26thICDERS July30th–August4th,2017 Boston,MA,USA

Correspondenceto:fureby@foi.se 1

OntheSupersonicFlameStructureintheHyShotIIScramjetCombustor

ChristerFurebyTheSwedishDefenceResearchOrganization

SE14725Tumba,Stockholm,Sweden

1 IntroductionandBackground

Understandingofthemulti-disciplinaryphysicalprocessesintheflow-pathofascramjetengineiscrucialfortheenablingofthistechnology,consideredthemostpromisingforhypersonicflight.Theflowinsuchenginesremainssupersonicthroughout,preventingthepressurelossesandstructuralchallengesinvolvedindeceleratingtheflowtosubsonicspeeds.However,thisnecessitatesthatthemixingandcombustionprocessesintheengineoccurwithinsupersonicflow,withresidencetimesofO(1)ms.Within thisshort time interval, the fuelandairmustmix, igniteandcombustprior todischargingthroughthenozzle.Laboratory,groundtestingandflight-testingexperiments,togetherwithhigh-fidelitynumericalsimulations,comprisethetoolsavailabletofillthegapinscramjetcom-bustorknowledge.Inthisstudy,wecombineresultsfromhigh-fidelityLargeEddySimulation(LES),using finite-rate chemistrymodels and skeletal reactionmechanisms,with experimentalpressuredata andvisualizationof the shock-train and theheat-release to elucidate thekey featuresof theflowoftheHyShotIIcombustor.WespecificallyfocusontheconditionsofexperimentsperformedintheHighEnthalpyShockTunnelGöttingen(HEG),emulatingflightconditionsat27kmaltitudes,[1].TheflamestructureischaracterizedusinganextendedWilliamsdiagram.

2 LargeEddySimulationModelsforSupersonicCombustion

TheLargeEddySimulation(LES)modelemployedisbasedonareacting-flowmodel inwhichthemixtureisassumedtobealinearviscousfluidwithFourierheatconductionandFickiandiffusion.TheviscosityiscalculatedusingSutherland’slawwhilethethermalconductivityandspeciesdiffu-sivitiesarecomputedfromtheviscosityusingconstantPrandtlandspeciesSchmidtnumbers.Themixture thermal and caloric equations-of-state areobtainedassuming that each species is a ther-mallyperfectgas.Thecombustionmodelisbasedonfinite-rateArrheniusreactionrates.

TheLESmodeluseimplicitly-filteredmass,momentum,energyandspeciesequations,[2],inwhichthesubgridstresstensorandfluxvectorsareclosedbythemixedmodel,[3].Thefilteredreaction-

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ratetermsaremodeledwiththePartiallyStirredReactor(PaSR)model,[4-5],whichisamulti-scalemodelbasedontheobservation,[6],thatcombustionoftentakesplaceindispersedfine-structureregionssurroundedbylowchemicalactivity.Here,thefilteredreactionratesareapproximatedasaweighted average of the fine-structure and surrounding reaction rates using the reacting volumefraction,γ*,astheweightingfunction.SubgridmassandenergyequationsaresolvedinallLEScellsfor both fine-structure and surroundingmass-fractions and temperature, using the fine-structureresidence time, τ*. Here, τ* and γ* aremodeled using the Kolmogorov, and global chemical time-scales,[4].TheLES-PaSRmodelhasbeenwidelyused,andisvalidatedforlaboratorycombustors,[7-8],afterburners,[9],gasturbines,[10],andscramjets,[11].

TheLESequationsaresolvedusingafully-explicit,density-based,compressiblefinite-volumecodebased on the OpenFOAM library, [12]. High-ordermonotonicity-preserving reconstruction of theconvectivefluxesandcentraldifferencingofthediffusivefluxes,[13],iscombinedwithatotalvaria-tiondiminishingbasedRunge-Kutta time integration scheme to result in a second-order accuratealgorithmwithaCourantnumberlimitationof∼0.2.Thechemicalsourcetermsareevaluatedusinganoperator-splittingapproachtogetherwithastiffRosenbrocksolver,[14].

Weusetheskeletal7-stepDavidenkoetal.(D7)reactionmechanism,[15],whichcomparefavorablywithcomprehensivemechanisms,e.g.[16],withrespecttotheadiabaticflametemperature,Tad,ig-nitiondelaytime,τign,extinctionstrainrate,σext,andlaminarflamespeed,su.Sensitivityanalysisre-vealsthatbothsuandσextaresensitiveprimarilytothechain-branchingreactionsH2+O⇔OH+HandH+O2⇔OH+OandtheinitiationstepH2+O2⇔OH+OH.D7capturesthissensitivitywell,andiscapa-bleofrepresentingtheexplosionlimitsofH2-airmixtures.

3 LESoftheHyShotIICombustor

ThecombustorconsideredistheHyShotIIcombustor,[1],experimentallystudiedintheHEGshocktunnel.Theflow-pathoftheHyShotIIHEGshocktunnelmodelduplicatestheflightconfiguration,[17] and consists of an intake ramp, a rectilinear combustor, and a single-sided exhaust nozzle.Here,wefocusontheHEGcombustorsection,showninfigure2,fromtestconditionXIII,[1],repre-sentingflightconditionsat28kmaltitude.Thecombustorhasacross-sectionof9.8×75.0mm2andalengthof0.3m,afterwhichaone-sideddiverging-areanozzleismounted.GaseousH2isinjectedor-thogonaltotheair-stream,havinganaveragevelocityof1720m/s,atemperatureof1350Kandapressureof127kPa,resultinginanequivalenceratioofφ≈0.28,throughfourφ2.0mmportholeMa1.0 injectors 58mm downstream of the combustor leading edge. The experimental data includeSchlierenandOH∗chemiluminescence,bodyandcowlwallpressuredata,andbodyheat-fluxdata,[1].Agridof∼100millioncells isusedwithclusteringatthecombustorwalls.Dirichletboundaryconditionsareusedforallvariablesattheinlet,withprofilesobtainedfromRANS,andattheH2in-jectors.Attheoutlet,allvariablesareextrapolated.Atthecombustorwalls,ano-slipLESwall-modelisusedtogetherwithzeroNeumannconditionsforallothervariables.

Figure2presentacompositefigureofthereactingflowintheHyShotIIcombustor.Thetwolargefigures,showingthefullcombustor,describetheflowintermsofaniso-surfaceofthesecondinvar-iantofthevelocitygradienttensor,λ2,coloredbytheaxialvelocity,vx,andthemixingandreactionprocesses in termsof volumetric renderingsof the temperature,T, and theH2O,OHandH2massfractions,YH2O,YOH,YH2,respectively.Thethreesmallfigures,showingasmallvolumearoundoneofthecentralinjectors,showaniso-surfaceofλ2,coloredbyvx,andsuperimposedvolumetricrender-ingsofH2O,OHandH2massfractions,andofthepressuregradient,∇p,andthechemicalexplosivemodeeigenvalue,λe,[18],describingtheshock-trainandthereactivestateofthemixture.

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Figure1.ReactingflowintheHyShotIIcombustorintermsofvolumetricrenderingsofthepressuregradient,∇p,chemicalexplosivemodeeigenvalue,λe, temperature,T,H2O,OHandH2massfractionsandiso-surfacesofthesecondinvariantofthevelocitygradienttensor,λ2,coloredbytheaxialvelocity,vx.

Theflowcanbroadlybedividedintoaninjectionandmixingregion,aself-ignitionregion,andaful-lydevelopedturbulentcombustionregion.The flow isgovernedby(i) fourhorseshoevortexsys-temswrappingaroundtheH2-jets,developinginfrontofeachinjectorasaresultoftheflowstagna-tionandboundary-layerseparation,thelatterresultinginalambda-shockaheadofthebow-shock;(ii)Fourcounter-rotatingvortexpairsalongtheaveragetrajectoryofeachH2-plume,startingattheleadingedgesofthejetshear-layers;(iii)Jetshear-layervorticeswrappingaroundthejets,andde-velopingduetoKelvin-Helmholtzinstabilitiesinthejet-shearlayers.Closebehindtheinjectors,the-se flow structuresoften appear as incoherent S-shaped side vortex arms, spanwise vortex rollersand small standing vortices,which furtherdownstreamcombine intoΩ-shapedvortex loops thatgraduallydevelops(byvortex-vortexinteractions)intolongitudinalvortices,

AsmallamountofH2ispeeled-offthejetsastheydischargeintothecombustor,andrapidlymixedwith the air by the jet shear-layer vortices, and ignited by the temperature increase due to thelambda-andbow-shocks.Thisresultsinradicals(e.g.O,H,OH),andH2O,formingathinsheetovereachH2plumebeingadvecteddownstream.Alongtheself-ignitionregion,thevortexloopsgradual-lybecomesmoreregularlyspaced,whilstprovidingthemixingofhotair,H2,radicalsandH2Ore-sulting in self-ignition of the H2-plumes, facilitated by the shock-plume interactions. Some H2 isdrawn into thehorseshoevortex systemswhere it graduallybecomesheatedandmixedwith thehotairandradicals.Whenthesestructuresareimpingedonbythereflectedshocks,ignitionoccurs.Neighboringhorseshoevortexsystemlegscombine,formingsmallΩ-shapedvortexloopsbetweentheprimaryH2plumes.Furtherdownstream,thevorticalstructuresgraduallylosetheircoherenceanddeveloplongitudinalvortices,andradicalsandproductspeciesoccurintermittently.

Thespecies(H2,OHandH2O)distributionsshowaratherentwinedandcomplexbehavior,typically,withOH,OandHoccurringbetweenH2,airandH2O.TheradicalsOandHoccurinthin,wrinkled,

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layersfragmentedbytheturbulence,whereasOHshowssuper-equilibriumlevelsalongthereactionfrontsandequilibriumlevelsontheproductside.Large-scaleturbulencecreates largescalewrin-klingandsmall-scaleturbulencecreatessmallscalewrinklingofthespeciesdistributions.Pocketsofradicals(O,HandOH)canbeobservedtoforminregionsinwhichshock-shock,shock-boundarylayerandparticularlyshock-plumeinteractionstakesplace.

Thechemicalexplosivemodeeigenvalue,λe,showpositivevalues(red),representativeofmixturespronetoigniteandburn,inthehorseshoevortexlegs,alongtheouteredgesoftheS-andΩ-shapedplumevortices,andinspotsjustdownstreamofwhereareflectedshockhasimpingedonaH2con-tainingmixturestate.λeshownegativevalues(blue),representativeofreactivebutnon-explosive,orburnedmixtures, in themiddle anddownstreampartof theplume.Thenegative regionsofλewidenwithdownstreamdistancefromtheinjectorsasmostofthefuelisconsumed.

Figures2aand2bcomparelongitudinalprofilesofthetime-averagedbody-sideandcowl-sidewall-pressures,〈p〉,andthebody-sideheat-flux,〈h〉,betweenexperimentaldata,[1],andRANS,[1],andLESpredictions.GoodagreementbetweenLESandRANSandtheexperimentaldataisobservedfor〈p〉,whichshowsalinearincreasealongthecombustorwithasuperimposedshock-traindevelopingfromthecombustorleadingedge.For〈h〉theLESpredictionsagreesignificantlybetterwiththeex-perimentaldatathantheRANSpredictions.ThedifferencesbetweentheLESandRANSaremainlyduetothehigherspatialresolutionandtheresolvedlarge-scaleunsteadiness.

(a) (b) (c)

Figure2.Predicted(lines)andmeasured,[1],(circles)(a)bodywallpressure,(b)cowlwallpressureand(c)bodyheatfluxfrom(—)RANS,[1],andfrom(—)LES.

FromthecomputationaldensitygradientandexperimentalSchlierenimages,[19],infigure3atheshock-trainandplumeareobservedtobe inacceptableagreement.TheplumeissomewhatmoreapparentintheLESthanintheSchlierenimages,whichmaybeduetotheabsenceofthesmallestscalesintheLES.Thecomputationalheat-releaseagreeswellintopologywiththeplumetopologyinboththeexperimentalSchlierenimagesandintheLES.

Figure3.ComputationalandexperimentalSchlierenimages,[19],ingrayscale(top)togetherwithcomputationalheat-releaseandexperimentalOHchemiluminescence(bottom).

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4 SupersonicFlameStructures

Themixingandflametopologyisverycomplicatedasobservedinfigure1,andinordertosimplifyit’sinterpretationwepresentinfigure4aa3Dscatterplotsofthetemperature,T,mixturefraction,z,andcoordinate,x,alongthecombustoraxis,coloredbythechemicalexplosivemodeeigenvalue,λe,[18].TheprojectionontheT-zplanerevealsadiffusionflamestructure,withapeakinTclosetozst, butwith a large variation in T, reminiscent of local extinction. The highest values ofλe occurclosetozst,butontheO2side,andtheshock-trainisvisibleasvariationsinTalongthex-axis.Thebranchstartingatz=1(atx=0.42)representstheH2richmixturefromtheinjectorsandisphysicallyassociatedwiththemainplumesandthehorseshoevortexsystems,alongwhichbothTandλe in-creasewithdownstreamdistance.Thisbranchmergeswiththeairbranchfromtheinlet(atx=0.34)alongwhichλe isnegativeas itconsistsofanon-reactivemixture.Whenthesebranchesmergeλeincreaseatfirstasthemixturebecomesexplosive(duetotheH2-O2mixingathighT),tothengrad-uallydecreasetonegativevalues,representingcombustionproducts(H2O).Someofinflowairpassthroughthecombustorwithoutparticipatinginthereactions(blue).Themixturetemperaturede-creasealongthenozzleastheflowacceleratesandthrustisgenerated.

Figure 4. (a) 3D scatter plots of the temperature, T,mixture fraction, z, and coordinate, x,alongthecombustoraxis,coloredbythechemicalexplosivemodeeigenvalue,λe,and(b)3Dscatterplotof theturbulentDamköhlernumber,Dat,Reynoldsnumber,Ret,andMachnum-ber,Mat,coloredbytheheat-releaseindexedTakenoflameindex.

Infigure4bwepresenta3DscatterplotoftheturbulentDamköhlernumber,Dat,Reynoldsnumber,Ret,andMachnumber,Mat,(basedonthevelocityfluctuations)coloredbytheheat-releaseindexedTakenoflameindex.ThisfigurecorrespondingtoanextendedversionoftheWilliamsdiagram,[20],andshowsthatscramjetcombustiontypicallyoccurs intheregion102<Ret<104and10–1<Dat<102,assuggestedbyWilliams,[20],butalsothatsignificantcompressibleeffectsoccursasevidentbythesurprisinglyhighMatnumbersobserved.RegionsofhighMat(Mat>0.75)occurinthecounter-rotat-ingvortexpairs,inregionsofshock-reflections,andinregionswhereshock-inducedignitionoccurs,i.e.inlocalizedregionsalongthehorseshoevortexlegsandinspotsontheplumeedgesinwhichthereflectedshocksimpingesonaheatedmixtureofH2,O2andradicals.ThehighMat-numberstateisprimarilyofnon-premixednature(blue)butwithsomepremixedelementsembedded.Thedetailedflamestructureinscramjetcombustionisnotverywellknown,anditwouldbeappropriatetotryandcharacterizethisusingDirectNumericalSimulations.

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5 Discussion

High-fidelityLESpredictionsoftheHyShotIIcombustorarepresentedandcomparedagainstexper-imentaldataandRANSpredictions.Goodagreementisgenerallyobserved, indicatingthattheLEScapturestheessentialphysics.TheLESresultsarethenusedtoelucidatetheflowandflamephysicswiththeintentofprovidingimprovedunderstandingoftheinteractingself-ignitionandflame-stabi-lizationmechanisms.Inparticularitisobservedthattheflametypicallyresideintheregion102<Ret<104and10–1<Dat<102,andexperiencesignificantturbulentManumbers,whichmayhaveaneffectontheturbulentflamestructure.Theobservationthatthemostprobableflameregimespanssever-alzonessuggestthatmethodscapableofhandlingvarious,aprioriunknown,flametopologies,suchasfiniteratechemistryLESmethodsshouldbeemployedinsimulations.

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