LES of CH4/H2/AirTurbulent Non-Premixed Flame

E. Giacomazzi∗, B. Favini†, C. Bruno†,F.R. Picchia∗, N. Arcidiacono∗

∗ENEA - C. R. CasacciaSec. ENE-IMPRome, Italy

†University “La Sapienza”Dept. Mech. and AeronauticsRome, Italy

European Combustion Meeting

25-28 October 2003Orléans, France

LES of�������������� ��

Turbulent Non-Premixed Flame

EugenioGiacomazzi��� , B. Favini � , C. Bruno� , F. R. Picchia� , N. Arcidiacono��ENE-IMP, ENEA - C. R. Casaccia,S.P. 081

Via Anguillarese,301- 00060- S.Mariadi Galeria,Roma(Italy)�Departmentof MechanicsandAeronautics

Universityof Rome“La Sapienza”Via Eudossiana18,00184- Roma(Italy)

AbstractWe perfomedLarge Eddy Simulationof a bluff-body stabilizedflame( ��������� � � �"!$# ) usingthe Fractal Model as%'&(%

model.Resultsshow thattheflameis stronglyunsteadyandthree-dimensional,mainly within therecirculationzone. Irregulareddiesareshedfrom the jet at differenthigh frequencies,while larger structuresareshedfrom theouteredgeat regular lower frequency. Intensestretchingin the neckregion of the flameproduceslocal extinction.Although the fastchemistryusedin the simulationis a too crudeassumption,resultingin a flameshorterthantheactualone,resultsevidencecomplex interactionbetweenchemistryandturbulence.

Introduction) �"* % ��+,�"* %(Reynolds or Favre Averaged

Navier Stokes) turbulent closureshave beenfor manyyears the only tool to numerically simulate complexflows of practical interest,but it is not suitablefor thesimulationof any problem:

) �"* % ��+,�"* %modeling

hasintrinsic limitations dueto its modelingof all scalesin the sameway. Today -/. %

(LargeEddy Simulation)seemsto betheanswerto this problembecauseit explic-itly computesthelargeststructuresof theflow (typicallystructureslargerthanthemeshsize)andmodelsonly theeffects of the small onesby meansof

%'&(%(Sub-Grid

Scale)modelsthatcanbemorephysicalandflexible clo-sures. At the extremeof numericalsimulationthereis0 * %

(Direct NumericalSimulation),but it canbeusedonly for “academic”flows.

Nowadays-/. %is widely usedfor practicalapplica-

tions,showing its power to provide multi-scaleinforma-tionandtocapturethedynamicsof aturbulentflow. -1. %resultsareimpressive; detailed,steadyandunsteadyex-perimentalmeasurementsare necessaryto validate the%'&(%

modelsassumed.The bluff-body burneranalyzedin this work [1]-[10] is a goodtestcaseto validatethesemodels: it has a simple geometry, with well definedboundaryconditions;it hascomplex flow patternssimi-lar to thosefoundin practicalcombustors;andit involvescomplex physicsrelatedto flamestabilization,localizedextinctionsandreignitionzones,providing a meanto an-alyzechemistry- turbulencecoupling. In this paperwe

perform -1. %of the proposed��� � ��� � �2�3!4# turbulent

nonpremixedflameassumingthe FractalModel +(5 as%'&(%closurefor turbulentcombustion.

Test Case DescriptionIn this work we analyzethe bluff-body burnerstud-

ied experimentallyat the University of Sydney [1]-[5],andnumericallyby differentgroups[6]-[8]; thedetailedmeasurementsrelatedto thisburnerareactuallyincludedin the Sandiadatabase[9], andareavailableon the web[10]. The burner consistsof a 6�798:8 diameter(

0<;)

bluff-body madeof brasswith a =?> @"8:8 centralfuel jet(0BA

). Theburneris unconfinedandcentredin awind tun-nelwhereair with a freestreamturbulenceof around

�DCflows. Thefaceof thebluff-bodyhasa E�> F�8G8 thick ce-ramic layer to withstandthehigh flametemperatureandto reduceheatlossesto thebodyof theburner.

This burner hasbeenexperimentallystudiedat dif-ferentconditionsandusingdifferentfuels. In this workwe numerically simulatethe following reactive condi-tion. The central jet is a fuel mixture H��IH (in volume)of ��������� � at HJHLKM8N�PO (bulk velocity) andthe coaxialjet is air at

� 738Q��O . Thestoichiometricmixture fractionis 7?> 7J6 and the adiabaticflametemperatureis

�P� @J6�R .Thejet Reynoldsnumbercalculatedwith thebulk veloc-ity, the jet diameterand the fuel kinematicviscosity, isS HT=J6�7J7 . The flame is at 6P7 C of the blow-off veloc-ity ( S � =J@�8N�PO ) which is obtainedwhentheflamestartsto extinguishintermittentlyin theneckzonedownstreamU

Correspondingauthor:eugenio@pcmerlino.ing.uniroma1.it Proceedingsof theEuropeanCombustionMeeting2003

of the recirculationzonewhich remainsburning stably.It wasfoundthat localizedextinctionsstartto happenatS @ ��C [3] of theblow-off velocity.

Dependingonthefuel-jetandcoflow-air velocitiesaswell asthe ratio

0<; � 0BAbetweenthebluff-body diame-

terandthecentralfuel-jetdiameter[11, 12], therearetwotypesof bluff-body stabilizedflames: fuel-jet dominantandcoflow-air dominant.Thisflameis fuel-jetdominant;it is characterizedby a stabilizingrecirculationzonefol-lowedbyaneckzoneandthenbyaburnoutregionfurtherdownstreamwheretheflamepropagatesin ajet-likeman-ner. At highenoughjet velocity, intenseturbulentmixingdevelopsin theneckzoneof theflameleadingto localex-tinction in this region; thereforethe neckzoneprovidesa meanto analyzefinite chemistry- turbulencecoupling.Stableburning exists further downstreamaswell in therecirculationzone.Stability characteristicsof this burnerareplottedin [2].

Numerics: Schemes, Boundary Conditions, GridTo simulate the bluff-body flame chosenwe used

our own codeparallelizedusing the 5WV,X procedures.Weimplementedathird-orderRunge-Kuttaexplicit time-steppingschemeandsecond-ordercentraldifferencingtonumericallyintegratethecompressible,reactive,Navier-Stokesequations.In this way we cantake into accountacousticseffect. Thestability conditionsimpose HL7IY�Z1Oastimestep,increasingthecomputationaltimebut allow-ing to resolve the high frequenciestypical of chemicalreactions.

Our calculationdomain has three zones: the mainzone, where combustion takes place, has the exit at� 7P7(8:8 downstreamof the bluff-body face; the othertwo inlet zonesare 6�7B8G8 long. The radial extensionis E�6B8G8 ( = 0�; � � ), wherethe coflowing air is undis-turbed on the baseof the experimentalmeasurements.The grid is structured. The numberof grid nodesare=J7P@,[NH � @([\= � , KJ7([QHJH3[]= � and KP7([]6P@([]= � , respec-tively for the main combustionzone,the fuel inlet zoneandthecoflow air zone.Numericalsimulationsshown in[5] have inlet conditionsspecifiedHT7P7^8G8 upstreamofthe faceof the bluff-body; the computationaldomainisextended=P7J7/8:8 downstreamof thebluff-bodyandhasaradialextensionof E�718:8 from theaxis.

As boundaryconditionswe assumedthe * % ��_9�method [13] (Navier-Stokes CharacteristicBoundaryConditions)at the inlet and outlet; this methodis nec-essaryparticularly at the outlet becauseit avoids largereflectionsof acousticswaves inside the numericaldo-main. At theoutletthepressurerelaxesto H/`Dab8 . At theinlet wespecifiedvelocity, temperatureandcomposition.Westressthattheexperimentalists[9] providedonly bulkvelocitiesandprofilesdownstreamof theexit; thesedata

arenotsufficient for goodspecificationof the -1. %prob-

lemat theinlet. At themaximumradialdistancefrom theaxis we assumeda slip condition; this assumptionis acrudesimplificationbecauseit makesthesimulatedflowconfined,whilst in factit is not.

We startedthesimulationwith aninitial still air fieldand forced transition to turbulenceoverimposingsomedisturbances,turnedoff aftertransition.

SGS Modeling+(5 [14, 15] is a%'&(%

modelbasedon fractal the-ory: it generatesa self-similarvortex/energy cascadeineachcell of a ��+ 0

domain. On the basisof the localReynoldsnumber

)�c�d�egf'dih ��j d , the energy . (perunit of mass)is transferedfrom the local scale

h(char-

acteristicof the cell dimension)down to *9k dissipativescalesl :. dm donp*BkMq . km ksrt u�vdh np*9k"q�j�k u �kl � (1)m d is the eddyturnover time of scale

h( n h � f'd

), m kis thedissipative time ( m k e l � �Pj�w ), j�k is thekinematicviscosityin the l structuresand u k theircharacteristicve-locity. Recallingthat

)�c k e u k�lx��j�k e H , thedissipativescalel is eventuallygivenby:

l e * �zy �k q|{ j kj d�} v y � q h)�c v y �d (2)

The ~b� d valuesare the filtered valuesin the cell, whilethe ~b� k arethesubgridvalues. +(5 assumesthat chem-ical reactionstake placein the “fine structures” l , andtherefore,their statewill bedifferentfrom the“filtered”stateof thecell; in particular, theterm �4j�kP��j d�� v y �

canbeof order HL7 . Detailsabouttheestimationof *9k (numberof dissipativescaleslocally generated)arein [14].

By the definition of l in eqn. (2), +(5 canpredictthe growth of the dissipative scalewith increasingtem-perature.Therefore,the +(5 “feels” andadaptsitself tothe local turbulenceregime. Where

h ��l e H themodelmustturn itself off (becausethelocal scale

his dissipa-

tive),enablinglocal0 * %

. This typically happensin thehottestreactingzoneof theflow. Where

h ��l���H , +(5modelssubgridturbulent stressesby meansof an “eddyviscosity” ��� , thatgoesautomaticallyto zeroin laminarregionsandin particularat walls [15]:

� � e�� qL*BkMq2� d�e�� q�� Y � q2� d q/��{ h l } � r H ��> (3)

where�

is thesoleengineering“calibrationconstant”ofthemodel,assumed7x>�H in thepresentsimulations.

2

+(5 treatsthereactive“fine structures”asaPerfectlyStirredReactor( V % )

); thisideais derivedfrom theEddyDissipationConcept( . 0 � ) of MagnussenandHjertager[16, 17]. Thisreactoris characterizedby aresidencetimem�� , assumedequalto thelocal “dissipativeeddyturnovertime” m k , and by a volume fraction � � (in each ��+ 0cell) [15]. � � is estimatedby meansof the local fractaldimension

0 v ,� �3� { h l }^��� Y v > (4)

Whereh ��l���H the local scale

his dissipative; no

modeling is locally appliedand therefore � � e H andthe local filteredandsubgridquantitiescoincide.Whereh ��l���H theheatreleasedby thechemicalreactionsin-sidethevolumeoccupiedby the“fine structures”is nat-urally modeledas a subgrideffect. The Favre filteredsourcetermsin the * speciesandenergy equationsaregivenby (accordingto theEDCmodel[16]):���� e � � � �� (5)

and ���  e¢¡£ ��¤ � � � � �� h<¥�¦§©¨(6)

where� �� is theinstantaneousproduction/destructionrateof the chemicalspecies! inside the reactor(given bytheArrheniusexpressionsof thechemicalmechanismas-sumed),and

h<¥ ¦§ª¨is theformationenthalpy of the ! r a ¥

species. � �� dependson the stateof the reactor, whichis definedby its concentrations« �� , temperature¬ � andpressure.We estimate« �� and ¬ � assumingthat 1) thepressureinsidethereactoris constantateachtimestepofthenumericalcalculation,andthepressure­ � in thereac-tor equalsthefilteredpressure

�­ in thecell; 2) thereactormassvariesin time,but is constantduringeachtimestep,andreactantsareperfectlymixed; 3) the local reactorismodeledasa steadyV % )

, closedandadiabaticat eachtimestep.

We solvemassandenergy equationsfor thereactor:« �� e �« ��® �ªH r � � � m��¯ � � �� (7)

and ¬ � e �¬ ® m�� �ªH r � � �¯ � � �° ¡£ �±¤ � � �� h<¥ ¦§ª¨(8)

WeobservethatassumingaclosedV % )meanstone-

glectthediffusivetransportin the“fine structures”,wherethemoleculartransportsareimportantinstead;moreover,we neglect the dynamicexpansionof the reactingstruc-turesdueto thehot products,which would have relevant

effect on the local divergenceof velocity (we will showanadvancedreactormodelingincludingtheseeffectsin afollowing paper).

Transport Properties and ChemistryAll moleculartransportproperties,exceptmassdif-

fusivities, arecalculatedby meansof kinetic theoryandusing look-up tablesand interpolationtecqniqueto re-ducecomputationtime. Weassumedthesamediffusivityfor all the speciesandcalculatedit by meansof a con-stantSchmidtnumber. We stressthatalthoughmixturesof fuelswith differentdiffusivities, suchas � � , �,² and�,² � , areexpectedto experiencesignificantdifferentialdiffusioneffects,resultsin [18] show that this is not thecasefor suchflameseven at modestjet Reynoldsnum-bers.Theeffectsof differentialdiffusionareexpectedtodecreasewith

)Mc Y �©y³� [19]; therefore,they arerelevantinlaminarflamecalculationsandat subgridlevel.

Experimentsandnumericalsimulationsin [8] showedthat the fastchemistryassumption(or flamelets)maybeadequateto computethe meantemperatureandcompo-sitionsin therecirculationzonedownstreamof thebluff-body. This hasbeenjustified following a thoroughin-vestigationof thereactivescalarstructure,whichshowedminor departuresfrom equilibrium [3]. Furtherdown-streamtheflameexperiencessomelocalizedextinctions;thereforedetailedchemicalkineticsis needed.

In ourcalculationsweestimatechemistryin thecrud-estway; in thenearfuturewewill assumeamoredetailedchemistryto take into accountextinction phenomena.Inparticular, for hydrogenoxidationweassumedfastchem-istry controlledby subgridturbulentmixing, accordingto. 0 � expression[17]:���´¶µ �) ´ e ¯D· � �m � �ªH r · � � � �« ´J¸ ¨º¹ (9)

where�« ´ ¸ ¨º¹ e 8:!4»½¼ �« ´�¾ �«�¿ÁÀ���# ´� is theminimumfuel

massfraction ableto react, # ´ beingthe oxidantto fuelmassratio ( K in caseof hydrogen).

For methaneoxidation we assumedthe single stepmechanismof WestbrookandDryer [20].

ResultsTheflameis characterizedby a stabilizingrecircula-

tion zonefollowedby a neckzoneandthenby a burnoutregion furtherdownstreamwheretheflamepropagatesina jet-like manner. Experimentsshow that the flame isverystableandhasavisible lengthof S � 7 0<;

( S H|8 );measurementsare only taken at axial locationsextend-ing to

� > � 0<;[2]. The recirculationzone extendstoS HJ> @ 0<;

( S KP7�8G8 ).

3

Fig. 1: Averagedtemperaturedistribution and streamlinesinside the recirculationzone downstreamof the bluff-body.The time window used for computing the averagedfield isöÄ�ÅTÆ Ç�ÈIÉ�Ê , insufficient to have a symmetricfield.

Wewantto stressthatdueto thefastoxidationmech-anismsassumed,our simulatedflamewill be inevitablyshorterthan the actualone; in fact, chemicalreactionshappenwithin S =P7P7Á8:8 from theinjectionin oursimu-lation. Anotherpoint to stressis thatwe useda too short

time window ( S @"8NO ) for statistics,i.e., for computingaveragedquantitiesand

) 5 %fluctuations;the lack of

symmetryin theaveragefield shown in Fig. 1 marksthispoint.

Recirculationzonestabilizestheflameby circulatingthe hot productsbackto the injectorexit planeandpro-viding acontinuousignition sourcefor theflame.Instan-taneouspicturesof this region areshown in Fig. 2. Thecold jet penetratesthrougha hot lower densitymediumandshiftsthestagnationpointfurtherdownstreamthaninthenonreactivecase[2, 3]; this shifting, i.e., thedecreas-ing of the meanvelocity decayrate, hasalso beenob-servedby Sheferet al. [21] in anotherbluff-bodyburner.

A time averagedview of the recirculationzoneob-tainedfrom measurementsindicatestheexistenceof onelargevortex ontheouteredgeandasecondnarrowervor-tex closeto the jet centerline[1]. Experimentsshowedthat the inner vortex exists only at low jet momentum[3]. The structureof the recirculationzoneis similar tothatfoundin isothermalbluff-bodyflowsatrelatively lowjet momentum[2], andto thatwe have alreadyfound inotherbluff-bodyflames[15, 22]. Therearethreemixinglayersin the recirculationzone[3, 5] identifiedby threeplateauxin the

) 5 %fluctuations,the third having the

highestpeak: accordingto measurementsthe first is at�P� 8:8 from the centerline,the secondat K r HL7,8:8 ,andthethird betweentheinnervortex andthefuel jet [5].

` ËFig. 2: Instantaneoustemperaturedistributionsandstreamlinesinsidethe recirculationzonedownstreamof thebluff-body. Thedelaytime betweenthetwo framesÌ and Í is ÃÎÆLÏ ÐiÅTÆÑÇ È�É Ê .

4

Looking at our computedaveragedfield, shown inFig. 1, wecanseethetwo vortices,but they haveroughlythe samesize; the length of our averagedrecirculationzone is S H 0 ;

, smaller than the experimentalone,S HP> @ 0 ;. The disagreementin the averagepicture is

probablydueto thetoosmalltimewindow ( S @�q2HL7 Y v O )that we usedfor statistics.We stressthat, in fact, someinstantaneousfields (seeFig. 2) arein betteragreementwith experimentaldata: the eddiesconstitutingthe in-stantaneousrecirculationzoneextendup to S HP> @ 0<;

.Also the threemeasuredshearlayerslocationsdisagreewith our averagedpredictionsbut agreewith the sameinstantaneouspicturesshown in Fig. 2 (tracingan idealhorizontalline at Ò S � 7�8G8 ).

Our simulationshows that the recirculationzonehasacomplex dynamics.Theoutertoroidalvortex is initiallysymmetric(seeFig. 2). Theevolution of the innerrecir-culationzoneis stronglythree-dimensionaldueto irreg-ular eddiesshedfrom theedgeof thejet at high frequen-cies( S E�FJ7"ÓpHT@P7J7���Ò ); theseeddiesenlargeandbreakthemselvesinto smallereddies,pushingtheoutervortexdownstream. While the outer initially regular vortex isbeingshed,it is stronglydeformedby the inner eddies,and its sheedingbecomesasymmetricwith a frequencyof ²<�©HL7J7 � ��Ò . Outervortex rotatesfrom theair sideto-wardsthecenterof theburnerandproducesentrainmentof the recirculatedflow into the air stream;the fuel-airmixing within therecirculationzoneis mainlycontrolledby theinnereddies.

Someirregularrolling eddies,withoutaregularshed-ding frequency, have beenalsoexperimentallyidentifiedon theinneredgeof theoutervortex [4]; thestreamlinesin Fig. 2 show thesestructuresinteractingwith thecoldjet and with reactingzones. Experiments[4] also re-vealedthat from the outer edgeof the burner thereareregular, periodiccoherentstructuresshedatacertainfre-quency, not reportedin [4]. Theouterlargevortex is in-termittentatthisoperatingcondition,affectingmainlytheflamestability andburningpattern;experimentsshowedthat it is not intermittent for higher fuel jet velocities.Also other authorsobserved vortex sheddingfrom theouteredgeof bluff-bodyflames[11, 23].

In the outer region the gradientsare very steepandthe scalardissipationratesarehigh; the missingof ²��in theinstantaneous-1XJ+ imagesin [4] indicatesthattheflameis intermittentcloseto theburnerexit within there-circulationzoneandsometimesis lifted from thejet exitplane[3]; this is in agreementwith Fig. 2. Therefore,thehigh temperaturesdetectedcloseto the burner are dueto the recirculatinghot products. The high gradientsinthe outer region lead also to artificially lower averagesof measuredtemperatureandreactive speciesmassfrac-tions. This is confirmedby temperaturescatterplots in

[3], showing theimportanceof extinguishedandburningparcelsin the averaging[24, 25, 26, 27]. Moreover, thehigh instantaneousvelocity gradientsacrossthe bound-ariesof theadjacentlargescalestructuresproduceanin-creaseof turbulencelevels insidethe recirculationzone,asmeasuredin [21].

Instantaneoustemperaturefields show simultaneousreactionzoneswithin the recirculationzonedue to thestrong three-dimensionalmixing of the inner vortices.This is confirmedby instantaneousmeasurementsof re-activescalarswithin therecirculationzone[4]. Unsteadyresultsshow eddiesstretchingtheflame;theseparatedre-actionzonesareconvecteddownstream,andcloseto theendof the recirculationzonethey mergeinto one,broadanddistributed,with someislandsof unreactedfreshmix-tureor cooledcombustionproducts;this is confirmedbyexperiments[4]. After this broadreactingzonebecomesa flat front at Ò S HP> K 0<;

; unburnt reactantsburn insidethis front while it propagatesdownstream;this makesdownstreamjet region leaner, resultingin the radial ap-proachingof theconicaljet flamefront closeto theaxis.Intensestretchingdevelopsin theneckzoneof theflameafterthepassageof theflat front, leadingto local extinc-tion andtemperaturedecreasing.

ConclusionsThebluff-bodyflameanalyzedhasastabilizingrecir-

culationzone,aneckzoneandaburnoutregionwheretheflamepropagatesin a jet-like manner. -1. %

resultsshowthattheflameis stronglyunsteadyandthree-dimensional,mainlywithin therecirculationzone.Irregulareddiesareshedfrom the jet at different high frequencies,mainlycontrolling fuel-air mixing, while larger structuresareshedfrom theouteredgeat regularfrequency.

It seemsthatthediscrepancy betweenthecalculationsat the momentavailable in literatureand the measure-mentsat downstreamlocationsin thejet andflame,maybe due to vortex sheddingon the outer (air side) edgeof the recirculatingregion. In our -/. %

simulationwecapturetheflow dynamics,but our fastoxidationmecha-nismsaretoo crudeto well predictexperimentaldata;inparticular, our flameis shorterthantheactualone.How-ever, resultsevidencecomplex interactionbetweenchem-istry andturbulence,showing alsolocalextinctionduetointensestretchingin theneckregionof theflame.

Theaveragepicturereportedin thispapersuffersof atoo small time window ( S @,qDHL7 Y v O ) usedfor statistics.The lack of symmetryindicatesthis point, and, in fact,someinstantaneousfields are in betteragreementwithexperimentaldata.

Moreover, the dataprovidedby the experimentalistsarenot sufficient to accuratelyspecifytheinlet boundaryconditionsof the -1. %

problem.

5

AcknowledgementsWe wish to thank the Informatic Dept. of ENEA

CasacciaResearchCenterwherewe performedcalcula-tion on theFERONIA Alpha/Linuxcluster.

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