On the Supersonic Flame Structure in the HyShot II...
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26 th ICDERS July 30 th – August 4 th , 2017 Boston, MA, USA Correspondence to: [email protected] 1 On the Supersonic Flame Structure in the HyShot II Scramjet Combustor Christer Fureby The Swedish Defence Research Organization SE 147 25 Tumba, Stockholm, Sweden 1 Introduction and Background Understanding of the multi-disciplinary physical processes in the flow-path of a scramjet engine is crucial for the enabling of this technology, considered the most promising for hypersonic flight. The flow in such engines remains supersonic throughout, preventing the pressure losses and structural challenges involved in decelerating the flow to subsonic speeds. However, this necessitates that the mixing and combustion processes in the engine occur within supersonic flow, with residence times of O(1) ms. Within this short time interval, the fuel and air must mix, ignite and combust prior to discharging through the nozzle. Laboratory, ground testing and flight-testing experiments, together with high-fidelity numerical simulations, comprise the tools available to fill the gap in scramjet com- bustor knowledge. In this study, we combine results from high-fidelity Large Eddy Simulation (LES), using finite-rate chemistry models and skeletal reaction mechanisms, with experimental pressure data and visualization of the shock-train and the heat-release to elucidate the key features of the flow of the HyShot II combustor. We specifically focus on the conditions of experiments performed in the High Enthalpy Shock Tunnel Göttingen (HEG), emulating flight conditions at 27 km altitudes, [1]. The flame structure is characterized using an extended Williams diagram. 2 Large Eddy Simulation Models for Supersonic Combustion The Large Eddy Simulation (LES) model employed is based on a reacting-flow model in which the mixture is assumed to be a linear viscous fluid with Fourier heat conduction and Fickian diffusion. The viscosity is calculated using Sutherland’s law while the thermal conductivity and species diffu- sivities are computed from the viscosity using constant Prandtl and species Schmidt numbers. The mixture thermal and caloric equations-of-state are obtained assuming that each species is a ther- mally perfect gas. The combustion model is based on finite-rate Arrhenius reaction rates. The LES model use implicitly-filtered mass, momentum, energy and species equations, [2], in which the subgrid stress tensor and flux vectors are closed by the mixed model, [3]. The filtered reaction-
Transcript of On the Supersonic Flame Structure in the HyShot II...
26thICDERS July30th–August4th,2017 Boston,MA,USA
Correspondenceto:[email protected] 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.
References
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