Controlled autoignition in stratified mixtures Combustion and Flame

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Combustion and Flame

journalhomepage:www.elsevier.com/locate/combustflame

Controlled autoignition in stratified mixtures

Fatma Cansu Yücel

^a,∗

, Fabian Habicht

^a

, Florian Arnold

^b

, Rudibert King

^b

, Myles Bohon

^c

, Christian Oliver Paschereit

^a

aChair of Fluid Dynamics Technische Universität Berlin Straße des 17. Juni 135, Berlin 10623, Germany

bChair of Measurement and Control Technische Universität Berlin Straße des 17. Juni 135, Berlin 10623, Germany

cChair of Pressure Gain Combustion Technische Universität Berlin Straße des 17. Juni 135, Berlin 10623, Germany

a rt i c l e i nf o

Article history:

Received 16 December 2020 Revised 25 May 2021 Accepted 26 May 2021 Available online 13 June 2021 Keywords:

Pressure gain combustion Shockless explosion combustion Fuel stratification

Controlled autoignition

a b s t r a c t

Theshocklessexplosioncombustion(SEC)isarecentlyproposedconceptaimingforpressuregaincom- bustionthroughanunsteadyprocessofmultiple,distributedautoignitionsoccurringsimultaneously.For this,astratifiedfuelprofileofdimethyletherisinjectedintoacontinuousairflow.Thisprofileistailored suchthatthemixtureresidencetimeandignitiondelaytimearematched,allowingmultipleignitionker- nelstoinitiatesimultaneouslyleadingtoanaerodynamicconfinementduringheatrelease.Thisworkfirst presentsaninjectionstrategyforinjectingadefinedmixtureprofileintoaconvectionairflowtocontrol thelocal equivalenceratio throughoutthecombustor.Line-of-sightmeasurements areappliedtovisu- alizetheconcentrationprofile andsubsequentlyused todevelopaone-dimensionaltooltopredictthe localequivalenceratiobeforeignition.Next,anextremumseekingcontrolalgorithmisappliedtoanex- istingSECtestrigtocontrolthecycleaveragedformationofdifferentautoignitionmodesbyoptimizing thefuelsupply.Pressureandionizationprobedataindicatethesuccessfulinitiationofspecificmodesof flamepropagationbyadjustingthefuelinjectiontrajectory.Thepreviouslydevelopedsimulationtoolis appliedtotheinjectiontrajectoriesoptimizedbythecontroller.Correlatingthefuelconcentrationdistri- butionandtheobtainedautoignitionmodesrevealthattheignitionprocesscanbeverywellcontrolled bythefuelinjectiontrajectory.Lastly,singlerepresentativeignitioncyclesarefurtherinvestigatedbyap- plyingopticalmeasurementtechniquestoobtainOH^∗andCH^∗chemiluminescence.Theresultsreveala complexinteractionbetweenheatreleaseandpressurewavesinfluencedbytemperature-dependentigni- tionbehavioroftheappliedfuel.Asaconclusion,fourdifferentflamepropagationmodesareidentified, namely:turbulentdeflagration,subsonicautoignition,supersonicautoignitionandaerodynamicconfine- mentbymultiplesimultaneousautoignitionfronts.

© 2021TheAuthor(s).PublishedbyElsevierInc.onbehalfofTheCombustionInstitute.

ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction

Implementationofpressuregaincombustion(PGC) intoa con- ventional gas turbine is a promising wayto achieve an increase in thermalefficiency.Oneconcept amongothersforrealizingthe PGCisthroughashocklessexplosioncombustion(SEC).TheSECis based on a periodic combustionprocess whichaims fora quasi- homogeneous autoignitioninside acombustor.Figure 1illustrates the differentphases (a, b,c,d)of asingle SECcycle. A stratified fuel profile is injected into a convecting air flow (Fig. 1a). This fuelprofileistailoredtocompensateforthevariationsinresidence time throughouttheinjectionduration.Therefore,theequivalence

∗Corresponding author.

E-mail address: f.yuecel@tu-berlin.de (F.C. Yücel).

ratio

ϕ

^{isaxiallystratifiedalongthecombustorlength,resultingin}

agradientinignitiondelaytime

τ

^.Hence,simultaneousautoigni- tionatmultipleignitionlocationsisachieved, leadingtoan aero- dynamically confinedvolume duringheatreleaseandtherefore a riseinpressuresimilartoconstantvolumecombustion(Fig.1b).A pressurewaveisthenobservedtravelingdownstreaminthecom- bustor.Attheopenendofthecombustor,thepressurewaveisre- flectedasanexpansionwavetravelingupstream(Fig.1c).Oncethe expansion wave reaches the combustor inlet, the pressure drops belowthesupplypressure,supportingtherefillingprocessandthe restartofthecycle(Fig.1d).

Althoughautoignitionasthedrivingmechanismforcombusting fuelis anew approachforgas turbineapplication,it alreadyhas been investigated in terms of internal combustion engines, such as diesel or homogeneous charge compression ignition engines.

https://doi.org/10.1016/j.combustflame.2021.111533

0010-2180/© 2021 The Author(s). Published by Elsevier Inc. on behalf of The Combustion Institute. This is an open access article under the CC BY-NC-ND license

Fig. 1. Sketch of the SEC cycle.

Table 1

Modes of autoignition.

ξ> 1 : subsonic autoignitive flame propagation or deflagration,

ξ≈1 : coupling of a reaction front with a pressure wave forming a detonation,

0 < ξ< 1 : supersonic autoignitive flame propagation,

ξ^{= 0 :} thermal explosion (homogeneous autoignition).

Particularly withrespect tolow temperaturecombustion, theau- toignitionprovidesseveraladvantagescomparedtothesparkigni- tionintermsofemissions[1].

Sinceautoignitionisprimarilydrivenbychemicalkinetics,itis highlydependentontheinitialstate ofthemixturesuch aspres- sure, temperature,andfuel–airratiomakingitsusceptibletohigh stochasticity inpractical approaches.Gradientsin theinitial state lead todeviationsinmixturereactivityandthus,induce different flamepropagationmodes.Theabilityofcontrollingtheoccurrence of these modes would be a leapfrogging step in combustion re- search.

The characterization of autoignition phenomena originating from gradients in reactivity has been intensively studied in the past intermsofdetonations andexplosions.An overviewon this topicisprovidedbyBartenevetal.[2].Thisphenomenonwasorig- inally investigated by Zel’dovich in his theoretical work defining different modes of flame propagation that initiate from ignition kernels[3].Zel’dovichdefineddifferentregimesbasedonthegra- dient inignition delaytime

τ

ai resultingin differentautoignition propagationvelocitiesu_ai

u_ai=

∂τ

ai

∂

^x

−1

=

∂τ

ai

∂ϕ ∂ϕ

∂

^x

−1

. (1)

Thedimensionlessparameter

ξ

^{,isintroduced}

ξ

⁼_u^a

ai =a

∂τ

ai

∂ϕ ∂ϕ

∂

^{x (2)}

withthespeedofsoundaandtheequivalenceratio

ϕ

^.Thisallows

forthedescriptionoffourregimeclassifications[3,4],summarized inTable1:

For

ξ

>1 a deflagration or an autoignition front propagating with a velocity below the speed of sound is observed. Propaga- tionvelocitiesoccurringclosetothespeedofsound(

ξ

≈1)might eventually lead to a coupling of the flame front and the gener- atedpressurewaveresultingintheonsetofadetonation.Perfectly homogeneous ignition(thermal explosion) is achievedforhomo- geneous initial conditions in pressure, temperature, and mixture composition leadingtoa constant ignitiondelaytime throughout themixture.Thisautoignitionmode,however,isatheoreticalcon- sideration corresponding to

ξ

=0.Inpractice,inhomogeneities in temperatureormixturefluctuationscausedby turbulenceleadto

gradients in reactivity, and thus, deviations in ignition time. For

ξ

<1asupersonicflameisobserved,burningthereactivemixture quasi-homogeneously,whichmeanseachparticleautoigniteswith- outbeingaffectedbyneighboringparticles.Acomparableignition behavior is observed inthe caseof multiple spatially distributed kernels igniting quasi-simultaneously leading to a confined vol- ume [2]. Both mechanisms result in a gradual increase in pres- suresimilar toconstant volumecombustion ratherthan inducing sharppressure peaksassociated withshockwaves.Withhis the- ory,Zel’dovichhighlightedtheimportanceofreactivitygradientsin mixtures.In mostapplicationsthesegradients are causedby tur- bulent fluctuations. For this, underlying aspects of the impact of turbulentfluctuations,whichare highlystochastic intheir nature, ontheautoignitionprocesshavebeenstudiedintermsoftemper- aturefluctuationandturbulenceintensity[5,6].

Besides the effect of turbulence, recent studies focus on the interaction of low and high temperature carbon chemistry lead- ingtodifferentcombustionmodes.Especiallyforfuelswithnega- tivetemperaturecoefficient(NTC)characteristics,suchasdimethyl ether (DME), these flames show differences in ignition behav- ior at low and high temperature conditions, resulting in either a two-stage or a single-stage autoignition [7]. Direct numerical simulations were performed by Luong et al. [8,9] for fuels with NTC behavior exposed to fluctuations in temperature and con- centration. Moreover, a tendency towards the formation of so- called double flames is observed. Such double flames are char- acterized by the appearance of hot and cool flame segments simultaneously [10–13]. A detailed analysis is provided by Ju[14]inhis recentstudies. However,moststudies are basedon numericalsimulations andexperimentaldata isscarcelyavailable duetothedifficultyofmeasuringtemperature,pressureandmix- turecompositionsimultaneouslywithveryhighresolutionintime and space. Optical measurement techniques help to gain funda- mentalinsights to understand the underlyingeffects by allowing formeasurementofelectronicallyexcitedspeciesduringhydrocar- boncombustion[15–18].

Thisworkexperimentallyinvestigatestheapplicabilityofacon- trol scheme to control the stochastic nature of an autoignition event. First, a fuel injection strategy is presented and its ability togeneratean axiallystratifiedfuel–airmixture throughoutcom- bustoris verifiedbyconcentration measurements withoutchemi- cal reactions.Subsequently, anumericaltool isintroduced, which allowsforapproximatingthefuelconcentrationdistributioninside thecombustorforadefinedfuelinjectiontrajectorywithsufficient accuracy.Asanextstep,anextremum-seekingcontrollerisapplied which adjusts the fuelinjection trajectory to optimize thecycle- averagedoperation. Theobjectiveisto increasetheprobability of a targeted combustion mode by generating the prescribed gradi- ent in mixture reactivity. However, a certain amount of stochas- ticity remains,which isvisibleinthe cycle-to-cyclevariation.For this, single cycles are analyzed using optical chemiluminescence and pressure measurements in order to better understand the causalityfortheobservedvariationsinthechemicalandphysical processes.

2. Experimentalsetup

Inthescopeofthisworkthreedifferent– butinherentlylinked – measurementswereconductedusinganexistingSECtestrig(see Fig.2).Theconductedmeasurementsarecategorizedasfuelstrat- ification,autoignition control,and singlecycleanalysis ofthe ig- nition distribution.For each measurement the combustorsection ofthetestrigisslightlymodifiedinordertoallowforchangesin instrumentationandoptical accessibility.Inthissection, theover-

Fig. 2. Sketch of the test rig. Sensors: low-speed, static pressure sensors (FA, FF), thermocouples (T1, T2), high-speed, static pressure sensors (P1–P5), ionization probes (I1–I8).

allexperimentalsetupandthesubsequentmodificationsmadefor eachmeasurementwillbedescribed.

The SECtest rigconsistsofa preheater,aninjectionstation,a convectiontube,andanexchangeablecombustorsection.Thecon- vectiontubeandcombustorhavealengthof500mm,respectively.

Thelengthoftheexhausttubeis1200mm.Alltubeshaveaninner diameterofd=40mm.Theinjectionstationisdesignedwithten circumferentially distributedports,each witha diameterof1mm.

Each port isequippedwith an individually controlled high-speed solenoidvalve(StaigerVA204–716),whichisdesignedforanoper- ationfrequencyupto250Hz.Ahigh-speeddome-loadedpressure regulatorismountedintothefuelsupplylinetominimizepressure fluctuations during fuel injection. While the concentration mea- surementsareconductedatnon-reactingconditionswithmethane, the reactingexperimentsare conductedwithDME asfueldueto itslowignitiondelaytimesunderatmosphericpressureconditions.

2.1. Fuelstratification

The instrumentation forinvestigating the fuel stratification in the experimental apparatusis highlighted in blue inFig. 2. Tun- ablediodelaser absorptionspectroscopy(TDLAS),asdescribedby Lietal.[19]andBlümneretal.[20],isappliedtothecombustorat 0.65mdownstreamofthefuelinjectionplaneallowingforaline- of-sight concentration measurement of methane in air. Methane is used astracer fuel asits absorption featureat 1.6537m coin- cides well withthe wavelengthof theavailable laser. Due tothe high Reynolds number,molecular diffusion isexpected to play a minor role. Thus, it is reasonable to conclude that gradients in fuel concentration obtainedwithmethanearereasonablycompa- rabletoreactivemeasurementusingDME.Wavelengthmodulation spectroscopywithamodulationfrequencyof10kHzandanampli- tudeof0.04nmisapplied,resultinginalargersignal-to-noisera- tiocomparedtodirectabsorptionspectroscopy.Theoutputsignal, whichiscalculatedasthesecondharmonicofthemodulationfre- quencydividedbythefirstharmonic,scales linearlywiththefuel concentration.Calibrationmeasurementswereconductedwithnu- merous well-defined steadystate mass flowrates offueland air.

Hence,theappliedTDLASisusedasanaccurate,quantitative,and time-resolved measure forthe fuel concentration atone distinct axial positioninthe combustor.After injection,the fuelprofileis exposed to turbulent mixingwhile convectingdownstream from theinjectionstationuntilreachingthemeasurementposition.

A previous study [21] demonstrated that the main effects on thefuelconcentrationprofilecanwellbecapturedbyTDLASmea- surements. Further, it wasshownthat theevolution of fuel con- centrationinthecombustorisdominatedbydiffusionintheaxial direction, whichwassuccessfullyreplicated bynumericalsimula-

tionsoftheone-dimensionaldiffusionequationgivenby

∂

^c

∂

^{t =D}

∂

^2c

∂

^{x2. (3)}

Here,tandxaretherespectivevariablesintimeandspace,cisthe localfuelconcentration,andDisthediffusioncoefficient.Compar- ingthenumericalresultstothemeasuredfuelconcentrationpro- filesrevealed that D linearly dependson the mean flow velocity

¯

u_air.Moreover, the spatial widthof the injected fuel–airpackage wasobservedto largelyaffectthe attenuationofgradients inthe fuelconcentrationdistribution.

In the scope of this work, fuel concentration measurements were conducted, at differentair flow temperatures startingfrom 293Kupto 800Kwith100Kincrements.Thisallows forevalu- atingthetransferabilityofthementionedfindingsfrominvestiga- tions atambienttemperatureconditions tocombustion measure- ments,whichareconductedatelevatedtemperatures.Toensurea constantconvectiontime forallmeasurements, theairmassflow ratem˙_airisadjustedforeachtemperaturesettingtoprovideacon- stantvolumetricairflowrate,andthus,aconstantairflowvelocity

¯

u_air=18m/s.Thisvelocitywaschosentomatchthereferencecase withchemicalreaction(T=1023K,p=1atmandm˙_air=30kg/h).

By this, the impact of the Reynoldsnumber, and thus, turbulent fluctuations can be evaluated. An internal proportional-integral- derivative controller allows a maximum fluctuation in air mass flow rate of about 0.5kg/h. The air temperature is measured at T1by acoatedthermocouple (typeK),whichextendsintotheair flowbyapproximately10mm.Thefuelsupplypressureissettoa constant value of p_fuel=4.5 barforall measurements ensuring a constantinjectionvelocity.Foragivencombustordiameterthere- quiredmassflowratem˙_aircanbecalculatedforeachappliedtem- peratureas

˙

m_air=

ρ

air

(

^T

)

^u¯air

π

^d2

4 . (4)

With an increasing temperature, the density

ρ

air(^T) ^decreases whilethedynamicviscosity

η

air(^T)^{increasesresultinginan over-} allreducedReynoldsnumberRe_air

Re_air=

ρ

air

(

^T

)

^u¯aird

η

air

(

^T

)

^{. (5)}

Foreachappliedtemperature,threedifferentfuelinjectiontra- jectories,showninFig.3,are injectedwithin aconstantinjection durationoft_inj=30ms.Eachtrajectoryisdefinedbytentimewin- dowswithan independently setnumber ofopen valves.Aseries of 150 injection cycles is performedfor every applied trajectory withafrequencyof5Hz.Inordertoexaminetheinfluenceofthe airtemperatureontheevolutionofthefuelconcentration,theob-

Fig. 3. Normalized fuel concentration at the injection station for an ideal injection and the applied model. The parameters of the valve response were optimized to achieve optimum agreement of the model results and the measured profiles.

tained profiles fora given injectiontrajectory are analyzed fora rangeoftemperatureconditions.

Toallow fortheassessment ofthefueldistribution insidethe SECforanarbitraryfuelinjectiontrajectory,atoolforthenumer- icalcalculationofthespatialdistributionofthefuelconcentration was implementedbased on the work publishedin [21].The tool aims forreproducingthreemechanisms: valveresponse,diffusion effectsandconvectiontime.Thecalculationsareperformedforthe normalizedfuelconcentrationcˆ,whichisdefinedastheactualfuel concentration c dividedby theconcentrationobtainedwhen con- tinuouslyoperatingasinglevalve.

The fuel injection inthe experiments isaffected by inertia in the valve response. Thus, the fuel concentration atthe injection station wasmodeled by apolynomial Bézier curveallowing fora gradual changein theinjected fuel flow rate. The initial opening speedandthetimeuntilthevalveiscompletelyopenareusedas parameters fortheadjustmentofthevalvebehavior. Additionally, dead-times for opening and closing are applied. The parameters were identified to replicate all measurementdata by thesimula- tionwithdifferentfuelinjectioncurves.Thenormalizedfuelcon- centrationcˆattheinjectionstationisshowninFig.3foranideal (black) and the modeled (red) fuel injection, respectively. Three differentfuelinjectiontrajectoriesareshown:tophat,localmaxi- mumandlocalminimumcurve.

EqualparametervaluesforthepolynomialBéziercurveandthe dead-times were applied forall injectiontrajectories. The shown profilesindicatethatthetriggeringofthevalvesresultsinagrad- ualincreaseinfuelmassflowafteracertaindeadtime.Thesame can be observed fortheclosing ofthe valves.Forall trajectories, thisresultsinacertainskewnessoftheinjectedfuelprofile.

To model dispersion effects, the numerical simulation of the one-dimensional diffusionequation(Eq.(3)) wasimplementedon a grid witha spatialresolutionof x=10 mm.In a preliminary study withvarying spatial resolutionof the simulation area, this gridsizewasfoundtobesufficienttoobtainaccurateresultswhile minimizing the computational effort. The spatial derivative

∂

/

∂

^x

wasimplementedbyacentraldifferencescheme.Thetimestepsof dt=0.05ms arediscretized bya 4thorderRunge–Kuttascheme.

Foragiventimestept_i,thefuelconcentrationattheinjectionsta- tion(x=0m)isincreasedbytheappropriatevalueobtainedfrom the valve opening. Subsequently, the spatial distribution in fuel concentrationforthenexttimestept_i+1=t_i+dtiscalculated.For

this,first,thesimulationdomainisshiftedbydx=u¯_airdt account- ing for convectiondue to the meanflow velocity. Then, the fuel concentration profile of thenext time step isdetermined by ap- plying thediscretized diffusionequation. Thediffusioncoefficient D wasdetermined iteratively to maximize the congruenceof the fuelconcentrationprofilesforsimulationsandexperiments.

The temporal evolution of the fuel profile was generated by observing the fuel concentration at a fixed spatial position (x= 0.65m)duringtheentiresimulationtime.Thisprocedureissimi- lartotheline-of-sightmeasurementusingTDLASandistherefore expectedtoproducesimilarresultsforagivenfuelprofile.

2.2. Autoignitioncontrol

Anextremum seeking control algorithmis definedtofind the optimum fuel injection trajectory to achieve reliable operation.

Twodifferentcostfunctionsareusedtoformulatethetargetofthe controllerbased oncycle-averagedmeasurementdata ofpressure orionizationprobes.

In this section, the injection optimization algorithm is intro- ducedandsubsequentlyappliedtotheSECtest riginSection3.2. Webasicallyextendedtheideaofacyclicextremum seekingcon- trol[22] to the integer-constraintcase andapplied the Broyden- Fletcher-Goldfarb-Shanno (BFGS) scheme with gradient informa- tion estimated from measurements for the underlying optimiza- tion. As theinteger-valued actuation is an uncommon restriction forextremumseekingcontrol,theappliedapproachisbrieflysum- marizedinthefollowing.

The fuel injectioncurve of a batch k,defined by n steps N_k,i, canbedescribedbythevector

n_k=

N_k,1,...,N_k,i,...,N_k,n

T

. (6)

Accordingly, the pressure signals p_k,j(^t) ^{of injectionperiod k are} functionsoftheinjectioncurven_k¹:

p_k,j

(

^t

)

= fj

(

ⁿk

) ∀

^j∈

{

^1,2,3,4

}

⁽⁷⁾

Thepressurerisecanbequantifiedbyacostfunction J_k=J

p_k,1

(

^t

)

,p_k,2

(

^t

)

,p_k,3

(

^t

)

,p_k,4

(

^t

)

=J

(

ⁿk

)

⁽⁸⁾

1Note that in this section we describe the approach only for pressure signals for easier readability. Nevertheless, the approach can be extended to all parame- ters that are influenced by the injection curve n k. An example is the ignition time detected by the ionization probes as described below.

that mapsthepressuresignalstoascalarvalue J_k.Theonlineop- timization aims to minimize the cost J_k over multiple injection batches.

Asasufficientmodelforthemappingofthefuelinjectioncurve to the pressure signals is not available, an approximation of the costfunctionisnecessary.Forsuchanapproximationweconsider aTaylorseriesuptothesecondorderterm

J

(

ⁿ k

)

≈J

(

ⁿk

)

+

∇

^J

(

ⁿk

)

^{T n}+1

2 n^THJ

(

ⁿk

)

^{n (9)}

with the deviated fuel injectioncurve n _k=n_k+ n. In Eq.(9),

∇

^J(ⁿk)^{denotesthegradientofthecostfunctionatthefuelinjec-} tion curve ofbatchk andH_J(ⁿk)^{denotes the}corresponding Hes- sianmatrix.Withoutanymodelinformation,ananalyticalcalcula- tionofthegradientandtheHessianmatrixisimpossible.Hence,a measurement-basedestimationisrequired.Forthat,thefuelinjec- tioncurvefrombatchkisperturbedintheupcoming2·nbatches.

Thefuelinjectioncurvesofthese2·nbatchesaredefinedby nk+2i−1=

Nk,1,...,Nk,i+1,...,Nk,n

=n⁺_k,i (10)

n_k+2i=

N_k,1,...,N_k,i−1,...,N_k,n

=n⁻_k,i. (11) Accordingly,thepressuresignals

p⁺_k,j,i

(

^t

)

=f_j

(

ⁿ⁺_k,i

) ∀

^j∈

{

^1,2,3,4

}

⁽¹²⁾

p⁻_k,j,i

(

^t

)

=fj

(

ⁿ⁻_k,i

) ∀

^j∈

{

^1,2,3,4

}

⁽¹³⁾

areobtainedforthecorrespondingfuelinjectioncurve definedby Eqs. (10) and(11). The pressure measurements are subsequently usedtocalculatethecosts

J_k⁺_,i=J

p⁺_k,1,i

(

^t

)

,p⁻_k,2,i

(

^t

)

,p⁺_k,3,i

(

^t

)

,p⁺_k,4,i

(

^t

)

=J

n⁺_k,i

(14)

J_k,i⁻ =J

p⁻_k,1,i

(

^t

)

,p⁻_k,2,i

(

^t

)

,p⁻_k,3,i

(

^t

)

,p⁻_k,4,i

(

^t

)

=J

n⁻_k,i

. (15)

After the perturbation phase,before batch k+11the gradient at thefuelinjectioncurvefrombatchk canbecalculatedusingcen- traldifferencescheme:

∇

^J

(

ⁿk

)

≈ 1 2

⎡

⎢ ⎢

⎢ ⎢

⎢ ⎣

J_k⁺_,1−J_k⁻_,1 .. . J_k⁺_,i−J_k⁻_,i

.. . J_k,n⁺ −J_k,n⁻

⎤

⎥ ⎥

⎥ ⎥

⎥ ⎦

. (16)

In whatfollowswe will refertothose batcheswhere anewgra- dient information is available as control steps with the counter p.Note that if a perturbation asdefined inEqs. (10) and(11) is not possibleduetotherestrictednumberofvalves,boththeper- turbation andtheensuing calculation ofthe gradient,haveto be adaptedappropriately.

Toavoidunnecessarydelayduringtheexperiments,aswell as toensureaquickresponsetodisturbancesintheoperationcondi- tion, thesecond orderderivative isestimatediterativelyfromthe gradientinformationwithoutapplyingacentraldifferencescheme.

For that,the commonBFGSalgorithm asdescribedin[23] is ex- ploited.TheHessianmatrixincontrolstep pcanbeapproximated by

HJ

(

^np

)

^≈

(

^I−

μ

^z

(

^np−1

)

^T

)

^·HJ

(

^np−1

)

^·

(

^I−

μ (

ⁿp−1

)

^zT

)

+

μ

^{zzT (17)}

with

n_p−1=np−n_p−1

z=

∇

^J

(

ⁿp

)

−

∇

^J

(

ⁿp−1

)

μ

= 1

z^T

(

ⁿp−1

)

^.

This estimationis subsequently applied within the approximated costfunctionfromEq.(9).

Thus,the optimaladjustmentofthefuelcurve incontrol step pisobtainedbysolvingtheinteger-valuedquadraticprogram:

np=argmin n n^THJ

(

ⁿp

)

ⁿ+

∇

^J

(

ⁿp

)

^{T n (18)}

subjectto n∈Nⁿ (19)

A n≤cT. (20)

Besides the restriction to an integer domain, Eq. (20) is used to incorporatedadditional linearinequality constrainslike themini- mumandmaximumaveragednumberofopenedvalvesinonein- jectioncycleaswellasthe restrictednumberofvalves.Thecon- straint for the average numberof opened valves is translated to linearconstraints

(

¹ⁿ

)

^Tnp+1≤n·8 and −

(

¹ⁿ

)

^Tnp+1≤ −n·6 (21) withrespecttoafuelinjectioncurveintheupcomingcontrolstep p+1.InEq.(21),1ⁿ denotesa sizencolumnvector ofones. Ac- cordingly,the limitednumberofvalves forthefuel injectioncan beexpressedby

Iⁿnp+1≤1ⁿ·10 and −Iⁿnp+1≤1ⁿ·0 (22) with the identity matrix Iⁿ of size n×n. Eqs. (21) and (22) is stackedtogethertoobtainthelinearconstraint

⎡

⎢ ⎣

Iⁿ

−Iⁿ

(

¹ⁿ

)

^T

−

(

¹ⁿ

)

^T

⎤

⎥ ⎦

A

np+1≤

⎡

⎢ ⎣

1ⁿ·10 1ⁿ·0

n·8

−n·6

⎤

⎥ ⎦

c

. (23)

AsthequadraticprograminEq.(18)isformulated fortheadjust- mentofthefuelinjectioncurve nbetweenthecontrolsteps,the constraintfromEq.(23)istransformedtoaformulationcompliant toEq.(20):

Anp+1≤c (24)

A

(

ⁿp+ n

)

≤c (25)

A n≤c−Anp

cT

. (26)

ThequadraticprograminEq.(18)canthusbeappliedtooptimize thefuelinjectioncurvefromonecontrolsteptothenext.

The experimental setupas describedearlierismodifiedto al- low for reactive measurements under atmospheric pressure con- ditions. For this, the optically accessible combustor is exchanged forastainlesssteelcombustionchamber,asshowninFig.2.DME isusedasthefuelduetoits sufficientlylowignitiondelaytimes (45ms<

τ

ign<80ms)underhightemperature(T_air=1023K)and atmosphericpressureconditionsfortheappliedequivalenceratios (

ϕ

∈[1.15,1.45]).Inordertoassuregaseous injection,DME isled throughavaporizerandguidedthroughaheatedfuellineat330K.

Thefuelsupplypressureissettop_fuel=4.5barwhichmatchesthe supplypressurefornon-reactivemeasurements.Bythis,thevolu- metricflow rateofthefueliskept constant inbothreactingand

Fig. 4. Optically accessible combustor and measurement setup consisting of a high- speed camera equipped with an intensifier and an image doubler, four PMTs, a spectroscope, pressure sensors P1–P4 and ionization probes I1–I5.

non-reactingcases.The airmassflow rateis settoasteadystate value ofm˙_air=30kg/h resulting in a flow velocity of18m/s fora temperatureof1023K.

Twostaticpressuresensors(FestoSPTW)areinstalledtomon- itorthefuel(labeledFF)andair(labeledFA) supplypressuredur- ingeachmeasurement.Fourhigh-speed,water-cooled,staticpres- suresensors(KuliteEWCTV-312)aremountedinsidethecombus- torwith100mmdistancetomeasurethepressurerisesubsequent to the ignitionevent. Seven ionization probes are installedto lo- catethe ignitionfront insidethe combustor.The datais sampled withanacquisitionrateof10kHz.

The test rig is operated with a frequency of 5Hz. At the be- ginning of each cycle a well-defined fuel profile is added to the continuousairmassflow.Thetotalinjectiondurationis30msfor all measurements. Thisduration issubdivided into injectionsec- tionsofeither3or6ms,resultingineither10or5valveoperation steps,respectively(examplegiveninFig.3for10operatingsteps).

The averagenumberofopenvalvesduringtheinjectionperiodis limitedtoa rangebetween6and8.Bythis, theglobalfuel mass flowrateduringeachcycleisrestricted.Foreachfuelinjectiontra- jectory applied by the controller, the test rig is operated for 40 cyclesofwhich thelast30are usedtocalculatea cycle-averaged valueforthegivencostfunction.Theapplied40consecutivecycles are referredto asbatch. Aconstantfuelprofilewithseven valves openischosenasaninitialinjectiontrajectoryforthefirstbatch.

2.3. Singlecycleanalysisofdistributedautoignition

Toallowforadetailedanalysisofsinglecycles,chemilumines- cence measurements are conducted. For this, the setup is again slightly modifiedbyintegratingan optically accessiblecombustor assembled fromfourquartz tubeseach withalength of120mm andheldtogether byfiveflangesasshowninFig.4.Ahighspeed camera (Photron SA-Z) and intensifier (Lambert Instruments) in combination with an image doubler is used to record the two- dimensional line-of-sight chemiluminescence distribution in the measurementsectionaroundtwocenterwavelengths(CWL)simul- taneously. 307 nm was chosen to capture the light emission by OH^∗speciesanda435nmslightlyoff themainCH^∗peakemission feature allows for thedetection of CH^∗ andformaldehyde simul- taneously.Notethatthetwo-dimensionalmeasurementsareover- layed with broadband emission spectrum ofCO₂.700 snapshots are recordedwithasamplerateof50,000 Hzresultinginatotal recordingtimeof14ms.

In addition to the two-dimensional measurements, time- resolved fiber-coupled line-of-sight measurements were con-

Table 2

Emission spectra of excited species during the com- bustion of dimethyl-ether in air [24,25] .

Emitting species Emission wavelength in nm CH 2O ^∗ 350–505

CO 2∗ 300–600

OH ^∗ 307

CH ^∗ 431

C 2∗ 470, 516

ducted. Forthis, a multi-connector optical cableis positioned in the center ofthe measurement section (see Fig. 4). This enables chemiluminescencemeasurementsformultiplewavelengthsatone distinctposition.The multi-connectorisconnectedtofourphoto- multiplier(PMT)sensorsandaspectroscope,respectively.ThePMT dataissampledatasamplerateof10kHz,whilethespectroscope operationfrequencyislimitedto5Hz.Thefilterwavelengths be- foreeachPMTare307nm,343nm,430nmand450nm.Thesig- nalsobtainedatwavelengths343nmand450nmareusedtocor- recttheCH^∗andOH^∗emissionsfromthebroadbandCO₂^∗andCH₂

∗emission.Fourhighspeedpressuresensorsaspreviously applied aremounted intotheflangestomeasurethepressure risesubse- quenttotheautoignition.

During the combustion of DME in air, several light emitting species are excited, including CH₂O^∗, CO₂^∗, OH^∗, CH^∗, and C₂^∗. In the emission spectrum CH₂O^∗ and CO₂^∗ are characterized by broad-band emission feature,while OH^∗,CH^∗,and C₂^∗ show dis- tinctsingleormultiplepeaks(Swanband)intheemissionspectra.

ThecharacteristicwavelengthsaresummarizedinTable2. Theformation offormaldehydehas beenobservedduringlow temperaturecombustion(LTC)[24]andisusedasanindicatorfor the onset of a first-stage ignition [18,26]. Its emission spectrum overlapstheemissionfeaturesofotherexcitedspeciessuchasCH^∗ andC₂^∗.Fortemperature rangesbelow 1000K emittedchemilu- minescence around the wavelengths of CH^∗ can be generally in- terpretedasformaldehydeformationwhileCH^∗ andOH^∗are typ- ically observed during high temperature combustion (HTC) [18]. Thus,theappearanceofCH^∗inabsenceofOH^∗mayreasonablybe interpreted as formaldehyde emission. The formation of C₂^∗ pri- marilyoccursunderfuelrichconditions.Additionally,accordingto Beckeretal.[27],so-calledhotandcoldOH^∗areformed,differing mainlyinthechemicalpathbywhichtheyareformed.HotOH^∗is mainlyformedbythereactionofCHwithmolecularoxygen.OH^∗ formedwithoutthepresenceofCHmoleculesisthereforeconsid- eredcoldOH^∗.

3. Results

Inthissectionfirstasimulationtoolisdevelopedbasedonthe TDLAS measurements describedin Section 2.1for replicating the fueldistributioninsidethecombustorforanarbitraryinjectiontra- jectory.Next,thecontrolapproachintroducedinSection2.2isap- pliedtothe SECtest rigandthecontroller performanceis evalu- atedbasedontheoptimizationoftwodifferentcostfunctions.Fi- nally,adetailedanalysisofsinglerepresentativecyclesisprovided basedonchemiluminescencedataasdescribedinSection2.3. 3.1. Fuelstratification

Themeasuredfuelconcentrationsforthreemodelinjectiontra- jectories,introducedinFig.3,werecomparedatdifferenttemper- atureswhich revealednosignificant affectofthe temperatureon thesteepnessofthegradientsinconcentrationwithintheconsid- eredrange.Hence,itisassumedthatthediffusionprocesseswhich

Fig. 5. Temporal evolution of the measured and modeled normalized fuel concentration at the measurement position for TDLAS.

are predominating the flow are mainly independent of the tem- peratureconditions.Therefore,wheninjectingagiventrajectoryin reactive experiments, a similar distribution in fuel concentration throughoutthecombustorasobtainedbyTDLASmeasurementsis expected.

Further, the measured fuel concentration profiles are used to validate the model parameters to predict the fuel concentration distribution inthecombustorforan arbitraryinjectiontrajectory, asdiscussedinSection2.1.Acomparisonofthemeasuredfuelpro- fileswiththemodeledfuelconcentrationatthemeasurementpo- sitionisshowninFig.5.

Excellent agreement can be seenfor thefirst andsecond fuel injection trajectories. Slightly greater deviations are observed for the thirdcurve dueto increasedcurvature ofthefuelprofilesre- sulting in promotion of inaccuracies. However, the main features including the position and amplitudeof the maximum fuel con- centrationare well reproducedby thesimulations. Thepresented results show,that thenumerical modelallows for the prediction ofthefuelconcentrationdistributioninside thecombustor.Inthe following,thistoolisusedtoestimatethefueldistributioninside the SEC before ignitionin measurements withchemical reaction.

Inthesecases,opticalfuelconcentration measurementscannotbe applied,whichmakes thereliablesimulationoftheinjectionpro- cessavaluabletoolfortheinterpretationofmeasurementdataat theseconditions.

3.2. Autoignitioncontrol

The control algorithm formulated in Section 2.2 is applied to thetestrigaimingforamaximizationofthepressurerisethrough distributedautoignition.Earlierobservationsshowedadistinctcor- relation between the maximum pressure andthe standard devi- ation of the autoignition front [28]. A low variation in ignition times across the combustor indicate a higher number of igni- tion points that occur simultaneously and/or a fast propagating flame front(s).This distributedignitionwasfound to resultinan aerodynamic confinement leadingto an overall increase in pres- sure amplitude. Based on these preliminary observations, a con- trol approach is developedthat optimizes thefuel injection asa function oftime-resolved outputsignals ofionization probes and pressure sensors. The first optimization goal is to maximize the pressurerisesubsequenttoautoignitionwhereasthesecond opti- mizationgoalistomaximizethehomogeneityoftheautoignition front.

Thecontrollerperformance isanalyzedbasedon twodifferent costfunctionsJ₁andJ₂.Thefirstcostfunctionisdefinedby J1

(

ⁿk

)

⁼⁻₂₀¹

30

m=11

summ

pj,max

(

ⁿk,m

)

(27)

with p_j,max(ⁿk,m)^{denoting the maximumpressure amplitudeof} sensor j for agiven trajectoryn_k in cyclem.summ indicates the sumoftheseamplitudesobtainedbyallsensors forcyclem.This approach aims at maximizing the cycle-averaged peak pressure amplitude generated by the autoignition events. The second ap- proachaimsatthesimultaneousdetectionoftheignitionfrontby theinstalledionizationprobes.ThecostfunctionJ₂isdefinedby J2

(

ⁿk

)

⁼₂₀¹

30

m=11

stdm

τ

io,j

(

ⁿk,m

)

(28)

with

τ

io,j(ⁿk,m)representingthetimewhenthereactionfrontin cyclem is detected ationization probe j,and std_m the standard deviationamongthesesevenionizationprobes.Thisapproachaims formaximizingthehomogeneityoftheignitionevent.

Figure 6 illustrates the maximum pressure amplitude J₁ ob- tainedbyeachsensorforallappliedcontrolsteps.Theorderofthe detectionindicateswhetherapropagatingpressurewaveorsimul- taneousriseofthepressurethroughoutthecombustorisachieved.

Thepresentedpressuredataisaveragedover30cycles.Thesedata arecomplementedby thevalueofstandarddeviationoftheigni- tion time obtained by the ionization probes J2(ⁿ)k as a measure ofthe autoignition homogeneitywith respectto the control step k.Comparingthegraphsforthetwocostfunctionsitcanbeseen that the choice of the optimization parameter has a significant impactonthecontrollerperformance.Asintended,usingJ₁results inan overallincreaseinpressureamplitudethroughouttheentire operationduration.Simultaneously,theadjustmentoftheinjection trajectorybythecontrolalgorithmleadstoanincrease intheho- mogeneityoftheignitionevent.Fromthis,itisobservedthatlarge pressure amplitudes tend to correlate with an increased ignition homogeneityasindicated by theoveralldecreaseinthe variation oftheobservedignitiontimes.Thesecondapproach,whichfocuses on directly minimizing the standard deviation of the observed ignitiontimes,turnedout tobelesseffectiveandroutinelyfailed to monotonically decrease the cost function. Here, a significant increaseintheignitionhomogeneityisonlyobservedfromcontrol step 3 to 4, and from 7 to 8, respectively. Simultaneously, this decreaseinJ₂ iscorrelatedtoaclearincreaseinthepressuream- plitude,whichagreeswellwiththefoundcorrelationformeasure-

Fig. 6. Maximum pressure measured by pressure sensors P1–P4 (black line) and standard deviation obtained by ionization probes I1–I7 (red line) for each control step averaged over 30 cycles when minimizing cost function J 1a) and J 2b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7. Maximum pressure over standard deviation of the ignition timing for each cycle optimizing cost function J 2. The chosen control steps 1, 4, 3 and 7 represent a broad range of values of the cost functional. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

mentwithJ₁.However, controlsteps3and7resultinlesshomo- geneous ignitions with aminor increase inpressure. Presumably, thecontrollerperformancebecomesmoresensitivetostochasticity ofthe systemwhen applyingcostfunctionJ₂,whichmakesit in- capableofconvergingtoasolution.However, inwhatfollows,the resultswillhelptoshedmorelightupontheunderlyingprocesses.

To better understand the causality of the applied control tra- jectory andthe resulting ignition behavior, four example control steps (1,3,4and7) fromFig.6bthatdistinctlydifferintheirob- tained pressure amplitudesare furtherexamined. The correlation betweenmaximum pressureamplitudeandstandarddeviationof theignition timeisshowninFig.7foreach cyclewhenapplying therespectivefuelinjectiontrajectories.Asmallstandarddeviation in

τ

io,jindicatesamorehomogeneousignitionwhichiscorrelated toa greaterriseinpressure.Althoughthereisanotablecycle-to-

cycle variation for a given injection trajectory, a distinct shift of thedata pointsby theapplicationofdifferent trajectoriescan be observed.Forexample,thetrajectoryinjectedduringcontrolstep4 resultsinamorehomogeneousignitionandhigherpressurescom- paredtocontrolstep3or7.Additionally,bothinjectiontrajectories arescatteringthroughoutthex-axis,whichwillbediscussedlater.

Controlstep1showsintermediatevaluesforboth,pressureampli- tudeandignition homogeneity.Thecycle-to-cycle variationisas- cribedtoastochasticprocess thatcannotbe predicted.Therefore, thecalculationofthecostfunctionbasedoncycle-averagedvalues isnecessary.

Tofurther investigate theresults, the respectivefuel injection trajectoriesappliedbythecontrollerarecorrelatedtotheobserved ignition characteristics.For this, the estimatedfuel concentration distribution inside the combustor at the time of the ignition is

Fig. 8. Applied fuel injection trajectory (black), calculated fuel profile using the simulation tool (shaded area) and gradient in concentration (red) for each control step. The simulation time was set to match the respective ignition timings. The average number of open valves during the injection duration representing the global fuel mass flow in one cycle is indicated. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

determined by applyingthe previously introduced 1D simulation tool. Figure 8 visualizesthe injected trajectories foreach applied controlstepshowninFig.6b.Thefueldistributionisvisualizedby the shaded area. The average number ofopen valves duringthe injection period, represented by a horizontal dashed line, varies between 6.2 and 8, which corresponds to the restriction of the total number of open valves.The red lineshows the gradient in fuelconcentrationalongthetubeaxis.Aconstantinjectiontrajec- torywithseven valvesopen(controlstep1)isgivenasastarting point for the controller, resulting in a broad region of gradually increasing fuelconcentration along thetubeaxis.As thefirst op- timization step (control step 2) the controller increasesthe total fuel mass flow ratewithout changing the shape of the injection pattern.Thisleadstoanincreaseinthemaximumpressure,while resulting insimilar values forthestandard deviation ofthe igni- tion timing, asshown in Fig.6. The injection trajectory for con- trol step 3 differs remarkably from the previously applied cases.

Theresultingfuelconcentrationprofilecontainstwodistinctmax- ima anda localminimum inthe centerof the profile.As shown in Fig.6, the measured datareveals agreatly reduced maximum pressure.Theapplicationoftheinjectiontrajectoryincontrolstep 4resultsinthehighestmeasuredincrease inpressurewhilehav- ingthelowesttotalfuelmassflowratetogetherwithcontrolstep 3.Theignitiontimingsindicateamorehomogeneousignition.The fueldistributionischaracterizedbyasingledistinctpeakfollowed byaregionwithasmoothdecreaseinfuelconcentration.Thisin- ducesagradualincrease infuelconcentration alongthetubeaxis inside the combustor. Control step 5 induces a very large maxi- mumvaluewithrathersteepgradients.Thisdistributionresultsin a significant decreasein pressurecompared tocontrol step 4,al- though a highvalue ofaveraged numberof open valvesleadsto large amountofinjectedfuel.Controlstep6hasafirst ’bump’in fuelconcentrationfollowedbyadominantglobalmaximum.Com- pared to control step 5 the total fuel mass flow rate is slightly lower. Nevertheless, there is a notable increase in pressure with a slightincrease inhomogeneity.The fuel concentrationdistribu- tion forcontrol step 7showssimilar features asthe controlstep 3 althoughtherespective injectiontrajectories differsignificantly.

Therefore,bothcasesresultincomparableignitionbehavior,asin- dicatedbythesimilardistributionsoftherespectivedatainFig.7. Most likely, the downstream peak in fuel concentration triggers an earlyignition leadingto apressurewave thatdoesnot couple

withtheflamefront.Thesecond peakignitesonlyafterthepres- surewaveinitiatedbythefirstflamefrontpropagatesthroughthe mixture.Bythis,noaerodynamicconfinementisachievedandthe mixtureundergoes adeflagrativecombustion.Moreover,the loca- tionofthe ignitionfronts atmorethan oneseparate locationsin thetube resultin thedetectionof eitherone flame frontor two subsequentlyappearingflamefronts,whichexplainsthescattering inignitiondelaytimeasearlierobservedinFig.7forcontrolsteps 3 and7.In contrast,the fuel profile withone distinct maximum followedbyaregionofgraduallydecreasingfuelconcentration,as achievedincontrolstep4,resultsinamorehomogeneousignition, andthus,inasignificantlyincreasedpressureamplitude.Allthese observationsreveal that by adjustingthe fuelinjectiontrajectory, the gradient in fuel distribution inside the combustion tube can becontrolledsuchthatmultipleignitionkernelsareinitiatedlead- ingtoaquasi-homogeneousautoignition.Thetotalfuelmassflow rateandthemaximumlocalfuelconcentrationare foundtohave aratherminorimpactonthepressurerise.Furthermore,thecon- trolalgorithmisagoodapproachforcycle-averagedoptimization.

However, in orderto achieve a reliable controller performance, a suitablecostfunctionisvital.

3.3. Detailedanalysisofdistributedautoignition

In the previous section, it was observed that the cost func- tionJ₂,byattemptingtominimizethevariationinignitiontiming, generatedseveral fundamentally differentignitionphenomenaby theapplied injectiontrajectories.Althoughthe final goalofpres- suremaximization was missed,the obtainedresults can be used tostudy theunderlying processes.Inthis part,adetailedexami- nationofsingleignitioncycleswithrespecttothechemilumines- cence,pressure,andionization measurementsis investigated.The objectiveistogainabetterunderstandingoftheignitionphenom- enaandhowtheycontribute tothe groupingorscatteringofthe individualeventsasdiscussedinFig.7.Forthis,thepreviouslyap- pliedtest rigis modifiedto allow for theoptical examination of underlyingaspectsthattriggerdifferentmodesofautoignitionand how those are distinguishable in terms of pressure and ignition characteristics.

The ignition behavior isexamined based on four differentin- jectiontrajectoriesasshowninFig.9.Thesetrajectorieshavebeen chosen since the predicted fuel distributions in the combustor

Fig. 9. Applied fuel injection trajectory (black), calculated fuel profile using the simulation tool (shaded area) and gradient in concentration (red) for four example injection trajectories. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. Maximum pressure rise over standard deviation of the ignition timing for curve green, blue and red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

showsimilarcharacteristicsthatwerefoundintheoperationwith the cost functionJ₂. Theair massflow rateofm˙_air=30kg/hand the temperatureof T_air=1023 Kare set to matchthe conditions for measurements with the controller. Due to the low heat con- duction property of the quartz tubes compared to the stainless steel combustor, a slightly decreased temperature is observed in the combustor. However, the goal is not to exactly replicate the measurements conductedintheprevious sectionbutrathertoin- vestigate fuel injection trajectories that are similar to those ob- servedinthecontrolleroptimization.

The appliedfuel injectiontrajectoriesresemblethefuel distri- bution derivedfromcontrolsteps1,3,4and7thatarediscussed in theprevious section (see Fig.8 highlighted ingreen,blue and red).Thecorrespondinginjectioncurvesarevisualizedinthesame colorandreferredto asgreen,blueandredcurve inthissection.

The graycurvewillbe discussedlater. Whencomparingthe igni- tion behaviorofthechosencurvesto therespectivecontrolsteps (showninFig.7)withregardtothecycle-to-cyclevariation,asim- ilarcorrelationbetweenthemaximumpressurepeakandthestan- darddeviationoftheignitiontimingisobserved(showninFig.10).

An increaseinmaximumpressuregoesalong withan increase in ignition homogeneityindicated by the decreasing standard devi- ation in ignition time. Here,the green curve indicates a lessho- mogeneous ignitionand, thus a minorrise in pressure compara- bleto controlsteps3and7.Thered curveignitesmorehomoge- neouslyleadingtonotableincreaseinpressureamplitudewhichis comparableto controlstep 4.The bluecurve showssimilarchar- acteristic as the control step 1 and can be assigned somewhere inbetween.Thisisaclearindicationthatthesespecifiedtrajecto-

riesarerepresentativeoftherespectivetrajectoriesappliedbythe controller.

Inthefollowingfirst,singlecyclesobtainedfromthreeexample fuelinjectiontrajectories(green,blueandred,asshowninFig.9) arecompared.Later,threecyclesobtainedfrominjectingthegray fuel trajectory will be compared allowing forthe examination of stochasticity.

ForeachcurveoneexamplecycleisshowninFig.11.Twonor- malized x–t diagramsare shownrepresenting the temporal evo- lution of the CH^∗ (first column) and OH^∗ (second column). For this, each snapshotis averaged over the tube diameter resulting in a one-dimensional array. The third and forth columns repre- sentthetime-resolved,CO₂^∗ correctedchemiluminescencesignals at a wavelength of 307 and 430 nm obtained by the PMTs and thepressuretracesforeachcycle.Column5showsthedatamea- sured by the spectroscope.Due to a limited sampling frequency of the spectroscope, the data is accumulatedover the entire ig- nition event, and is not time-resolved. The obtained peaks are thereforenot quantitativelycomparabletothedataobtainedfrom PMTs and high-speed imaging. In order to compare the tempo- ral evolution ofthe ignitionobtained fromtwo-dimensional data totheone-dimensionalmeasurements, fivedatapointsinthex–t diagrams atthe respective position of the optical sensor are av- eraged resulting in a 1D array. The resulting time-resolved data (white line) as well as the uncorrected PMT data (dotted line) are overlayed in the x–t diagrams. For convenience, the fuel in- jectiontrajectory isvisualized inthebottom left foreachsample shot.

When comparing the one-dimensional temporal evolution of the chemiluminescence data obtainedfrom the uncorrected PMT

Fig. 11. Three example cycles for injection curve green (top), blue (middle) and red (bottom). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

data to the x–t diagrams, it can be seen that both are in good agreement.Thisisagoodvalidationofthemeasurementmethod- ology and revealsthat both, PMTandhigh-speed imaging, result in similar measurement signals. The two-dimensional snapshots are impacted by CO₂^∗ chemiluminescence in the background, which has to be considered when interpreting. Comparing the pressure tracesofeach cycle, itcan bestatedthat the maximum obtained pressure rise applying the green is the lowest and red curve is the highest. The blue curve can be categorized in the intermediate range. Similar behavior regarding the shape of the fuel distribution andthe resulting maximum pressure amplitude wasobservedinthecontrolleroptimizationforcontrol steps1,3, 4and7,respectively.

Two propagating flame fronts can be observed when ap- plying the green curve (see Fig. 11a). The shape of the fuel concentration distribution is characterized by two spatially separated maxima. These peaks ignite inside the combustor at two different ignition times and locations initiating two propagating flame fronts. Both flame fronts propagate through the reactive mixture independently leading to a non-confined volume and therefore a low pressure amplitude. When com- paring the temporal position of the first pressure peak to the temporal positionofthefirst peak inthePMTdata,an increased time delay can be observed. This agrees well with the previ- ous observation shown in Fig. 10 in which an increased time delay is associated with a less homogeneous autoigni- tion/deflagration. The pressure traces reveal three independent pressure rises corresponding to each individual ignition event and a downstream propagating pressure wave reflected at the combustor inlet.Bothflame fronts are characterized bythe pres- ence of CH^∗ and OH^∗. In general, the simultaneous presence of CH^∗ andOH^∗ is an indicator ofthe reaction zone. When further investigating thePMT data,itcan be seen that thesecond flame frontischaracterizedbyastrongpeakintheCH^∗data.Thiscorre-

lateswiththe larger propagationvelocity than thefirst observed flame front, which is linked to an increased reaction rate. The second increaseinOH^∗ ismoregradual andremainsfora longer periodoftimecomparedtotheemittedOH^∗bytheprimaryflame front.OH^∗withoutthepresenceofCH^∗,asvisibleinthePMTand x–t data, is considered cold OH^∗ and is characteristicfor purged exhaust.

Theignitionobservedforthebluecurve(seeFig.11b)ischarac- terizedbyafairlyhomogeneousignitionwhileshowingaconsider- ablespatialvariationinCH^∗andOH^∗chemiluminescencealongthe combustoraxisindicatedbythex–t diagrams.Thepressuretraces revealaslightincreaseinthepressurepriortothemainpressure peak,whichoccursbeforethedetectionofCH^∗andOH^∗chemilu- minescence.Potentially,a firststage ignitionis takingplace lead- ing toslowrise inpressure.Terashimaetal.[13]numericallyin- vestigatedtheroleoflow-temperaturecombustioninend-gas au- toignitionandpressurewave generation.Theyfound outthatlow temperature combustion in DME–air mixtures leads to a consid- erable heat release rate which is correlated to the formation of CH₂Oandpromotespressurewaves.Iftheheatreleaseofthefirst stage ignitionislarge enough,a transitiontoHTCis likelyto oc- cur. This two-stageignition behavior was further investigatedby Savard etal.[11].Theirresultsreveal thata reducedreactivityin theproducts ofthecoolflamecanlimit subsequentHTC.Thus,if LTC isobserved overan extended time frame withouttransition- ingintoHTC,thehot flamespeedisretardedduetothedecrease inreactivityofthe coolflameproducts. Inthe presentcycle,this decreaseinreactivitypriortoHTC,whichisindicatedbyOH^∗and CH^∗chemiluminescence,leadstoalimitedpressureincrease.How- ever,thiscannotbedefinitivelyverifiedinthechemiluminescence dataduetoweakchemiluminescenceofformaldehydewhichisan indicatorforthefirststageignition.Futureworkisplannedtofur- therinvestigatetheroleofformaldehydeintheobservedignition phenomena.