December 2003

NASA/CR-2003-212689

Numerical Analysis of the SCHOLARSupersonic Combustor

Carlos G. RodriguezAllied Aerospace, GASL Division, Hampton, Virginia

Andrew D. CutlerThe George Washington UniversityJoint Institute for Advancement of Flight SciencesLangley Research Center, Hampton, Virginia

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December 2003

NASA/CR-2003-212689

Numerical Analysis of the SCHOLARSupersonic Combustor

Carlos G. RodriguezAllied Aerospace, GASL Division, Hampton, Virginia

Andrew D. CutlerThe George Washington UniversityJoint Institute for Advancement of Flight SciencesLangley Research Center, Hampton, Virginia

Available from:

NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)7121 Standard Drive 5285 Port Royal RoadHanover, MD 21076-1320 Springfield, VA 22161-2171(301) 621-0390 (703) 605-6000

iii

List of Symbols

k specific turbulence kinetic energy [m2/s2]

M Mach number

p pressure [Pa]

Pr Prandtl number

Sc Schmidt number

T temperature [K]

x axial coordinate [m]

y vertical coordinate [m]

yi mass-fraction of specie i

z lateral coordinate [m]

y+ dimensionless vertical wall-turbulence coordinate

ρ mass density [kg/m3]

γ specific-heat ratio

ω specific dissipation rate [1/s]

τ relative turbulence intensity

µ viscosity [N s/m2]

Subscripts:

L laminar

T turbulent

01 total inflow conditions

02 pitot value

iv

1. Introduction

Most ComputationalFluid Dynamic (CFD) codesusedin practicalapplicationsarebasedon theReynolds-AveragedNavier-Stokes(RANS) set of equations.Theseequationsemploy many ad hocassumptionsandempiricalcoefficientsin themodelingof theturbulentviscous-fluxesandthechemicalspecie-productionsource-terms.Therefore,thesemodelshaveto be validatedwith experimentaldatabeforebeingappliedwith anyconfidenceto a givenclassof flows. Thetypesof flow of interestfor thepresent work are those found in scramjet applications.

A supersonic-combustionscramjetmodelknownasSCHOLARhasbeentestedatNASA Langley’sDirect-ConnectSupersonicCombustionTestFacility (DCSCTF)1,2. This experimentwasdesignedtoprovidea testcasefor validationof CFD codes,involving supersonicinjection,mixing andcombustionin aduct.Themodelhasasimplegeometry,andlargeregionsof subsonic/recirculatingareavoided;theenthalpyof the testgascorrespondsto a Mach-7flight condition(approximately1200K at combustorentrance).During thedesignof theexperimentit wasbelievedthattheresultingflow would bemixing-limited (i.e.,with chemicalreactiontowardsequilibriumbeingmuchfasterthanthemixing process);aswill beseenlater,this turnedoutnot to bethecase.Somenumericalsimulationsof thisexperimenthavealready been reported by other authors3.

The present work documentssome preliminary results in the numerical simulation of theSCHOLARscramjetusingVULCAN, a RANS computercodedevelopedat NASA Langley4. Thepur-poseof thesimulationis to assesstheeffectsof themodelingassumptionsandparametersin theflow-field predictions.A brief descriptionof theexperimentandsummaryof thedatais presentedfirst. It isfollowedby thenumericalanalysisof thefacility nozzle,whichwill providethenecessaryinflow condi-tionsfor thesimulationof thedirect-connectcombustor.Theanalysisof thescramjetproperbeginswiththedefinitionof abaselineconfigurationfor thenumericalmodeling.Thisconfigurationprovidesa ref-erencesolutionwhich is usedfor a qualitativeanalysisof the flowfield, grid convergencestudy,andcomparisonwith thedata.Themainobjectiveof theinvestigationis to quantifytheeffectson this solu-tion dueto changesin someof thenumericalparameters.This reportconcentrateson turbulenceparam-eterssuchasnumericalmodels,SchmidtandPrandtlnumbers,andinflow turbulence.Futurework willinclude the effects of chemistry models, inflow conditions and the presence of radicals.

2

2. Experiment

The SCHOLAR experiment has been extensively described in references 1 and 2. Only a briefdescription of the experimental set-up and a summary of the data will be presented here.

2.1 Description of the Facility

In the DCSCTF facility, vitiated air is produced at high enthalpy in the heater by combustion ofhydrogen with premixed oxygen and air; the nominal enthalpy corresponds to Mach 7 flight. This air isaccelerated through a water-cooled Mach-2 nozzle before entering the test section (operating conditionswill be given later in the report). The complete layout and dimensions of the combustor model areshown in figure 1 (a). The duct consist of a constant-area isolator, which ends in a small step on the topwall. Downstream of the step there is another short constant-area section. This section is followed by a3° divergence on the top wall, which extends all the way to the exit of the model. The span of the modelis constant throughout its entire length. The injection nozzle provides hydrogen fuel at a 30° angle [fig-ure 1 (b)]. This nozzle was designed to produce a Mach 2.5, one-dimensional flow at its exit (injectionconditions and equivalence ratio to be given later). Also shown in the figure are 5 pilot injectors thatwere used in some runs to pilot the main injector; these injectors were not modeled in the present calcu-lations.

The model was built in two sections: the upstream section (containing the isolator and injector) wasmade of copper, while the downstream section (containing most of the divergent section) was made ofsteel. The conductivity of these materials and the thickness of the walls allowed the duct to be run with-out cooling. There are 7 transverse slots in the model to allow for measurement of static temperaturesfields by CARS beams; the locations shown in figure 1 (numbered 1, 3, 5, 6, 7) are the ones used in thisstudy. The model itself is instrumented with both pressure taps and wall-temperature probes. Pressuretaps are located at the centerline of the bottom wall, on the top wall (close to the sidewall for the coppersection and centerline for the steel section), and on the sidewall (midpoints of the steel section). Ther-mocouples are located on the top wall, six for each section of the duct.

2.2 Summary of Data

Wall-pressure distributions for the pressure taps at the bottom centerline are shown in Figure 2.Data are shown at 10 s and 24 s; note that the heater is started at 1 s and fuel injection commences at 6.4s. Comparison between measurements at these two times reveals only small differences. Also shown isthe average over the total time run; this average will be used throughout the present work for compari-son with numerical results. Pressures vary widely in the upstream region, probably due to the shock-wave system created by the injector and step; a small discontinuity in cross-section between nozzle andcombustor, due to a stainless-steel flange, may also account for the pressure variations. Pressure gener-ally falls moving downstream due to the divergence in the duct, until about 0.5 m. At that location itrises rapidly to a peak at about 0.75 m, and then falls slowly as the gas flows towards the exit. Very littlecombustion appears to take place upstream of 0.5 m, but by 0.75 m most of the mixed fuel seems tohave burned; further mixing and combustion is expected to occur downstream.

Since the duct is uncooled, surface temperatures vary greatly during the course of the run; represen-tative temperature histories and fits (top wall, unpiloted) are presented in figure 3. In the copper section,temperature is typically about 350 K at the beginning of the fuel injection and rises to as high as 600 Kat the end. For the steel section, those numbers are typically 450 K and 950 K, respectively.

3

Figure 4 contains three-dimensional cutaway views of the duct showing contour-plots of the fittedCARS temperature data; the data are all fit to cosine-series bivariate functions. Flow-direction is fromtop-left to bottom-right; main fuel injector is on the top wall between planes 1 and 3. Planes 3 and 5show a region of low temperature (between 250 and 550 K) at the center, which is the injected fuel-plume; there is no evidence of combustion between these two planes. At planes 6 and 7 temperatureshave risen abruptly, suggesting near complete combustion. The hot regions at the top and bottom wallsare probably near stoichiometric, with the cooler region at the center likely to be fuel-rich. Injected fuelhas probably not penetrated to the sidewalls. There is some asymmetry in the data, probably due toinflow perturbations and the data fit.

4

3. Analysis of the Facility Nozzle

As mentioned,a two-dimensional,converging-diverging,water-coolednozzlewasusedto acceler-atethevitiated flow to thenominaltestconditionsat thecombustorinlet. Theconditionsat thenozzleexit wereprobedwith apitot raketo mapthepitot pressure(p02). Thesemeasurementswerereportedinreference5, togetherwith comparisonsto CFD calculationsperformedwith the VULCAN code.Thefacility nozzle was modeled in the present work to provide inflow conditions to the duct calculations.

3.1 Solution Procedure

The three-dimensionalgrid usedfor thenozzlesimulationis shownin figure 5; its dimensionsare129× 129× 145(axial × vertical× lateral).Thehalf-width andfull heightof thenozzlewasmodeled,the latter becauseof slight asymmetriesbetweentop andbottom(curved) walls. The grid wassubdi-vided into 32 blocks,to take advantageof the MessagePassingInterface(MPI) capabilitiesof VUL-CAN. It had a wall-spacing of 5× 10-5 m, resulting in a maximum y+ of 65.

The inlet boundarywas modeledas subsonicinflow, with a total pressureand temperatureof767250Paand1828K, respectively.Theinflow turbulenceintensityτ andturbulent-to-laminarviscos-ity ratio µT/µL weresetat25%and600,respectively(which resultin a turbulencelength-scaleof about1 mm at inflow conditions).All solid (water-cooled)walls weremodeledasno-slip isothermalbound-aries;following reference5, thewall-temperaturewasassumedto be500K. Theexit boundarywassetassupersonicextrapolation.Finally, theverticalcenterplanewasmodeledasa symmetryboundary.Asmentioned,the inflow to the nozzlewasvitiated air. One-dimensionalcalculationsassumingequilib-rium andfrozencompositionsdifferedlittle in majorspecies,temperatureandpressure1. Becauseof thisandtherangeof temperaturesunderconsideration,thegaswasmodeledascaloricallyperfectin ordertoreducecomputationalexpense.Following the one-dimensionalresults,the molecularweight andspe-cific-heat ratioγ were assumed to be 25.9098 and 1.28909, respectively.

The inviscid fluxeswerecalculatedusingEdwards’low-dissipationflux-split scheme6, with third-orderMUSCL interpolation.Time-integrationwasdoneusingthe implicit diagonalizedapproximate-factorizationscheme7; the entire domainwas run fully elliptic. Wilcox’s 1998 k-ω model and wall-matchingfunctions8 wereusedfor modelingturbulentviscousstressesandheat-transfer;the turbulentPrandtlnumber(PrT) wasassumedto be0.90.CalculationsweredoneonanSGI Origin 2000,using32processors.Grid sequencingwith threelevelswasusedfor convergenceacceleration,andalsoasamea-sureof grid convergence,as will be seenin the results.Convergencewas consideredto havebeenachievedwhenthe residualdroppedfour ordersof magnitude,which occurredafter 1500iterationsinthe fine sequence.

3.2. Results

Figure6 showsthe nozzlecenterplaneMach contours.The effectsof the wall asymmetryarejustapparentin thecontours.Thecalculatednozzle-exitpitot-profilesarepresentedin figure7 for theverti-cal centerplane,andin figure 8 for thehorizontalcenterplane.Both showadequateagreementwith theexperimentaldata,althoughthe latter oneshowsmoreasymmetryandthicker boundary-layers(espe-cially in thehorizontalcenterplane).It shouldbenotedthedatawasobtainedatslightly differentoperat-ing conditions than those of the SCHOLAR test used here. Also, the pitot rake was locatedapproximately2 mmdownstreamof thenozzleexit (with theductremoved);thenumericalresultsweretakenat the exit itself. Finally, measurementsmay be affectedby the probediameternot beingsmallenough with respect to the boundary-layer thickness.

5

A detail of figure 7 is shown in figure 9 for the medium- and fine-sequence calculations, togetherwith 1% error bars on the data. The fine-sequence solution falls within the error bars for most of thepoints, although the data shows a greater dip near the center. There are some differences betweenmedium and fine calculations, but for the most part these differences are of the order of the experimentalerror; therefore, the solution can be considered to be grid-converged.

The values of the inflow turbulence-parameters quoted before were chosen in order to providescramjet-inlet turbulence-intensity and viscosity-ratio of the order of 1% and 100, respectively (giving aturbulence length-scale of the order of 1 mm at exit conditions). There is no way to quantify the turbu-lence velocity and length scales of the experiment. To determine the effects of these parameters on thescramjet simulation, several combinations were chosen. It was found difficult to predict a priori whichinflow values would give desired values at the exit, but after some trial-and-error the inflow parametersshown in table 1 were found to give adequate values at the exit potential flow (also given in the table).In particular, the values of the inflow turbulence parameters given earlier provide exit conditions with2.5% turbulence intensity and 300 viscosity-ratio. The effects on the nozzle-exit vertical-profiles of thedifferent combinations of turbulent parameters given in the table can be seen in figure 10. In general,higher values of τ and µT/µL appear to give better agreement with the nozzle experimental data. Theeffects of these parameters on the flow within the combustor proper will be shown in the next section.

6

4. Scramjet Baseline Solution

4.1 Solution Procedure

A referencesolutionwassoughtthatwould providea first approximationto theproblem,andfromwhich parametricstudiescouldbedone.This solution,andtheprocedureandconditionsusedto obtainit, will hereafterbereferredto as“baseline”.Unlessotherwisenoted,this numericalconfigurationhavebeen used for all calculations reported here.

The half-width combustorwasdiscretizedwith a grid that hadapproximately3.6 million controlvolumes(CVs), uniformly distributedamong80 blocks (again,to take advantageVULCAN’s MPIcapability).A detailof thegrid in theneighborhoodof theinjectoris shownin figure11.To reducegridrequirements,non-C(0)block-boundarieswereextensivelyused(asmaybeseenfrom thegrid disconti-nuitiesin thefigure).Theverticalgrid-dimensionsvariedbetween61and85,andthelateralbetween61and81.Thegrid spacingat thewall variedbetween1.5× 10-4 m and3.0× 10-4 m. For themostpart,theresulting values of y+ are below 100, which is just about right for the use of wall functions.

For inflow conditionsat thecombustorinlet, theprofilesobtainedfrom thenozzlecalculationwereimposedon theboundary.To allow for multi-speciescalculations,speciesmass-fractionswereadded.The vitiated compositionfrom the one-dimensionalcalculationspreviouslymentionedincludedabouttwo dozenspecies.For thechemistrymodelsusedin thepresentcalculations(which couldnot accountfor mostof thevitiation species),theinflow wasassumedto containonly N2, O2 andH2O with uniformmass-fractions0.5638,0.2321and0.2041,respectivelya; thesewereobtainedfrom theone-dimensionalanalysisusingthesamemolefractionsfor O2 andH2O (themolefractionof N2 wasslightly adjustedtogive a total mole-fractionof 1.0). The inflow conditionsat the inlet of the hydrogeninjector wereassumedto besubsonicwith totalpressureandtemperatureof 3.44MPaand302K, respectively.Theseconditionsresultedin anequivalenceratio of approximately1.0.Thesolid walls weremodeledasno-slip isothermal,with wall temperaturessetat400K and500K for thecopperandsteelsections,respec-tively (basedon the wall-temperaturesshownin figure 3). The exit boundarywasmodeledassuper-sonic extrapolation, and the vertical centerplane was modeled as a symmetry boundary.

The inviscid spaceand time integrationschemeswere the sameas for the nozzlecalculations,unlessotherwisenoted.Theburnerwasranfully-elliptic, to accountfor possiblesubsonic/recirculationregions;somecalculationsweredoneusinga semi-ellipticapproachto be describedbelow.The flowwasmodeledasa mixture of thermally-perfectgases.The chemistrymodelusedwasDrummond’s9-specie/18-reaction(9×18) mechanism9; the ignition-regionfeaturein VULCAN wasneededto ignitethis modelat thepresentconditions.Thermodynamicpropertiesof thechemicalspeciesweremodeledwith a one-curvepolynomialfit includedin VULCAN, andbasedon the datafrom reference10. TheWilcox k-ω turbulencemodelandwall functionswereagainused.They weresupplementedwith theWilcox compressibilitycorrection,usedto reducespreadingrates(or turbulence)asa function of thelocal turbulenceMachnumber8. Not includedwasthePopecorrectionfor theround-jet/plane-jetanom-aly, which is standardin Wilcox’s model.The turbulencePrandtl(PrT) and Schmidt(ScT) numberswere set at 1.0.

A three-levelgrid sequencingwasagainusedfor convergenceaccelerationandto estimategrid con-vergence.Computationsweredoneon 80 500-MHz processorsof an SGI Origin 2000computer;the

aThe effects of radicals such as OH present in the inflow will be the subject of future work.

7

ideal parallel speed-upobtainedwith the presentgrid was78.3.Also usedwere16 DEC Alpha 667MHz nodes in a BEOWULF cluster.

4.2. Results

A total of 10,000iterationsweredoneon themediumsequence,and45,000on the fine sequence.For both sequences,the residualwould drop abouttwo ordersof magnitudebeforeundergoingslowoscillations.For the medium-gridsolution, convergencewas assumedwhen no variation would beobservedin eithertheoverall flowfield or thewall-pressuredistributions;thesolutionwasmostlycon-vergedafter2,000-3,000iterations.For thefine-gridsolution,aminimumof 35,000wereneededbeforethe solution would show no further changes.

Figure12 showsthecenterplaneMachcontoursfor thebaselinesolution(notethat in this andsub-sequentcenterplaneplots the vertical scaleis twice the horizontalfor betterresolution).The jet pene-tratesat approximately30° for a certaindistance,but it is immediatelyturnedin the directionof themainflow while continuingto penetratefurthertowardstheoppositewall. Theexpansionafterthestep,andcompressionfrom the jet areclearlyseen.A region of slower flow is apparentdownstreamof x ~0.50 m.

Thewatermass-fractioncontours(figure13)suggeststhatignition takesplacebetween0.45and0.5m. This is alsoshownby the temperaturecontourplots (figure 14). TheCARSmeasurementssamplesonly indicate that heat-releaseoccursafter 0.4 m. The fuel core (indicatedby the low-temperatureregions)seemsto penetratefurther in thenumericalsimulation.Themixing andcombustionefficiencydistributionsarepresentedin figure 15; they aredefined11 asmixed-fuelover total-fuel, and reacted(water)-fuelover total-fuel, respectively,and correctedfor vitiation12. Initially, the combustionlagswith respectto themixing, but it raisesrapidlyafter0.5m, andby 0.8m mostof themixedfuel appearsto have reacted. Overall, just over 60% of the fuel seems to mix and react with the inflow air.

Theseobservationsareconfirmedby theanalysisof thebottom-wallcenterlinepressuredistribution(figure16).Theexperimentaldatasamplingcanonly locatetheignition delaysomewherebetween0.45and0.57m. CFDpredictstheflameto beginneartheupstreamlimit; this is likely to beanunderpredic-tion of the delay.The pressurelevelsfrom the medium-andfine-sequencesolutionsarecomparedinfigure 17. At the inlet, the medium-solutionlevelsareslightly higher than the fine-solution;this hasbeenobservedin otherVULCAN calculations13, andmay be dueto post-processingof the medium-sequencesolution.Themaindifferencebetweenbothsolutionsis in theignition delay,which is consid-erably greaterfor the mediumsolution (and closer to the data).This is counter-intuitive,since thegreaternumericaldiffusion of thecoarsergrid shouldresultin greatermixing, andthereforelessigni-tion delay(seebelow). In any case,theseresultsshowthat grid convergenceat the very leasthasnotbeen proven on the current grid.

This preliminarysolutionindicatesthat thebaselinemodellikely underpredictsthe ignition delay,or timefor a fuel-airmixtureto form aflamein theabsenceof ignition sources14. Thisdelayis thecom-binationof aphysicaldelay(dependingonfuel mixing) andachemicaldelay(timefor flameproductionafter the formationof a homogeneousfuel-air mixture). In the numericalsolution,the former mostlydependson theturbulencemodelandthelatteron thechemistrymodel.Therefore,theunderpredictionof theignition delaymaybedueto anoverpredictionof themixing by theturbulencemodel,anunder-predictionof thechemicaldelayby thechemistrymodel,or a combinationof both.Anotherdeficiencyis the overpredictionof the penetrationof the fuel plume; it is likely due to the turbulencemodel,although this is subject to further verification.

8

Someof the following calculationswereobtainedwith a “semi-elliptic” integrationapproach,inorderto reducecomputationalrequirements.In this approach,thefirst 48 upstreamblocksweresolvedelliptically, with a first-orderextrapolationboundary-conditionappliedat the downstreamendof theresultingregion(at x ~ 0.35m). Convergenceon this regionwasfairly rapid,owing to theabsenceofsignificant reaction.The remaining32 blocks were then solved,also elliptically, for about15,000-20,000iterations.Theresultsfor thebaselineconditionareshownin figures18 and19.Thesolutionisalmostindistinguishablefrom the fully-elliptic calculation.Sincemostof the computationis spentinthesecond(reacting)region,this approachreducesthecomputationaleffort by almost60%.Thecalcu-lations performed with this approach will be explicitly noted.

As explainedin theIntroduction,for thepresentwork theeffectsin theturbulenceparameterswerestudied.Two additionalturbulencemodelsweretested:Menter’sk-ω model15, andanexplicit algebraicstressmodelextensionb (EASM) of the Wilcox modelbasedon GatskiandSpeziale’smodel16; thesecalculationsweredoneusingthe semi-elliptic integrationdescribedabove.Menter’smodelcombinesthe Wilcox k-ω modelnearsolid walls, with the standardk-ε modeleverywhereelse(particularly inshear-dominatedflow-regions).Theresultsfor thismodel(figures20and21)showthatit slightly over-predictsignition delay,andhaslessfuel-plumepenetrationthantheWilcox model.Ontheotherhand,itconsiderablyoverpredictsthe pressure-risein the reactionregion.The EASM model is essentiallyanextensionof theBoussinesqapproximation,providinga non-linearconstitutiverelationbetweenturbu-lent stressesandstrain-rates.Theyaccountfor theanisotropyof thenormalReynoldsstresses,which inturn allows for the simulationof stress-inducedmotions.Thesemotionsareof importancein corner-flow regions,were they may delay the onsetof separationdueto adversepressuregradients.For thepresentapplication,it canbe seen(figures22 and23) that the EASM modelprovidesan acceptableapproximationto the ignition delay and pressure-rise,but at the expenseof overpredictingthe fuel-plume penetration.

Theeffectsof loweringScT andPrT by half from theirbaselinevaluesareshownin figures24to 27.LoweringScT (figures24 and25) appearsto havelittle impacton fuel-plumepenetration,but theigni-tion-delayandpressure-risepredictionsareunacceptable.Ontheotherhand,a lowerPrT haslittle effecton pressure-riseandignition-delaywhile havinga somewhatlower penetrationof the fuel-plume.ThevaluesPrT = ScT = 0.50areusuallyrecommendedfor shear-dominatedflows17. No attemptwasmadeto testvalueshigherthanthebaselineones,sinceit wasconsideredthatthesewerealreadyhighenough.

Theeffectsof thedifferentcombinationsof inflow turbulence-parametersof table1 aregivenin fig-ures28 to 31.Thehigh-turbulenceinflow (figures28 and29),which appearedto give betteragreementwith the nozzledata,is shownhereto give a somewhatbetterapproximationto jet-penetration,at theexpenseof theagreementwith ignition delayandpressure-rise.The low-turbulenceinflow (figures30and31) seemsto overpredictignition delayandpenetration,andsomewhatunderpredictpressure-rise.In brief, a changeof approximately50%in τ anda factorof 3 in µT/µL with respectto baselinevaluescangive drasticallydifferentsolutions.Theseparametersarenot usuallyestimatedin experiments,andin any case can only be done so in an order-of-magnitude basis.

Onecommonthreadthroughall thesecalculationsis the apparentinability of currentturbulence-modeling to accuratelypredict ignition delay, combustionpressure-riseand fuel-plume penetrationsimultaneously. So far, only two of the three parameters at best could be adequately captured.

bIt should be noted that this model is still under development within VULCAN.

9

5. Conclusions

TheSCHOLARscramjetis thesubjectof anongoingnumericalinvestigation,with thepurposeofvalidatingthe VULCAN codeandits turbulenceandchemistrymodels.The facility nozzlewasmod-eledfirst, in orderto provideadequateinflow conditionsto thecombustor.Resultsfor the latter showthatCFDcouldpredictits qualitativebehavior,particularlyreaction-limitedheat-releasedueto ignitiondelay.From a quantitativepoint of view, at leasttwo problemswereidentified: the inability to provegrid-convergencefor thegrid currentlyused,andthedifficulty of accuratelypredictingall threeparam-etersrelevantfor thepresentapplication:ignition delay,combustionpressure-rise,andfuel-plumepen-etration.

Regardinggrid convergence,this couldnot beprovedusingsimplegrid-sequencing.Additionally,thetrendsbetweenthesequenceswerenotwhatwouldbeexpectedin termsof numericaldiffusion.Onepossiblecausefor thisbehaviorcouldbein theextensiveuseof non-C(0)zonalboundaries,bothnormalandparallelto the flow. The latter onescould adverselyaffect the numericalflowfield by introducingextended areas of numerical diffusion.

Thesecondproblemis associatedwith theaccuracyof turbulenceandchemistrymodels.Only thefirst oneswereinvestigatedhere,andthenumericalsolutionwasshownto besensitiveto them.Differ-entturbulencemodelsgavequalitativelydissimilarsolutions.Furthermore,arelativelyhighvalueof 1.0hadto beusedfor theturbulentSchmidtnumber,if theignition delaywasto becapturedatall. Anotherissueis that of inflow turbulence-parameters.Theseare not usually determinedin experiments,andappearto havea considerableimpactin numericalsolutions.It is not immediatelyobviouswhatcombi-nation,if any,of modelingparameterswould allow to simultaneouslypredictthethreeflow-parametersmentioned above with any acceptable accuracy.

Futurework will initially concentrateon obtaininga grid-convergedsolution.A newgrid is underdevelopmentin which thediscontinuousboundarieshavebeenrestrictedto a limited numbernormaltotheflow; thecomputationalpriceto payis analmostdoublingof thetotal numberof CVs.Basedon theresultsfrom this grid, it will be determinedwhetherthe numericalresultsobtainedso far arevalid orneedto berecalculated.Thenextstepwill beto includetheeffectsof chemistryparametersasdescribedin the Introduction.Theoverallobjectivewill be to determinethesensibilityof thesolutionto thedif-ferentparameterspresentin mostnumericalmodels,andperhapsestablishan“envelope”in somesolu-tion space were the “correct” answer may be expected.

10

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2. Cutler, A.D., Diskin, G.S.,Danehy, P.M., andDrummond,J.P., “FundamentalMixing andCombustionExperi-ments for Propelled Hypersonic Flight”, AIAA Paper 2002-3879, 2002.

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13. Rodriguez, C.G., “CFD Analysis of the CIAM/NASA Scramjet”, AIAA 2002-4128, 2002.

14. Laster, W.R., andSojka,P.E., “Autoignition of H2-Air: The Effect of NOx Addition”, Journal of Propulsionand Power, Vol. 5, No. 4, July-August 1989, pp. 385-390.

15.Menter, F.R., “ImprovedTwo-Equationk-ω TurbulenceModelsfor AerodynamicFlows”, NASA TM 103975,October 1992.

16.Gatski,T.B., andSpeziale,C.G.,“On Explicit AlgebraicStressModelsfor Complex TurbulentFlows”, Journalof Fluid Mechanics, Vol.254, 1993, pp. 59-78.

17. Schetz, J.A.,Boundary Layer Analysis, Prentice-Hall, New jersey, 1993.

11

Tables

Table 1. Nozzle Inflow and Outflow Turbulence Parameters

Description*

*Based on exit conditions

Inlet Exit†

†Values are approximate potential-core averages.

τ µΤ/µL τ µΤ/µL

Baseline 0.25 600 0.025 300

High turbulence 0.10 600 0.035 850

Low turbulence 0.25 300 0.015 100

12

Figures

Figure 1. Layout of the combustor model:(a) Nozzle and complete combustor. (b) Detail in the region of the injector.

13

Figure 2. Bottom-wall experimental pressure distributions.

Figure 3. Top-wall temperature history.

x [mm]

p[P

a]

0 500 1000 15000

50000

100000

150000

t = 10.00 st = 24.00 sAverage over t

t [s]

Tw

all[K

]

0 5 10 15 20300

400

500

600

700

800

900

x = 197 mmx = 426 mmx = 978 mm

14

Figure 4. Cutaway planes with contours of mean temperature(dimensions in meters).

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

15

Figure 5. Three-dimensional nozzle grid (every other grid-line shown).

Figure 6. Nozzle centerplane Mach contours.

-0.04

-0.02

0

0.02

0.04

00.020.04

-0.20

-0.15

-0.10

-0.05

0.00

X

Y

Z

x [m]

y[m

]

-0.2 -0.15 -0.1 -0.05 0-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Mach

16

Figure 7. Nozzle vertical-centerplane pitot-pressure profiles.

Figure 8. Nozzle horizontal-centerplane pitot-pressure profiles.

p02/p01

y[m

]

0 0.25 0.5 0.75 1-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

ExperimentalNumerical

z [m]

p02

/p01

-0.04 -0.02 0 0.02 0.040.1

0.2

0.3

0.4

0.5

0.6

0.7

ExperimentalNumerical

17

Figure 9. Nozzle vertical-centerplane pitot-pressure profiles: grid sequencing.

Figure 10. Nozzle vertical-centerplane pitot-pressure profiles: effects of inflow turbulence.

p02/p01

y[m

]

0.6 0.65 0.7 0.75 0.8-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

ExperimentalFine sequenceMedium sequence

p02/p01

y[m

]

0.6 0.65 0.7 0.75 0.8-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

ExperimentalBaselineτin = 10% - µT/µL = 600τin = 25% - µT/µL = 100

18

Figure 11. Scramjet: three-dimensional grid (every third grid-line shown).

-0.02

0

0.02

00.020.04

0.1

0.2

0.3

4

X

Y

Z

19

Figure 12. Centerplane Mach contours - baseline solution.

Figure 13. Centerplane water contours - baseline solution.

x [m]

y[m

]

0 0.25 0.5 0.75 1 1.25 1.5-0.05

0

0.05

0.1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Mach

x [m]

y[m

]

0 0.25 0.5 0.75 1 1.25 1.5-0.05

0

0.05

0.1

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

yH2O

20

Figure 14. Temperature contours - baseline solution.

Figure 15. Efficiencies distributions - baseline solution.

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

Numerical

Experimental

x [m]

η

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ηmix

ηc

21

Figure 16. Bottom-wall centerline pressures- baseline solution.

Figure 17. Effect of grid sequencing on wall-pressures - baseline solution.

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalNumerical

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalFine sequenceMedium sequence

22

Figure 18. Water contours - Semi-elliptic integration.

Figure 19. Wall-pressure distribution - Semi-elliptic integration.

x [m]

y[m

]

0 0.25 0.5 0.75 1 1.25 1.5-0.05

0

0.05

0.1

0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

yH2O

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalSemi-elliptic integrationFully-elliptic integration

23

Figure 20. Temperature contours - Menter’s turbulence model.

Figure 21. Wall-pressure distribution - Menter’s turbulence model.

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

Numerical

Experimental

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalMenterWilcox

24

Figure 22. Temperature contours - EASM turbulence model.

Figure 23. Wall-pressure distribution - EASM turbulence model.

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

Numerical

Experimental

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalEASMWilcox

25

Figure 24. Temperature contours - Sc = 0.50.

Figure 25. Wall-pressure distribution - Sc = 0.50.

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

Numerical

Experimental

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalSc = 0.5Sc = 1.0

26

Figure 26. Temperature contours - Pr = 0.50.

Figure 27. Wall-pressure distribution - Pr = 0.50.

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

Numerical

Experimental

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalPr = 0.5Pr = 1.0

27

Figure 28. Temperature contours - High inflow-turbulence.

Figure 29. Wall-pressure distribution - High inflow-turbulence.

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

Numerical

Experimental

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalHigh inflow-turbulenceBaseline

28

Figure 30. Temperature contours - Low inflow-turbulence.

Figure 31. Wall-pressure distribution - Low inflow-turbulence.

0

0.5

1

-0.0400.04-0.02

0

0.02

0.04

0.06

0.08

X

Y

Z

2200200018001600140012001000800600400200

T [K]1

3

5

6

7

Numerical

Experimental

x [m]

p[P

a]

0 0.25 0.5 0.75 1 1.25 1.50

50000

100000

150000

200000

ExperimentalLow inflow-turbulenceBaseline

REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188

2. REPORT TYPE

Contractor Report 4. TITLE AND SUBTITLE

Numerical Analysis of the SCHOLAR Supersonic Combustor5a. CONTRACT NUMBER

NAS1-97110

6. AUTHOR(S)

Rodriguez, Carlos G.; Cutler, Andrew D.

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Allied Aerospace, GASL Division, Hampton, VA 23681-2199The George Washington University, JIAFS, Hampton, VA 23681-2199NASA Langley Research Center, Hampton, VA 23681-2199

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National Aeronautics and Space AdministrationWashington, DC 20546-0001

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10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTESRodriguez: Allied Aerospace; Cutler: The George Washington UniversityLangley Technical Monitor: David E. Reubush An electronic version can be found at http://techreports.larc.nasa.gov/ltrs/ or http://ntrs.nasa.gov

12. DISTRIBUTION/AVAILABILITY STATEMENTUnclassified - UnlimitedSubject Category 34Availability: NASA CASI (301) 621-0390 Distribution: Nonstandard

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

The SCHOLAR scramjet experiment is the subject of an ongoing numerical investigation. The facility nozzle and combustor were solved separate and sequentially, with the exit conditions of the former used as inlet conditions for the latter. A baseline configuration for the numerical model was compared with the available experimental data. It was found that ignition-delay was underpredicted and fuel-plume penetration overpredicted, while the pressure rise was close to experimental values. In addition, grid-convergence by means of grid-sequencing could not be established. The effects of the different turbulence parameters were quantified. It was found that it was not possible to simultaneously predict the three main parameters of this flow: pressure-rise, ignition-delay, and fuel-plume penetration.

15. SUBJECT TERMS

Supersonic combustion; Scramjet; Computational fluid dynamics; Turbulence

18. NUMBER OF PAGES

35

19b. TELEPHONE NUMBER (Include area code)

(301) 621-0390

a. REPORT

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Prescribed by ANSI Std. Z39.18Standard Form 298 (Rev. 8-98)

3. DATES COVERED (From - To)

5b. GRANT NUMBER

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23-745-30-10

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