poresizeof183m.FigureA3displaysthemeasuredpressuredrop forallairmassﬂowsat=0.8andP_H=0.1and0.2.

AppendixB.Velocityexitproﬁlesoftheinjectors

Toinvestigatethe exitvelocity profiles,aswell asthe volume flow distribution over the injectors (i.e. the flow asymmetry in thecombustor),hot-wiremeasurementswereperformedunderat- mospheric and cold flow conditions. The setup in use is a Dan- tec StreamlinePro-systemequippedwitha miniature singlewire (55P11)witha probesize of1.25mm. Theprofile wasmeasured 2mm downstream ofthe dump plane andthe probewasorien- tated both parallel andperpendicular to the traversing direction.

The investigated flow rate is m˙a=91.87gs⁻¹ and the measure- mentswereperformedinatmosphericconditions.FigureA4shows theresultsfortwotraversingdirectionswiththeprobeorientated inparallel.Theprofileshowsaverysymmetricpattern.Intermsof theflowasymmetryofthefullannulus,severalinjectorswerein- vestigated.Acomparisonofthemassflowscalculatedbasedonthe measuredvelocityrevealedlessthan5%differencebetweenthein- jectors.Thisindicatesaverysymmetricflowdistribution.

AppendixC. Temperaturemeasurements

ThetemperaturemeasurementswereperformedwithanOptris CTLaser3MHinfraredthermometer(spectralrange2.3m,temper- aturerange0–600^◦Candresponsetime2ms).Themeasuringspot hasasizeof4.5–8mmdependingonthemeasuredlocation.

As the IRthermometer cannot measure temperatures through ﬂames, theburner hasto be switchedoff to read object temper-

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Fig. A4. Velocity proﬁle in x and y direction for one injector.

Fig. A5. Temperature T 1-T 3 corresponding to temperatures measured at the bluff body, base plate and inner wall for differing H 2content.

atures (see approach of [49]). Subsequently for the full stability map,onlytheﬁnaltemperaturesofthebluff bodywere recorded.

For thetwo operatingconditions detailedinthiswork, morede- tailedmeasurementswereperformedatthreelocations:Bluff body (=30^◦),back planeinbetweentwo bluff bodies(=45^◦) and at the inner wall (=45^◦) 45 mm above the dump plane (see Fig.A6).

Toretrievethetransients,thetemperatureswere evaluatedaf- ter different run-times,startingfromtheinstant when thetarget airﬂowratewasreached(t=10s).Practically,thecombustorwas ignited,runforacertaintime,switchedoff andcooleddownuntil a threshold temperatureofthe bluff bodywas reachedandthen ignitedagain.FigureA5depictsthemeanvaluesofthreerunsfor each run time up to1m. Onenotes thatthe wall andbluff body temperaturesstartreachingthermalequilibriumafter50s andlie attemperaturesabout350−400^◦C.

AppendixD. Watercooling

The water cooling is divided into three cooling circuits: back plate, innerwall andouter wall.Thevolumeflow ismeasuredby Omega FPB1400 paddle wheel meters and adjusted with control valves. For all operating conditions the flows are set to constant values: V˙_inner≈33Lmin⁻¹, V˙outer≈28Lmin⁻¹, V˙_back≈15Lmin⁻¹. The inlet watertemperature fluctuates between 8-10^◦C. Depend-

Fig. A6. Detailed view of the combustion chamber showing the measuring posi- tions of the temperatures. Red circle depicts measuring spot.

Table D.2

Volume ﬂow rates V ˙ , inlet and outlet temperatures T in, T out and heat transfer P cool

for m ˙ a= 91 . 87 gs ⁻¹at = 0 . 8 and P H= 0 . 1 and P H= 0 . 2 .

Circuit V [L min ˙ ⁻¹] T in[ ^◦C] T out[ ^◦C] P cool[kW]

P H= 0.1 Inner 32.9 8.1 55.6 109

Outer 28.2 8.1 35 52.9

Back 15.3 8.1 22.9 15.8

P H= 0.2 Inner 33 8 57.2 113.2

Outer 28.1 8 35.2 53.3

Back 15 8 22.8 13

ingontheconditionthecombustorisoperatedat,theoutletwater temperatureandtherebytheheattransferoverthewallscanvary signiﬁcantly.Forbrevity,wewilllimittheinformationonthetwo operatingconditionswhichwereinvestigatedindetail.Therespec- tiveinformationcanbefoundinTableD.2.

AppendixE

Supplementarymaterial

Supplementary material associated with this article can be found,intheonlineversion,atdoi:10.1016/j.combustﬂame.2021.02.

015. References

[1] M.A. Gonzalez-Salazar , T. Kirsten , L. Prchlik , Review of the operational ﬂexibil- ity and emissions of gas- and coal-ﬁred power plants in a future with growing renewables, Renew. Sustain. Energy Rev. 82 (2018) 1497–1513 .

[2] M.R. Bothien , A. Ciani , J.P. Wood , G. Fruechtel , Toward decarbonized power generation with gas turbines by using sequential combustion for burning hydrogen, J. Eng. Gas Turbines Power 141 (2019) 121013 .

[3] F. Halter , C. Chauveau , I. Gokalp , Characterization of the effects of hydrogen addition in premixed methane/air ﬂames, Int. J. Hydrog. Energy 32 (2007) 2585–2592 .

[4] E. Æsøy , J.G. Aguilar , S. Wiseman , M.R. Bothien , N.A. Worth , J.R. Dawson , Scal- ing and prediction of transfer functions in lean premixed h2/CH4-ﬂames, Com- bust. Flame 215 (2020) 269–282 .

[5] L. Rayleigh , The explanation of certain acoustic phenomena, Nature 18 (1878) 319–321 .

[6] T. Poinsot , Prediction and control of combustion instabilities in real engines, Proc. Combust. Inst. 36 (2017) 1–28 .

[7] B.T. Zinn, T.C. Lieuwen, Combustion Instabilities in Gas Turbine Engines: Op- erational Experience, Fundamental Mechanisms, and Modeling, The American Institute of Aeronautics and Astronautics, Inc., pp. 1–26.

[8] W. Krebs , P. Flohr , B. Prade , S. Hoffmann , Thermoacoustic stability chart for high intensity gas turbine combustion systems, Combust. Sci. Technol. 174 (2002) 99–128 .