HIGHFIDELITYNUMERICALSIMULATIONSOFTURBULENTJETIGNITIONANDCOMBUSTIONByAbdoulAhadValidiADISSERTATIONSubmittedtoMichiganStateUniversityinpartialentoftherequirementsforthedegreeofMechanicalEngineering-DoctorofPhilosophy2016ABSTRACTHIGHFIDELITYNUMERICALSIMULATIONSOFTURBULENTJETIGNITIONANDCOMBUSTIONByAbdoulAhadValidiTurbulentjetignition(TJI)isanovelignitionenhancementmethod,whichfacilitatesthecombustionofleanandultra-leanmixturesincomplexpropulsionsystemsandengines.Here,acomprehensivestudyofTJIintcombustionsystemsisconductedwithdirectnumericalsimulation(DNS)andlargeeddysimulation(LES)methods.DNSofTJI-assistedcombustionofleanhydrogen-airisperformedinathree-dimensionalplanarjetforvariousthermo-chemicalandwconditions.Fullycompressiblegasdynamicsandspeciesequationsaresolvedwithhighordermethodsandadetailedchemicalkineticsmechanism.SeveralinterestingphenomenainvolvedinTJI-assistedcombustionincludinglocalizedmeextinction/reignitionandsimultaneousareinvestigatedbyconsideringw/combustionvariablesliketheheatrelease,temperature,speciesconcentrations,vorticity,Baroclinictorque,andanewlyTJIprogressvariable.NumericalsimulationsofTJI-assistedcombustioninarapidcompressionmachine(RCM)arealsoconductedbyahybridEulerian-LagrangianLESmethodbasedonthemassdensityfunction(FMDF)model.AnimmersedboundarymethodisdevelopedandusedintheLEStofacilitatemorphingthecomplexgeometriesanddecreasetheMonteCarlo(MC)particlesearchandlocateoperationsinFMDF.ItalsohelpstoproperlyhandlegridsandMCparticlesattheboundarieswhilemaintainingthehighaccuracyofthesimulator.IntheTJI-RCMsystem,ahotproductturbulentjetrapidlypropagatesfromapre-chamber(PCh)toamainchamber(MCh).ThreemaincombustionphasesofTJI-assistedcombustioninaRCMaredelineatedasi)coldfueljet,ii)turbulenthotproductjet,andiii)reversefuel-air/productjet.Theofvariousparametersonthesephasesarestudiednumerically,includingtheignitertimingandlocation,lean/rich/N2-dilutedmixtures,andadiabaticvs.non-adiabaticwalls.ItisfoundthattheturbulentjetcharacteristicsandtheMChcombustionarehighlybythePChturbulenceintensityaswellastheignitionparameters.Forexample,ignitingthePChatthelowerlocationsclosetothenozzleforcesthePChchargetofullypar-ticipateinthePChignition/combustionprocessesandpreventstheunburnedfuelsleakingtotheMCh.ItalsoenhancestheMChcombustionbygeneratinglowervelocityhotproductjetsforalongertime.ThepressuretracespredictedbyLES/FMDFarefoundtobeingoodcomparisonwiththeavailableexperimentaldata.Thetemperaturecontoursarealsowellcomparablewiththeexperiments.TomyparentsParvinandAhmadivACKNOWLEDGMENTSIamsincerelygratefultomyadvisorProfessorFarhadJaberiforhisinvaluableguidanceandsupport.Thisworkwouldnothavebeensuccessfulwithouthispatienceandencour-agement.Ithasbeentrulyanhonorandanenlighteningexperienceworkingforhim.MysincerethanksgotomydoctoralcommitteemembersDr.HaroldSchock,Dr.CarlLira,andDr.ElisaToulsonfortheirconstructivecomments.Dr.Touslon'sinsightsonrapidcompressionmachineswereveryhelpful.ThisstudywasconductedwiththesupportofNationalScienceFoundationandDepart-mentofEnergyundergrantnumberCBET-1258581.IexpressmygratitudetotheInstituteforCyber-EnabledResearchHighPerformanceComputingCenteratMichiganStateUniversityfortheirsupportinprovidingthecomputationalfacilitiesforthisstudy.TechnicalhelpfromDr.DirkColbry,JimLeikert,andAndrewKeenisgreatlyappreciated.IwouldalsoliketoacknowledgetheTexasAdvancedComputingCenter(TACC)atTheUniversityofTexasatAustinforprovidingapartofcomputationalresourcesforthisstudythroughXSEDEprogram.Lastbutnottheleast,Iamever-indebtedtomyparentsandmytwosistersfortheirunconditionallove,support,andbehindeverythingIhaveachievedinlife,includingthisdissertation.vTABLEOFCONTENTSLISTOFTABLES........................................viiiLISTOFFIGURES.......................................ixKEYTOSYMBOLSANDABBREVIATIONS....................xviChapter1FundamentalStudyofTurbulentJetIgnitionandCombustioninaLeanPremixedwithDNS............11.1Chaptersummary....................................11.2Introduction........................................21.3Governingequationsandnumericalmethodology..................61.4Flow....................................91.5Resultsanddiscussions:wandfeaturesofTJI-assistedcombustion.141.5.1Flostructure..............................161.5.2Turbulentspeed.............................321.5.3Temporalandspatialvariationsofturbulentvariables..........341.6Resultsanddiscussions:jetandwondevelopmentofpremixedandnon-premixedincludinglocalizedextinctioninTJI-assistedcombustion481.6.1FlamevariableforTJI-assisted........................551.6.2wcomposition...........................591.6.3Incomingjetthermo-chemical....................741.7Chapterconclusions...................................79Chapter2LES/FMDFofTurbulentJetIgnitionassistedRapidCom-pressionMachines...............................822.1Chaptersummary....................................822.2Introduction........................................832.3Governingequations...................................872.3.1FilteredcompressibleNavier-Stokesequations...............872.3.2CompressiblesinglephasescalarFMDFequations............912.3.3Numericalapproach...............................962.3.4MCparticletrackingandparallelization..................982.3.5ImmersedboundarymethodforLES/FMDF...............992.4TJI-RCMsetupandcomputationaldomain.....................1002.5Resultsanddiscussions.................................1032.5.1Compressionstage................................1032.5.2Combustionphase................................1082.5.2.1Comparisonwithexperimentandparametricanalysis.....1162.6Chapterconclusions...................................142viBIBLIOGRAPHY........................................144viiLISTOFTABLESTable1.1:Thermo-chemicalpropertiesoftheincomingjetsandcows.....11Table1.2:Thespeciesmassfractionsintheincomingjets..............11Table1.3:DetailedchemistrymodelforH2~O2system................12Table2.1:SpofTJI-assistedRCMcomputationaldomain.......102Table2.2:Igniterparametersusedinexperimentandenergydepositionmodel(EDM)......................................109Table2.3:Thermo-chemicalandphysicalparametersofsimulatedTJI-assistedRCM.......................................116viiiLISTOFFIGURESFigure1.1:Schematicofturbulentjetignitionofturbulentplanejet,TJI-TPJ,..................................10Figure1.2:Thegridresolutionatthefront,idenbasedon˚H,andaviewofthefrontbyafactorof261...........13Figure1.3:Instantaneouscontoursofthetemperatureatamiddlespanwiseplane,‹z1:5D“,atttimesduringwtransitionfromanon-reactingwtoareactingone.(˝ig3˝0).................15Figure1.4:Instantaneousheatreleaseratecontourafter17˝0.(Contourspre-sentedinthelowerareforthey0:5Dplane(Surfxzin1.1)....................................17Figure1.5:Variouszonesinthedevelopedregionofthesimulatedturbulentpla-narjetwithturbulentjetignition......................19Figure1.6:MarginalPDFsof(a)Temperatureand(b)Hradicalmassfraction.(c)ScatterplotofHradicalmassfractionandtemperature......20Figure1.7:InstantaneousTemperaturecontoursfor:(a)Non-reactingand(b)Reactingcasesafter17wthroughtime,˝0...............23Figure1.8:Instantaneous(a)OHand(b)Hconcentrationcontoursforreactingwatt17˝0..................................24Figure1.9:Scatterplotsof_Qe,˚H,and˚OH,anillustrationofthespatialcor-relationbetweenheatreleaserateand(a)OHmassfractionand(b)Hmassfraction................................25Figure1.10:Normalizedspeciesmassfractionsversusat(a)˘4and(b)˘16.27Figure1.11:ConditionaljointandmarginalPDFs.(a)ConditionaljointPDFoftemperatureand˚H,P‹T;˚HS1000DTD1800“(b)ConditionalmarginalPDFoftemperature,P‹TS4104D˚HD6104“....28Figure1.12:Instantaneousvorticitymagnitude,!,contoursfor(a)Non-reactingand(b)Reactingcasesatt17˝0......................29ixFigure1.13:InstantaneousBaroclinictorque,contoursfor:(a)Non-reactingand(b)Reactingcasesatt17˝0.........................31Figure1.14:MarginalPDFof,P‹˚“..........................31Figure1.15:Conditionalmeansandboundsof(a)Baroclinictorque,,and(b)scalardissipationrateofHradical...............33Figure1.16:Contoursoftimeandspanwiseaveragedtemperatureandthejetspanspreadratefor(a)Non-reactingand(b)Reactingcases........35Figure1.17:(a)Turbulentspeed,ST,andturbulenceintensity,I,atfrontvs.streamwisewdirection,(b)Conditionalmeananddenceboundsofturbulenceintensity.....................35Figure1.18:(a-c)instantaneousvariationsofu1,T1,and˚H1intime;(d-f)PDFofu1,T1,and˚H1;and(g)associated,˙,S,andK..........37Figure1.19:(a-c)instantaneousvariationsofu2,T2,and˚H2intime;(d-f)PDFofu2,T2,and˚H2;and(g)associated,˙,S,andK..........38Figure1.20:(a-c)instantaneousvariationsofu3,T3,and˚H3intime;(d-f)PDFofu3,T3,and˚H3;and(g)associated,˙,S,andK..........39Figure1.21:(a-c)instantaneousvariationsofu4,T4,and˚H4intime;(d-f)PDFofu4,T4,and˚H4;and(g)associated,˙,S,andK..........41Figure1.22:(a-c)instantaneousvariationsofu5,T5,and˚H5intime;(d-f)PDFofu5,T3,and˚H5;and(g)associated,˙,S,andK..........42Figure1.23:Streamwisevariationsofaveragedvalues(a)streamwisevelocitycom-ponentand(b)temperatureattcross-streamloca-tions.(`esreferstobothtimeandspanwiseaveragedvalue.Thickandthinlinesrepresentthereactingandnon-reactingcases,respec-tively)......................................44Figure1.24:Cross-streamvariationsof(a)meanstreamwisevelocity,(b)rmsofstreamwisevelocity,(c)meantemperature,and(d)rmsoftempera-ture.(Thickandthinlinesrepresentthereactingandnon-reactingcases,respectively)...............................46Figure1.25:Instantaneoustemperaturecontoursatthemiddlespanwiseplane‹z1:5D“andt17˝0for(a)Case1,(b)Case2,(c)Case3,(d)Case4,(e)Case5,and(f)Case6.......................49xFigure1.26:Timeandspanwiseaveragedtemperaturevalues,aTfs,at(a)˘1and(b)˘2versuscross-streamdirection,,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6....................................52Figure1.27:Meanandintervalsofyzplaneandtimeaveragedtem-perature,‹`Teyz“˙‹`Teyz“,inthecombustionzonesversusstream-wisedirection,˘,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6..........54Figure1.28:Normalizedthermalhalfwidthjetbytheincomingjetwidth,Dhalf~D,versusstreamwisedirection(˘).(i)Contourofrmsoftemperature,Trms,atthemiddlespanwiseplane,‹z1:5D“,schematicallyshownforCase3.....................................55Figure1.29:Meanandintervalsoftemperature,‹T“˙‹T“,inthecombustionzonesatt17˝0versus(a)elementalmixturefraction,fand(b)TJIcombustionprogressvariable,R,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6.(i)Scatterplotoftemperature,T,inthecombustionzonesatt17˝0versusTJIcombustionprogressvariable,R,forCase6,identifyingthesimultaneousexistenceofthepremixedandnon-premixedcombustionregimes.....................58Figure1.30:TJIcombustionprogressvariable,R,versuscross-streamdirectionatamiddlespanwiseplane,‹z1:5D“,andt17˝0at(a)˘1and(b)˘3versuscross-streamaxis,,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6..59Figure1.31:InstantaneouscontoursoftheH2Omassfraction,˚H2O,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4.(Notethatthescalelimitsaresettotheavailablevaluesineachcontourandarenotthesame.).........61Figure1.32:InstantaneouscontoursoftheOHmassfraction,˚OH,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4..............................62Figure1.33:InstantaneouscontoursoftheHmassfraction,˚H,atamiddlespan-wiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4.(Notethatthescalelimitsaresettotheavailableval-uesineachcontourandarenotthesame.)................63xiFigure1.34:Instantaneouscontoursoftheheatreleaserate,_Qe‹W“,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4.(Notethatthescalelimitsaresettotheavailablevaluesineachcontourandarenotthesame.).........65Figure1.35:Meanandintervalsofyzplaneaveragedheatreleaserate,‹`_Qeeyz“˙‹`_Qeeyz“,att17˝0versusstreamwisedirection,˘,forfourcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,and(l)Case4.................................66Figure1.36:Localizedextinctionandre-ignitionatsheetidenbasedonheatreleaseandamviewofthembyafactorof5:1,occurredinultra-leancow(Case1)..........................67Figure1.37:Scatterplotoftheheatreleaserate,_Qe‹W“,versusTJIcombustionprogressvariable,R,for(a)Case1,(b)Case2,(c)Case3,and(d)Case4attstreamwisesectionsrepresentedby(h)Sec1,(X)Sec2,and(⁄)Sec3...............................69Figure1.38:Scatterplotoftheheatreleaserate,_Qe‹W“,versusstrainrate,_‹1~s“,for(a)Case1and(b)Case4attstreamwisesectionsrepresentedby(h)Sec1,(X)Sec2,and(⁄)Sec3............71Figure1.39:(a)Cross-streamlocationofmax‹Trms“andmax‹I“,(b)turbulenceintensity,I,valuesatmax‹Trms“andmax‹I“locations,and(c)vor-ticitymagnitude,!,atmax‹Trms“andmax‹I“locations,versusstreamwisedirection,˘,forfourcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,and(l)Case4.Thicksolidandthindashedlinescorrespondtomax‹Trms“andmax‹I“,respectively........72Figure1.40:InstantaneouscontoursoftheOHmassfraction,˚OH,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case5and(b)Case6..75Figure1.41:InstantaneouscontoursoftheHmassfraction,˚H,atamiddlespan-wiseplane,z1:5D,andt17˝0for(a)Case5and(b)Case6.(Notethatthescalelimitsaresettotheavailablevaluesineachcontourandarenotthesame.)............................76Figure1.42:Instantaneouscontoursoftheheatreleaserate,_Qe‹W“,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case5and(b)Case6.(c)Meanandintervalsofyzplaneaveragedheatreleaserate,‹`_Qeeyz“˙‹`_Qeeyz“,att17˝0versusstreamwisedirection,˘,forthreecasesrepresentedby(⁄)Case3,()Case5,and(P)Case6.......................................78xiiFigure1.43:Scatterplotoftheheatreleaserate,_Qe‹W“,versusTJIcombus-tionprogressvariable,R,for(a)Case5and(b)Case6attstreamwisesectionsrepresentedby(h)Sec1,(X)Sec2,and(⁄)Sec3.79Figure2.1:TheattributesofthehybridLES/FMDFmodel..............97Figure2.2:Schematicofthegridpoints,largeblackcircles;MCparticles,smallpurplecircles;controlvolumes,dashedgreenlinesaroundthegridpoints;FDmesh,solidyellowline;andsweepingdirectionstodeter-mineithandjthcomponentsofthepointq................99Figure2.3:SchematicofapproximateddomainusingIBmethod.fluid,outofdomainout,approximatedboundary(thickline),actualboundary(parallellines),andMonteCarloparticlesY................100Figure2.4:(a)TJI-RCMcombustionsystemand(b)3DviewoftheTJI-RCMmesh........................................102Figure2.5:TJI-RCMwstructuresattheendofthecompressionstage:(a)Contourplotofiso-surfacesofvelocitymagnitude,SÑUS‹m~s“,and(b)Contourplotofvorticitymagnitude,SÑ!S‹1~s“,inthemiddleofthedomainatxyandxzplanes.......................104Figure2.6:TimeevolutionofthePChwduringthecompressionstageconsideringcontourplotsofvelocitymagnitude,SÑUS‹m~s“.......105Figure2.7:TimeevolutionofthePChwduringthecompressionstageconsideringcontourplotsofvorticitymagnitude,SÑ!S‹1~s“........106Figure2.8:Schematicofthewallheattransfermodelandrelatedquantities....107Figure2.9:TemperaturecontoursofTJI-assistedRCMattheendofthecom-pressionstage,pistonlocatedatTDC,forthecaseswith(a)adiabaticand(b)conductivewalls............................107Figure2.10:Quantitativecomparisonofthepredictedpressuresofbothcasesus-ingadiabaticandconductivewallswithavailableexperimentaldataduringthecompressionstageoftheTJI-RCM...............108Figure2.11:TJI-RCMcombustionphasesbasedonthecompositionanddirectionofthewatthenozzle............................110Figure2.12:ThephaseoftheTJI-assistedRCMcombustionstage.Instan-taneousiso-surfacesofvelocitymagnitudecoloredby(a)fuelmassfraction,˚CH4,and(b)Temperature,T,att1:0‹ms“........112xiiiFigure2.13:ThesecondphaseoftheTJI-assistedRCMcombustionstage.Instan-taneousiso-surfacesofvelocitymagnitudecoloredby(a)fuelmassfraction,˚CH4,and(b)Temperature,T,att2:5‹ms“........113Figure2.14:ThereverseunburnedfueljetofthethirdphaseoftheTJI-assistedRCMcombustionstage;instantaneousiso-surfacesofvelocitymagni-tudecoloredby(a)fuelmassfraction,˚CH4,and(b)Temperature,Tatt4:0‹ms“.ThereversehotproductjetofthethirdphaseoftheTJI-assistedRCMcombustionstage;instantaneousiso-surfacesofvelocitymagnitudecoloredby(c)fuelmassfraction,˚CH4,and(d)Temperature,T,att8:0‹ms“.....................115Figure2.15:QualitativecomparisonbetweenLES/FMDFandexperimentalre-sults:(a1)-(a3):Experimentalpictures;(b1)-(b3):LES/FMDFspan-wisedaveragedtemperaturecontoursat;and(c1)-(c3):LES/FMDFtemperaturecontoursinthemiddleoftheMCh..............118Figure2.16:Comparingtheexperimental(l)andsimulatedpressuretracesatPointMChinCase1(X)andCase2(h)..................119Figure2.17:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase1.....121Figure2.18:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase2.....122Figure2.19:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase3.....124Figure2.20:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase4.....125Figure2.21:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase5.....127Figure2.22:(a)SimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase3(X),Case4(h),andCase5(⁄).(b)-(e)Simulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase2toCase5.Thestreamwisevelocityvaluesarealsoshown.................................129Figure2.23:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase6.....130xivFigure2.24:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase7.....131Figure2.25:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase8.....132Figure2.26:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase9.....133Figure2.27:(a)SimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase6(h),Case7(X),Case8(⁄),andCase9().(b)-(e)Simulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase6toCase9.Thestreamwisevelocityvaluesarealsoshown........................135Figure2.28:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase10.....136Figure2.29:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase11.....137Figure2.30:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase12.....138Figure2.31:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase13.....139Figure2.32:(a)SimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase10(h),Case11(X),Case12(⁄),andCase13().(b)-(e)Simulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase10toCase13.Thestreamwisevelocityvaluesarealsoshown.................141xvKEYTOSYMBOLSANDABBREVIATIONSAbbreviationsCFDComputationaldynamicsEDMEnergydepositionmodelFDFiniteFDFFiltereddensityfunctionFMDFFilteredmassdensityfunctionIBImmersedboundaryICInternalcombustionLESLargeeddysimulationMChMainchamberPChPrechamberPDFProbabilitydensityfunctionRCMRapidcompressionmachinermsrootmeansquareSDEStochastictialequationSGSSub-gridscaleSISparkignitionSUServiceunitTJITurbulentjetignitionDNSDirectnumericalsimulationTJITurbulentjetignitionTPJTurbulentplanejetConventions‹“Timeaveragedvalue`esspanwiseaveragedvaluexvi`SeLConditionalFavrevalue`eTimeaveragedvalue`elorFilteredvalue`eLor~Favrevalue`elœSecondaryfunctionSymbolsh0fEnthalpyofformationofspecies,J/Kg_QeHeatreleaserate,J/(Kgs)KKurtosisSSkewnessMean˚Massfractionofspecies˙Standarddeviation˝0Flow-throughtime,setTotalenergy,J/KgBaroclinictorquemagnitude,1~s2DiracdeltafunctionGFiltersize,m_!Reactionrateofspecies,1/s_QHeatreleaserate,J/Kg.s_SRateofmassproduction/destructionperunitvolumeforspeciesduetochem-icalreaction,Kg/sKolmogrovlength,mt;x;y;zMetriccotsofthecoordinatetransformation;tandturbulentsioncots,Kg/m.s^F;^G;^HInviscid^Fv;^Gv;^HvViscousxviie;⁄Thermal,e,conductivity,J/m.s.KS~SSStrainratemagnitude,1/se;⁄Molecular,e,kinematicviscosity,Kg/m.s!Vortivitymagnitude,1~smMixingfrequency,1/sCompositionvector˚ParabolicrepresentationsofscalarCompositionsamplespacevectorˆDensity,Kg/m3˙Fine-graineddensity˝ijViscousstresstensorijTotalstresstensor˘;;;˝Independentvariablesintransformeddomain˘t;˘x;˘y;˘zMetriccotsofthecoordinatetransformationt;x;y;zMetriccotsofthecoordinatetransformationaSpeedofsound,m/sCmMKEVmodelconstantC!MixingmodelconstantCpSpheatofspecies,J/Kg.KDWidthofturbulentplanejet,mETotalinternalenergy,J/kgGFilterfunctionHTotalenthalpy,J/KghEnthalpyofspecies,J/KgITurbulenceintensityJJacobiantransformationJiSpeciesterm,m2/sxviiinNormaldirectiontotheimmersedsurfaceNsNumberofspeciespPressure,PaPrtTurbulentPrandtlnumberqiHeatvector,Kg/s3RMixturegasconstant,J/Kg.KR0Universalgasconstant,J/Kg.KruVelocityratiorGridsize,›xyz”13ScSchmidtnumberTTemperature,KtTime,sUSolutionvectoruœ;vœ;wœFluctuationsofvelocitycomponents,m/suiVelocitycomponentinithdirection,m/sUjJetvelocity,m/sUcowvelocity,m/sWWienerprocess,s0:5w‹n“WeightofthenthMonteCarloparticleWMolecularweightofspecies,Kg/molex;y;andzstreamwise,cross-stream,andspanwisedirectionsxiithcomponentofthepositionvector,mXiProbabilisticrepresentationofposition,mxPositionvector,mxixChapter1FundamentalStudyofTurbulentJetIgnitionandCombustioninaLeanPremixedwithDNS1.1ChaptersummaryDirectnumericalsimulations(DNS)ofturbulentjetignition(TJI)-assistedcombustionofleanpremixedfuel-airmixturesareperformedinathree-dimensionalplanarjetforvariousthermo-chemicalandwconditions.TJIisanovelignitionenhancementmethodwhichfacilitatesthecombustionofleanandultra-leanmixturesbyrapidlyexposingthemtohightemperaturecombustionproducts.Itisalsoantmethodforinitiatingandcontrollingcombustioninultra-leancombustionsystems.Fullycompressiblegasdynamicsandspeciesequationsaresolvedwithhighordermethods.Thehydrogen-airreactionissimulatedwithadetailedchemicalkineticsmechanismconsistingof9speciesand38elementaryreactions.ThephysicalprocessesinvolvedintheTJI-assistedcombus-tionincludinglocalizedpremixedextinctionandsimultaneouspremixed/non-premixedareinvestigatedbyconsideringtheheatrelease,temperature,speciesconcen-trations,scalardissipation,vorticity,Baroclinictorque,andanewlyTJIprogress1variable.Thecomplexturbulentandwstructuresaredelineatedinthreemaincom-bustionzonesasi)hotproductjetzone,ii)burned-mixedzone,andiii)zone.Thewstructuresandstatistics,temperatureandspeciesdistributions,andthefeatures(suchasthespeedandtemperature)intheTJI-assistedcombustionarefoundtobequitetthanthosein\standard"turbulentpremixedcombustion.Thearemainlyduetointensiveinteractionsoftheturbulewithahighenergyturbulenthotproductjetzone.1.2IntroductionTurbulentjetignition(TJI)isanovelmethodforinitiatingandcontrollingultra-leancom-bustionininternalcombustion(IC)engines[63],high-speedcombustors[46],andothercom-bustionsystems[66].TJIfacilitatesleancombustionbyprovidingandpropagatingpocketsofhotandoftenfuel-richmixtureproductsasenergyandfuelsourcesthroughoutthecom-bustor.Itnotonlyincreasestheanddecreasestheemissionsbutalsoprovidesmorecontrolovertheentirecombustionprocess.TJI-assistedcombustionsystemstypicallyincludeamainchamber,apre-chamber,andpassagewaystoconnectthem.Anignitionde-vice(e.g.asparkplug)isinstalledinthepre-chambertoignitethechargeandcreatahighvelocityhotproductjetexitingoutintothemainchamber.Thisjetinitiatesandmaintainsthemaincombustion.TJI-assistedcombustionofpremixedmixtureshavebeenstudiedinthepastbyseveralinvestigator,focusingonthetransitionandtheviabilityofthedesigned[15,94,39,20,22,80].Injectingahotproductjetintoafuel-airmixturemayalsobeasourceofstrong[16]andevendetonationcombustion[22],whichareimportanttothesafetyoftherelatedindustrialsystems[28].2Theignitionandcombustionofpremixedmixturesbyturbulentjetshavebeenstudiedandanalyzedbothnumericallyandexperimentallyintcoandforvariousfuels[15,94,39,20,22,80].Theworkof[94],forexample,providesincreasedunderstandingoftheofthejettemperatureandturbulentmixingonignition.Inthestudyconductedby[39],theofjetReynoldsnumberandreactantyonignitionhavebeeninvestigated.Generally,themainfocusofthesestudiesandotherpreviousjetignitionstudieswasonthetransitionandtheviabilityofthedesignedThereiscertainlyaneedforin-depthstudiesoftheverycomplicatedphysicalandchemicalprocessesinvolvedintheTJI-assistedcombustion.OneofthemajorchallengesofnumericallysimulatingtheTJI-assistedcombustionistopredicterenttypes(premixed,non-premixed,melet,distributed)atthesametime.ThemeletcombustionmodelsbasedonG-equation[77,78]andmixturefraction[81],eacharecapableofmodelingeitherpremixedornon-premixedregimes.Themodelsbasedonmomentclosure[52]canbeusedinnon-premixedregimes.Lineareddy[51]andscale-similaritymodels[43]mightbebettercandidatesforsimulatingtcombustionregimes.However,theseassumptionsmaybeinappropriateforquantitiesthataredominatedbysmallscales(e.g.chemicalreactionsandscalardissipation)andtherefore,highReynoldsnumberzonesareunlikelytoberesolved.ThemostpromisingmodelingapproacheswhicharecapableofdealingwithtcombustionregimesinTJI-assistedcombustionprocessesaretheonesdevelopedbasedonprobabilitydensityfunction(pdf)methods[87]andMonteCarlosimulationtechniquesviathedensityfunction[41].ThecomplexitiesandchallengesofTJIsimulationsalsoarisefromthestrongcouplingofthewandthermo-chemicalvariablesoverawiderangeoftemporalandspatialscales,andthehighlynonlinear,multicomponent,andunsteadynatureoftheheatandmasstransportandchemicalreactions3[45,89].Anaccurateandreliablenumericalapproachisclearlyrequiredtodelineateandcapturetheeandturbulencestructuresinsuchsystems.Here,forthetime,westudyTJIandcombustioninawellcharacterizedthree-dimensionalturbulentplanarjet(TPJ)[35,32,86,89,38]viadirectnumericalsimula-tion(DNS).Thisisdesignedsuchthatafteratlylongtime,thew/combustionreachesa\stationary"condition.ThisuniquesetupmakesthecurrentworkdistinguishablefromthepreviousstudiesinthisareaandattractiveforfundamentalinvestigationsofTJI.TheTPJiscomposedofhotproductsofcombustionofstoichiometrichydrogen-airmixture.Thisjetisinjectedintoarelativelycoolerleanpremixedhydrogen-airwmixture.Thewandcombustionparameters(e.g.,thejetwidth,thestreamwise,cross-stream,andspanwisedomainlengths,themainjetandwproperties,andtheboundaryconditions)areimportantfactorsindesigningtheTJI-TPJtoreachawellde-velopedreactingcondition.Bothnon-reactingandreactingsimulationswithsimilarwconditionshavebeenperformed.Onemayhaveltytosetupthenon-reactingcaseex-perimentally,becausetheincominghotturbulentjetnaturallyignitesthepremixedmixture.Nevertheless,thiscaseprovidestheopportunitytoisolateandstudythecombustiononthedevelopingturbulentscalarandhydrodynamicsAlso,thenon-reactingwre-sultscanbecomparedwiththoseavailableintheliteraturefornon-isothermalnon-reactingjets[89,38,37,86].OurdirectnumericalsimulationsprovideawealthofdataforabetterunderstandingofvariousphenomenainvolvedinTJI.ThesedatacanalsobeusedtodevelopreliablemodelsforReynolds-averageNavier-Stokes(RANS)andlargeeddysimulation(LES)ofTJI.Here,westudythedetailsofTJI-TPJandinvestigatesomeofitsuniquefeaturesbyanalyzingarangeofw/combustionvariables.Thereactingwisspatiallydividedintoanddevelopedregions.Inthelaterregion,threemainw/combustionzones4areideni)remnantofthehotproductjetzone,ii)burned-mixedzonewheretheproductsofthewcombustionmixwiththeremnantofthehotjet,andiii)zonethatseparatestheunburnedwandburned-mixedzones.Detailsofthestructuresineachzoneincludingtheassociatedstatisticsarepresentedinlatersections.TheuniqueTPJ-TJIsetupprovidesfundamentalinsightsonthecomplexandturbulencestructuresinTJI-assistedcombustionsystems.Itcanbeusedforparametricstudiesofkeyw/combustionparameters.Amongimportantparameters,here,weconsidertheveryimportantthermo-chemicalconditionsofthewandtheincomingjettodevelopinsightsintothetemporaldevelopmentofinteractionsandvariouscombustionzones.Awiderangeofwcompositionsisconsidered,fromultra-leantoleanmixtureswithequivalenceratiosof˚0:1,0:2,0:35,and0:5.ItisfoundthatTJIiscapableofinitiatingultra-leancombustionbyexposingthemixture,constantlyandforalongerduration,toahightemperaturejet.ItisshownthatthelowabilitylimitofHydrogen-fuelmixture,˚0:14,canbedecreasedmoredespitetheexistenceofthelocalizedextinctions.Weobservesanimportantchangeintypebychangingthejetcompositionfromtheproductsofleantostoichiometric,andthentorichmixtures.Eventhoughtheismostlyofpremixedtypeinallsimulatedows,incaseswithveryrichinitialthemixturethegeneratedjetincludesunburnedhightemperaturefuel,whichresultsintothesimultaneousgenerationofthepremixedandsionThisphenomenonthecombustionprocesses,tly,byincreasingoveralltemperatureandheatrelease.OurunderstandingofTJI-assistedcombustionwouldbtremendouslyfromtheDNSdataandanalysisprovidedinthisstudy.Thischapterisorganizedasfollows.In§1.3,thegoverningequationsandnumeri-calmethodologyarepresented.In§1.4,thewisdescribed.Section1.55providesdetailedanalysisofthewandthetemporalandspatialevolutionsofvariousw/combustionquantitiessuchasheatreleaserate,temperature,speciesconcentrations,vorticity,Baroclinictorque,andspeed.Insection1.6,theofthewandincomingjetthermo-chemicalpropertiesarestudiedconsideringvariousw/combustionquantitiessuchasheatreleaserate,temperature,speciesconcentrations,vorticity,andanewlyTJIprogressvariable.Section1.7summarizesthemainandconclu-sion.Section1.7summarizesthemaindingsandconclusions.1.3GoverningequationsandnumericalmethodologyForthisDNSstudy,anin-housecodeisdevelopedinwhichtheconservativeformoffullycompressible,three-dimensionalNavier-Stokesequationsissolvedwithhighordernumericalmethods.Thegoverningequationsincludethefollowingcontinuity,momentum,energy,andspeciesequations:@ˆ@t@@xi‹ˆui“0‹i1;2;3“;(1.1)@@t‹ˆui“@@xj›ˆuiuj”@p@xi@˝ij@xj;(1.2)@‹ˆet“@t@@xi‹ˆuiet“@qi@xi@@xj›ijui”_QeˆNsQ1˚›uiu;i;(1.3)and@@t‹ˆ˚“@@xi‹ˆui˚“@Ji@xiˆ_S:(1.4)Inequations1.1-1.4,theprimaryvariablesarethedensity,ˆ,thevelocitycomponentinithdirection,ui,thetotalenergy,et,andthescalarmassfraction,˚;1;:::;Ns(Ns6representsthenumberofspecies).ijisthetotalstresstensorij˝ijij:(1.5)Theviscousstresstensor,˝ij,isobtainedbythefollowingNewtonianmodel:˝ij2Re12„@ui@xj@uj@xi‚13@uk@xkij:(1.6)Theheatvector,qi,isobtainedbasedontheFourierlawasqi‹1“RePrM2ª@T@xi;(1.7)andthespeciestermJiˆ˚u;i;(1.8)isevaluatedbasedontheFick'slaw,whereu;iistheithcomponentofvelocityforspecies.Inequations1.3and1.4,_Sistherateofmassproduction/destructionperunitvolumeforspeciesbychemicalreactionand_Qerepresentstheheatreleaseratecalculatedas_QeNsQ1_Sh:(1.9)Thetotalenergyandspeciesenthalpy,h,areexpressedasetNsQ1h˚p~ˆ12uiui;(1.10)7andhTST0Cp‹T“dTh0f;(1.11)whereCpandh0farethespheatandenthalpyofformationofspecies,respec-tively.Theconservationequationsareclosedbytheequationofstate,pˆR0TNsQ1˚W;(1.12)whereWandR0arethemolecularweightofspeciesandtheuniversalgasconstant.TheChemkinthermodynamicdatabase[49]isusedtoobtainspeciesthermodynamicsandtransportproperties.Theential[44]areexpectedtobeimportantinthestudiedhydrogenandareincludedinthecalculations.Thecombustionofhydrogen-airismodeledwiththedetailedchemicalkineticsmechanismdevelopedby[102].Thismechanism,whichisextensivelyusedinseveralpreviousstudiesonhydrogencombustion[47,108,7,13],consistsof38elementaryreactionsand9species‹H2,O2,O,OH,H2O,H,HO2,H2O2,andN2“.Table1.3showsalltheforwardandbackwardelementaryreactions,notreadilyavailableintheliterature.Reversedrateconstantsinthismechanismarecomputedfromtheforwardrateandequilibriumconstants.Thediscretizationofthegoverningequationsisbasedonthecompactscheme[84,57],whichyieldsuptoeighthorderspatialaccuracy.Inordertoavoidnumericalinstabilitiesandremovethespurioushighfrequencynsinthesolutions,alowpass,highorder(uptosixthorder),spatialimplicitoperatorisused.ThetimeisbasedonthethirdorderlowstorageexplicitRungeKuttamethod[50].ThenumericalmethodutilizedherehasbeenusedpreviouslyinDNSandLESoflowspeedandhighspeed8turbulentreactingws[10,3,58,11]andisproventobequiteaccurateandsuitableforthecurrentstudy.1.4FlowThecomputationalconsideredinthisstudyconsistsofaspatiallydeveloping,three-dimensionalturbulentjetissuinghotcombustionproductsintoanambientcombustibleleanpremixedw.Aschematicofthewtogetherwiththespofphysicaldimensionsarepresentedin1.1.Thewevolvesspatiallyinthestream-wisedirection‹x“.Thefreestreamboundaryconditionsareimposedinthecross-streamdirection‹y“,andperiodicboundaryconditionsareimplementedinthespanwisedirection‹z“[84].IntheTJI-TPJ,thejetexpansionishighlybythewmomentum,fuel-airequivalenceratio,andturbulence-controlledspeed.Apre-studywasperformedfordesigningawelldevelopedreactingTJI-TPJration.TheTJI-TPJwhydro-dynamics,thermo-chemicalproperties,andgeometrieshavebeendesignedsuchthatstablecombustionregionsandzonesareestablished.Table1.1providesthewandthejetthermo-chemicalproperties,whereTco,Uco,ZHco,and˚corepresentthetemperature,thestreamwisevelocity,theelementalmassfrac-tionofHradical,andtheequivalenceratioofthew.TheequivalentvariablesfortheincomingjetaredenotedbyTj,Uj,ZHj,and˚ij.However,˚ijistheequivalenceratioofaninitialhydrogen-airmixtureatatemperatureequalsto1000‹K“,whichitscombustionprod-uctsandtemperatureareassignedtotheincomingjets.Thespeciesmassfractionvaluesofthejetsforallsixcasesareprovidedintable1.2.InCase1toCase4,thewcompositionsvaryfromultra-leantolean(˚co0:1,0:2,0:35,and0:5),withthesamewtemperature9Figure1.1:Schematicofturbulentjetignitionofturbulentplanejet,TJI-TPJ,andvelocity,Tco850‹K“andUco150‹m~s“.Thesecaseshavethesamehotproductjetwith˚ij1:0andTj2556:0‹K“andcangreatlyhelptoanalyzethewontheturbulence-combustioninteractions.Theyexhibitverytbehaviorfromfastburningtomixedwiththemistryandevenlocalextinction.Theofthejetcompositionorequivalenceratio(leanandrichwith˚ij0:5and2:0)areinvestigatedbyconsideringCase5andCase6.Inthesecases,thesamewconditions(equivalenceratio,etc.)asCase3areconsidered.Notethatbychangingtheinitialmixtureequivalenceratiofrom0:to2:0,elythefuelconcentrationintheproductsischangedfromnonetot,alsothejettemperatureischangedfromTj2050to2350‹K“.Inallsixcasesconsideredhere,thejetvelocityissettobethreetimesofthewvelocity,Uj3Uco450‹m~s“.Inordertoisolatethecombustionwithinthethreewthroughtime,thereactionsourcetermsintheenergyandspeciesequations(equations1.310and1.4)areturnedsothatthewandturbulencebecomefullydevelopedbyt3˝0.Thesimulationsperformeduptot17˝0inordertoaccuratelycalculatethetimeaveragedstatistics.TheselectedallowstheunderstandingofspTJI-TPJphysicalfeaturesthatarebelievedtobeinvariantofthegeometryandcommoninpracticalTJI-assistedcombustionsystems[103].Table1.1:Thermo-chemicalpropertiesoftheincomingjetsandws.Case#Tj‹K“Tco‹K“˚ij˚coZHjZHcoCase125568501.0e01.0e-12.85e-24.03e-2Case225568501.0e02.0e-12.85e-27.74e-2Case325568501.0e03.5e-12.85e-21.28e-1Case425568501.0e05.0e-12.85e-21.73e-1Case520508505.0e-13.5e-11.44e-21.28e-1Case623508502.0e03.5e-15.54e-21.28e-1Table1.2:Thespeciesmassfractionsintheincomingjets.Case#˚H2˚H˚O2˚O˚OH˚H2O˚HO2˚H2O2˚N2Case1-42.0e-72.1e-41.2e-21.2e-39.9e-32.2e-12.1e-43.4e-77.57e-1Case51.9e-71.3e-61.1e-11.7e-41.8e-31.2e-11.6e-61.7e-77.55e-1Case62.7e-23.3e-41.2e-51.5e-59.9e-42.4e-16.7e-96.8e-97.24e-1Thegridandtimeresolutioninthesimulationsarecarefullychosentoresolveallturbulentandwstructures.Sinceadetailedchemicalkineticsmechanism[102]isincorporatedtodescribethehydrogen-aircombustion,thestructuresandscalararecantlycomplex.Therefore,ameshisincorporatedforcapturingthezoneasrepre-sentedbyintermediateradicals,e.g.H[91].UniformgridspacingsofyD~6062:5,x1:5y,andz1:9yareusedinthecross-stream,streamwise,andspanwisedirections,respectively.ThegridpointsaroundalocallymaximumHmassfractionareaareshownin1.2,illustratingaregionofthefront.Theminimumgridpointscoveringthethickness(basedonHradical)intheentirecomputationaldomainisfoundtobe9.Theminimumgridnumberforcapturingthezonebased11Table1.3:DetailedchemistrymodelforH2~O2system.AExpofTENo.Mechanism(cm/mol/s)(kJ/mol)1O2HXOHOkf2.20E140.007.03E01kb1.72E130.003.52E002H2OXOHHkf5.06E042.672.63E01kb2.22E042.671.82E013H2OHXH2OHkf1.00E081.601.38E01kb4.31E081.607.64E014OHOHXH2OOkf1.50E091.140.42E00kb1.47E101.147.10E015HHMXH2Mkf1.80E18-1.000.00E00kb7.26E18-1.004.36E026HOHMXH2OMkf2.20E22-2.000.00E00kb3.83E23-2.004.99E027OOMXO2Mkf2.90E17-1.000.00E00kb6.55E18-1.004.95E028HO2MXHO2Mkf2.30E18-0.800.00E00kb3.19E18-0.801.95E029HO2HXOHOHkf1.50E140.004.20E00kb1.50E130.001.70E0210HO2HXH2O2kf2.50E130.002.90E00kb7.27E130.002.44E0211HO2HXH2OOkf3.00E130.007.20E00kb2.95E130.002.44E0212HO2OXOHO2kf1.80E130.001.70E00kb2.30E130.002.31E0213HO2OHXH2OO2kf6.00E130.000.00E00kb7.52E140.003.04E0214HO2HO2X2HO2kf2.50E110.005.20E00kb0.00E000.000.00E0015OHOHMXH2O2Mkf3.25E22-2.000.00E00kb1.69E24-2.002.02E0216H2O2HXH2O2kf1.70E120.0015.70E00kb1.32E120.0083.59E0017H2O2HXH2OOHkf1.00E130.0015.00E00kb3.34E120.003.12E0218H2O2OHXH2OHO2kf2.80E130.0026.80E00kb9.51E120.008.68E0119H2O2OHXH2OHO2kf5.40E120.004.20E00kb1.80E130.001.34E02kA:Tn:exp‹Ea~RT“;units:mol,cm3,K,andkcal.Third-BodyMisH26:5H2O0:4O20:4N2OOHHO2H2O2:12Figure1.2:Thegridresolutionatthefront,idenbasedon˚H,andadviewofthefrontbyafactorof261.onthehydroxylradicalOHismorethan15.Theconcentrationvariationsofotherspecies(notshownhere)alsocothescalareldstobeaccuratelycomputedwiththeadoptedgrids.However,tofurtherassesstheadequacyofgridresolutionintandtur-bulencezones,speciallythezone,wehavecomputedthelocalvaluesoftheKolmogrovlengthscale,‰3’1~4,andfoundthemtobelowerthanthegridsize›xyz”13.Therefore,thedesignedcomputationalmeshisbelievedtobeenoughtoaccuratelyre-solvealltemporalandspatialstructuresofw,turbulence,andscalars.Inordertoensurethegridindependence,allsimulationsareconductedwiththehighestresolutioninvolving82066095uniformgridpoints.Thecomputationaltimeincrementissettobesmallerthanthesmallestcharacteristictimescalesassociatedwiththehydrodynamicsandchemistry.Toproduceawelldevelopedturbulentw,turbulenttionsbasedonanisotropicturbulenceareaddedtotheincominghotproductjetvelocityThis13isgeneratedbysolvingthegoverningequationswithperiodicboundaryconditionsandaninitiallyrandom,solenoidal,andGaussianvelocityforalongtime[116].Theturbulence(velocity)intensityischosentobe10%ofthehotjetvelocity.Toobtaintemporalstatistics,thesimulationsareadvancedforatlylongtime,17˝0(˝0218:75,fortheaveragevelocityofUrefUjUco2300‹m~s“,andthestreamwisedomainlengthofLx17:5D65:625103‹m“).Eachsimulationutilizesabout0:2millionServiceUnits(SU)son250IntelmachinesatMichiganStateUniversityandUniversityofTexasatAustin.Toproduceawelldevelopedturbulentw,turbulenttionsbasedonanisotropicturbulenceareaddedtotheincominghotproductjetvelocityThisisgeneratedbysolvingthegoverningequationswithperiodicboundaryconditionsandaninitiallyrandom,solenoidal,andGaussianvelocityforalongtime[116].Theturbulenceintensityischosentobe10%ofthehotjetvelocity.Toobtainstatistics,thesimulationisadvancedforthreew-throughtime,˝0,beforeaveragingthevariablesforalongtime,17˝0(˝0218:75,fortheaveragevelocityofUrefUjUco2300‹m~s“,andthestreamwisedomainlengthofLx17:5D65:625103‹m“).Eachsimulationutilizesabout0:3millionServiceUnits(SU)son250IntelmachinesatMichiganStateUniversity[1]andUniversityofTexasatAustin[2].1.5Resultsanddiscussions:wandfeaturesofTJI-assistedcombustionInthissection,theresultsassociatedwiththewhydrodynamicsandthermo-chemicalconditionsofCase3(shownintables1.2and1.1)forbothnon-reactingandreactingwsarepresentedandanalyzedwithafocusonthereactingw.Withinthethreew14(a)(b)(c)(d)Figure1.3:Instantaneouscontoursofthetemperatureatamiddlespanwiseplane,‹z1:5D“,atttimesduringwtransitionfromanon-reactingwtoareactingone.(˝ig3˝0)throughtime,thereactionsourcetermsintheenergyandspeciesequations(equations1.3and1.4)areturnedsothatthewandturbulencebecomefullydevelopedbyt3˝0asseenin1.3(a).Thebasiccharacteristicsofisothermalandnon-isothermalmixingjetsfortthermo-chemicalandhydrodynamicsconditionshavebeendiscussedindetailsinpreviousstudies[86,83,103,21,74,92,4,114,113].Here,thenon-reactingTPJissimulatedasabenchmark,providingauniqueopportunitytoisolatethecombustiononthewandturbulence.ThereactingTJI-TPJsimulatedinthisstudyistheofitskind.151.5.1FlostructureThewtransitionfromnon-reactingtoreactingconditionsisshownin1.3,wherethetemporalvariationsoftheinstantaneoustemperaturecontoursareconsidered.Thistransitionmaynotbereproducibleexperimentallysincethereactioncannotbesuddenlyinitiatedfromafullydevelopedandmixedturbulenthotproductandfuel-airmixture.Figure1.3(a)showsthealreadydevelopednon-reactingjetatt3˝0,justbeforethecombustionstarts.Figures1.3(b)and(c)showthat,incomparisontothenon-reactingjet,thereactingjetspreadsmuchmoreinthecross-streamdirectionasthejettemperatureincreasesbytheformationofzonessurroundingthejetedges.Oneofthemainofthecombustionappearstobeontherelativelysmallwscales.Thesequenceoftemperaturecontoursin1.3(a)-(d)clearlyshowsthatsmall-scaleturbulentstructuresinthejetzonearegraduallyremovedbythecombustion.Yet,theturbulencewrinklesandaltersthelocalestructuresobservedtobeformedintheregionssurroundingthemainjet1.3d).Despitetheirsimilaritiestothoseobservedin\standard"turbulentpremixed[93],thewandstructuresintheTJI-TPJaretlybytheexistenceofthehotproductturbulentjetbehindtheintheburnedzone.TobetterdescribethecomplexameandturbulenceintheTJI-TPJ,itisusefultodividetheentirewintotregionsandcombustionzones.Primarily,theowisdi-videdspatiallyintoseparateregionsbasedonthephysicalstructures,idenbytheheatofreaction.Thecombustionheatreleaserate,_Qe,isacriticalquantitytodiscernandtheirlocationsinturbulentreactingws.Thespatialdistributionof_Qeistlydependentonthee-turbulenceinteractions.Despiteitsmeasuring_Qeisachallengingtask[75,71].Here,_Qeisconvenientlyobtainedbyequation1.9[69].Figure1.416Figure1.4:Instantaneousheatreleaseratecontourafter17˝0.(Contourspresentedinthelowerareforthey0:5Dplane(Surfxzin1.1)showstheinstantaneouscontoursofheatreleaserateat17˝0.Thisureindicatesthatthewcanindeedbedividedintotworegionsinthestreamwisedirection:i)ne‹xB4D“andii)developed‹xC4D“regionswithveryntfeatures.Intheregion,thehotincomingjetessentiallycausesautoignitionatthejetshearlayerandsurroundingareas,wherethejetheatsthepremixedwandultimatelysustainstheinanultra-leanfuel-airmixture.Inadditiontothecombustion,highlydistortedturbulentstructuresaredevelopedinthisregionwhichenhancethemixing.Theprocessofe-turbulenceinteractionsandmixingoftheincominghotjetwithcoolerpremixedwinthereactingshearlayercreatesrelativelythickandgeometricallycomplexThethicknessisdeterminedmainlybasedonthedistributed_Qevalues.Marchinginthestreamwisedirection,aspatiallycontinuousanddistortedameisdeveloped.Whilethemovesawayfromthemainturbulentjetandspreadsinthew,itbecomesthinner.The_Qecontourplotsin1.4clearlyshowtheseparationoftheunburnedand17burnedzonesinthedevelopedregionwiththecross-streamspreadingoftherelativelythindistortedturbulentfront.Thelowercontoursinthisshowthe_QedistributioninthespanwisedirectioninaxzplaneatyD~2.Itisobservedthatthedistributedhighheatreleaseratevaluesvirtuallyvanishfromthemainjetasthewmoveawayfromthetothedevelopedregion.Eventhoughtheandturbulencefeaturesvaryovertime(asshownin§1.5.3),theyappeartobewellstabilizedinthedevelopedregion.InthedevelopedregionofthesimulatedTJI-TPJ,thewcanbedividedintofourmainzonesbasedontheparameters.Figure1.5showstheschematicofthesefourzones:I.hotproductjetzone,II.burned-mixedzone,III.zone,andIV.premixedwzone.Inordertoidentifytheabovezones,weprimarilyusedthetemperature,theHradicalmassfraction,andtheheatreleaserateeventhoughotherquantitiessuchasOHmassfraction,˚OH,vorticity,Ð!,andBaroclinictorque,Ð,mayalsobeused.Theprobabilitydensityfunctions(PDF)softemperature,P‹T“,andHradicalmassfraction,P‹˚H“,andthescatterplotof˚HversusTareshownin1.6(a)-(c).ThePDFplotsareusefulindelineatingthewintotzonesasshownin1.5.ThethreedistinguishablepeaksofP‹T“andP‹˚H“in1.6(a)and(b)arerelatedtothethreeactivecombustionzones.ThedataassociatedwiththewarenotincludedintheseItisworthwhiletomentionthatdetailsofthewandmayvarywithchangesinthermo-chemicaland18Figure1.5:Variouszonesinthedevelopedregionofthesimulatedturbulentplanarjetwithturbulentjetignition.hydrodynamicsconditions,butthegeneralcharacteristicsofvariouszonesidenedintheTJI-TPJstaythesame.Thehotproductjetzone(labeledaszoneI)isidenbytheP‹T“peaklocatedatthehighesttemperaturevaluesin1.6(a)andbytheP‹˚H“peaklocatedatthemoderate˚Hvaluesin1.6(b).Inthenon-reactingw,asexpectedandshownin1.3(a)(and1.23b),thejettemperaturedecreasesby30%inabout16Dfromthejetinletduetoheattransferandmixingofhotjetwiththecoolerw.Thereisalsoatemperaturereductioninthereactingjetbecausethetemperatureoftheleanwmixtureisconsiderablylowerthanthetemperatureofthehotproductincomingjet.However,thetemperaturereductionislessthan10%,duetoheatingoftheremnanthotproductjetzonebythereaction.Theinitialvalueof˚Hinthehotproductjetisalsoincreasedfrom0:4104to2:1104,whichisconsistentwiththeamountofHradicalgeneratedthroughcombustionoftheleanwmixture.TheP‹T“peakintheintermediatetemperaturerangein1.6(a)andtheP‹˚H“peakinthelowest˚Hrangein1.6(b)arebothassociatedwiththeburned-mixedzone,whichislabeledaszoneII.Thereisatinteractionbetweenturbulenceandand,asitcanbeobservedinthescatterplotof˚HversusTin1.6(c),there19(a)(b)(c)Figure1.6:MarginalPDFsof(a)Temperatureand(b)Hradicalmassfraction.(c)ScatterplotofHradicalmassfractionandtemperature.20maynotbewellandboundariesbetweenzoneIIanditsneighboringzones,particularly,thehotproductjetzone.TheP‹T“peakfallsinbetweentheadiabatictemperatureoftheleanwandthehotproductjettemperature.ThisclearlyindicatesthatonaveragethewmixtureisexposedtoatamountofheattoinitiateandsustainthecombustionaszoneIIistlybythehotproductjet.Incontrast,thepeakofP‹˚H“occursatthesmallest˚Hvalues.Asareliablevariabletoidentifythefront,themaximumvaluesof˚Hoccuratthefront.The˚Hvaluesintheburned-mixedzonearelessthantheirvaluesinthehotproductjetandfrontzonesastheleanpremixedcombustionheatandproductsaretowardthemaininnerjetandw.Theburned-mixedzoneintheTJI-TPJhassomesimilaritieswiththeburnedzoneappearinginstandardturbulentpremixed[88,93,17],butwithrelativelyhighertemperatureandproductspeciesmassfractionvalues.ThecomplexityofthiszonearisesfromthestronginteractionsoftheinnerhotproductjetturbulenceandcompositionwiththeleanpremixedturbulentTheP‹T“peakinthelowesttemperaturerangeorzoneIIIof1.6(a)andtheP‹˚H“peakinthehighest˚Hrangein1.6(b)areassociatedwiththemetemperatureand˚Hatthefrontofcombustionofleanhydrogen-airmixture(withequivalenceratioof0:35andinitialtemperatureof850‹K“).Thesetwopeaksclearlyidentifythezone.Similartowhathasbeensuggestedforstandardturbulentpremixed[23,88,93,17,14],threeareasinthezonescanbeidenIII.1)Preheatedzonewhichislocatedveryclosetothefrontbutinsidetheunburnedfreshwmixture.Thiszoneisshownin1.6(c)andalsoin1.5byashadowareaontopofthefront.21III.2)Flamefrontwhichisidenbythehighest˚Hvaluesandarelativelyhighertem-peraturethantheadiabatictemperatureofleanmixture.Thiszoneisathinwrinkledsheetseparatingunburnedzoneformtheotherzonesasshowninres1.5and1.6(c).III.3)Behindtheamefrontinburned-mixedzonewhichhasa˚Hlevellessthanthatinthefront1.6c).ItisworthwhiletoemphasizethatthetemperatureandHmassfractioninareaIII.3andtheentirezonearegreaterthanthoseexpectedforastandardturbulentpremixed[30,61,33,55,60]becauseoftheheattransferandmixingwiththehotproductjet.Havingvariouscombustionzonesinthedsidenwecanstudytheofcombustiononthesezonesbyexaminingscalarvariables(likeT,H2,OH,andH)andhydrodynamicsvariables(like!,andBaroclinictorque).Figure1.7showsthetemper-aturecontoursforbothnon-reactingandreactingwsat17˝0.Comparingtheseresultstotheonespresentedin1.3(a)and(d)thatthereactingwisalreadywelldevelopedatt4˝0anditisqualitativelysimilartothatshownatt17˝0.Oursimulationsareconductedforalongtimetocalculatethestatistics.Thesmallturbulentwstructuresinnon-reactingw,asseenin1.7,arevirtuallyeliminatedbythecombustion.Inthespanwisedirection,thewisshowntobeinitiallyhomogeneousandisotropicduetotheimposedturbulentw.Itstayshomogeneousfurtherdownstream,butwithconsiderablylargerturbulentscales.Evidently,reactioncausestheformationofcomplexcombustionzones,particularly,attheshearlayersandalsoconsiderablejetspreadingandheating.However,thestructuresatthezonesarenotwellcharacter-izedbythetemperaturecontours,sincetheincomingjettemperatureisconsiderablyhigher22(a)(b)Figure1.7:InstantaneousTemperaturecontoursfor:(a)Non-reactingand(b)Reactingcasesafter17wthroughtime,˝0.thantheadiabatictemperatureoftheleanwcombustion.Tosuitablemarkerswhichcorrelatewellwiththeand_Qe,thespatialdistributionsofvariousspeciesintheTJI-TPJwhavebeenexaminedindetails.Thefuelmassfractioncontours(notshownhere)generallyrepresentthemainreactiveareas;however,moredetailsofthescalarcanbeobtainedbyconsideringtherad-icalspecieslikeOHandH.Asthejetcompositionismadeoftheproductsofstoichiometrichydrogen-airmixturecombustion,the˚OHvaluesinthehotjetarerelativelyhigh,asop-posedtothatintheleanpremixedwcombustion.Naturally,inthenon-reactingwthehighOHandHconcentrationsinthehotproductjetareconsiderablydilutedthroughmixingwiththew,exhibitingqualitativelysimilarbehaviortotemperaturein1.7(a).Inthereactingcase,asshownin1.8(a),theOHradicalgeneratedbythecombustion(veryintensivelyintheneregionandlessintensivelyinthedevelopedregion)addsuptotheinitialamountofOHinthejet,causingthemaximum˚OHtooccurinthehotproductzoneandnotinthezone.InstandardpremixedOHradi-calscanidentifythezone[64,111,13].Figure1.8(a)showsthatthe˚OHvaluesare23(a)(b)Figure1.8:Instantaneous(a)OHand(b)Hconcentrationcontoursforreactingwatt17˝0.indeedhigherinthefrontthanthoseintheimmediatesurrounding.However,sincetheOHconcentrationinthestoichiometricly-burnedproductjetisalreadyt,isolationofthefrontby˚OHbecomessomewhatIncontrasttoOH,theHradicallevelisrelativelylowinthehotproductjet,Consequently,asshownin1.8(b),˚Hbetteridenthelocationofthefront.Withintheldregion,thehighvaluesof˚HinitiallyoccurattheedgesoftheincomingjetbeforespreadingintothejetasshearlayersdevelopandgeneraterelativelythickInthedevelopedregion,˚Hvaluesmaximizeatthefrontanddroptoverylowvaluesintheburned-mixedzone,consistentwiththeheatreleaseratecontourplotsin1.4.Thescatterplotof˚OHversus_Qe,coloredbasedonw/combustionzones,in1.9(a)quantherelationshipbetweenthesetwovariables.Lowcorrelation(withcorre-lationcotof0:35)between˚OHand_QeindicatesthattheOHradicalisnotsuitableforisolatingtheintheTJI-TPJtion.Incontrast,thescatterplotof˚Hand_Qeine1.9(b)exhibitsahighcorrelation(withcorrelationcontof0:88)betweenthesetwoquantities.Inconclusion,becauseofrelativelylow˚Hintheproductjet,Hrad-24(a)(b)Figure1.9:Scatterplotsof_Qe,˚H,and˚OH,anillustrationofthespatialcorrelationbetweenheatreleaserateand(a)OHmassfractionand(b)Hmassfraction.ical(andotherspecieswithsimilarbehaviorlikeO,HO2,andH2O2)isbetterrepresentingtheleanfrontinthesimulatedTJI-TPJbyprovidingclearboundariesbetweentheunburnedandburned-mixedzones.Notethat1.9(a)and(b)areassociatedwiththewinthedevelopedregion.Duetomoretinteractionsofandwintheregion,thecorrespondingcorrelationcotsarelower(0:32for˚OHwith_Qeand0:84for˚Hwith_Qe)inthisregion.TofurtherinvestigatethebehaviorofOH,H,andotherspeciesinthesimulatedTJI-TPJthespatialdistributionofallreactivespeciesisexamined.Figures1.10(a)and(b)showthenormalizedspeciesmassfractionsattwostreamwiselocations˘x~D4and16(shownin1.1)versusthecross-streamdistancefromcenterline,normalizedbythethejethalfwidth,i.e.y~‹D~2“.Thespeciesmassfractionsarenormalizedbytheirlocalmaximumvalues.Evidentlyandexpectedly,thereactivespeciesfollowttrendsintzones.Whilethefueliscompletelyconsumedinthezoneandhaszeroconcentrationintheburned-mixedandhotjetzones,considerableamountofO2istransportedtoandmixedwiththemaincorejet.HandOradicalsaswellasHO2and25H2O2speciesfollowasimilartrend.Theirmassfractionvaluesremainrelativelysmallintheburned-mixedandhotjetzonesandincreaseatthefrontat5:5BB5:8.Incontrast,theOHandH2Omassfractionsmaximizeinthehotproductjetzoneandnotatthefront,wheretheirvaluesarenotdistinguishablefromthoseintheneighboringzones.Acloseexaminationof1.10(a)and(b)indicatesthattheH2,H,O2,O,HO2,andH2O2massfractionsat˘4and16aresimilaratthefront,indicatingselfsimilartrendsinthespeciesdistributioninthiszone,butnotnecessarilyattheburned-mixedandhotjetzones.TheOHandH2Oarequitetalongthesetwolocations,whereselfsimilaritycannotbeachievedforthesetwospeciesinthesimulatedw.TheuenceofcombustiononthewvariablesaroundtheamezoneisfurtherstudiedbyconsideringtheconditionaljointPDFofthetemperatureandHmassfractioninareaswith1000DTD1800,P‹T;˚HS1000DTD1800“,in1.11(a).Similartoure1.6(c),anormalbellshapedcanbeobservedforthejointT-˚HPDF.Intheareaswithtemperatureslessthantheadiabatictemperature(e.g.,inthepreheatedzoneveryclosetothefrontinsidetheunburnedw)˚HandTvarywithinthesamerangeastheydoatthefront.However,thevaluesofP‹T;˚HST“atthefrontarelowerthanthosebehindthefront.Infact,theareabehindthefrontinsidetheburned-mixedzoneaccountsformajorityofthehightemperaturevaluesinzoneIII.3in1.6(c).Thisthatthefrontisathinzonesurroundedbyhotpremixedmixtureandproducts.TheseresultsareconsistentwiththeconditionalmarginalPDFoftemperatureinthezone,conditionedon4D˚H104D6,in1.11(b).Asshownin1.6(c)(zoneIII.2),4D˚H104D6correspondstothefront.ThePDFoftemperaturewithinthezone,P‹TS˚H“,issomewhatsimilartothatonenormallyseeninastandardleanpremixedautoignitedat850‹K“.Itisclosetoanormal26(a)(b)Figure1.10:Normalizedspeciesmassfractionsversusat(a)˘4and(b)˘16.27(a)(b)Figure1.11:ConditionaljointandmarginalPDFs.(a)ConditionaljointPDFoftemperatureand˚H,P‹T;˚HS1000DTD1800“(b)ConditionalmarginalPDFoftemperature,P‹TS4104D˚HD6104“.distributionwithapeakaround1480‹K“andatvariance.However,theisskewedtowardhighertemperatures,mostlybecauseofpreheatingofthebythehotjet.TheplateauattherightendoftheP‹TS˚H“,wherethestartstodiminish,isassociatedwiththeburned-mixedzone.SincethestandarddeviationofP‹TS˚H“isrelativelyhigh,thetemperaturemightnotbeagoodindicatorforthelocationinthesimulatedTJI-TPJasopposedtostandardturbulentpremixedInadditiontoheatrelease,temperature,andspecieswehavealsoconsideredthebehav-iorofturbulentvariableslikevorticityintheTJI-TPJ.Figure1.12showsthecontoursofvorticitymagnitude,!SÐ!S,forbothnon-reactingandreactingcases.Thecontourvalueshavebeenadjustedsothatquantitativecomparisonscanbemade.Itcanbeseenin1.12(a)thatthesimulatednon-isothermaljetishighlyturbulentwithtatalllength(andtime)scales.Overall,asimilarvorticityisobservedinreactingandnon-reactingws,eventhoughthesmall-scaleturbulentstructuresareclearlydepletedby28(a)(b)Figure1.12:Instantaneousvorticitymagnitude,!,contoursfor(a)Non-reactingand(b)Reactingcasesatt17˝0.thecombustion.Intheregion,thevortexstretchingandcompressibilityarethesourcesofthevorticityproduction.Furtherdownstreaminthedevelopedregion,thesig-tvariationsindensityandpressurecausetheBaroclinictorque,Ð1ˆ©ˆ©P,toplayamoreimportantroleingeneratingvorticity.Thisbehaviorisgenerallythesameinbothnon-reactingandreactingws.Closetothezone,theBaroclinictorqueandthevortexstretchingarethemainsourcesofgeneratingvorticity.However,inthecombustionzonesthevorticityisnegativelybythereactionbecauseheatreleaseinducesvolumetricwexpansionandtemperaturedependencyofviscosityincreasesthedissipationofvorticity.Thesurfacesareconvected,wrinkled,andstrained(muchmoreintenselyintheregion)bytheturbulencepropagatingwithrelativelyhighvelocitiesparallelandperpendiculartothew.Yet,evenfortheleanpremixedconsideredhere,theturbulenceisnotstrongenoughtocauseanoticeablelocalextinctionandsurfacebreakupasobservedin1.8(b).Thereisapressureassociatedwiththeheatofreactionofthewrinkledandexpandedw,thatindirectlythesheet29evolutionthroughoscillationsinthevelocityAsexpected,therearealsolocallylargedensitydropsinthecombustionzones.TheaccumulativeofpressureanddensitygradientsandtheirmisalignmentmaketheBaroclinictorque(orthemagnitudeofit,SÐS)asuitableturbulent\hydrodynamic"variableforcharacterizingthesimulatedTJI-TPJ.In1.13(a)itcanbeobservedthatevenintheabsenceofthereaction,tisgeneratedattheshearlayerduetodensityjumpbetweenhotjetandw.Furtherdownstream,turbulentmixingcausesmoredistributedvaluesoflowlevelthroughoutthedomain,particularly,atsmall-scales.Thesamegeneralbehaviorcanbeobservedtoexistin1.13(b)forthereactingcase.Infact,theBaroclinictorquedistributionintheregionisverysimilareventhoughtheyaretinthedevelopedregionwhenthereiscombustion.Intheregionandinsidethereactivezonesattheoverlapofthehotproductandburned-mixedzones,isgeneratedmainlyduetodensitybetweentheincominghotjetandproductsoftheleanwcombustion.Inthedevelopedregion,thedominantmechanismforBaroclinictorquegenerationischangingasthedensitygradientsdecrease.Largescalevariationsinarevirtuallyeliminatedbythecombustioninthereactingw.Theimportanceofinrepresentingthefrontisclearlyevidentin1.13(b),whereitisshownthatthelocalmaximumvaluesofinthezoneareremarkablysimilartothelocalmaximumvaluesof_Qeand˚H.ThesinglepointmarginalPDFsofBaroclinictorquefornon-reactingandreactingcasesareshownin1.14.Consistentwith1.13(a)and(b),awiderangeofBaroclinictorquevaluesexistsinthedomaininbothcases.Thisalsothatthehighvaluesseeninthenon-reactingwdisappearinthereactingwandtherelativelysmallvaluesbecomedominant.ThisindicatesthatinthesimulatedTJI-TPJcombustionnegativelythelargeandsmall-scalevorticitynotonlybecauseofvolumetricwexpansionand30(a)(b)Figure1.13:InstantaneousBaroclinictorque,contoursfor:(a)Non-reactingand(b)Reactingcasesatt17˝0.Figure1.14:MarginalPDFof,P‹˚“.increaseinviscosity,butalsobecauseofreductioninhighBaroclinictorquegeneration.Figure1.15(a)showstheconditionalmeanandintervalsoftheBaroclinictorque,˙,conditionedon˚H.Thewvaluesareincludedintheseconditionalplots.Notethatbyincreasing˚Honeelymovesfromthewandburned-mixedzonestowardtheremnanthotjetzoneand,afterward,tothezone.Figure1.15(a)showsthatatlow˚Hvalues,associatedwiththeburnedmixedzone,themeanBaroclinictorqueissmall.increasesinthehotjetzonebutitmaximizesatthezone.A31similarbehaviortoisobservedforthescalardissipationrateofHradical,˜H,as[101]˜HD@˚H@x’2‰@˚H@y’2‰@˚H@z’2;(1.13)whereDistheycot,afunctionoftemperature.ThescalardissipationrateistiedtotheturbulentvelocitySince˜Handbotharetransportedbyturbulencefromthejettothewinasimilarway,˜Hfollowssimilartrendstothosefor.Thestructurecanbecapturedby˜H.Figure1.15(b)showstheconditionalmeanandintervalsof˜H,˜H˙˜H,versus˚H.Therelativelylowvaluesof˜Hintheburned-mixedandwzonesareduetothesmallandsomewhatuniformvaluesof˚Hinthesezones.Intheremnanthotjetzone,˜Hincreasesduetostrongervariationsin˚HandalsoD.Highwrinklingresultsintolargescalargradientsor˜Hatthefrontwhere5104D˚HD6104(areaIII.2in1.6c).However,inthetwosidesofthe(zonesIII.1andIII.2in1.6c),behindthefrontintheburned-mixedzonesideandinthepreheatedzoneinthewside,˜Hdecreases.Thus,thehighestvaluesof˜Hareassociatedwiththefront,whichcanalsobeusedtoidentifyitslocation.Comparisonbetween1.15(a)and(b)additionallythatisasuitableturbulent(hydrodynamic)quantityforidentifyingtheintheTJI-TPJuration.1.5.2TurbulentspeedAsimplemethodisusedtocalculatetheturbulentspeed.Figures1.16(a)and(b)showthetimeandspanwiseaveragedtemperatureaTfsfornon-reactingandreactingcases.Thejetspreadrateinthereactingwisconsiderablygreaterthanthatinthenon-reacting32(a)(b)Figure1.15:Conditionalmeansandboundsof(a)Baroclinictorque,,and(b)scalardissipationrateofHradical.w,mainly,becauseoftheturbulentburningvelocity.Thecombustioninducedchangesinthewandturbulencewithintheburned-mixedandhotproductjetzonesalsohavesomeonthejetspreadrate.Thesecannotbewellcharacterizedandareexpectedtobelesstthanthepropagationspeed;thus,theyarenotincludedinourspeedcalculations.AssumepointspNandpRin1.16tobelocatedattheedgeofthenon-reactingandreactingjetsatthegeometricallocationsof›xpN;ypN”and›xpR;ypR”,wherexpNxpR.ThejetanglescanbecalculatedasNtan1‰ypNxpN’andRtan1‰ypRxpR’,assumingtheoriginoftheanglesislocatedatthevirtualjetorigin[53].TheturbulentspeedatanyaxiallocationcanthenbecalculatedasSTypRypNtT,wheretTuxpNanduaretimeandconvectivevelocity.Figure1.17(a)showsthevariationsofthecalculatedturbulentspeed,ST,andtheturbulenceintensity,I‰uœ2vœ2wœ2’12Uref,atthefront,whereUrefUcoUj2300‹m~s“istheaverageofthewandhotproductjetvelocities.Itisobservedthattheturbulenceintensityconstantlydecreasesalongthejet,asthejet33spreadingandcombustionsimultaneouslydissipateturbulentstructuresinsidethejetandatthefront.Itisalsoshownthattheturbulentspeedisdirectlycorrelatedtotheturbulenceintensity;thehigherturbulenceintensity,thehigherturbulentspeed.Theseresultsareconsistentwithpreviousstudies[59,12].Variousanalytical,numerical,andexperimentalstudieshavebeenpreviouslyusedtocalculatethehydrogenturbulentspeed[112,97].Despiteinthermo-chemicalconditions,thecalculatedhydrogenturbulentspeedsarefoundtobecomparablebutslightlyhigherthanthosereportedintheliteraturepossiblyduetotstructuresintheburnedzoneandtheexistenceofthehotjet.Closeexaminationoftheinstantaneoustemperature,heatrelease,andspeciesdistributionsatttimesindicatesstrongvariationsinstructureandturbulenceintensity,whichisnotevidentinthemeanspeedin1.17(a).Figure1.17(b)showstheconditional(conditionedon˚H)meanandintervalsofI,I˙I,versus˚Hfortheentirew.Thehighstandarddeviationofturbulenceintensityatthezone,where4104D˚HD6104,isanindicatorofastrongvariationinlocalspeed.ContrarytothestandardturbulentpremixedinthestudiedTJI-TPJahightemperatureandmomentumturbulentwexistsbehindthefrontintheburnedzone,whichenhancesthecombustionatthezoneandincreasestheburningvelocity,ST.Thisisevidentin1.17(b),whichshowsrelativelyhighturbulenceintensitiesintheburned-mixedandhotjetzones(1104D˚HD4104).1.5.3TemporalandspatialvariationsofturbulentvariablesInordertoquantitativelycharacterizetheandturbulencedynamicsintheTJI-TPJ,timesignalsofthestreamwisevelocity,temperature,andHradicalmassfraction,withthecorrespondingPDF,mean,,standarddeviation,˙,Skewness,S,andKurtosis,K,forCase334(a)(b)Figure1.16:Contoursoftimeandspanwiseaveragedtemperatureandthejetspanspreadratefor(a)Non-reactingand(b)Reactingcases.(a)(b)Figure1.17:(a)Turbulentspeed,ST,andturbulenceintensity,I,atfrontvs.streamwisewdirection,(b)Conditionalmeanandboundsofturbulenceintensity.35presentedintable1.1arepresentedin1.18-1.22forthedurationof17˝0to20˝0attpointsshownin1.1.Point1:Thispointislocatedinsidethewfarawayfromthefront.Figure1.18providestheessentialinformationrequiredtounderstandthewvariationsatthispoint.Figures1.18(a)-(c)showthetimevariationofinstantaneousstreamwisevelocity,u1,temperature,T1,andHradicalmassfraction,˚H1,while1.18(d)-(f)presenttheassociatedPDFs.Thestatisticsarepresentedin1.18(g).ThetimesignalsofT1,u1,and˚H1showoscillationsaroundthewvaluesclosetothoseprovidedintable1.1forCase3.Themeanandstandarddeviationofvelocityareu1149‹m~s“and˙u11:62‹m~s“,consistentwiththewvalues.ThesmallnegativevalueofSu1isconsistentwiththeP‹u1“tobenegativelyskewed.Ku1isequalto2:75,closetothevalueforanormaldistribution.TheT1signalispositivelyskewed,withsmallstandarddeviation.SincePoint1islocatedoutofthecombustionzones,˚H1and˙˚H1arezero.Nevertheless,largepositivevaluesofS˚H1andK˚H1indicatethatsmallresidualsoftheHradicalproducedinthezonearesporadicallytransportedtoPoint1.Point2:Thispointislocatedinthepreheatedzoneveryclosetothefront(inthewside).However,thewatthispointisstillstronglybythew;thestreamwisevelocitycomponentoscillatesintherangeofUcoasshownin1.19(a)and(d).Themeanvelocityu2isequalto160‹m~s“withrelativelysmallstandarddeviation,˙u23:12‹m~s“.Theu2signalsalsoshowanasymmetric,negativelyskewedbehavior.T2signalsshowabimodaldistributionoftemperaturevaryingwidelyfromowtemperatureTcototheadiabatictemperatureoftheleanmixtureasnormallyexpectedinthepreheatedzoneofpremixed[17].P‹˚H2“formsatrimodaldistributionindicating36(a)(b)(c)(d)(e)(f)(g),˙,S,andKatPoint1˙SKu11491.62-0.2512.5T18490.60.312.75˚H11040.00.07.162.4Figure1.18:(a-c)instantaneousvariationsofu1,T1,and˚H1intime;(d-f)PDFofu1,T1,and˚H1;and(g)associated,˙,S,andK.37(a)(b)(c)(d)(e)(f)(g),˙,S,andKatPoint2˙SKu21603.12-0.443.09T21345285-0.71.90˚H21041.91.750.742.11Figure1.19:(a-c)instantaneousvariationsofu2,T2,and˚H2intime;(d-f)PDFofu2,T2,and˚H2;and(g)associated,˙,S,andK.thatintimethreettypesofthewpassthroughPoint2,namelythoseseeninthew,thepreheated,andzones.Atthispoint,the˚Hvaluesvaryfromzero(thew),to1104(thepreheatedzone),to5104(thefront).Point3:Thispointisalsolocatedatthefrontbutinsidethereactingzone.ThewatPoint3isbytheburned-mixedzone.Figures1.20(a)and(d)showthattheturbulentwatthispointhashighervelocitythanthew,therefore,u3169‹m~s“and˙u211:46‹m~s“arelargerthantheircorrespondingvaluesatPoint2.P‹u3“ispositivelyskewedwiththehighestKurtosis,Ku34:04,ascomparedtothoseatotherpoints.Itisshownin1.20(b)and(e)thatPoint3temperatureoscillatesbetweenthefronttemperatureandthehighertemperaturesassociatedwiththeburned-mixed38(a)(b)(c)(d)(e)(f)(g),˙,S,andKatPoint3˙SKu316911.460.784.04T317571301.053.50˚H31040.20.111.826.71Figure1.20:(a-c)instantaneousvariationsofu3,T3,and˚H3intime;(d-f)PDFofu3,T3,and˚H3;and(g)associated,˙,S,andK.zonewithT3and˙T3of1757‹K“and130‹K“,respectively.P‹T3“isarightskeweddistribution,whichsuggeststhatthispointisindeedbytheburned-mixedzone.Asexpected,the˚H3valuesarelowerthanthoseinthezone.P‹˚H3“alsoshowsarightskeweddistributionwitharelativelysmallpeakvaluesandlessweightingattherighttail.Sincethefrontishighlydistortedandtheamelocationchangesintime,thecharacterizationofthebyspatialpointsiscult.OurexaminationofheatreleaserateandHradicalcontoursindicatesthatthefrontkersbetweenPoint2andPoint3intime.Thus,thesimultaneousresultsinthesepointsprovideabetterunderstandingofthebehaviorandassociatedscalarandhydrodynamicintime.39Point4:Thispointislocatedinsidetheburned-mixedzone,whereunlikePoint3,thewistlybythehotproductjet.Figures1.21(a)and(d)showthatthevelocityatthispointiswidelychangingintimewiththemeanvelocityofu4262‹m~s“andrelativelyhighstandarddeviationof˙u435:55‹m~s“,anindicationofintensiveturbulence.AGaussiandistributioncanbetoP‹u4“sinceitgeneratesanearzeroskewnessofSu40:02andKurtosisofKu42:31.TheesofthehotproductjetcanbemoreclearlyobservedintheT4signalswhichtheyaregenerallygreaterthanT3.Themeanandstandarddeviationoftemperatureatthispoint,T4and˙T4,areequalto2065‹K“and116‹K“,respectively.P‹T4“isanegativelyskeweddistributionwithahighpeakaroundthemeanvaluesofT42065‹K“.Similarly,˚H4ishigherthan˚H3,indicatingagaintheofthehotjetwhichconsistsofhigherHradicals.ThePDFof˚H4,P‹˚H4“,ispositivelyskewedandhasaconcentrateddistributionandahighpeakaroundthemeanvalueof0:5104.Point5:Thispointislocateddeepinsidethehotproductjet,exhibitingthefeaturesex-pectedforareactinghotturbulentjetmixingwithacoolerpremixedfuel-airmixture.Figure1.22providestheessentialinformationforstudyingthetemporalwfeaturesatthispoint.Thevelocityvaluesarethehighestwhencomparedtothoseatotherpointswithu5316‹m~s“and˙u532:1‹m~s“.TheSkewnessandKurtosisforthevelocitydistri-butionareequalto0:002and2:651.22g)whichsuggestasymmetricandnearlyGaussiandistribution.Thetemperaturesignalsatthispoint1.22b)showabimodalP‹T5“distribution1.22e),indicatingtheinofbothburned-mixedandhotjetzones.Thissuggeststhatdistinguishingburned-mixedzonefromthehotproductzonemaynotbetrivialandthereisanoverlapbetweenthesetwozonesevenatthecenterofthe40(a)(b)(c)(d)(e)(f)(g),˙,S,andKatPoint4˙SKu426235.550.022.31T42065116-0.613.12˚H41040.50.210.362.45Figure1.21:(a-c)instantaneousvariationsofu4,T4,and˚H4intime;(d-f)PDFofu4,T4,and˚H4;and(g)associated,˙,S,andK.41(a)(b)(c)(d)(e)(f)(g),˙,S,andKatPoint5˙SKu531632.10-0.0022.65T5216891-0.42.72˚H51040.70.26-0.0092.453Figure1.22:(a-c)instantaneousvariationsofu5,T5,and˚H5intime;(d-f)PDFofu5,T3,and˚H5;and(g)associated,˙,S,andK.hotjet.However,highertemperatureandHradicalmassfractionatPoint51.22bandc),incomparisontothoseatPint4,indicatethatthedominantatPoint5arethoseduehotproductjet.Thisisalsoshownin1.22(e)and(f),wheretheP‹T5“andP‹˚H5“areobservedtopeakaroundhigherTand˚H5values.Theresultsin1.18-1.22showthetimehistoryofthewvariablesandappropriatestatisticsatlimitednumberofpoints.TobettershowtheaveragespatialvariationsofwvariablesintheTJI-TPJ,themeanandrootmeansquare(rms)valuesofthestreamwisevelocityandtemperaturealongseveralaxialandlateraldirectionsareconsidered.Theseresultsareobtainedbytimeaveragingforabout17˝0whichisatlylongtimetoassessthehighorderstatistics.Toanalyzetheselfsimilarity[86,32]ofthesevariablesinthe42simulatedTJI-TPJuration,onemaynormalizethecalculatedstatisticsbyspatiallyvariablenormalizationfactors;forexample,velocitycomponentsmightbenormalizedbythemaximumlocalvelocity.However,herewescalethevariablesbyconstantfactors(i.e.thewvelocityandtemperature,UcoandTco)inordertoshowtheirspatialbehavior.Figure1.23showsthemeanvelocityandtemperature,`ues~UcoandaTfs~Tco,versusthestreamwisedirection(˘x~D)aty~‹D~2“0;4;and8.Notethattheoriginofisatthemiddleofcomputationaldomain,sothat0and8correspondtothejetcenterlineandcw,respectively.Itcanbeobservedin1.23(a)thatforbothreactingandnon-reactingwsinsidethehotproductjetzonethemeanvelocitygenerallydecreasesalongthestreamwisedirection,veryrapidlyinthenregionthenslowlyinthedevelopedregion.Thebehaviorissimilarforbothwsinthenearregion.However,inthedevelopedregion`ues~Ucodecreaseslessinthereactingwthaninthenon-reactingw,suggestingthattheheatofcombustionnotonlycausesthejettospreadinthecross-stream,italsoenhancesthejetvelocityinthestreamwisedirection.Thenon-reacting`ues~Ucovaluesinsidethew(8)stayunchanged,whereasthereactingvaluesslightlyincreaseattheintersectionofthewandcombustionzones.ThestreamwisevariationsofaTfs~Tcoasshownin1.23(b)exhibitmoreinterestingtrends.ThemaximumvalueofaTfs~TcoisequaltoTj~Tco2556~8503:01forbothnon-reactingandreactingwsandoccursattheinlet.Asexpected,alongthejetcenterline(0)themeantemperatureisdecreasedlessandisevenslightlyincreasedinthereactingcasebecauseofthecombustion.Thespatialshiftsbetweentwzonescanbebetterrepresentedalong4,wherethewisinitiallythedominantzone.Atthiscross-streamlocation,aTfs~Tcoofthereactingwincreasesfrom1at˘8to2:2at˘16,indicatingthechangeofwfromthewzonetotheburned-mixedzone.However,themean43(a)(b)Figure1.23:Streamwisevariationsofaveragedvalues(a)streamwisevelocitycomponentand(b)temperaturepattcross-streamlocations.(`esreferstobothtimeandspanwiseaveragedvalue.Thickandthinlinesrepresentthereactingandnon-reactingcases,respectively)temperatureinthenon-reactingwstartstoslightlyincreaseat˘C10:5.Thewat8forbothcasesstayswithinthewzoneasaTfs~Tcoremainsconstantandequalsto1.Thecross-streamof`ues~Ucoand`urmses~Ucoatthreetstreamwiselo-cationsareshownin1.24(a)and(b).Theseareconsistentwiththetimevaryingvelocitiesin1.18-1.22,wherethemeanvelocityisshowntocontinuouslyde-creasefromthejetcenterlinetothewandthemaximumrmsofvelocitytooccuratthejetedges.Thetrendsaresimilarinnon-reactingandreactingws.Intheregion,thepeakrmsvelocityoccursclosetothezonewherethermstemperatureisthehighest,indicatingtoftheturbulenceoncombustionandviceversainthisregion.Furtherawayfromtheinlet,themaximumvaluesofrmsvelocityandtemperatureoccurattcross-streamlocations,indicatingmuchlessinteractionsbetweenthejetandezones.Nevertheless,theratioofurms`uesinbothwsarelessthan0:03,which44showsthattheturbulenceisnotunusuallystronginthesimulatedTJI-TPJ,ratheritiscompatiblewiththosereportedinthestudiesonnon-isothermalnon-reactingplanarjets[114,113]andthusisnotabletobreakthesurfaceandcreatecantlocalextinctioninthesimulatedw.Figure1.24(c)presentstheaTfs~Tcoforbothnon-reactingandreactingcasesatthreetstreamwiselocationsalongthecross-streamdirection.Asitisalsoobservedin1.23,themaximumjettemperaturedecreasesinstreamwisedirectionmuchlessinthereactingw.TheaTfs~Tcoreductionratefrom˘16to4is%74forthenon-reactingcase,whereasitis%93forthereactingcase.Consistentwith1.18-1.22,timeaveragedtemperaturevaluesdecreasecontinuouslyfromthehotjetzonetothewzoneeveninthereactingwsincethemaximumtemperatureofthecombustionoftheleanwislessthanthejettemperature.Thecombustionontemperaturesorrmsarerathert.Thevaluesof`Trmses~Tcoversusthelateralaxisforbothnon-reactingandreactingcasesatthreetstreamwiselocations,˘4;10;and16,areshownin1.24(d).Maximumvaluesofnon-reacting`Trmses~Tco,consistentwiththevelocityrms,occurclosetothejetedgesanddecreaseinthestreamwisedirection.Thisbehaviorisexpectedforaheatedturbulentjetmixingwiththecolderw.Figure1.24(d)alsorevealsthatthejetexpandstoabout2:3Dat˘16inthenon-reactingcase,whereasjetspanis4:3Datthesameaxiallocationinthereactingcase.Themaximumvaluesof`Trmses~Tcooccurclosetothejetedgesforbothcases.Inthedevelopedregionofthereactingw,thepeakrmstemperature,whichoccursatthecross-streamlocationsisverytthanthepeakofthermsvelocity.Sincehightemperaturevariationslocallyhappenatthezone,Trmscanbeusedtoidentifythiszone,inadditionof_Qe,˚H,and.45(a)(b)(c)(d)Figure1.24:Cross-streamvariationsof(a)meanstreamwisevelocity,(b)rmsofstreamwisevelocity,(c)meantemperature,and(d)rmsoftemperature.(Thickandthinlinesrepresentthereactingandnon-reactingcases,respectively)46Comparisonofthemeanvelocityandtemperature(shownin1.23aand1.23c)andthermsofvelocityandtemperature(shownin1.24band1.24d)indicatesthatcombustiononthescalararemuchmorenotableascomparedwiththevelocityItalsoshowsthatthesetwoarenotcorrelatedspeciallyatthezone.ThisismoreimportantandhastobeconsideredindevelopingclosuremodelsforLESandRANSofTJI-assistedcombustionsystems.471.6Resultsanddiscussions:jetandwondevelopmentofpremixedandnon-premixedincludinglocalizedextinctioninTJI-assistedcom-bustionInthissection,resultsconcerningtheofwandjetconditionsonthephysicalprocessesinvolvedintheTJI-assistedcombustionarepresentedanddiscussed.Figures1.25(a)-(f)presenttheinstantaneoustemperaturecontoursinaxyplaneatthemiddleofthethree-dimensionaldomainfortheconditionspresentedintable1.1att17˝0‹s“.Thecontourrangevaluesof850‹K“jTj2600‹K“arechosenforallcasessothatabettercomparisonscanbemade.Intheregion,˘x~Dn4,thehotincomingjetcausestautoignitionatthejetshearlayerandsurroundingareas,wherethejetheatsthepremixedwand,ultimately,sustainstheeven,inultra-leanfuel-airmixtures.Inadditiontothecombustion,highlydistortedturbulentstructuresaredevelopedinthisregion,whichstronglyinteractwiththecombustion.Theme-turbulenceinteractionsandmixingoftheincominghotjetwithcoolerpremixedwinthereactingshearlayercreatesrelativelythickandgeometricallycomplexintheregion.Independentofthewcompositions,visually,similarstructuresandshearlayersaredevelopedintheldregioninallcases,indicatingthedominanceoftheincomingjethydrodynamics.EventhoughthewcompositionisthesameinCase3,Case5,andCase6,temperaturecontoursin1.25(e)and(f)whencomparedto1.25(c),thatthejetvariablesareindeeddmorebytheincomingjetthanthewcombustion.48(a)(b)(c)(d)(e)(f)Figure1.25:Instantaneoustemperaturecontoursatthemiddlespanwiseplane‹z1:5D“andt17˝0for(a)Case1,(b)Case2,(c)Case3,(d)Case4,(e)Case5,and(f)Case6.49Marchinginthestreamwisedirectioninthedevelopedregion(˘k4),wherespatiallycontinuousanddistortedreactingandzonesaregenerated,theofwequiva-lenceratioismoreclear.Inthisregion,theturbulentpremixedseparatesfromthejetandactiveturbulentwregionsasitspreadsintothewincross-streamdirection.ThisseparationdevelopsvariouscombustionzonesinthesimulatedTJI-TPJbasedontheparametersasi)hotproductjetzone,ii)premixedzone,andiii)burned-mixedzone.Thehotproductjetzoneisidenbythehighesttemperaturevalues.Thezoneisidenbyrelativelylowtemperaturevaluesassociatedwiththeadiabatictemperatureofleanhydrogen-aircombustionwithinitialwtemperatureof850‹K“.Theburned-mixedzoneisrecognizedbasedontheintermediatetemperaturevalues.Theburned-mixedzoneintheTJI-TPJhassomesimilaritieswiththeburnedzoneappearinginstandardturbulentpremixed[88,93,17],butithasarelativelyhighertemperatureandproductspeciesmassfractionvalues.ThecomplexityofthisregionarisesfromthestronginteractionsoftheinnerhotproductjetturbulenceandcompositionwiththeleanpremixedturbulentTherefore,theremaynotbewellbound-ariesbetweenthiszoneanditsneighboringzones,particularly,withthehotproductjetzone.Inthespanwisedirection(notshownhere),thewisinitiallyhomogeneousandisotropicduetotheimposedturbulentw.Itstayshomogeneousfurtherdownstream,butwithconsiderablylargerturbulentscales.DetailedfeaturesofvariouszonesandregionsinTJI-assistedcombustionsystemshavebeendiscussedinreference[109].Figure1.25showsthattheprogressionorthejetgrowthrateofjetthermalhalfwidthinthedevelopedregion(˘k4)ishighlydependentonthewmixtureconditions.ForCase3andCase4withwequivalenceratiosof0:35and0:5theisstableandwidelyspreadsinthecross-streamdirections1.25candd).However,thecombustion50ofultra-leanmixturesinCase1andCase2withequivalenceratiosof0:1and0:2isweakasshownin1.25(a)and(b)hardlyestablishesstableanddistinguishablecombustionzones,showingtlocalizedextinctionandre-ignition(moredetailsarepro-videdinsection1.6.2).Despitetburnedjetthermo-chemicalconditions,thegrowthandstructureofcombustionzonesforCase5andCase61.25eandf)arealmostthesameasthoseforCase31.25c),suggestingthattheinitialenergyprovidedbythein-comingproductjetisttoinitiateastablecombustionintheregion.Theseresultsindicatethatthecombustioninthedevelopedregionisverysensitivetothewcompositionbutislessbytheincominghotproductjetcomposition.Expectedly,theunburnedhotfuelintheincomingjet1.25fforCase6)rapidlymixesandreactswiththeavailableoxidizer,establishingwithinthemainjetsurroundedbythepremixedHowever,theheatreleasebythehaslittleontheoverallbehaviorofthesurroundingpremixedThelowtemperatureincomingjetinCase5,also,slightlythegrowthrateofthecombustionzones.Toqualitativelycomparethewandthetimeandspanwiseaveragedvaluesoftemperature,aTfs,forallsixcasesareillustratedin1.26)(a)and(b)versusthecross-steamdirection,,attwostreamwiselocations,˘13and˘215.Itcanbeobservedin1.26(a)thatintheregionthetemperaturearenearlythesameforthecaseswithsimilarincomingjetthermo-chemicalconditions(Case1-4).However,1.26(b)showsthatthetemperaturedevelopverytlyforcaseswithtwandincomingjetconditions.Intheregion,themaximumtemperaturelocatedatthejetcenterlineislowerforcaseswithleanandrichinitialmixtures.Thetemperatureintheshearlayersseemtobedependentmoreonthewcompositionthantheincomingjet.Closeexaminationoftheresultsin1.26indicatesthatthe51maximumtemperaturedecreasesmuchmoreinCase1.ThisshowsthatthemixingwithcoolerwhasmoreontemperaturethantheweakcombustioninCase1.ThemaximumtemperaturevalueinCase6doesnotdroptly,indicatingthatthenon-premixedcombustioninsidethejetzonesustainsthejettemperatureatahighlevel.Amongthecaseswithtwcompositions,expectedly,themaximumtemperatureofCase4ishigherthantheothersandthemaximumtemperatureforCase1isthelowest.ButthemaximumtemperaturestaysalmostthesameinCase5.(a)(b)Figure1.26:Timeandspanwiseaveragedtemperaturevalues,aTfs,at(a)˘1and(b)˘2versuscross-streamdirection,,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6.Theoveralleofthecowandincomingjetconditionsareexploredmorein1.27,whichshowsthemeanandintervalsofyzplaneandtimeaveragedtem-perature,‹`Teyz“˙‹`Teyz“,versusstreamwisedirectionforallsimulatedcases.Thetimeaveragedstatisticsarecalculatedbasedonthesimulateddataforacientlylongtime,17˝0.Thewdataareexcludedinthisbutthepreheatedzonesofthepremixedzonesareincluded,which,potentially,lowerthemeantemperaturevalues.Evidently,theplotsassociatedwiththeregionareverysimilarforCase1toCase4,whichshowstheimportanceanddominanceoftheincomingjethydrodynamicsanditsmixingwiththe52w.SimilarbehaviorcanbeobservedforCase5andCase6,eventhoughtheincomingjettemperaturesaregenerallylowerinthesetwocases.Thetransitionfromtheregiontothedevelopedregionapproximatelystartsat˘3.Inthedevelopedregion,theaveragedtemperaturevaluescontinuouslydecreasealongthejetbutwithmuchhigherrateinCase1withequivalenceratioof0:1thancomparedtothoseinCase4withequivalenceratioof0:5.ThisshowstheexistenceofweakerandlowertemperaturecombustioninCase1.Case5withaleaninitialmixture,˚ij0:5,exhibitsratherttrendincomparisonwithothercases.Forthiscase,theaveragedtemperaturestartswithaconsiderablylowerinitialvaluethenincreasesinthedevelopedafterasuddendropintheregionreachingtoaplateaufurtherdownstream.ComparisonbetweenCase5andCase3indicatesthat,eventhoughthewandcombustionaresimilarintheregion,theoveralltemperatureislowerinCase5sincethetemperatureoftheincomingjetislower.InthedevelopedregionofCase6witharichinitialmixture,˚ij2:0,theaveragedtemperatureplateausafterasmallincrease,whichissimilartoCase5butisfortreasons.TheincomingjettemperatureinCase6islowerthanthatinCase3,butunliketheCase5,theaveragedtemperatureeventuallybecomeshigherthanthatinCase3.Expectedly,theunburnedhotfuelinsidetheincomingjetreactswiththeremainingoxidizeroftheleanwpremixedcombustion,creatingastableinthehotproductjetzone.Thenon-premixedcombustion,canalsobeobservedin1.25(f),wherethetemperatureinsidethecombus-tionzonesisshowntobemuchhigher.Theevidently,increasestheaveragedtemperatureevenhigherthanthatincase3,despitethesamewconditions.Ithasbeensuggestedinreference[109]thatthethermalhalfwidthjet,Dhalf,inTJI-assistedcombustion,canbecomputedbasedonthepeakrootmeansquare(rms)oftem-perature,Trms‹T2T2“1~2,sincehightemperaturevariationsusuallyoccuratthe53Figure1.27:Meanandintervalsofyzplaneandtimeaveragedtemperature,‹`Teyz“˙‹`Teyz“,inthecombustionzonesversusstreamwisedirection,˘,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6.zone.Figure1.28(i)showstheTrmscontoursforCase3inthemidplane.HighvalueTrmszonesalsoexistintheregionwhichrepresenttheaveragedlocationofrelativelythickpreminthisregion.However,thefocushereisthepremixedinthedevelopedregionandtheexpansionofcombustionzonesundervariouswandincomingjetconditions.Dhalfismeasured,simply,byastraightline(dashedblacklineshownin1.28(i))tothelocalmaximumTrmsvalues.Figure1.28showsthestreamwisevariationsofthermalhalfwidthjetnormalizedbytheincomingjetwidth,Dhalf~D,fortcases.ThemaximumandminimumDhalfvaluescorrespondtoCase4andCase1,withthehighestandthelowestwequivalenceratios.Evidently,forCase3,Case5,andCase6,Dhalf,unlikelychangetlybychangingthethermo-chemicalpropertiesoftheincomingjet.Nevertheless,DhalfforCase6isslightlygreaterthanthatforCase3,whichsuggestsaninsignttofthecombustiononDhalf.ItcanbeconcludedthatDhalfismainlycontrolledbythepremixedcombustion.Fortheconditions54thatthepremixedarelocatedfarawayfromtheincomingjet,Dhalfisunlikelytobebytheinteractionswiththeincomingjetturbulence.Figure1.28:Normalizedthermalhalfwidthjetbytheincomingjetwidth,Dhalf~D,versusstreamwisedirection(˘).(i)Contourofrmsoftemperature,Trms,atthemiddlespanwiseplane,‹z1:5D“,schematicallyshownforCase3.1.6.1FlamevariableforTJI-assistedOurprimarilyanalysisofTJI-assistedcombustioninTPJrevealthatthistypeofcombustioninvolvesawiderangeofpremixedto(non-premixed)ToclassifytheTJI-assistedcombustionregimesandundervariousconditions,asuitablevariableneedstobeThepremixeddevelopedinthistypeofcombustionsystemsis,essentially,areacting"wave"initiatedbythehotjetinthenearregionwhichpropagatesintotheunburnedmixtureorow.Thebasicparameter,knownastheprogressvariable,inanalyzingthestandardpremixedisascpremixedTTfTbTf;(1.14)55whereTfandTbrepresenttheandburnedzonetemperatures,respectively.Theprogressvariableisconventionallysettozeroandoneintheunburnedmixtureandburnedgaszones,respectively.Theintermediatevaluesareassociatedwiththesheet.How-ever,intheleanTJI-assistedcombustionthemaximumtemperatureisnormallyassociatedwiththeincominghotjetandnotnecessarilytheburnedgasesinthepremixedzone.Therefore,thestandardon(equation1.14)oftheprogressvariableisnotveryusefulvalidforouranalysis;theinformationconcerningthelocal,incomingjet,andwtemperaturesmustbeincluded.ThechallengeofaprogressvariableforTJI-assistedcombustionalsoarisesfromthecoexistenceofandpremixedThisphenomenon,thesimultaneousexis-tenceofpremixedandnon-premixedcombustionregimes,occursinthecasesthattheburnedproductjetcontainsextrafuel(i.e.˚iji1forCase6),inwhichtheunburnedhotfuelinsidetheincomingjetgetsmixedandreactswiththeremainderofleanpremixedcombustionoxygen.IntheTJI-assistedcombustionsystems,thefuelandairstreamsaregettingex-posedtoeachothermostlyinthehotproductjetzone(thenon-premixedcanoccupyatpartofthiszone)bythepremixedinsteadofasheetasnormallyseenin"standard"Consequently,thelocationandstrengthcanbecontrolledbythehydrodynam-icsandthermo-chemicalconditionsofboththeincomingjetandthew.Thefuelandoxidizerfeedtheattratesduringthetransitionfromtheoxidizerintheburned-mixedzonetothefuelsideinthehotproductjetzone.Sincethistypeofismainlycharacterizedbytheinter-penetrationoffuelandoxidizer,conveniently,atracerofthemixturestateisintroducedbasedonthecombinationoftransportequationsofthosetwostreams.Onemayarguethatsincetheproductsexistinbothfuelandoxidizerstreamsofthe56non-premixedregimeoftheTJI-assistedcombustion,aproperalternativeofthemixturefractionmightbebasedontheelementalconservationequations.Butthecombina-tionofthefuel,oxidizer,orelementaltransportequationsisderivedwiththeapproximation,which,ultimately,suppressestheofthetemperature.Figure1.29(a)showsthemeanandintervalsoftemperatureinthecombustionzonesversusel-ementalmixturefraction(basedonelementH),fZHZHjZHcoZHj,forall6casesprovidedintable1.1.WhereZHNsP1aHWHW˚,ZHcoNsP1aHWHW˚co,andZHjNsP1aHWHW˚jarelocal,w,andtheincomingjetelementalmassfractions.aHisthenumberofelementHwithmolecularwightWHinspecieswithmolecularweightW.Thepoorperformanceoffisevidentasforafvaluevarioustemperaturevaluesarepredictedandtheofthejetandwcannotbedistinguished.Hence,TJI-assistedprogressvariablenotonlyhastotracethefuelandairstreams,butalsohastoincludethetemperatureinafunctionalformlikeRg‹T;Tj;Tco“h‹˚fuel;˚oxidizer“.Basedontheaboveargument,here,weanormalizedRsuchthatitrepresentsboththemixtureandthetemperatureasR„TjTTjTco‚˚;(1.15)where˚isthelocalequivalenceratio.Figure1.29(b)presentsthemeanandintervalsoftemperatureinthecombustionzonesversusRforall6cases.Atbothsidesofeachplot,RvaluesdescribetheassociatedcombustionzoneconditionssuchasifTÐTcothenRÐ˚co,whichrepresentsthepreheatedzoneofthepremixedwinsidethew.Thestraightlinewithnegativeslopeshowsthetransitionofthewfromunburnedfreshwtotheburned-mixedzonepassingthroughapremixedAttheothersideofwifTÐTjthenRÐ0,whichrepresentsthehotproductjetzone.Inthecaseswith57extrafuelintheincomingjet,˚jcontributestoR,resultinginsmallbutgreaterthanzeroRvalues,i.e.TÐTjthenRÐ˚j,whichessentiallyidentheTheintermediateRvaluesrepresenttheburned-mixedzone.(a)(b)Figure1.29:Meanandintervalsoftemperature,‹T“˙‹T“,inthecombustionzonesatt17˝0versus(a)elementalmixturefraction,fand(b)TJIcombustionprogressvariable,R,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6.(i)Scatterplotoftemperature,T,inthecombustionzonesatt17˝0versusTJIcombustionprogressvariable,R,forCase6,identifyingthesimultaneousexistenceofthepremixedandnon-premixedcombustionregimes.TofurtherexaminetheperformanceofRinidentifyingvarioustypesandcom-bustionzones,theinstantaneousvaluesofRattwostreamwiselocations,˘1and˘2,atthelatesttime,t17˝0,versuscross-streamdirectionareplottedinFigures1.30(a)and(b)forallcases.Itcanbeobservedingure1.30(a)thatintheregionat˘1,RvaluesareverysmallinsidethejetforCase1toCase5,butsubstantiallyincreaseinthepremixedzoneallthewaytothewandstayconstantequaltothecorrespondentwequiva-lenceratios.tbehaviorisobservedforCase6;theinitiallylargevaluesofRareduetoextraamountoffuelwhichcreatesintheinnerjet.Movingforwardinthestreamwisedirection1.30b),similarbehaviorsareexpectedforCases1-5,andless58intenseforCase6.Interestingly,thesharptransitionsfromthecombustionzonestothefreshunburnedwinthepremixedzoneiscapturedbysuddenincreaseinRvalues,ingtheabilityofRinlocatingthepremixedinthescalarspace.(a)(b)Figure1.30:TJIcombustionprogressvariable,R,versuscross-streamdirectionatamiddlespanwiseplane,‹z1:5D“,andt17˝0at(a)˘1and(b)˘3versuscross-streamaxis,,forallcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,(l)Case4,()Case5,and(P)Case6.Inthenextsection,theofwequivalenceratioontheincludingthelocalizedextinctionandre-ignitioninultra-leanmixturesareexamined.Changesinthewconditiontlythestructureanditsinteractionswiththeturbulence.1.6.2wcompositionThespatialdistributionsofvariousspeciesinthesimulatedTJI-assistedTPJhavebeenexaminedindetailsinordertodevelopabetterunderstandingofpremixedinteractionswiththeturbulencefortconditionsintheTJI-TPJ.Thefuelmassfractioncontours(notshownhere)aresimilartothetemperaturecontoursin1.25,generallyshowingthesimilarityofthejetandcombustionintheregionandtheverytinthedevelopedregionregardingthepropagationandjetstructure.More59detailsoftheamecanbeextractedfromotherspecieslikeH2O,O2,OH,andH.Figures1.31(a)-(d)illustratetheinstantaneousH2OmassfractioncontoursforCase1toCase4.Sincetheincomingjetconditionsarethesameinthesefourcases,the˚H2Ocontoursstaysomewhatsimilarintheregions.TheproducedH2Ospeciesduringtheleanpremixedcombustionareaddedtotheinitialvaluesinthedevelopedregions.Expectedly,the˚H2Oareproducedmoreincaseswithhigherowequivalenceratio.InCase1,thegeneratedwaterissmall,makingthemixingofhotproductjetwithcoolerw(notthecombustion)thedominantprocess.Wherethehigh˚H2Ovaluesinthehotproductjetare,considerably,dilutedthroughthemixingwiththezerolevel˚H2Ow,exhibitingqualitativelysimilarbehaviortothetemperaturecontoursin1.25(a).ByincreasingtheequivalenceratioinCase2,Case3,andCase4,sheetswithconsiderablyhigher˚H2Olevelsappearwithinthejetwithconsistentlygreaterjetgrowthrateinlatercases.InthedevelopedregionofCase4,threeareasaredistinguishablewith˚H2Olevelsof0:22,0:17,and0:0inthemainhotproductjetzone,burned-mixedzone,andw.Thevaguetransitionfromtheburned-mixedzonetothewthatthezonecannotbeidenbyH2O,eventhoughtheturbulentmixingandhighlynatureofthepremixedcanbeobservedinthe˚H2Ocontours.TheO2massfractioncontours(notshownhere),whilehaveanoppositebehaviorofH2Ocontours,alsoindicatethatthefrontcannotbecapturedbyO2.InthestandardpremixedOHradicalisoftenusedforidentifyingthezone[64,111,13].Figures1.32(a)-(d)showtheOHmassfractioncontoursforfoursimulatedTJI-assistedTPJcases.AsitcanbeobservedintheseOHradicalsproducedbythecombustion(veryintensivelyintheregionandlessintensivelyinthedevelopedregion)adduptotheinitialOHoftheincomingproductjet,causingthemaximum˚OH60(a)(b)(c)(d)Figure1.31:InstantaneouscontoursoftheH2Omassfraction,˚H2O,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4.(Notethatthescalelimitsaresettotheavailablevaluesineachcontourandarenotthesame.)tooccursomewhereinthehotproductjetandnotatleanpremixedfront.TheOHgenerationinCase1andCase2,duetoweakcombustionoftheultra-leanwmixtures,insuchanextentisrelativelysmall.Thelocalmaximumvaluesof˚OHintheregionareconsiderablylargerthanthoseinthedevelopedregion.Expectedly,theOHlevelinCase3andCase4increase,onaverage,duetomorestableandstrongercombustion.Figures1.32(c)and1.32(d)showthat˚OHvaluesarealso,locally,higherinthezonethanthoseintheimmediatesurroundings.Thus,whileOHmightbeafairindicatorofewhenthecombustionisstrongenough,anditmaynotbeabletolocatethefrontandalsoextinctedinultra-leanmixtures.OtherradicalssuchasHinhydrogencombustionorCHinhydrocarboncombustionarepotentiallymorehelpful.61(a)(b)(c)(d)Figure1.32:InstantaneouscontoursoftheOHmassfraction,˚OH,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4.Figures1.33(a)-(d)presentthecontoursofHmassfractionforCase1toCase4.Itcanbeobservedthat,interestingly,themaximumvalueof˚Hoccursrightatthefrontwhileitsvalueinsidetheincomingjet,incontrastto˚OH,isrelativelylow.ThisbehaviorsuggeststhattheradicalHmaybeusedasanaccurateemarkerinTJI-assistedTPJcombustion.Notethatthecontourcolormapsin1.33(a)-(d)arescaledtlytotherangeofdataforbettercapturingofHradicalbehavior.Forallwmixturefractionsconsideredinthisstudy,thehighvaluesof˚Hoccurattheedgesoftheincomingjetintheregionasshearlayersdevelopandgeneraterelativelythickes.InthedevelopedregionsofCase2,Case3,andCase4,˚Hvaluesmaximizeatthefrontanddroptoverylowvaluesintheburned-mixedandhotproductzones.InCase1,wherethelocalized62extinctionoccur,similartrendisobservedbutwithmuchsmallerlocalmaximum˚Hvaluesatthefront.Ithasbeenshownin[109]thatHradicalmassfractionvaluesarewellcorrelatedwiththeheatofreaction,especially,inthedevelopedregions.(a)(b)(c)(d)Figure1.33:InstantaneouscontoursoftheHmassfraction,˚H,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4.(Notethatthescalelimitsaresettotheavailablevaluesineachcontourandarenotthesame.)Thecombustionheatreleaserate,_Qe,isanimportantquantitytodiscernandtheirlocationsinturbulentreactingwssuchastheTJI-TPJ.Thespatialdistributionof_Qeishighlydependentontheinteractionsaswellasthechemicalreaction.Despitethenceof_Qe,measuringitischallenging[75,71].Here,_Qeis,conveniently,obtainedbyequation1.9[69].Figures1.34(a)-(d)showtheinstantaneouscontoursofheatreleaserateforfourcaseswithtwequivalenceratios.Theprocessofturbulenceinteractionsandmixingoftheincominghotjetwithcoolerpremixedwin63theregionatthereactingshearlayerscreatesrelativelythickandgeometricallycomplexintheTJI-TPJ.TheregionofTJI-assistedTPJcombustionmightbesimilartothecorrugatedanddistributedburningzonesinstandardpremixedwheretheintenseturbulencegenerateseddiesstronglycoupledwiththecombustionprocess,thickeningthezonewhilethefrontbeingwrinkled.Itisexpectedthattheeddiesgeneratedintheregionareinthetailoftheenergyspectrumsuchthattheirlifetimeisveryshortandtheirimpactsonthecombustionzonesinthedevelopedregionarethuslimited.Itisobservedthatthedistributedreactionandhighheatreleaseratevaluesvirtuallyvanishfromthemainjetasthewtransientsfromtheldtothedevelopedregions.Movinginthestreamwisedirection,aspatiallycontinuous,distorted,andconcentratedisdeveloped.Whilethepremixedmovesawayfromtheincomingturbulentjetandpropagatesintothew,itbecomesthinnerandmuchlessdbythejetturbulence.The_Qecontoursshownin1.34(b)-(d)clearlyshowtheseparationoftheunburnedandburned-mixedzonesinthedevelopedregioninthecross-streamdirectionandtherelativelythindistortedpremixedturbulentzone.Eventhoughtheandturbulencefeaturesvaryovertime,theyappeartobewellstabilizedinthedevelopedregion,particularly,inCase2,Case3,andCase4.Theheatreleasecontoursshowninures1.34(a),consistentwithH,illustratesrelativelyhighandlow(closetozero)_Qevaluesalongthefront.Itindicatesthatthewcompositionlaysonthelowerylimitsofhydrogen-airmixtures.Thelean(lower)yequivalenceratioforhydrogen-airmixtureatT359‹K“isreportedtobe0:14[119].ConsideringthatthewtemperatureinCase1ishigherthanthatconsideredinexperimentalmeasurementsoflowylimitsandsincethefuel-airmixturesarecontinuouslyexposedtoahightemperaturejet,itisnotsurprisingthattheTJI-assistedcombustionhasamuchlowerleanylimits64thanthestandardpremixedcombustion.(a)(b)(c)(d)Figure1.34:Instantaneouscontoursoftheheatreleaserate,_Qe‹W“,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case1,(b)Case2,(c)Case3,and(d)Case4.(Notethatthescalelimitsaresettotheavailablevaluesineachcontourandarenotthesame.)In1.35themeanandboundsofthe(yz)planeaveragedheatreleaserates,‹`_Qeeyz“˙‹`_Qeeyz“,areplottedversusstreamwisedirection.Theamountofcom-bustionheatis,expectedly,increasedbythewequivalenceratio.Nevertheless,inallcasestheaveragedheatisgeneratedthemostattheendoftheregion.Clearly,theheatreleasepeaksareditbutoccuralmostatthesamestreamwiselocationinallcases.Thissuggeststhattautoignitionhappensatallwequivalenceratioswheretheresidencetimeislargeenough,eventhoughthecombustionisalreadyinitiatedattheshearlayers.Thisthedominanceoftheincomingjethydrodynamicsinthisregion.Surely,tbehaviorsareexpectedforvariousjethydrodynamics.Inthe65developedregion,descendingheatreleasecanbeobservedforallcasesindicatingcoolingofthecombustionzones.However,theyconvergetotvalueswithtrates.Incase1,`_Qeeyzreachestonearlyzeroattheendofthecomputationaldomain,indicatingaveryweakcombustionandsitextinction.Figure1.35:Meanandenceintervalsofyzplaneaveragedheatreleaserate,‹`_Qeeyz“˙‹`_Qeeyz“,att17˝0versusstreamwisedirection,˘,forfourcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,and(l)Case4.Thestabilityandextinctiondependonthevolumetricheatlossfromtheincomparisontoitsheat(energy)release.Heatlossisrelativelyt,particularly,closetotheleanlitylimitcondition.In1.36,thecontoursof_Qeareshownagainfortheultraleanw.Inthisthescaledinthedevelopedregionwherethelocallyextinctandre-ignitearealsoshown.Thelocalextinctionandre-ignitioneventsareillustratedbyeandr,respectively.Thestretchingandfolding,inducedbythemeanvelocitygradientandthesmall-scaleturbulence,changeintimeandspaceoverthepremixedsurface.Ifthestretchingincreaseslocally,thespacebetweenthebothsidesofthedecreases,leadingtothelocaleextinctionandincompletecombustion.Thelocalextinctioneventsareseentobeaccompanied66Figure1.36:Localizedextinctionandre-ignitionatsheetidenbasedonheatreleaseandamviewofthembyafactorof5:1,occurredinultra-leanw(Case1).byalargedropinheatreleaseeventovaluesclosetozero.Asobservedintheimage,whenthefrontgetsfurtherawayfromthehotincomingjet,morelocalextinctioneventsoccur.Also,morere-ignitioneventsareseenatthelocationsclosetothehotproductjetzone,whererelativelyhighheatreleasevaluesreappearamongtheextinctzones.Thesethatinsituationswherethepremixedisclosetothehotproductjet,theintenseinteractionsandheattransferfromtheincomingjethelpsthetore-igniteafterextinction.Aslongasthefrontisconnected,leanwmixturesstaylargelyseparatedfromthefrontandhotproductinsideburned-mixedzone.However,asequenceoflocalizedextinctionandre-ignitionoccursacrosstheindicatingdiscontinuitiesintheeforultraleanmixtures.Whenthefrontis67interrupted,thecombustioninducedhigh-viscositydilatationlayerisnolongerpresenttoformabarrierforhightemperatureturbulenteddies,hence,theycanescapethroughtheholesinthezoneandintothew.Themixingofthehotproductswithwincreasesthetemperatureofthepreheatedzoneofthepremixedeatthewsidethatmaysubsequentlyleadtore-ignition.Tobetterunderstandthelocalextinctionandreignitioninultraleanmixture,thescatterplotsof_QeversusRareshowningure1.37forCase1toCase4.TheresultsforvariouspartsorsectionsofthewareincludedsuchthatSec1,(h),representstheregion0j˘j4,Sec2,(l),representstheinitialpartofthedevelopedregion4j˘j10,andSec3,(⁄),representstheendpartofthedevelopedregion10j˘j17.Theresultsin1.37basicallyshowthecompositionalstructure.ThegeneralbehaviorinthisisthatthemaximumheatreleasehappensatRvaluescorrespondingtothefront,i.e.R0:02,0:04,0:065,and0:1.Theareaswithgreaterthanthesevaluescorrespondtothepreheatedzoneofthepremixedzone.TheareaswithsmallerRvaluesrepresenteitherthehotproductzoneortheburned-mixedzone.Therelativeextentofscatterinthe_QeRplotalsoshowtheextentoflocalextinctioninthew.Theverywidescatterof_QeRdataintheultraleanmixtureinCase1indicatesthattheratechemistryareveryimportantandthelocalheatlossismorethantheheatreleaseandstablecontinuousezonescannolongerbemaintained.Thisismoreclearwhenthedataintsectionsofthewarecompared.Thebehaviorchangesinthestreamwisedirectionfromatlythickpremixedintheregiontoalocalizedthinextincted-reignitedinthedevelopedregioninCase1.Consequentlyasshownin1.37(a),theisstableandcontinuouslyprovidestamountofheat.Thisisrepresentedbyhigh_QevaluesoflowRsandisalsosupportedbyHand_Qecontoursin681.34(a)and1.33(a).MovinginthestreamwisedirectiontoSec2,lower_QevaluesatagivenRbecomemoret.InSec3theextinctionisdominantandscatterindataisimportantinallregions.Asimilar(butlessintensive)behaviorisshownin1.37(b)forCase2.Forcase3andCase4,therelativelynarrowbandofscatterinthe_QeRdatainallsectionssupportstheexistenceofstrong,continuous,andstablepremixedcombustion.Itshouldbeaddedherethatasitcanbeseenin1.25(a),thetemperaturevariationsbetweenthelocallyextinctedandre-ignitedaret,unlikethestandardturbulentpremixedwhichnormallyhavelowtemperatureinregionswithtextinction.(a)(b)(c)(d)Figure1.37:Scatterplotoftheheatreleaserate,_Qe‹W“,versusTJIcombustionprogressvariable,R,for(a)Case1,(b)Case2,(c)Case3,and(d)Case4attstreamwisesectionsrepresentedby(h)Sec1,(X)Sec2,and(⁄)Sec3.69TheofturbulenceandwstrainrateontheTJI-assistedcombustionandstabilizationaretthanthoseinstandardpropagatingturbulentpremixedIntheregion,wherethestrainrate,_,ishigh,thewresidencetimeisrelativelysmall,which,theoretically,mightleadtotheincompletereaction.However,highwmixingandturbulencelevelintheregionalsofacilitatestheheattransferofthehotproductjetwiththew.Thisovertakesthenegativeofthehighstrainrateandpreventslocalextinctioninthisregion.Inthedevelopedregion,Sec2andSec3in1.38(a),thehighstrainratevalues,inonehandmightcausethetoextinct,butinanotherhandtheyhelpthereignitionprocessbyconvectingheattotheextinctedThisprocessstabilizesthecombustionand,eventually,canlowertheleanylimit.Figure1.38(a)and(b)presentthescattersoftheheatreleaserate(_Qe)versusstrainrate(_)forCase1andCase4.Thescatterdataareseparatedforthethreetsectionsinstreamwiselocations.Evidently,theheatreleaserateisbythestrainratesincethemagnitudesofstrainratearethesameinthesetwocases,onewithandonewithoutextinctedmes.Unlikethestandardpremixedes,acriticalstrainratecannotbefortheTJI-assistedcombustion.Here,theofthewcombustionontheturbulenceandviceversaareinves-tigatedbyconsideringthermalhalfwidthjet,turbulenceintensity,andvorticityin1.39.Thesolidthicklinesshowtheresultsatmaximumrmsoftemperature,max‹Trms“,andthedashedthinlinesdenotethoseatmaximumturbulenceintensity,max(I),whereI−uœ2vœ2wœ2‘12UrefandUrefUcoUj2300‹m~s“istheaverageofthecowandhotproductjetvelocities.Figure1.39(a)showsthelocationofthemaximumTrmsandIinthecross-streamdirectionversusthestreamwisedirection.ThemaximumTrmscanbeusedto70(a)(b)Figure1.38:Scatterplotoftheheatreleaserate,_Qe‹W“,versusstrainrate,_‹1~s“,for(a)Case1and(b)Case4attstreamwisesectionsrepresentedby(h)Sec1,(X)Sec2,and(⁄)Sec3.identifytheapproximatedlocationofthepremixedandthethermalhalfwidthjetintheTJI-assistedcombustionasitwasshownin1.28(i).ThelocationofthemaximumturbulenceI,clearly,fromthelocationoformaximumTrms.Thisshowsthatasthepremixedpropagatesintothewitgetsseparatedfromthemainjet.ItalsothatthetemperatureisnotwellcorrelatedwiththehydrodynamicsinthedevelopedregionoftheTJI-TPJ[109].However,thejetspan,estimatedbasedonthemaximumI,isincreasingbyincreasingthewequivalenceratio,sincethepremixedmovesfurtherawayfromtheincomingjet,leadingtolessinteractionsbetweenthesetwozones.ThesmallestjetwidthcorrespondstotheCase1wherethepremixedisveryclosetotheturbulentjetandhasthemosttdampingonthegrowthoftheincomingjetinthecross-streamdirection.TheIvaluesatmaximumTrmsandIlocations,versusthestreamwisedirectionareplottedinure1.39(b).TheIvaluesattheselocationsareinitiallyalmostthesameclosetojetinletinallfourcases.Thesmallmightberelatedtosmallvariationsinthewdensity.TheIvaluesatlocationormax‹Trms“inCase4andCase3droprapidly71(a)(b)(c)Figure1.39:(a)Cross-streamlocationofmax‹Trms“andmax‹I“,(b)turbulenceintensity,I,valuesatmax‹Trms“andmax‹I“locations,and(c)vorticitymagnitude,!,atmax‹Trms“andmax‹I“locations,versusstreamwisedirection,˘,forfourcasesrepresentedby(h)Case1,(X)Case2,(⁄)Case3,and(l)Case4.Thicksolidandthindashedlinescorrespondtomax‹Trms“andmax‹I“,respectively.toverysmall,closetozerovalues,duetorelativelystrongerpremixedcombustioninthesetwocases;thehigherthewequivalenceratio,thelowertheI.ThehigherIvaluesforCase1andCase2suggestastrongerinteractionofthepremixedfrontwiththeinnerjet.TheIvaluesatthemax‹I“locationssimilarlydecreaseinthestreamwisedirection,however,theyareaboutoneorderofmagnitudehigherthanthoseatlocation,whichshowsthenearlyindependentbehaviorofthehydrodynamics.TheIvaluesatanylocationsinthedevelopedregionaregreaterforthecaseswithhigherequivalenceratios,Case4and72Case3,which,again,thelessinteractionsofthewithturbulenceinthesetwocases.Inre1.39(c),thestreamwisevariationsofvorticitymagnitude,!SÐ!S,atmaximumTrmsandIlocationsfortcasesarecompared.The!levelsintheregionarerelativelyhighbecauseoftheintenseinteractionsbetweentheincomingjet,thickpre-mixedandturbulence.Inthedevelopedregion,however,theseinteractionarelesstialontheoverallturbulenceofthew.Asobservedin1.39(c),thevorticityatmax‹Trms“locationsreachtoverylowvaluesinthecaseshavingverystableandstrongcombustion(Case3andCase4);supportingthefactthatthecombustionhasadissipativeonturbulence.Thesimulatedhotproductjetishighlyturbulentwithntwvariableatalllength(andtime)scales,eventhoughthesmall-scaleturbulentstructuresaredepletedbythecombustion.Highvaluesof!atmaximumIlocationsindicatethattheincomingjetisstilleinthehotproductjetzone.Intheregionandatmax‹I“locations,thevortexstretchingandcompressibilityarethesourcesofthevorticityproduction.Furtherdownstreaminthedevelopedregion,thetvariationsinden-sityandpressurecausetheBaroclinictorque,Ð1ˆ©ˆ©P,toplayamoreimportantroleingeneratingthevorticity.Closetothezoneatmax‹Trms“locations,theBaroclinictorqueandthevortexstretchingarethemainsourcesofgeneratingvorticity.Nevertheless,closetotheethevorticityldisnegativelybythereactionbecauseofheatreleaseinducedvolumetricwexpansionandtemperaturedependencyofviscosity.Intheregion,Ðisgeneratedmainlyduetodensitybetweentheincominghotjetandwandthedensity/pressuregradientgeneratedintheinnerjetcorebycomplexthickInthedevelopedregion,however,thedominantmechanismsfortheBaroclinictorquegenerationarethetransportandleanpremixedcombustionintheouteredgeofw.73Asreportedin[109],vorticalstructureswiththesameBaroclinictorquemagnitudeexistintheweventhoughthelocalizedmaximumcanidentifythepremixedfront.1.6.3Incomingjetthermo-chemicalInthissection,theofincomingjetthermo-chemicalconditionsontheTJI-assistedTPJcombustionareinvestigatedconsideringtheresultsofCase3,Case5,andCase6.Inthesecasestheequivalenceratiooftheinitialmixtureandconsequentlytheincomingjetcompositionandtemperaturearetwhiletheowconditionsarethesame.InCase5,theinitialmixtureequivalenceratioischosentobeontheleansidewith˚ij0:5,thusthejetmainlyconsistsofO2andH2OwithrelativelylowtemperatureofTj2050‹K“(tables1.1and1.2).InCase6,theinitialmixtureconsideredtobeontherichsidesothattheincomingjetcarriesunburnedhotfuelalongwiththeproducts.ThemainjetspeciesareH2andH2OspecieswithtemperatureofTj2350‹K“.Thejethydrodynamicpropertiesareconsideredtobethesameinthesethreecases.Figures1.40(a)and1.40(b)showtheinstantaneousOHmassfractioncontoursatthelatesttimet17˝0forCase5andCase6,respectively.IntheregionsofthesecasestheintenseandsimilarproductionofOHradicalonceagainshowtheofreactionandstrongwinteractionswiththecombustion.InCase5,theOHmassfractionintheincomingjetisrelativelylow,around1:8e3(table1.2),buthigh˚OHvaluesexistinthedevelopedregion,particularly,intheburned-mixedandproductjetzones.Thislevelof˚OHismostlyduetotheproductsofthecombustionwhicharetransportedintothedownstreambytheturbulentjet.Thiscanbebythe_Qeresultsin1.42,whichshowsthattheheatreleaseinthedevelopedregionandthementionedcombustionzonesisverysmall.InCase6,thejetOHmassfractionisequalto9:9e4which74istheminimumvalueamongallothercases.However,thehighest˚OHvaluesareseeninthedevelopedregionforthiscase,whichismainlyduetothecombustionoftheunburnedfuelinsidetheincomingjetwiththeoxygenoftheleanwmixture.Partofthehigh˚OHisduetothetransportedandOHradicalsfromtheregiontothisregion.Theseresultssuggestthat,thepremixedandnon-premixedinTJI-assistedcombustionaresomewhatculttocapturedbytheOHradical.(a)(b)Figure1.40:InstantaneouscontoursoftheOHmassfraction,˚OH,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case5and(b)Case6.Figures1.41(a)and1.41(b)presenttheHmassfractioncontoursforCase5andCase6.The˚Hlevelsintheincomingjetsareverylow,1:3e6and3:3e4(table1.2).Therefore,themainHradicalsinthedomainareproducedbytheleancombustion.Intheregion,tHradicalisgeneratedbytheverycomplicated,thick,distributedcombustioninbothcases,eventhoughinthecasewithextrafuelitisgeneratedmuchmore.Inthedevelopedregion,theHradicaldistributionprovidesusefulinformationconcerning.InCase5,similartoCase1toCase4,themaximumvalueof˚Hislocatedatthepremixedleanwhile˚Hvaluesarerelativelyverylowinothercombustionzones.InCase6,Hradicalconcentrationistnotonlyatthepremixedezones,butalsoinsidethehotproductzonescontainingstrongFigure1.41(b)showsthatH75generationismuchmoretintheinnerjet.Thisbehavioriswellcorrelatedwiththeheatreleasecontours.(a)(b)Figure1.41:InstantaneouscontoursoftheHmassfraction,˚H,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case5and(b)Case6.(Notethatthescalelimitsaresettotheavailablevaluesineachcontourandarenotthesame.)Figure1.42(a)and1.42(b)presenttheinstantaneouscontoursofheatreleaserateforCase5andCase6att17˝0.ThestructuresintheeldanddevelopedregionsofCase5areverysimilartothoseshownbeforeforCase3.However,duetolowerincomingjettemperaturetheamountofheatreleaseintheregionisslightlylower,whichindicateslessheattransferandtheinitiationofcombustionatlowertemperatures.Itwasobservedin1.25(c)and1.25(e)thattheoverallcombustionzonetemperaturesinCase5islowerthanthatinCase3duetolessheattransferfromtheincomingjettoitssurroundings.Sincethecombustioninthedevelopedregionismainlycontrolledbythew,almostthesameamountofheatreleaseisgenerated.Thisalsocanbeseenin1.42(c),wherethemeanandtheboundsofyzplaneaveragedof_Qeinthecombustionzonesareplottedversusstreamwisedirection.DespiteoverallsimilaritiesofthethermalhalfwidthjetgrowthinCase6withthatinCase5andCase3,thetypeandcombustionbehaviorinthiscasearequitet76thanothers.Forthiscasetheinteractionsintheregionaremorecomplexduetotheexistenceofunburnedhotfuelintheincomingjetandverytinthejetzone.Thewideandhighlevelof_Qeintheregionrepre-sentstheextensiveoverlapofthickanddistributedpremixedwiththeusionMarchinginthestreamwisedirection,similartoCase5andCase3,aspatiallycontinuousanddistortedpremixedisdevelopedwhichgraduallypropagatesandgetsseparatedfromthejet.Thisisrepresentedbymoderatelevelof_Qeattheedgeofthew.However,thehighlevelof_QevaluesintheinnerjetaremostlyduetosionFigure1.42(c)showsthattheplanaraveragedheatreleasevaluesinCase6areconsiderablyhigherthanthoseinothercaseseventhoughthewconditionsarethesame.Thissupportstheexistenceofcombustionoftheadditionalfuelinsidetheincomingjet.Notethatdespitethecombustion,someoftheextrafuelintheincomingjetcouldsurviveandunburnedfuelstillexistsinthecombustionzones,whichisduetolackofoxygenorlongmixingtime.Theamountofleftoverfuelcanbecontrolledbytheinitialmixtureandwequivalenceratios,˚ijand˚co,andtheturbulenceinthejetandevenw.Lower(butstillgreaterthanone)valuesof˚ijresultsinlowerunburnedfuelintheincomingjetandlower˚coleadstohigherleftoveroxidizerafterthepremixedcombustion.Ingures1.43(a)and1.43(b)thescatterplotof_QeversusRareplottedforCase5andCase6attwsections.SimilartoCase3,themaximumheatreleaseoccursatR0:065whichcorrespondstothepremixedfront.Theobservationsandexpla-nationsmadebeforeforCase3arealsovalidforthepremixedcombustioninCase5andCase6.However,interestingly,thenon-premixedmesinCase6canalsobeidenviaRsimultaneouslywiththepremixedes.Thenon-premixedzoneofthesimulatedTJI-assistedcombustionsystem,inwhichthetemperatureisrelativelyhighbuttheequiv-77(a)(b)(c)Figure1.42:Instantaneouscontoursoftheheatreleaserate,_Qe‹W“,atamiddlespanwiseplane,z1:5D,andt17˝0for(a)Case5and(b)Case6.(c)Meanandintervalsofyzplaneaveragedheatreleaserate,‹`_Qeeyz“˙‹`_Qeeyz“,att17˝0versusstreamwisedirection,˘,forthreecasesrepresentedby(⁄)Case3,()Case5,and(P)Case6.alenceratioisgreaterthanzero,subsequentlyleadstolargerRvaluesinCase6comparedtoCase3.Asitcanbeseenin1.43(b),theRvaluesconstantlydecreasealongthestreamwisedirection,indicatingstrongernon-premixedcombustionintheregion.Thiswasalsoshownine1.29(i)wherethescatterplotoftemperature,T,inthecom-bustionzonesisplottedversusRforCase6.LargerRvaluesathightemperaturezonesrepresentthenon-premixedcombustion.78(a)(b)Figure1.43:Scatterplotoftheheatreleaserate,_Qe‹W“,versusTJIcombustionprogressvariable,R,for(a)Case5and(b)Case6attstreamwisesectionsrepresentedby(h)Sec1,(X)Sec2,and(⁄)Sec3.1.7ChapterconclusionsThethermo-physicalprocessesinvolvedinturbulentjetignition-assistedcombustionsystemsareexploredandstudiedbydirectnumericalsimulationsofahotproductturbulentplanarjetinjectedintoaveryleanpremixedhydrogen-airw.The\stationary"jetwissimulatedutilizinghighordermethodsanddetailedchemicalkinetics.ThesimulatedTJI-assistedreactingwcanbedividedspatiallyintwoi)eldandii)developedregions.Intheregion,whichinvolvesverycomplexturbulenceevolution,thestronginteractionsandmixingofthepremixedwwiththehotincomingjetleadtoasitautoignition.Stablethickarebeingestablishedinthisregion,whicheventuallysustaintheultra-leancombustiondownstream.Inthedevelopedregion,threedistinguishablecombustionzonesareideni)hotproductjet,ii)burned-mixed,andiii)zones.Theandturbulencestructuresofthesezoneshavebeenexaminedbyanalyzingvariousscalarandhydrodynamicsquantities.Despitethesimilaritiesofsimulatedwwith\standard"turbulentpremixedcombustion,theTJI-TPJexhibitstsuchashighertemperaturesandturbulentburningvelocities.Theseerences,79whichareduetotheinteractionsofthezonewiththehotandhighlyturbulentinnerjet,maketheTJI-assistedcombustionprocessunique,challengingincombustionsafetystudies,andrathertomodel.Eventhoughstablecombustionzonesareestablished,thezonalboundariesextensivelyoverlapandoscillateintimethroughouttheentirewNevertheless,thespeedisshowntobewellcorrelatedwithturbulenceintensityinthezone.TheHradical,thedissipationrateofHradical,thermsoftemperature,andtheBaroclinictorquearefoundtoconsistentlyidentifythesimilartotheheatreleaserate.Comparisonofvelocityandtemperaturestatisticsindicatesthatwhilethesetwoaresimilarinnon-reactingws,thetemperaturearemoretthanthevelocityinreactingw.Thesebehaviors,particularlyinthedevelopedregion,showtheseparationofturbulenceinthemainjetfromthehighlywrinkledleanpremixedTheyalsothatthesearenotverywellcorrelatedespeciallyatthezone,whichisanimportantfactorindevelopingclosuremodelsfortheseDirectnumericalsimulationsofvarioushotproduct-fuelturbulentplanarjetsinjectedintodtleanpremixedhydrogen-airmixturesws)areperformedusingdetailedchemicalkinetics.Thethermaljetwidthisshowntobemorebythewthermo-chemicalconditionsandlessbytheincomingjetcompositionandproperties.However,thecombustionzonesarehighlybythejetpropertiessuchastemperatureandunburnedfuel.Theunburnedhotfuelavailableinthejetreactingwiththeremainderoxidizeroftheleanpremixedcombustioncreatesacomplexsimultaneouspremixedandnon-premixedcombustionwhichishardtomodel.Toidentifytheetypeandstructure,aTJIcombustionprogressvariableisdwhichincludestheoftemperatureandmixturecomposition.Furtherinvestigationsofthecombustionregionsandzonesareperformedconsideringthereactionheatrelease,temperature,andspeciesconcentrations.Thelow80ylimitisshowntobeloweredbyexposingthepremixedfuel-airmixturetoahotturbulentjetdespitetheexistenceoflocalizedextinctions.Theinteractionsbetweenthepremixedzoneandthehotandhighlyturbulentinnerjetaremoreintenseintheultra-leanwmixtures,whichmaycauselocalizedextinctionandre-ignition.Intheleanmixtures,thepremixedgetsseparatedfromtheinnerturbulentjetasthepropagatesintothew.Thistheinnerjetdevelopmentinthestreamwisedirectionandalsotheturbulenceonthesheet.Turbulenceintensityandvorticityvaluesareshowntobemuchsmallerinthepremixedpropagatingfasterintothewwhiletheyalwaysmaximizeattheedgeofthejetlocated,onaverage,attheshearlayersoftheinnerjet.Itisalsofoundthatthetemperatureandhydrodynamicarenotwellcorrelated,whichisanimportantfactorinmodelingofTJI-assistedcombustionsystems.81Chapter2LES/FMDFofTurbulentJetIgnitionassistedRapidCompressionMachines2.1ChaptersummaryNumericalsimulationsofturbulentjetignition(TJI)andcombustioninarapidcompres-sionmachine(RCM)areconductedbyahybridEulerian-Lagrangianlargeeddysimu-massdensityfunction(LES/FMDF)computationalmodel.AnimmersedboundarymethodisdevelopedandusedintheLEStofacilitatemorphingthecomplexge-ometries,todecreasetheMonteCarlo(MC)particlesearchandlocateoperationsinFMDF,andtoproperlyhandlecegridsandMCparticlesattheboundaries,whilemaintainingthehighaccuracyofthemodel.TJIisanovelmethodforinitiatingcombus-tioninultraleanmixtures.InTJI-assistedcombustionsystems,ahotproductturbulentjetrapidlypropagatesfromapre-chamber(PCh)toamainchamber(MCh).Here,forthetimewedelineatedthreemaincombustionphasesinTJI-assistedcombustioninaRCMasi)coldfueljet,ii)turbulenthotproductjet,andiii)reversefuel-air/productjet.Theofvariousparametersonthesephasesarestudiednumerically,includingtheignitertimingandlocation,lean/rich/N2-dilutedmixtures,andadiabaticandnon-adiabaticwalls.ItisfoundthattheturbulentjetcharacteristicsandtheMChcombustionarehighlyaf-fectedbyPChturbulenceintensityaswellastheignitionprocess.IgnitingthePChatthe82lowerlocationsclosetothenozzle,enforcesthePChchargetofullyparticipateinthePChignition/combustionprocessesandpreventstheunburnedfuelsleavingtotheMCh.ThisalsoleadstolowervelocityhotproductjetspropagatingintotheMChforalongertime,enhancingtheMChcombustion.ThepressuretracespredictedbyLES/FMDFarefoundtobequitewellcomparablewiththeavailableexperimentaldata.Also,thequalitativecom-parisonsoftemperaturecontourswithexperimentalpicturestheaccuracyandthewealthvalueofthisstudy.2.2IntroductionTurbulentjetignition(TJI)isanignitionenhancementprocesswhichenablesthecombus-tionofultraleanandlowtemperaturemixtures.TJI-assistedcombustionsystems,typically,consistofarelativelysmallpre-chamber(PCh),amainchamber(MCh),andanozzlecon-nectingthem.AsparkplugandalsoinjectorsareinstalledinthePChtoigniteitschargeandprovidedesiredamountsofauxiliaryfuelandair.Anzoneis,usually,createdinsidethePChwithalowignitionenergydemandwhichpotentiallyminimizestherequire-mentsoftheconventionalignitionsystemsandtlyinitiatesandcontrolstheMChcombustion[34].ThecombustionprocessesoferentTJI-assistedcombustionsystemsinvolvingPCh-MChhavebeenreviewedinreferences[105,107,95].Morerecently,TJIhasbeenusedinrapidcompressionmachines(RCM)[104,65,36,68,9,8].Thesemachinesaretypicallyusedforinterrogatingtheoflow-to-intermediatetem-peratureautoignitionbycompressingfuel-airmixtures,uniformly,toengine-likeconditions.InTJI-assistedRCMcombustionsystems2.4a),aPChisinstalledattheendsideoftheRCM,referredtoastheMCh.ThePChisconnectedtotheMChthroughanozzle83(orseveralnozzles),allowingthehotproductjet(s)torapidlyentering/propagatingintheMCh[26].Ideally,theincomingjetshouldcausenearlyvolumetricallyandhomogeneouscombustion,enablingtheimplementationofleanburnedtechnologyininternalcombustion(IC)engines.Sincetheheatreleaseoccursalmostsimultaneouslyandrapidlyinallthecombustionsites,theoverallreactionactivitiesareexpectedtobecomparabletothoseinsparkignition(SI)engines.ThisallowstheTJI-RCMsystemstooperateatoptimumigni-tiontiming,whichextendstheknocklimits.LeanburnedTJI-assistedcombustionsystems,tly,reducethepumpingloss,improveenginedrivecycle,anddecreasecarbonemissionssincetheyoperatelessthrottled.Theleanhomogeneouscombustionhasalsolowertemperatureandnitrogenoxidesemissions.TheperformanceofTJI-assistedRCMisdependentonthecomplicatedandoftencou-pledofvariousfactorssuchastheinitialthermo-chemicalconditions,thePChandMChgeometries,theignitionprocess(timing,location,amount,anddurationofigniterdischargedenergy),thefuel-air-productsmixing,andthefuelchemistry.ItisnottrivialtoexperimentallypredicttheTJI-RCMbehaviorforvariousoperatingconditions.High-ycomputationalmodelssuchasthosedevelopedbasedonthelargeeddysimulation(LES)concept[89,90,82,85,79,25,72]cangreatlyhelpwiththedevelopmentandassess-mentofthesesystems.However,LESmodelshavenotbeenfullyusedforthispurposeduetothechallengesinmodelingofsub-gridscales(SGS)correlations.Thesearemoreculttomodel,especially,incompressibleturbulentreactingwsbecauseoftheadditionalnonlinearityofchemicalreactionsandtheintricatecomplexitiesofturbulence/reactioninter-actions[115].Additionally,inTJI-assistedcombustionsystemsabroadrangeoftypesincludingtype,distributed,premixed,non-premixed,andcanexist,simultaneously,incombustionzones[109].Therefore,thecombustionclosuremodelswhich84aredevelopedbasedontheassumptionofexistingonetypemightnotbeusedtopre-dicttheoverallbehaviorofsuchcombustionsystems,sincetheymaynotbeabletocapturethedetailsofthestructuresaccurately.SeveralreviewsandbooksareavailableontheadvantagesandchallengesofLESmodels[89,90,82,85,79,25,72].ThemodelsdevelopedbasedonthesolutionoftheSGSprobabilitydensityfunction(PDF),knownasthedensityfunction(FDF)[116,40,58,45,42,29,41,18,31],areamongthemostpromis-ingmodelsdevelopedforLESofturbulentreactingws.IntheFDFapproach,thejointstatisticsofturbulentvariablesatthesub-gridlevelareobtainedfromtheFDFtransportequation.ThemainadvantageoftheFDFapproachisthatalltermsinvolvingsingle-pointstatisticslikereactiontermsintheFDFequationappearinaclosedform.However,thesingle-pointFDFequationisnotclosedandfurthermodelingformulti-pointcorrelationsisneeded.Jaberietal.[41]developedaFDFmodelforLESofcompressibleturbulentreactingwsbasedonthescalarmassdensityfunction(FMDF).Thismodelisbasicallythemassweightedvalueofthedensityofenergyandspeciesmassfractions.TheFMDFmodelwasextendedtothevelocity-scalar[99,70]andvelocity-scalar-frequencyFMDF[100].ThescalarFMDFhasbeenusedtosimulateavarietyofcombustionsystems[98,118]withoutincludingthectofpressureontheFMDF,whichmightbeareasonableassumptionforlowMachnumberandconstantpressurecombustion.ThisisalsoincludedintheFMDFmodeltoaccuratelysimulatehigh-speedws[11].Inpreviousstudies[11,10,3],successfulsimulationshavebeenperformedbyusingLES/FMDFalongwithH-HO-Hgrid[56]forcylindricalgeometries.Despiteapplicabil-itytowsincomplexgeometries,thesearchandlocateMonteCarlo(MC)particlesinFMDFwillbemuchfasterandmoreaccurateforsimplergrids.Toaddressthisissueand85alsoincorporateauniformCartesianmeshinanygeometry,wedevelopedaversionofim-mersedboundary(IB)method[67]compatiblewiththeunderlyingsolvertotreatthe(FD)gridsandMCparticlesattheboundaries.TheIBmethodwasstintro-ducedbyPeskin[76]tocomputethebloodwinthecardiovascularsystems.Therehavebeennumerous[24,117,106]toassessitsaccuracyandstabilityinawiderangeofap-plicationssuchascompressible[27,62]andturbulentws[48,73].TheLES/FMDFmodelalongwithIBmethods,inadditionofsimplifyingthegridgenerationprocess,requireslesscalculationsintheproceduresofsearchingandlocatingtheMCparticles.Also,itallowsthemaximumuseofavailablecomputationalcapacity,sincethecomputationalloadsareequallydividedbetweenallparallelprocessor.Overall,incorporatingIBmethodintheLES/FMDFmodel,considerably,decreasesthecomputationalcostofsimulatingturbulentreactingwsincomplexgeometries,whilemaintainingtheaccuracy.Inthisstudy,weusethedevelopedcomputationalmodelinordertoinvestigateinde-tailstheTJI-assistedRCMcombustionprocessesandtheofvariousparametersonthem.Insection2.3,thegoverningequations,thecompressiblesinglephaseFMDFfor-mulation,thenumericalapproach,andtheIBmethodaredescribed.Insection2.4,thesimulatedTJI-RCMisdescribed.Insection2.5,theresultsforbothcompressionandcom-bustionstagesarepresentedandcomparedwiththeavailableexperimentaldata.Insection2.5.2.1,aparametricstudyisperformed,coveringtheignitertimingandlocations,vari-ouslean/rich/N2-dilutedmixtures,andadiabatic/heattransfermodelwalls.Section2.6summarizesthemainandconclusions.862.3GoverningequationsThehybridcompressibleLES/FMDFmethodologyinvolvestwosetsofEulerianandLa-grangianequations,whicharesolvedconjointlyforvelocityandscalar(speciesmassfrac-tionsandenthalpy)TheconservationformofthefullycompressibleLESequationsandtheFMDFequationarepresentedinthefollowingsections.2.3.1FilteredcompressibleNavier-StokesequationsThestandardFavre[6]compressiblecontinuity,momentum,energy,andscalarequa-tionsincurvilinearcoordinatesystemscanbecombinedintothefollowingvectorcompactform,@‹JU“@˝@›^F^Fv”@˘@›^G^Gv”@@›^H^Hv”@J^S;(2.1)whereU›ˆ;ˆ~u;ˆ~v;ˆ~w;ˆ~E;ˆ~˚”andJ@‹x;y;z;t“@‹˘;˝“arethesolutionvectorandtheJacobiantransformation,respectively.Theprimaryvariablesarethedensity,ˆ,theFavrevelocitycomponents,~u;~v;~w,theFavretotalenergy~E~e12~ui~ui,andtheFavrescalarmassfraction,~˚.Thecoordinatetransformationbetweenthephysicaldomain,‹x;y;z“,andcomputationaldomain,‹˘;;“,isbyxx‹˘;;“;yy‹˘;;“;zz‹˘;;“:(2.2)Thespatialngoperationisasf‹x;t“`f‹x;t“e`Sf›xœ;t”Òh›xœ;x”dxœ;(2.3)87wheref‹x;t“(or`f‹x;t“e`)representsthevalueofthetransportvariable,f‹x;t“,forthefunctionÒh.However,incompressiblewsitismoreconvenienttoconsidertheFavrevariables,where~f‹x;t“`f‹x;t“eL`ˆfe`~`ˆe`.Inequation2.1,theinviscidvectorsareas^F<@@@@@@@@@@@@@@@@@@@@>ˆ^Uˆ~u^Up^˘xˆ~v^Up^˘yˆ~w^Up^˘z›ˆ~Ep”^U^˘t=AAAAAAAAAAAAAAAAAAAA?;^G<@@@@@@@@@@@@@@@@@@@@>ˆ^Vˆ~u^Vp^xˆ~v^Vp^yˆ~w^Vp^z›ˆ~Ep”^V^t=AAAAAAAAAAAAAAAAAAAA?;^H<@@@@@@@@@@@@@@@@@@@@>ˆ^Wˆ~u^Wp^xˆ~v^Wp^yˆ~w^Wp^z›ˆ~Ep”^W^t=AAAAAAAAAAAAAAAAAAAA?(2.4)where¢¨¨¨¨¨¨¨¨¨¨¨¨¦¨¨¨¨¨¨¨¨¨¨¨¨¤^F^˘xÑF^˘yÑG^˘zÑH^G^xÑF^yÑG^zÑH^H^xÑF^yÑG^zÑHand¢¨¨¨¨¨¨¨¨¨¨¨¨¦¨¨¨¨¨¨¨¨¨¨¨¨¤^U^˘t^˘x~u^˘y~v^˘z~w^V^t^x~u^y~v^z~w^W^t^x~u^y~v^z~w:(2.5)88TheviscousFv,Gv,andHvincurvilinearcoordinatesystemscanbewrittenas^Fv<@@@@@@@@@@@@@@@@@@@@>0eŽ2L1~u23‹L1~uL2~vL3~wže‹L1~vL2~ue‹L1~wL3~u~uF2~vF3~wF41~TtPrtL1~H=AAAAAAAAAAAAAAAAAAAA?;^Gv<@@@@@@@@@@@@@@@@@@@@>0e‹L1~vL2~ueŽ2L2~v23‹L1~uL2~vL3~wže‹L2~wL3~v~uG2~vG3~wG42~TtPrtL2~H=AAAAAAAAAAAAAAAAAAAA?;^Hv<@@@@@@@@@@@@@@@@@@@@>0e‹L1~wL3~ue‹L2~wL3~veŽ2L3~w23‹L1~uL2~vL3~wž~uH2~vH3~wH43~TtPrtL3~H=AAAAAAAAAAAAAAAAAAAA?.(2.6)inwhichtheoperatorsare¢¨¨¨¨¨¨¨¨¨¨¨¨¦¨¨¨¨¨¨¨¨¨¨¨¨¤L1˘x@@˘x@@x@@L2˘y@@˘y@@y@@L3˘z@@˘z@@z@@:(2.7)89Here,themetriccots^˘t;^˘x;:::;^zareas^˘tJ@˘~@t,^˘xJ@˘~@x,:::,^zJ@~@z.Intheproceedingequations,,t,andPrtarethethermalconductivity,SGSviscosity,andSGSturbulentPrandtlnumber.ThequantitiesFn,Gn,andHnarethenthcomponentsofFv,Gv,andHvvectors.Forthetemperature,theFavreinternalenergyequationissolved,whiletheSGSpartofthekineticenergyisneglected.Furthermore,thesubgridstresstermsinequation2.1aremodeledbyagradienttypeclosure,inwhichtheeviscosity,e,isafunctionofmolecularviscosity,,andtheturbulentkinematicviscosity,t(i.e.et).TurbulentkinematicviscosityismodeledbyeithertheSmagorinskyclosuremodel(primarilyusedinthisstudy),t‹CsG“2S~SS;(2.8)orthemokinematicenergyvelocity(MKEV)model,tCmG¼S~u⁄i~u⁄ia~u⁄iflœa~u⁄iflœS:(2.9)IntheSmagorinskymodel,CsisthemodelconstantandS~SSisthemagnitudeofstrainratetensorcalculatedbyS~SS¼2~Sij~Sij:(2.10)Similarly,intheMKEVmodelCmisthemodelcotanda~u⁄ifisasa~u⁄if~uiuref(urefisaddedtoensuretheGalileaninvarianceandlœdenotesthesecondaryfunction).Inbothmodels,Gisthecharacteristicsizeofthefunction.Innon-reactingsimulations,thesourceterm^Sinequation2.1isanullvector,whereasinreactingsimulationsitisobtainedfromtheFMDF.Favreredheatisas~H~Epˆ90andthesubgridheatclosure,HSGSij,iscalculatedbasedonagradientmodelHSGSitPrt@~H@xi:(2.11)2.3.2CompressiblesinglephasescalarFMDFequationsThescalarFMDFisthejointPDFofthescalarvectoratsub-gridlevelandisasPL‹x;t“Sˆ›xœ;t”˙;›xœ;tG›xœx”dxœ;(2.12)whereGrepresentsthefunction,isthescalarvectorinthesamplespace.˙isthedensitybasedonaseriesofdeltafunctions,,by˙;›xœ;tNs1M1‹ ˚‹x;t““:(2.13)Nsrepresentsthenumberofthespeciesandthescalarvector,˚;‹1;:::;Ns1“,includesthespeciesmassfractionsandthespenthalpy›˚Ns1”.ThetransportequationfortheFMDFcanbederivedfromthefollowingscalarequationinCartesiancoordinatesystem:ˆ@˚@tˆui@˚@xi@@xi‰@˚@xi’ˆ›SRScmp”:(2.14)Thesourceterm,SR_!,representstheproductionorconsumptionofspecies‹1;:::;Ns“duetoreaction.ForEnergy(orEnthalpy)equation(Ns1),thesourcetermSR_QisthecombustionheatandScmp1ˆ‰@p@tui@p@xi˝ij@ui@xj’iscompressibilityterm.Theexact91FMDFequationcanbederivedfromthetimederivativeofFMDFequation2.12asPL‹x;t“@t@@ @˚@tShlPL‹x;t;(2.15)where`fSelrepresentstheconditionalvalueoffunctionf.TheFMDFtransportequationcanbeobtainedbyinsertingequation2.14intoequation2.15as@PL@t@‹`uiSelPL“@xic‰1ˆ@ˆ@t@‹ˆui“@xiS hlPL@@ ‰1ˆ@@xi@˚@xi’ShlPL@@ SRSflPL@@ ScmpSflPL:(2.16)Thespeciesandenergysourcetermsinequation2.16areas¢¨¨¨¨¨¨¨¦¨¨¨¨¨¨¨¤SR_!;Scmp0;1;:::;NsSR_Q;Scmp1ˆ„@p@tui@p@xi˝ij@ui@xj‚;Ns1:(2.17)Thechemicalreactionsourceterm,@@ SRSflPL,isclosedwhentheSGSpres-sureareignored.Thisterminthescalarequationandconven-tionalLESmethodsisnotclosed,therefore,theFMDFequationcannotbesolveddirectlyduetopresenceofthreeunclosedterms:@›auiSflPL”@xi,@@ −1ˆ@@xi@˚@xi‘SglPL,and@@ SRSflPL.Theunclosedconvectionterm,@›auiSflPL”@xi,canbedecomposedintotwolargeandSGS92convectiontermsas`uiSelPL`uieLPL‹`uiSelPL`uieLPL“:(2.18)TheSGSconvectiontermismodeledviaagradienttypeclosureas‹`uiSelPL`uieLPL“t@‹PL~`ˆel“@xi;(2.19)wheret`ˆelt~PrtistheturbulentyandPrtistheturbulentPrandtlnumber.ThesecondunclosedtermisdecomposedintwomolecularandSGSdissipationtermsas@@ ‰1ˆ@@xi@˚@xi’ShlPL@@xi@‹PL~`ˆel“@xi@@ m‹ `˚el“PL:(2.20)TheSGSdissipationismodeledviathelinearmeansquareestimation(LMSE)orthein-teractionbyexchangewiththemeanmodel(IEM)withthemtobetheSGSmixingfrequency,whichcanbeobtainedfromthemolecularandSGSturbulenty‹andt“andthesize‹G“asmC!tG`ˆel:(2.21)TheReynolds-averagedNavierStokes(RANS)PDFmethodforcompressiblewswasextendedbyDelarueandPope[19],inwhichpressureisconsideredasoneoftherandomvariablesinthePDFformulationandasetofmodeledstochasticequationsissolvedforthejointvelocity-frequency-energy-pressurePDF.Inthisstudy,thepressureisnotdirectly93includedintheFMDFformulationandonlytheofpressureonthescalarFMDFisconsidered.Thelastterminequation2.16representstheofpressureandviscosityonthescalars,wherethetemporalderivativeofpressurecanbewrittenasc‰1ˆ@p@t’ShlPL1`ˆel@`pel@tPLNs1:(2.22)ThespatialderivativepartisdecomposedintotheresolvedandSGSparts,c‰1ˆui@p@xi’ShlPL1`ˆel`uieL@`pel@xiPL„c‰1ˆui@p@xi’ShlPL1`ˆel`uieL@`pel@xiPL‚Ns1:(2.23)Similarly,theviscousdissipationpartisdecomposedintotheresolvedandSGSparts,d„1ˆ˝ij@ui@xj‚SilPL1`ˆela˝ijfL@`uiel@xjPL„d„1ˆ˝ij@ui@xj‚SilPL1`ˆela˝ijfL@`uiel@xjPL‚Ns1:(2.24)However,theSGSpressureterminequation2.23andtheSGSviscousterminequation2.24areignored.Byinsertingequations2.18-2.24intoequation2.14,thenalformoftheFMDF94transportequationforsingle-phasecompressiblereactingsystemcanbederivedas@PL@t@‹`uieLPL“@xi@@xit“@‹PL~`ˆel“@xi@@ m‹ `˚eL“PL@@ SR‹ “PL@@ ~Scmp‹ “PL,(2.25)where¢¨¨¨¨¨¨¨¦¨¨¨¨¨¨¨¤SR_!;~Scmp0;1;:::;NsSR_Q;~Scmp1`ˆel„@`pel@t`uieL@`pel@xia˝ijfL@`uieL@xj‚;Ns1(2.26)ThescalarcanbeobtainedfromthemodeledscalarFMDFtransportequation,whichisclosedandprovidesallsingle-pointspatialandtemporalstatisticsofspeciesandtemperature.However,tocheckthemathematicalconsistencybetweentheFMDFandtheconventionalLESmethods,thetransportequationsforthescalarvariablescanalsobesolveddirectlybyFDmethods.Here,weonlysolvetheFDequationforoneofthereactivespecies.952.3.3NumericalapproachTheattributesofthehybridLES/FMDFmodelareshownin2.1.Inthismodel,thevelocityandpressureareobtainedbysolvingequation2.1withtheconventionalFDmethods,whilethespeciesmassfractionsandtemperaturearecomputedusingtheFMDF-MCapproach.Inthisapproach,themodeledFMDFequationissolvedbytheLagrangianMCprocedurewiththeknownvelocityandpressureInthisprocedure,equa-tion2.20issolvedindirectlyviaequivalentstochasticequations.EachMCparticleisspatiallytransportedinthephysicalspaceduetothelargescaleconvection,andsub-gridandmoleculardThisisimplementedthroughasetofSDEsasdXiUieL1`ˆel@‹t“@xidt<@@@@>¿ÁÁÀ2‹t“`ˆel=AAAA?dWi‹t“;(2.27)whereWidenotestheWienerprocess.ThechangeinthecompositionspaceoccursduetoSGSandmolecularmixing,chemicalreaction,viscousdissipation,andpressurevariationintimeandspace,whichisdescribedbythefollowingSDEs:d˚m‹˚`˚eL“dt›SR‹˚“~Scmp”dt1;:::;Ns1:(2.28)Thecombinationofallprocessesdescribedbyequations2.27and2.28yieldsaFokker-Planckequation,whichisidenticaltotheFMDFtransportequation(equation2.25).ThisequationgovernsthePDFsofstochasticprocesses,inwhichthelargescale,SGS,molecularmixing,andthechemicalreactionsareincorporated.ThenumberofMCparticlesaremanagedviaaprocedureinvolvingtheuseofnonuniformweights.Thevariableweightingallowstheparticlenumbertovarybetweencertainminimumandmaximumnumbers.MC96LES-FDsolver:`ˆel;`uieL;`pel;`TeL;`˚eL`uieLOverlap:`ˆel;`˚eL;`TeLFMDF-MCsolver:`ˆel;`SeL;`TeL;`˚eL`SreacelFigure2.1:TheattributesofthehybridLES/FMDFmodel.particlesareweightaveragedoveraboxofsizeEcenteredatthepointofinteresttocalculatetheFavrevaluesofvariablesatagivenpoint.Itcanbeshownthatthesummationofweightswithintheensembleaveragingdomain,E,isrelatedtotheltereddensityas`ˆelmVEQn>Ew‹n“;(2.29)whereVEisthedomainvolume,mistheMCparticlemasswithaunitweight,andw‹n“representstheMCparticleweightwithintheensembledomain.TheFavalueofanyfunctionofscalars,`QeL,isobtainedfromthefollowingweightedaveragingoperation,`QeLPn>Ew‹n“Q‹˚“Pn>Ew‹n“:(2.30)ThediscretizationofgasdynamicsequationsisbasedonthecompactFDscheme[57],whichyieldsuptosixth(orhigher)orderspatialaccuracy.Inordertoavoidnumericalinstabilitiesandremovethenumericalnoisesgeneratedbythegrowthofnumericalerrorsathighwavenumbermodes,alowpass,highorder,spatialimplicitoperatorisused[57].ThetimegisbasedonathirdorderlowstorageRungeKuttamethod[10].972.3.4MCparticletrackingandparallelizationThesearchandlocateprocedureofMCparticlescouldbecomecomputationallyintensiveintheLES/FMDFmethod[11,10,3].Here,anemethodhasbeendevelopedtoreduceitscostbyusingastructured,orthogonal,uniform,andmulti-blockEuleriangridsystem.Figure2.2showstheFDmesh(solidyellowlines),MCparticles(smallpurplecircles),andimaginarycontrolvolumes(dashedgreenlines)aroundthegridpoints.Theprocedureisthree-dimensionalbuttobetterdescribeit,atwodimensionalschematicisconsidered.In2.2,thequadrilateralqrstisformedaroundtheFDgridpointO,whichisagoodrepresentativeforthiscell.Theparticleswithintheqrstareusedinensembleaveraging.ToperformensembleaveragingandinterpolationforMCparticles,thisquadrilateralhastobedetermined.Foralltheparticleslocatedinsidetheqrst,thevaluesatthecornersareused.Ageneralformofthisprocedurefornon-orthogonalgridisdescribedhere.InordertolocatetheMCparticle,initially,thecorrespondingcomputationalprocessorindexisidenThereafter,thequadrilateralqrstisspbythe3indexesofpointp.Todeterminetheithcomponentofpointq,theauxiliaryvectorsÐsp,Ðsq,andÐAareÐAisthenormalvectortoÐst,whereitsdirectioncouldbeeitherway.Therefore,G‹q“isasG‹q“−ÐspÐA‘−ÐsqÐA‘:(2.31)ThesignoftheG‹q“idenwhethertheparticlepandpointqlieonthesamesideofÐstornot.Sweepingstartpointisassumedtobei1andisperformedinthedirectionofincreasingi.PointqisthepointwithpositiveGvalue.Theparticlesaretrackedinthreetgridlinedirections,separately,andasimilarprocedureisusedinotherthreegridlinedirectionsasshowninre2.2.Astheithcomponentofqisdetermined,the98Figure2.2:Schematicofthegridpoints,largeblackcircles;MCparticles,smallpurplecircles;controlvolumes,dashedgreenlinesaroundthegridpoints;FDmesh,solidyellowline;andsweepingdirectionstodetermineithandjthcomponentsofthepointq.kthcomponentcouldbespbysearchinginagridplane.Byknowingtheithandkthcomponents,jthcomponentisdeterminedsimplybysweepinginasegmentformedbygridlines.Tointerpolatethepropertiestotheparticlelocation,alinearinterpolationisused.Sincetheuniformgridisusedhere,nofurtherinterpolationisneededfromthephysicaldomaintothecomputationaldomain.Therefore,thevelocityoftheparticlepiscomputedbyaninterpolationofthevaluesatthecornerofthequadrilateralqrst.ThisschemehasbeensuccessfullyimplementedintheunderlyingLES/FMDFsolver.boundaryconditionisusedforMCparticlesattheboundariesasdescribedbelow.2.3.5ImmersedboundarymethodforLES/FMDFAversionofimmersedboundary(IB)methodcompatiblewiththeLES/FMDFcomputa-tionalmodelisdevelopedandusedhere.Forthis,thesolutionalgorithmismodlocallybyenforcingthedesiredboundaryconditionsforbothFDgridsandMCparticles.Therefore,aCartesianmeshisusedanditisnotrequiredtomorphthecomputationalmeshtothephysicalboundaries.WiththeIBmethod,theLES/FMDFmodelretainsmostofthefavor-99Figure2.3:SchematicofapproximateddomainusingIBmethod.fluid,outofdomainout,approximatedboundary(thickline),actualboundary(parallellines),andMonteCarloparticlesY.ablepropertiesofstructuredgridsandalsoprovidesahighlevelofyintacklingwsandMCparticlesfortworeasons.First,theprocedureofsearchandlocateMCparticlesrequireslesscalculations.Second,thecomputationalloadisalmostequallydividedbetweentheprocessors,whichfacilitatesthemaximumutilizationofavailableparallelcomputationalprocessorswithsimpleandlessexpensivecommunicationprocedures.Figure2.3showstheactualboundaries,approximateddomain(shadedarea,fluid),approximatedboundary(thickline),andtheoutofdomainareaout).TheconservationofmassiswithinthefluidandDirichletboundaryconditionisusedforvelocitycomponentsattheapproximatedboundaries.TheparameterdMCBdenotesthedistancebetweenaMCparticleandtheassociateboundary.conditionswithnewdMCBequalsto1106‹m“areusedtorelocatetheparticleshittingtheboundaries.2.4TJI-RCMsetupandcomputationaldomainThesimulatedTJI-RCMissimilartotheopticallyaccessibleTJI-RCMexperimentatMichi-ganStateUniversity,operatingwithacompressionratioof8:5[26].Thismachineismainly100composedofthreeseparatepneumatic,hydraulic,andcombustioncylinderpistons,whicharemechanicallycoupled.Initially,theRCMcylinderisevacuatedbeforeitwithafuelandairmixtureataspequivalenceratio,andpreheatingto353K.Themixttureisthenrapidlycompressedtothedesiredelevatedtemperatureandpressure.Attheendofthecompressionprocess,thefuelandairmixtureiswelland(ideally)homogeneouslymixed.Thismixtureisheldataconstantvolume,whilethePChigniterisbeingchargedforadura-tionofabout5ms.ThePChcombustionisinitiatedbyasparkplug.ThePChisarelativelysmallchamberwithabout2%oftheMChvolumeandseparatefuelandairinjectors,igniter,andapressuretransducer2.4a).Afterasuccessfulignition,ahotproductturbulentjetisgeneratedandinjectedintotheMCh,whichstartstheMChcombustion.Theentireprocessisdescribedinmoredetailsinsection2.5.TheLES/FMDFequationsaresolvedontheorthogonaluniformmeshalongwithIBmethodtosimulatethethecurvedsurfaces.ANeumannboundaryconditionisimposedforthedensity,(@ˆ@n0,wherenisthedirectionnormaltotheimmersedsurface)andno-slipboundaryconditionisusedforthevelocitycomponentsattheapproximatedboundaries.Accordingtothepreviousstudies[63,10,11],moderateheattransferoccursatthecombus-tionchamberwall,whichhassomeonthetemperaturedistributioninbothPChandMCh.Here,weprimarilyuseadiabaticwalls,however,aconductiveheattransfermodelisalsodevelopedandused.Inordertoensurethegridqualitythroughoutthedomain,allsimulationsareconductedwithauniformgridspacingequalsto2:5104‹m“inalldirections.In2.4(b)andtable2.1,thespofthesimulatedthree-dimensionalmeshandcomputationaldomainarepresented.Ingeneratingthecomputationalgeometry,thevolumesoccupiedbytheigniterandfuelandairinjectorsinsidethePCharesubtractedfromtheactualvolume101(a)(b)Figure2.4:(a)TJI-RCMcombustionsystemand(b)3DviewoftheTJI-RCMmesh.tomakethecomputationalvolumeequaltotheexperimentalvolume.Thecomputationaldomainismassivelypartitionedintwostreamwiseandcross-streamdirections.Inordertomaintaintheaccuracyacrosstheparallelprocessorsandgridblockboundaries,5overlapgridsareusedusingordercompactFDscheme[57].ThecomputationalresourcesareprovidedbyhighperformancecomputingcenteratMichiganStateUniversity[1]andUniversityofTexasatAustin[2].Atypicalsimulationon100Intelprocessorsforabout1msofcombustionandcompressionstagesrequires3:0103and1:5103serviceunit(SU),respectively.Table2.1:SpofTJI-assistedRCMcomputationaldomain.ChamberRadius(mm)Height/Width(mm)PChSec.I6.7514.00Sec.II4.2516.00Sec.III1.503.00MCh25.3526.701022.5ResultsanddiscussionsThew/combustionintheTJI-assistedRCMcanbedividedintwomaini)compressionandii)combustionstages,whicharedescribedindetailsinthefollowingsubsections.2.5.1CompressionstageHere,thecompressionstageofTJI-RCMissimulatedincorporatingastaticmeshandim-posingtheavailableexperimentalpressuretraces,ppexperiment,andNeumannboundaryconditionsfortemperatureandvelocitycomponents,i.e.dTdz0andduidz0,onthepistonsideoftheRCM2.4b).Figure2.5(a)presentsthethree-dimensionaliso-surfacesofvelocitymagnitude,SÑUS‹m~s“,insidetheTJI-RCMattheendofthecompressionstage,wherepistonstaysatthetopdeadcenter(TDC).In2.5(b),thecontourplotsofvorticitymagnitude,SÑ!S‹1~s“,atthemiddleoftheRCMareplottedinxyandzyplanes.Forabetterrepresentationofthewstructures,thevelocitycontoursinhalfofthedomainareplotted.Asitcanbeobservedinthisahighlydistortedlowvelocityturbulentwisgeneratedduringthecompressionstage.ThegeneratedturbulentinsidethePChfacilitatesthecombustionbyenhancingtheburningvelocity.ThetemporalevolutionofthePChwduringthecompressionstageisshownthroughcontourplotsofvelocityandvorticitymagnitudesin2.6and2.7.Initially,therelativelylowpressurebetweenMChandPCh,gently,pushesthepremixedfuel-airmixtureintotheinitiallystagnantPCh2.6(a)-(c)and2.7(a)-(c)).However,afterabout14‹ms“,awelldevelopedunsteadyturbulentroundjetpenetratesintothePCh2.6dand2.7d).Thepistonacceleration,whichoccursapproximatelyinthetimeframeof17‹ms“ßtß27‹ms“,tly,increasesthejetvelocityandvorticity103(a)(b)Figure2.5:TJI-RCMwstructuresattheendofthecompressionstage:(a)Contourplotofiso-surfacesofvelocitymagnitude,SÑUS‹m~s“,and(b)Contourplotofvorticitymagnitude,SÑ!S‹1~s“,inthemiddleofthedomainatxyandxzplanes.magnitudes2.6e-gand2.7e-g).Whilethefuel-airjetpenetratesintothePChandreachesthesurroundingwallstrongvorticiesareappeared,initiatinganintenseturbulentwinsidethePCh.Thepistonbeginsdeceleratingaround27‹ms“ßtandasitcanbeobservedins2.6(h)-(i)and2.7(h)-(i),thePChwspeeddecreasesandthejetvanisheswhenthepistonreachestheTDCatt30‹ms“.Atthispoint,asomewhathomogeneousturbulentowdominatesthePChres2.6jand2.7j),whichmaycauseinstabilizingtheinthePChduringignition.Intheexperiments,about5‹ms“afterthepistonreachestheTDC,theigniterisdischarged.Thisdelayhelpstostabilizethehowever,itotherprocessesincludingPChturbulenceintensity,speed,and,eventually,thecharacteristicsofthegeneratedhotproductjet.Thecompressionstageissimulatedincorporatingtwoadiabaticandnon-adiabaticwallconditions.Thus,aheattransfermodelisdevelopedbasedontheenergybalancebetweenthew,innerandouterwallstocalculatetheinnerwalltemperature.Figure2.8showsaschematicofthemodelandtherelatedquantities.Here,Tgisthemeantemperatureof104(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)Figure2.6:TimeevolutionofthePChwduringthecompressionstageconsideringcontourplotsofvelocitymagnitude,SÑUS‹m~s“.theinsidew,Twiisthetemperatureoftheinnerwall,Twoistheassignedtemperatureoftheouterwall,hcgisthemeanconvectionheattransfercot,kcwisthethermalconductivityforthewall,xwisthewallthickness,andQistheheatByapplyingtheenergybalance,itisobtainedthatQkcwA›TwiTwo”xwhcgA›TgTwi”:(2.32)Thus,thetemperatureoftheinnerwallisgivenbyTwihcgTg‹kcw~xw“Twohcg‹kcw~xw“;(2.33)105(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)Figure2.7:TimeevolutionofthePChwduringthecompressionstageconsideringcontourplotsofvorticitymagnitude,SÑ!S‹1~s“.wherethemeanconvectiveheattransfercotiscalculatedashcgNugkcgD:(2.34)Here,kcgrepresentsthegasthermalconductivity,DisthePChorMChdiameterbasedonthelocationofthewall.NugisthemeanNusseltnumbercalculatedasNug0:035Re0:8,whereReisthemeanReynoldsnumber.Theouterwalltemperatureissetequalsto353K.Theheattransferfromthewallstotheinteriorwgaswasnotallowed.Figures2.9(a)and2.9(b)showthepredictedtemperaturecontoursattheendofthecompressionstageforcaseswithadiabaticandconductivewalls.Asitcanbeseeninthese106Figure2.8:Schematicofthewallheattransfermodelandrelatedquantities.twotheMChgastemperaturedistributionsarenearlyhomogeneouswithmeanvaluesequalto754Kand742K.HomogeneoustemperaturedistributionsarealsoobservedinthePCh.However,thePChmeantemperatureforthecasewithconductivewallsislowerthanthatforthecasewithadiabaticwalls.ThisnceisbecauseofthehighratioofthePChwall-surfacesareatovolume,whichincreasestheheatloss.(a)(b)Figure2.9:TemperaturecontoursofTJI-assistedRCMattheendofthecompressionstage,pistonlocatedatTDC,forthecaseswith(a)adiabaticand(b)conductivewalls.In2.10thepredictedMChandPChpressuretracesduringthecompressionstagearecomparedwiththeavailableexperimentaldata[26].Itcanbeobservedthatthenumerical107andexperimentalpressurevaluesareveryclosethroughoutthecompressionphasebeforeTDC(t28ms).Thistrendcontinuesuptotheignitionpoint(t36ms)whentheconductivewallsareused.Asexpected,thepressurestaysconstantbetweenTDCandignitionwhenadiabaticwallsareused.Theexperimentalandnumericalpressuresattheignitionpointarelessthan2%tforthecasewithadiabaticwallsandlessthan0:3%tforthecasewithconductivewalls.Figure2.10:QuantitativecomparisonofthepredictedpressuresofbothcasesusingadiabaticandconductivewallswithavailableexperimentaldataduringthecompressionstageoftheTJI-RCM.2.5.2CombustionphaseIntheTJI-assistedRCM,thetransitionfroma(non-reacting)compressedwtoareactingwisveryfastandcomplex.ThecombustionisusuallyinitiatedbyasparkpluginstalledinsidethePCh.ThePChignitionprocessisacrucialphaseinstabilizingaanditdepends,ratherverytly,ontheturbulenceintensityandmixturehomogeneitylevels[54].AsuccessfulkernelinitiationdoesnotnecessarilyleadtoastableandasuccessfulTJI-assistedcombustion.Forinstance,kernelsmaybegenerated,butthentheinthePChmaybeblownduetointensivew/turbulenceandhighstrain108ratestructures[5].Here,theigniterismodeledbyanenergydepositionmodel(EDM)[54],inwhichthefollowingsourceterm,Qig,anexponentialfunctionofbothspaceandtime,isusedintheenergyequation.Qigˆ"4ˇ23ig˝igexp™Œfl12›XiXig”22igfiŠŁexp™fl12‹ttm“2˝2igfiŁ:(2.35)Here,"isthetotalamountofenergydepositedinthevicinityofthesparkplugwiththediameterigforthetimeperiodof˝igandXiandXigaretheMCparticleandsparkpluglocations,respectively.IntheFD-basedLES,sub-gridscale(SGS)modelshavetocapturethesparkonthegasmixtureastheignitionenergyhastobedischargedinanareasmallerthantheLESsize.However,intheLES/FMDFmodelthisenergyisdepositedontheMCparticles,whichcancapturethelocalThemodeledigniterdiameterigissuggested[54]tobesetequaltothreetimesoftheexperimentalsparkplugclearancegap(30:8mm).Itisfoundthatthesameamountofenergyreportedtobegeneratedbythesparkplugintheexperimentsistforasuccessfulignition.Thedurationofthedepositionis200.ThemainexperimentalsparkandtheEDMparametersareprovidedintable2.2.Table2.2:Igniterparametersusedinexperimentandenergydepositionmodel(EDM).EnergyamountDurationSparkwidth(mJ)(s)(mm)Experimental1502000.8EDM1502002.4Figure2.11showsthevariationsofzyplaneaveragedtemperature(solidblueline),andfuelmassfraction(dashedredline),attheintimemarkedbythedirectionofthestreamwisevelocitycomponent,u.ThejetmovingfromthePChintotheMCh(i.e.uC0:0)isshownbyyellowsquaresÌandthejetgoinginoppositedirectionfromtheMCh109intothePCh(i.e.uB0:0)isshownbygreencirclesY.Thestreamwisejetvelocityvaluesatthearealsodisplayedonthetemperatureplot.TheresultsinthisrepresenttheoverallbehaviorofTJI-RCMw,aswellasthemixturecompositionanddirectionsofthedevelopedjetspassingthroughthefrom/totheMCh.Notethatgure2.11andalso2.12-2.14representtheresultscorrespondingtoCase1withthethermo-chemicalconditionsshownintable2.3.ThreemainphasesaredelineatedintheTJI-assistedRCMcombustionstage.Thedetailedfeaturesofeachphasemayvaryforerentthermo-chemicalconditions,buttheoverallcharacteristicsarebelievedtoremainthesame.Thesecombustionphaseshavebeenidenasi)coldfueljetphase,ii)turbulenthotproductjetphase,andiii)reversefuel-air/productjetphase.Theimportantfeaturesofeachphasearedescribedbelow.Figure2.11:TJI-RCMcombustionphasesbasedonthecompositionanddirectionofthewatthenozzle.110I.Coldfueljetphase:ThephaseoftheTJI-RCMcombustionstageconsistsoftheignition,expansionofgas,andformationoftheunburnedfueljet.Itcanbeobservedin2.11(PhaseI)thatatearlypartofthisphase,whiletheenergyisbeingdischargedbytheig-niter,suddentemperatureanddensitychangescausesomewanductuationsinthemixturevariablesasalowvelocitystreamatthefromtheMChtothePChisgenerated.Thesetwhicharemainlydependentontheamountandthedurationofthedischargedenergy,vanishrapidlyandmaynotthemaincombustion.Havingasuccessfulignitionprocess,turbulentformandpropagatethroughoutthePChand,accordingly,thePChpressurerisecausesthecoldfueljettopushthroughtheintotheMCh.Figure2.11(PhaseI)showstheproper-tiesofthecoldfueljetatthetemperatureofT750K,fuelmassfractionof˚CH40:05,andstreamwisevelocityof0:0juj200‹m~s“.Thisisalsoobservedin2.12(a)and2.12(b),wherethevelocitymagnitudeiso-surfacescoloredbythefuelmassfractionandtemperatureareshown.Evidently,arelativelycoldandhighfuelconcentrationjet(incomparisontotheMCh)indeedpassestheAsitcanbeobservedin2.12(a),thefuelmassfractioninPChishigherthanthatinMCh.SincethefuelmassfractionofthecoldfueljetisthesameasthePChfuelmassfraction,itcanbeeasilydistinguishedfromtheMChingure2.12(a).However,thetemperatureofPChandMCharealmostthesameandtrackingthecoldfueljetbasedonitstemperature2.12b)maynotbetrivial.ThemaincharacteristicsofthisjetaredependentonthePChcompositionandturbulenceintensityaswellastheparametersinvolvedintheignition.Forexample,higherequivalenceratioandturbulenceintensityinthePChgenerallyleadtohighervelocityofthecoldfueljet.111(a)(b)Figure2.12:ThephaseoftheTJI-assistedRCMcombustionstage.Instantaneousiso-surfacesofvelocitymagnitudecoloredby(a)fuelmassfraction,˚CH4,and(b)Temperature,T,att1:0‹ms“TheamountoffuelleavingthePChtotheMChisanimportantfactorindesigningtheauxiliaryairandfuelinjectors.ThemainroleoftheauxiliaryfuelinjectoristoimprovethePChcombustioninitiationbyincreasingtheequivalenceratio.Ideally,alltheexistingfuelinsidethePChhastoparticipateinthePChcombustion.However,inpracticesomeoftheauxiliaryfueldoesnotparticipateinthePChcombustionandissimplyaddedtotheMChcharge.ThisfuelmighthelpthecombustioninMCh,butitusuallyhaselittleanditisbettertobeburnedinsidethePCh.Asexplainedinthenextsection,locatingtheigniterclosetothenozzleinsidethePChpreventscoldfuelleavingthePCh,whichenablestheultra-leanpremixedcombustionandlowersthelowylimitofpremixedcombustion.II.Turbulenthotproductjetphase:Afterasuccessfulignition,duringtheevolutionofthePChcombustion,aturbulenthotproduct/fueljetisdevelopedpassingthroughthefromthePChtotheMCh.Thefeaturesofthisjet,whicharebyvariousparametersincludingPChandMCh112(a)(b)Figure2.13:ThesecondphaseoftheTJI-assistedRCMcombustionstage.Instantaneousiso-surfacesofvelocitymagnitudecoloredby(a)fuelmassfraction,˚CH4,and(b)Temperature,T,att2:5‹ms“thermo-chemicalconditions,areimportanttotheMChcombustion.Unlikethecoldfueljet,thehotproductjetcanalsobeidenedbythevelocitymagnitudeiso-surfacescoloredbytemperature.Itcanbeseenin2.11thatthejettemperature,rapidly,increasesfromT750KuptoT2400KandthefuelmassfractiondropstozeroinPhaseII.Initially,thejetvelocity,rapidly,increasesandreachestoveryhighvalues(about500‹m~s“)attheduetothehighPCh-MChpressureLateronwhentheMChcombustionisinitiated,thejetconfrontsrelativelyhigherpressurezonesintheMCh,whilethePChcombustionbecomeslesse,therefore,thedrivingforcetosustainthehighvelocityhotproductjetis,quickly,weakened.Figures2.13(a)and2.13(b)showthejetcompositionandtemperature,whenithitsthelowersectionoftheMCh.III.Reversefuel-air/productjetphase.ThehotproductturbulentjetdevelopedinthephaseIIprovideshighenergycon-tentignitionsitesthroughouttheMCh.Sincethefuel-airmixtureresidencetimeis113relativelyhigheratthelowersectionoftheMCh,combustionmainlystartsatthislo-cation.DuringtheMChcombustion,expectedly,MChtemperatureandconsequentlyitspressureincrease,unevenly,inalldirections;developinginversejetsfromtheMChtothePCh.Thisphasecanbedividedintotwosub-phases,basedonthecompositionandtemperatureofthereversejets.Ideally,theentireamountoftheavailablefuelmustbeconsumedinthemainchamber.However,asitalsocanbeobservedinPhaseIII.apartof2.11,anunburnedfuelstreamwithrelativelylowtemperatureandvelocityofabout100m~sispassingthefromtheMChtothePCh.Thissub-phaseisalsoshownin2.14(a)and2.14(b).Theinversejetpropertieschangesintimetohighertemperaturesandlowerfuelmassfractions;asindicationsofareversehotproductjetleakingintothePCh.Thetemporalvariationsofthecomposition,thetemperature,andthevelocityofthisjetareshowninPhaseIII.bpartof2.11.Asitcanalsobeobservedin2.14(c)and2.14(d),thetransitionfromoneinversejettotheotherdependsontheMChcombustion.ItisexpectedthatallthefuelintheMChtobeburnedbytheendofthisphase,however,someoftheunburnedfuelleakedfromtheMChtothePChstayunburnedforalongtimeand,negatively,theperformanceoftheTJI-RCMsystem.In-terestingly,attheveryendoftheTJI-RCMcombustionstage,theremnantunburnedfuel-airtrappedinthePChduringthepreviousphasesmightgenerateamixtureofunburnedfuel-airandproductstreamfromthePChtotheMCh.Sincethetempera-tureofthisjetisrelativelyhighanditsresidencetimeisshort,itburnsquicklyasitgetsintotheMCh.Thisjetmighthelpwiththecombustionsustainabilityatthelatertimes,however,italsostretchestheendofTJI-RCMcombustionstage.Preventingthefuelfromescapingmaynotbetrivialbycontrollingthethermo-chemicalparameters.114(a)(b)(c)(d)Figure2.14:ThereverseunburnedfueljetofthethirdphaseoftheTJI-assistedRCMcombustionstage;instantaneousiso-surfacesofvelocitymagnitudecoloredby(a)fuelmassfraction,˚CH4,and(b)Temperature,Tatt4:0‹ms“.ThereversehotproductjetofthethirdphaseoftheTJI-assistedRCMcombustionstage;instantaneousiso-surfacesofvelocitymagnitudecoloredby(c)fuelmassfraction,˚CH4,and(d)Temperature,T,att8:0‹ms“.However,asitisstudiedinCase10toCase13oftable2.3,loweringthelocationoftheignitershortensthecombustiondurationandalsopreventstheunburnedfuelattheuppersectionoftheMChleaksintothePCh.Here,westudytheofvariousthermo-chemicalandphysicalparametersaspro-videdintable2.3,whicharecategorizedinthreesetsasa)initialconditionandwallheattransfermodel(Case1toCase5),b)N2dilutionandMChandPChequivalenceratios(Case6115toCase9),andc)igniterlocation(Case10toCase13).ThereferenceMChandPChcompo-sitions,˚MCh0:485and˚PCh0:787,andtheigniterlocation,dig4‹mm“,havebeenchosenintheLES/FMDFsimulationsbasedontheavailableexperimentaldata[110].IntheexperimentsafterthepistonreachestheTDC,theRCMishelduntouchedwhiletheigniterisbeingcharged.TheetimeoftheigniterenergydischargeisobservedtobeaboutTDC6‹ms“,therefore,thesimulationofthecompressionphasewascontinued.Accord-ingly,thethermo-hydrodynamicsatTDC6‹ms“areusedastheinitialconditionsinthesimulations,exceptinCase5whichtherelatedatTDCareused.Table2.3:Thermo-chemicalandphysicalparametersofsimulatedTJI-assistedRCM.Case#˚MCh˚PChICattigWallHTtig(ms)N2%dig(mm)10.4850.787idealadiabatictTDC+60.0420.4850.787idealmodeltTDC+60.0430.4850.787realisticadiabatictTDC+60.0440.4850.787realisticmodeltTDC+60.0450.4850.787realisticadiabatictTDC0.0460.4850.787realisticadiabatictTDC+620.0470.4850.787realisticadiabatictTDC+630.0480.30.787realisticadiabatictTDC+600.0490.32.0realisticadiabatictTDC+600.04100.4850.787realisticadiabatictTDC+600.013110.4850.787realisticadiabatictTDC+600.025120.30.787realisticadiabatictTDC+600.025130.20.787realisticadiabatictTDC+600.0252.5.2.1ComparisonwithexperimentandparametricanalysisThecorrespondingsimulationresultsinCase1areutilizedin2.15foraqualitativecomparisonbetweentheavailableexperimentaldata[110]andLES/FMDFtemperaturecontours.Theexperimentalimagesshownin2.15(a1)-(a3)presenttheMChlumi-nosityforttime.Here,tjisasthetimewherethetipofthehotproductjet(bothinexperimentsandnumerics)reachesthemiddleoftheMChasitcanbeobservedin2.15(a1),2.15(b1),and2.15(c1).Thecontrastandbrightnessofthecolorimages116wereenhancedusingImage-Jsoftware[96].IntheexperimentalimagestheentireMChinspanwisedirectioniscaptured.Forthesakeofbettercomparisons,2.15(b1)-(b3)showthespanwiseaveragedofthesimulatedtemperaturecontours,whicharemoresimilartotheexperimentalimages.ItmightbechallengingtocapturethewinaparticularplaneinsidetheMChexperimentally,butthiscanbeeasilydonenumerically.Figures2.15(c1)-(c3)showthetemperaturecontoursinaplanelocatedatthemiddleoftheMChwhichpresentmoredetailsofthehighlyturbulenthotproductjet.Itcanbeseenin2.15(a2),2.15(b2),and2.15(c2)thatatthetimetj0:2‹ms“boththepredictedandexperimentalhotproductjetsarereachedtothelowerpartoftheMCh.Thepredictedtipjetvelocity,consistentwithexperiments,isabout125‹m~s“onaverage.Afterabouttj0:4,combustionisalreadyini-tiatedandpropagatedinbothspanwiseandcrossstreamdirections2.15a3,2.15b3,and2.15c3).Thequalitativecomparisonoftheserevealsthehighaccuracyofournumericalapproach.Aquantitativecomparisonhasalsobeenmadebetweentheavailableexperimentalpres-suredata[110]andLES/FMDFpressuresobtainedfromCase1andCase2providedintable2.3.In2.16,theexperimentalpressuretraceisshownby(l).Thepressuretrans-ducerintheexperimentalsetupislocatedatthelowersectionoftheMCh.Thesimulatedpressurevaluesatthelocationofthepressuretransducer,PointMCh,areshownby(X)forCase1andby(h)forCase2.DuringtheearlyphasesoftheTJI-RCMcombustion,bothexperimentalandnumericalpressurevaluesarereasonablyinanaccurateagreement.Inthelaterphases,thesetwopressuretracesdeviatefromeachother.Inthenumericalpointofview,thisbehaviormightbeduetothechemicalkineticsmodeland/orwallconditionusedinthesimulations.Thediscrepanciesbetweenthereportedandactualinitialexperimentalconditionsincludingtheinitialfuelequivalenceratio,temperature,pressure,andauxiliary117TimeExperimentalLES/FMDFLES/FMDF(ms)imagespanwiseaveragedmid-planetj(a1)(b1)(c1)tj0:2(a2)(b2)(c2)tj0:4(a3)(b3)(c3)Figure2.15:QualitativecomparisonbetweenLES/FMDFandexperimentalresults:(a1)-(a3):Experimentalpictures;(b1)-(b3):LES/FMDFspan-wisedaveragedtemperaturecon-toursat;and(c1)-(c3):LES/FMDFtemperaturecontoursinthemiddleoftheMCh.118Figure2.16:Comparingtheexperimental(l)andsimulatedpressuretracesatPointMChinCase1(X)andCase2(h).amountoffuel,aswellasthepossibleleakageintheexperimentalsetupmightcausethepressureTherepeatabilityoftheexperimentalpressuretraceswasexaminedrepeatingtheexperimentswiththesameconditions;anuncertaintyfactorequalsto10%fromthemeanvalues,reasonably,representthepossiblealeatoryandepistemicuncertain-ties.Theexperimentalpressure(uncertainty)boundsareshownbyshadedgrayareain2.16.Despiteofpressurethesimulatedpressuretraces,accept-ably,followthecorrespondingexperimentalvalueswithinthebounds.InCase1theadiabaticwallsareusedandthegeneratedheatofcombustionstaysinthesystemandexpectedlythepredictedpressureisrelativelyhigher.InCase2wheretheheattransferwallmodelisused,themaximumpredictedpressureislowerthanitinCase1andclosertotheexperimentalresults.ItcanbeseenthattheTJI-assistedRCMcombustionprocessissensitivetotheheattransfermodelatthewallsevenforthesameinitialthermo-chemicalconditions.Moredetailsareprovidedbelow.Figure2.17showsthecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforCase1.Intheseandsimilarforallcases,thecontoursofeachquantityatthe119middleandsideplanesoftheTJI-RCMareshownatttimes,e.g.ttig0:5‹ms“,tig02:0‹ms“,tig05:0‹ms“,andtig10:0‹ms“inthesamerow.InCase1,theinitialthermo-chemicalconditionsaresetbasedontheexperimentalresults.However,sincethemixtureisheldatrestforafairlylongtime,stagnantconditioninMChmightbeareasonableassumption,however,duetothehighturbulencelevelinsidethePCh,turbulentareinitiallyadded.Thesetionsaregeneratedbysolvingthegoverningequationswithperiodicboundaryconditionsandaninitiallyrandom,solenoidal,andGaussianvelocityldforalongtime[116].Themaximumvaluesofthevelocitycomponentsarewithinthe10%oftheinitialhotproductjetvelocitypassingthenozzle(e.g.300‹m~s“).Thewallsareassumedtobeadiabatic.Itcanbeseenthatwithin0:5‹ms“theignitionprocessiscompletedandthecoldfueljetisreachedtothemiddlesectionoftheMCh,suggestingthatlessamountofcoldfuelisexitingouttotheMChandmorefuelparticipatesinthePChignitionprocesses.After2‹ms“ahighlyturbulenthotproductjetisalreadydevelopedandreachedthelowersectionoftheMChinitiatingitscombustion.TheMChcombustiongeneratesvortexshapestructureswhicheventuallypropagateintheentiredomainandleadtoanearlyvolumetriccombustion.Asitcanbeseenafter10‹ms“theMChandPChcombustionarecompleted.Thethermo-chemicalandhydrodynamicconditionsusedinsimulatingCase2arethesameasthoseusedinsimulatingCase1.However,inthiscasetheconductiveheattransfermodel(equation2.33)isusedtocalculatethewalltemperatures.Itcanbeseenin2.18thateventhoughthecombustioniscompletedby10‹ms“,itisgenerallydelayed.ThejetisalreadyreachedtothelowersectionoftheMChandcombustionisinitiatedby2‹ms“afterignition,butthepropagateslessincomparisontoCase1.Alsoafter5‹ms“thereverescoldfueljetisdeveloped,buthightemperaturezonesintheMCharelessdeveloped.120Case1tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(realistic)Fuelmassfraction(realistic)Velocitymagnitude(realistic)Figure2.17:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase1.121Case2tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(realistic)Fuelmassfraction(realistic)Velocitymagnitude(realistic)Figure2.18:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase2.122Figure2.19showsthecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforCase3.Inthiscase,consistentwiththeexperiments,thesimulationofthecompressionphaseiscontinuedforanother6‹ms“afterthepistonreachestotheTDC.Withinthistime-lagtheMChandPChturbulencesrelax,whichmightallowthesparkplugtobetterignitethePChcharge,butitnegativelythespeedandpressureriseinsidethePChduringtheignitionprocess.After0:5‹ms“thePChignitionprocessisnotcompletedandthecoldfueljetisexitingouttotheMCh.About2‹ms“afterignition,ahotproductturbulentjethitsthelowerpartoftheMChandinitiatesthemaincombustion.DuetothepressureriseoftheMChareversecoldfueljetisgettingintothePChatabout5‹ms“.Within10‹ms“thecombustionisfairlycompletedandallavailablefuelinsidethesystemisconsumed.AsitcanbeseeninSÑUS‹m~s“contoursthereareatthenozzlebetweenMChandPChwhichbalancethepressureofbothchambers.Figure2.20showsthecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforCase4.Inthiscasethewalltemperaturesarecalculatedbasedontheconductiveheattransfermodel(equation2.33).Thecompressionsimulationusingwallheattransfermodelwascontinuedforextra6‹ms“afterthepistonreachestheTDCandthewisusedastheinitialhydrodynamicscondition.ThefuelmassfractioninsidetheMChandPCharethesameastheminCase3.Asitcanbeseenintemperatureandfuelmassfractioncontoursin2.20,thePChignitionprocesstakeslongerabout2‹ms“mainlyduetotheheatlossofthePCh.Thecombustionwasalreadyinitiatedbefore5‹ms“butatthistime,comparetopreviouscases,lessamountoftheMChchargeparticipatedinthecombustion,theoftheheatlossoftheMCh.Eventhoughthecombustioniscompletedafter10‹ms“,theentireprocessofcombustionis,reasonably,delayedinthiscasedueheatlossacrosstheMChandPChwalls.123Case3tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(realistic)Fuelmassfraction(realistic)Velocitymagnitude(realistic)Figure2.19:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase3.124Case4tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(wallHTmodel)Fuelmassfraction(wallHTmodel)Velocitymagnitude(wallHTmodel)Figure2.20:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase4.125Figure2.21showsthecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforCase5.InthiscasetheignitiontimingisshiftedtothetimewhenthepistonstopsattheTDC.Atthistime,theinitialturbulenceinsidebothMChandPChisrelativelyhigherthanitinCase3which,ultimately,generateshighervelocityhotproductjetattheearliertimesandcombustionisinitiatedfaster.However,conductingthiscasemightbeexperimentally,sincethesparkplugmustinitiatethePChcombustioninahigherlevelturbulence.ThisissuemightbeaddressedbydischargingmoreenergyforalongertimeduringthePChignitionprocess.Asitcanbeseenin2.21,thePChignitionprocessintheuppersectionofthePChiscompletedwithin0:5‹ms“andtheMChcombustionisinitiatedby2‹ms“.ThehotproductjetvelocityisrelativelyhigherthanitinCase3duetofasterignitionprocessesandrapidpressureriseinthePCh.Expectedly,theMChcombustioniscompletedby10:0‹ms“.ThemaininCase2toCase5istheinitialhydrodynamicscondition,thereforethecorrespondingresultsforthesesimulationsareanalyzedtogether.Inure2.22(a)thesimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase3(X),Case4(h),andCase5(⁄)areshown.In2.22(b)-(e)thesimulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atonepointlocatedatapointinthenozzleexitintheMChsideversustimeforCase2toCase5arepresentedwhichthestreamwisevelocityvaluesareassignedtothetemperatureplot.Thisformatisalsousedlaterin2.27and2.32forCase6toCase9andCase10toCase13.InitiallyalocalpressurerisecanbeobservedinPChpressureduringtheignitionprocess.Thispressurerise,whichdeterminesthevelocityofbothcoldfuelandhotproductjets,ishighlydependentontheinitialPChturbulenceandwallheattransfer.InCase5,sincethePChturbulenceisrelativelyhigher,thelargerpressurerisesinthePChareobserved.126Case5tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(tigtTDC)Fuelmassfraction(tigtTDC)Velocitymagnitude(tigtTDC)Figure2.21:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase5.127WhenthehotjetreachesthelowersectionsoftheMChandinitiatesthemaincombustion,expectedly,theMChpressurerises.ThepressurebetweenMChandPChdrivestheMChmixtureattheuppersections(unburnedmixture)intothePCh.Eventually,whencombustioniscompleted,bothpressuresreachestothesamelevel.Asitcanbeobservedin2.22(b)-(e),thisbehaviorisvalidinallcases,exceptinCase2andCase4whichtheheatlossismorethanitinothercasesand,accordingly,thetemperatureandpressureareslightlylower.Theinitialcoldfueljetcanbedelineatedbythewcharacteristicsatapointinsidethedomainclosetothenozzle.Itcanbeobservedin2.22(b)-(e)thatthehighlevel˚CH4andlowtemperature(750‹K“)passesthroughthispointwithrelativelylowmagnitudenegativestreamwisevelocityvalues.Thedurationofthisphase,expectedly,isshorterinCase2andCase5andlongerinCase4.AfterthecompletionofthePChignitionprocess,thehotturbulentjetexitsouttotheMCh.Thevelocityofthisjetisdependentontheignitionprocess.Thehighestvelocitymagnitudes,509‹m~s“and418‹m~s“,occurredintheCase2andCase5inwhichthePChignitiontimingisshorter.Duetothesamethermo-chemicalconditions,theMChcombustiontakesplace,fairly,inthesametime,exceptforCase4whichoccursoveralongerperiodoftimeduetoMChheatreleasethroughthewalls.Inthesecondsetofthesimulationswestudytheofinitialthermo-chemicalcondi-tionsonthecombustionprocessesbydilutingtheoriginalmixturewith20%N2and30%N2inCase6andCase7andloweringtheMChequivalenceratioto0:3inCase8.AlsotheofrichPChandunburnedfuelinsidethehotproductjetisstudiedinCase9byaddingextrafueltothePChcompositionandprovidearichPChwith˚PCh2:0.Figures2.23and2.24showthecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforCase6andCase7,respectively.FairlysimilarPChignitionprocessandMChcombustioninitiationis128(a)(b)(c)(d)(e)Figure2.22:(a)SimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase3(X),Case4(h),andCase5(⁄).(b)-(e)Simulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase2toCase5.Thestreamwisevelocityvaluesarealsoshown.129Case6tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(20%N2)Fuelmassfraction(20%N2)Velocitymagnitude(20%N2)Figure2.23:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase6.observedinthesecases,however,theMChcombustionprocessisdelayedmoreinCase7,duetoexistenceofmoreN2intheMCh.Itcanbeseenin2.23after5‹ms“thepropagatesthroughouttheMChleadingtothecombustioncompletion.However,gure2.24forthesametimerevealsthatthepropagatesinthelowersideoftheMChandsustainsthecombustioninthisarea.Italsocanbeseenthatthecombustioniscompletedinbothcasesafter10‹ms“.Figure2.25showsthecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforCase8,inwhichtheMChequivalenceratioisequalto0:3.SincethePChthermo-chemicalandhydrodynamicsisthesameasCase3,thesimilarignitionprocessoccurs.However,theleanMChontheinitiationoftheMChcombustion.Asitcanbeseenafter5‹ms“ignition,aweakcombustionisinitiatedandmostoftheMChchargestaysunburned.130Case7tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(30%N2)Fuelmassfraction(30%N2)Velocitymagnitude(30%N2)Figure2.24:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase7.131Case8tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(˚MCh0:3)Fuelmassfraction(˚MCh0:3)Velocitymagnitude(˚MCh0:3)Figure2.25:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase8.Howeverthecombustioniscompletedafter10‹ms“,expectedly,withlowertemperature.Figure2.26showstheassociatedcontoursforCase9.InthiscasethePChcompositionconsistsofarichpremixedfuel-airmixture,˚PCh2:0.Theignitionprocesstakesmorethanitintheothercasessincethetemperatureoftherichmixtureisrelativelylower.Itcanbeseenin2.26thatafter2‹ms“thehotproductjetisnotyetdeveloped.FuelcontoursrevealthatthemostofthefuelinsidethePChexitsouttotheMChduringtheignitionprocess,whichmaychangetheleannessoftheMChcomposition.Itcanbeseenafter5‹ms“oftheignitionthehotjetisdevelopedandgettingintotheMCh.However,thecompositionofthisjetconsistsofproductsandalsounburnedfuel.ThisamountoffuelmighthelptoinitiatetheMChcombustion,butthejettemperatureisrelativelyloweranddelaystheMChcombustion.Itcanbeseenthatafter5‹ms“theMChcombustionis132Case9tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(˚PCh2:0)Fuelmassfraction(˚PCh2:0)Velocitymagnitude(˚PCh2:0)Figure2.26:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase9.initiatedatthelowersectionswithconsiderableamountofunburnedfuelinsidethePChandMCh.Eventually,theentirefuelparticipatesineitherPChorMChcombustion.SincetheinitialhydrodynamicsconditionsarethesameinCase6toCase9andthemainarerelatedtotheircompositions,theresultsofthesecasesareanalyzedhere.In2.27(a)thesimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase6(h),Case7(X),Case8(⁄),andCase9()areshown.ItcanbeobservedthattheinitialpressureriseinPChisthesameinCase6toCase8anditisdelayedinCase9.TheMChcombustionandpressureriseisalsodelayedinallcases.ThemaximumpressuredropsinCase6toCase9.However,maximumpressureinCase9isslightlyhigherthanitinCase8,sincetheextraamountoffuelinsidethePCh,eventually,participatesinthecombustionprocesses.In2.27(b)-(e)thesimulatedtemperature133(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase6toCase9arepresentedwhichthestreamwisevelocityvaluesareassignedtothetemperaturecurves.FairlysimilarbehaviorareobservedforCase6toCase9.AndinCase9thefuelmassfractionofthecoldfueljetisconsiderablyhigherthanitinothercasesanditisexitingouttotheMChforslightlylongertime.ThemainideaofTJI-assistedcombustionis,constantly,exposingaleanmixturetoahotjet.Aswehaveseeninthepreviouscases,initially,duringtheignitionprocessacoldfueljetisdevelopedandexitsouttotheMChandmightchangetheleannessoftheleanMCh.Thisfuel,ideally,mustparticipateinthePChignitionandcombustionprocesses.ThisjetisacoldjetanditunlikelyhelpstheinitiationoftheMChcombustion,however,itparticipatesintheMChcombustionlaterifthecombustionissustained.InordertopreventthecoldfueljetfromgettingintotheMChandalsoforceittoparticipateinthePChcombustionprocess,wesuggesttochangethelocationoftheigniter,whichisalsopossibleexperimentally.Loweringtheigniterlocationleadstocombustioninitiationinthemiddle(orlow)sectionsofthePCh.ThemixtureattheuppersectionsofthePChistrappedinbythepremixedaroundtheigniterlocationandgraduallyisfedtothereactingzonesdevelopedduringthePChignitionandcombustionprocesses.Atthesametime,ahotproductjetgetsoutofthePChintoMCh.InthisapproachthemaingoalofTJI-assistedcombustionisbydevelopingahotjetforalongertime,which,eventually,allowstolowerthelowylimitofthepremixedcombustion.Here,westudythecombustionprocessesoftheTJI-assistedRCMbychangingtheigniterlocations.Figures2.28and2.29showthecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforCase10andCase11,inwhichtheigniterdistancesfromthetopofthePCharedig13‹mm“anddig25‹mm“,respectively.Asitcanbeseenin2.28134(a)(b)(c)(d)(e)Figure2.27:(a)SimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase6(h),Case7(X),Case8(⁄),andCase9().(b)-(e)Simulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase6toCase9.Thestreamwisevelocityvaluesarealsoshown.135Case10tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(dig13‹mm“)Fuelmassfraction(dig13‹mm“)Velocitymagnitude(dig13‹mm“)Figure2.28:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase10.after0:5‹ms“astablereactingzoneinthemiddleofthePChisdevelopedandthemixtureaboveitistrappedandstayedunburned,while,still,acoldfueljetisbeinginjectedintotheMCh.Combustionisalreadyinitiatedafter2:0‹ms“butanunburnedfuelsstillcanbeseenafter5:0‹ms“.However,itcanbeseenin2.29thatafter0:5‹ms“,thecoldfueljetisvirtuallyvanishedandahotproductjetisalreadydevelopedandbeinginjectedintotheMChandcombustioniscompletedafter5:0‹ms“.Tofurtheranalyzetheoftheigniterlocationontheleanandultra-leanpremixedcombustionprocesses,itisatthesamelocationasitinCase11andtheMChequiva-lenceratioarechangedto0:3and0:2inCase12andCase13,respectively.Thecontoursoftemperature,fuelmassfraction,andvelocitymagnitudeforthesecasesareshownin2.30and2.31.ThePChignitionprocessesare,fairly,similartotheminCase11.Itcanbe136Case11tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(dig25‹mm“)Fuelmassfraction(dig25‹mm“)Velocitymagnitude(dig25‹mm“)Figure2.29:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase11.137Case12tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(˚MCh0:3;dig25)Fuelmassfraction(˚MCh0:3;dig25)Velocitymagnitude(˚MCh0:3;dig25)Figure2.30:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase12.seenin2.30thatafter5‹ms“mostoftheMChmixtureisburned(comparetotheresultsshownforCase8in2.25after5‹ms“).Italsocanbeseenine2.31thatthecombustionofanultraleanmixtureisinitiatedandcompletedby10‹ms“.ThemaininCase10toCase13isthelocationoftheigniterandtoevaluateitsontheentirecombustionprocesstheresultsofthesescasesareanalyzedtogether.Inure2.32(a)thesimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase10(h),Case11(X),Case12(⁄),andCase13()areshown.AsitcanbeseentheMChcombustionsare,generally,advanced.Asitwasshown138Case13tig00:5‹ms“tig02:0‹ms“tig05:0‹ms“tig10:0‹ms“Temperature(˚MCh0:2;dig25)Fuelmassfraction(˚MCh0:2;dig25)Velocitymagnitude(˚MCh0:2;dig25)Figure2.31:Temporalevolutionofsimulatedtemperature,T,fuelmassfraction,˚CH4,andvelocitymagnitude,SÑUS‹m~s“,contoursforCase13.139forCase3in2.22(a),thecombustionwascompletedwithin10‹ms“,whileforthesamethermo-chemicalandhydrodynamicsconditionbutlowerigniterlocationinCase10itiscompletedwithin7‹ms“.ItcanbeobservedinCase11(thesameconditionsbutlowerigniterlocationclosetothenozzle)thatthemaincombustiondurationcanbedecreasedmoretolessthan5‹ms“.Theoftheigniterlocationisinvestigatedmoreinleanerandultra-leanMChcompositionsinCase12andCase13,whichcombustionisinitiatedandcompletedinashortperiodoftime.In2.32(b)-(e)thesimulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase10toCase13arepresentedwhichthestreamwisevelocityvaluesareassignedtothetemperaturecurves.ItcanbeseenthatinCase102.32b),still,forashorterperiodoftimeacoldfueljetispassingthroughthenozzleintotheMCh,but,immediatelyafterthatahotproductjetisgettingintotheMChandtheMChcombustionisinitiatedandcompletedfaster.Itcanbeobservedin2.32(c)forCase11thatitisunlikelytodevelopacoldfueljetsincethepremixedbehavesasabarrierandtrapsthemixtureattheuppersectionofthePCh.ItcanbeseenthatimmediatelyafterdischargingtheigniterenergyahotproductjetisdevelopedpropagatingintotheMCh.Similarbehaviorcanbeseenin2.32(d)and2.32(e)butwithlowertemperaturesincetheMChchargeisleanandultra-lean.Usingthisapproachallowstheultra-leancombustiontoburnnearlyvolumetricwithinaveryshortperiodoftime.140(a)(b)(c)(d)(e)Figure2.32:(a)SimulatedpressuretracesinPch(dashedthinlines)andMch(solidthicklines)versustimeforCase10(h),Case11(X),Case12(⁄),andCase13().(b)-(e)Simulatedtemperature(bluesolidlines)andfuelmassfraction(reddashedlines)atapointinthenozzleexitintheMChsideversustimeforCase10toCase13.Thestreamwisevelocityvaluesarealsoshown.1412.6ChapterconclusionsTurbulentjetignitionassistedrapidcompressionmachines(TJI-assistedRCM)aresimulatedforvariousthermo-chemicalandhydrodynamicsconditionsbylargeeddysimulation/massdensitymassfunction(LES/FMDF)modelingapproachusinganimmersedboundary(IB)method.ThehybridLES/FMDFequationsforthecompressiblereactingwswhichinvolvestwosetsofEulerianandLagrangianequations,aresolved,conjointly,forvelocityandscalars.Thesimulationresultsareinagoodagreementwithavailableexperimen-taldata,quantitavelyandqualitatively.ThreemaincombustionphasesaredelineatedinaTJI-assistedRCMcombustionsystemasi)coldfueljet,ii)turbulenthotproduct/fueljet,andiii)reversefuel-air/productjet.Astheresultsofasuccessfulpre-chamber(PCh)ignition/combustionprocess,aturbulenthotproduct/fueljetisbeingdevelopedpropagat-ingintothemainchamber(MCh)andinitiatingitscombustionbyprovidinghotignitionsitesthroughoutthechamber.TheMChcombustioninitiationanddurationfeaturesaredependentonthePChandMChinitialthermo-chemicalandhydrodynamicsconditions,aswellastheamountofheattransferringthroughthewalls.HigherturbulencelevelinsidethePChleadstofasterhotjetandshorterMChcombustionduration.IntheprocessofPChignition,ajetofunburnedfuelexitsouttotheMCh,whichisanundesirableoflocatingtheigniterfarawayfromthenozzle.Wesuggestedandstudiedaremedytocontrolandeliminatethisjetbychangingthelocationoftheigniter.IgnitingthePChchargeclosetothenozzlepreventstheunburnedfuelgettingoutintotheMCh,sincethedevelopedpremixedinsidethePChactasbarrierstrappingthePChchargeintheupperside,whichlatertheyare,constantlyandgradually,fedintothePChcombustionduringtheMChcombustion.Loweringtheigniterlocation,whichcanbedoneexperimen-142tally,causestheMChchargegettingexposedtoahotjetforarelativelylongertime.Thiscandecreasethelowylimitofthepremixedcombustionsandallowthefastandnearlyvolumetriccombustioninultra-leanpremixedmixtures.143BIBLIOGRAPHY144BIBLIOGRAPHY[1]InstituteforCyber-EnabledResearch(ICER)atMichiganStateUniversity.http://icer.msu.edu/.[2]TexasAdvancedComputingCenter(TACC)atheUniversityofTexasatAustin.http://www.tacc.utexas.edu.[3]A.Afshari,F.Jaberi,andT.P.Shih.Large-eddysimulationsofturbulentwsinanaxisymmetricdumpcombustor.AIAAJournal,46(7),2008.[4]D.Ahlman,G.Velter,G.Brethouwer,andA.Johansson.Directnumericalsimulationofnonisothermalturbulentwalljets.PhysicsofFluids,21(3),2009.[5]S.AhmedandE.Mastorakos.SparkignitionofliftedturbulentjetCombustionandFlame,146(12):215{231,2006.[6]A.Aldama.Filteringtechniquesforturbulentwsimulations.LectureNotesinEngineering,SpringerVerlag,49,1990.[7]C.Arndt,R.Schiel,J.Gounder,W.Meier,andM.Aigner.Flamestabilizationandauto-ignitionofpulsedmethanejetsinahotw:oftemperature.Pro-ceedingsoftheCombustionInstitute,34(1):1483{1490,2013.[8]W.AttardandH.Blaxill.Asinglefuelpre-chamberjetignitionpowertrainachievinghighload,highandnearzeronoxemissions.SAEInt.J.Engines,5:734{746,082011.[9]W.AttardandP.Parsons.Flamekerneldevelopmentforasparkinitiatedpre-chambercombustionsystemcapableofhighload,highandnearzeronoxemissions.SAEInt.J.Engines,3:408{427,102010.[10]A.Banaeizadeh,A.Afshari,H.Schock,andF.Jaberi.Large-eddysimulationsofturbulentwsininternalcombustionengines.InternationalJournalofHeatandMassTransfer,60:781{796,2013.[11]A.Banaeizadeh,Z.Li,andF.Jaberi.Compressiblescalarmassdensityfunctionmodelforhigh-speedturbulentws.AIAAJournal,49(10),2011.145[12]D.Beerer,V.McDonell,P.Therkelsen,andR.K.Cheng.Flashbackandturbulentspeedmeasurementsinhydrogen/methanestabilizedbyalow-swirlinjec-toratelevatedpressuresandtemperature.JournalofEngineeringforGasTurbinesandPower,136:20242{20254,2014.[13]L.Bezgin,V.Kopchenov,A.Sharipov,N.Titova,andA.Starik.Evaluationofpre-dictionabilityofdetailedreactionmechanismsinthecombustionperformanceinhy-drogen/airsupersonicws.CombustionScienceandTechnology,185(1):62{94,2013.[14]M.Boger,D.Veynante,H.Boughanem,andA.Trouv.Directnumericalsimulationanalysisofsurfacedensityconceptforlargeeddysimulationofturbulentpre-mixedcombustion.Symposium(International)onCombustion,27(1):917{925,1998.[15]P.Boivin,A.Dauptain,C.Jimnez,andB.Cuenot.Simulationofasupersonichydro-genairautoignition-stabilizedusingreducedchemistry.CombustionandFlame,159(4):1779{1790,2012.[16]J.Carpio,I.Iglesias,M.Vera,A.Snchez,andA.Lin.Criticalradiusforhot-jetignitionofhydrogenairmixtures.InternationalJournalofHydrogenEnergy,38(7):3105{3109,2013.[17]P.Clavin.Dynamicbehaviorofpremixedfrontsinlaminarandturbulentws.ProgressinEnergyandComb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