wind validation cases: computational study of thermally

1American Institute of Aeronautics and Astronautics

Abstract

The ability of the WIND Navier-Stokescodeto predict the physics of multi-species gasesisinvestigatedin support of futur e high-speed,high-temperature propulsion applications relevant toNASA’s Space Transportation efforts. Thr eebenchmark casesare investigatedto evaluate thecapability of the WIND chemistry model to accu-rately predict the aerodynamics of multi-specieschemically non-reacting (fr ozen) gases. Case 1representsturb ulent mixing of sonichydrogenandsupersonicvitiated air. Case2 consistsof heatedand unheated round supersonic jet exiting toambient. Case 3 represents2-D flow thr ough aconverging-diverging Mach 2 nozzle. For Case1,the WIND results agree fairly well with experi-mental results and that significant mixing occursdownstream of the hydrogeninjection point. ForCase2, the resultsshow that the Wilk e and Suth-erland viscosity laws gave similar results,and theavailable SST turb ulence model doesnot predictround supersonic nozzle flows accurately. ForCase 3, results show that experimental, fr ozen,and 1-D gasresultsagreefairly well, and that fr o-zen, homogeneous,multi-species gas calculationscan be approximated by running in perfect gasmode while specifying the mixtur e gas constantand Ratio of Specific Heats.

WIND VALID ATION CASES: COMPUTATION AL STUDY OF

THERMALL Y-PERFECT GASES

T. DalBello*Institute for Computational Mechanics in Propulsion (ICOMP)

NASA Glenn Research Center, Cleveland, OH 44135

* Senior Research Associate, Department of Mechan-ical Engineering,Universityof Toledo,Toledo,Ohio.MemberAIAA. Email: [email protected] document is intended to be viewed in color. v2.

Copyright 2003by theAmericanInstituteof Aeronauticsand Astronautics, Inc. No copyright is asserted in theUnited States title 17, US code. The US Government has aroyalty-freelicenseto exerciseall rightsunderthecopyrightclaimedhereinfor Governmentalpurposes.All otherrightsare reserved by the copyright owner.

1. Intr oduction

HIS PAPER presentstheresultsof benchmarkval-idationstudiesusedto evaluatethecapabilityof

WIND1 to predict the physicsof a mixture of gasesininternal geometriesin support of future high-speed,high-temperaturepropulsion applications relevant toNASA’s SpaceTransportationefforts. Accuratepredic-tion of the aerodynamicsrequirescorrectmodelingofthe macroscopicchemistryeffects, which includestheproductionand consumptionof species(combustion),thermal and massdiffusion and other speciesinterac-tions. Development, verification,andvalidationof theNPARC Alliance WIND solver has been proceedingover the pastseveral years. Recentwork hasincludedimproving the thermally-perfectgas (frozen), equilib-rium air, and non-equilibriumair models. This paperfocuseson thevalidationof thermally-perfectgasmod-els in which no chemical reactions are taking place.

The evaluation casesused here to benchmarkrecentchangesto WIND, collectedfrom the National

CombustionCode(NCC)2 validationarchive,consistofcalculationson chemically non-reacting(frozen) mix-turesof gases,intendedto studymixing and,ultimately,combustionin a simplifiedenginenozzleor combustor.Frozengasesobey the perfectgas law but have locallyvarying specific heats. The internal flow problemsshown in thearchivecangive indicationsaboutdeficien-ciesinherit to theturbulencemodels,chemistrymodels,reactionrateandthermodynamiccoefficients,andmainflow equations.For thispaper, experimentalandnumer-ical resultsfor threecasesarecomparedto calculationsusing WIND version 5.

The first caserepresentsmixing of sonichydrogen

and a supersonicvitiated airstream3. The secondcaseconsistsof calculationson a heatedand unheated

roundsupersonicjet exiting to ambient4. Finally, the

T

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viscosityis still a functionof temperature,but is poten-tially moreaccuratein that it is calculatedusing infor-mationaboutthemolecularcompositionof themixture.The mixture thermal conductivity is also calculatedusing Wilke’s law but with different reference values.

Thermodynamic,transport and finite rate coeffi-cients usedby the chemistryequationsare not hard-codedinto WIND, allowing theuserfreedomto specifydifferentchemicalmechanisms.Changesto thesecoef-ficients can have significant effects on the results,asobserved in some undocumentedtrials. For frozencases,only the thermodynamicand transport coeffi-cientslisted in thechemistryinput files areusedby thechemistryequations(the reactionratesarezerofor fro-zenreactions). Holding total temperatureandpressurefixed at the inflow planewhen using chemistryis cur-rently not implementedin WIND. As a result,unlessotherwisespecified,all inflow valuesare specifiedasstatic valuesin this report. For Case2, thesevalueswereadjustedslightly so that thefinal total temperatureand pressure matched the conditions of the experiment.

Two-dimensional,structured,computationalgridswere generatedfor all casesusing Pointwise, Inc’s

GRIDGEN8 software. Averagey+ valuesontheviscouswalls were specified to be approximately 1.

The convergencecriterion consistedof monitoringthe speciesmassfractionsat the computationaldomainexit for changeswith iteration, at least two ordersofmagnitudereductionof theL2 Norm residual,andmassflow conservation.

3. Description of Cases and Results

Case 1: Mixing

Case1 representsnon-combustingturbulentmixingof two supersonicstreamswhosechemicalcompositionis fixed(frozen). It consistsof ahot,high-speedvitiatedmixture enteringaboveandparallelto asonicstreamofpure hydrogen.Both streamsenter into the 3.66 inchhigh by 14 inch long combustor. The hydrogeninjec-tion heightat theinjectionstepis 0.157inchesfrom thebottomwall, followedby a lip regionof 0.03inches,and3.5 inches of freestream.

This casewas modeledusing a 2-D, 5-zonegrid(see Figure 1) with 363 points streamwiseand 159points vertically representingthe mixing (test) sectionof the experiment,and a 50 by 81 zone upstreamtodevelop boundary layers in the vitiated stream.Thelower viscouswall of the mixing sectionis slopedtoaccount for thickening of the boundary layer. Gridpoints were clusteredalong the lower viscouswall toresolve the turbulent boundarylayer and in the shearlayer between the two streams.

The conditionsfor Case1 are shown in Table 1.

third caserepresentsflow through a 2-D converging-

diverging Mach 2 nozzle5.

2. Numerical Model

Calculations were conducted with WIND v5.0alpha, a general purpose 3-D ComputationalFluidDynamics(CFD) codewhich solvestheturbulent,time-dependent, Reynolds-Averaged Navier-Stokes equa-tions,in additionto theequationswhich governequilib-rium air, non-equilibriumair andfrozengaschemistry.For thecalculationspresentedhere,thesolver wascon-figured to run with the following specifications:

• Two-dimensional or axisymmetric, steady-state• Frozen chemistry and perfect gas models• Sutherland and Wilke viscosity laws• Node-centered finite-volume approach• Second order Roe upwind scheme• Two-equationMenterSST(ShearStressTransport)

turbulence model

WIND was configuredto run in multi-processormode on an SGI Origin 2000. As mentioned,

Sutherland6 andWilke7 laws areboth usedto computelaminarviscosityfor thethreecasesstudied. For frozenand perfect gas runs, the local static temperatureandassociatedreferencevalues(for air) areusedto computeviscosity in Sutherland’s law:

whereT is thelocalstatictemperature,andµΟ, SandTO

are reference values for air.Wilke’s law, an extensionof the Sutherland-type

equationto multi-componentsystemsobtainedon thebasis of the kinetic theory and several simplifyingassumptions,is usedin WIND to computethe laminarviscosity for multi-species gases:

where

where φi,j is the mixing coefficient, X is the speciesmolefraction,M is thespeciesmolecularweight,andµis the specieslaminarviscositycomputedwith Suther-land’s law. Becausethespeciesviscosityin Wilke’s lawis initially computedwith Sutherland’s law, themixture

φi j,1

8------- 1

MiM j-------+

1 2⁄–

1µiµ j------

M jMi-------

1 4⁄

+2

=

µlam

Xi µi⋅

X j φi j,⋅j 1=

N

∑----------------------------------

i 1=

N

∑=

µlam µoT

To-------

32--- To S+

T S+----------------

=


Turbulent mixing and movement of hydrogen awayfrom the wall and replacementwith H2O and N2 pro-gressively further down the duct canbe seen. Signifi-cant mixing starts to occur at about five inchesdownstreamof the hydrogen injection point (plottingalongthewall). This turbulentmixing processis criticalto existenceof combustion, and the specific ignitionlocation(assumingit wascombusting). Massfractionsof speciesat theentranceandexit of mixing sectionareconserveddown to sevendecimalplaces.Thehydrogenstreamentersthemixing sectionslightly underexpandedin the final solution (although the initial pressuresbetweenthetwo streamsweresetequal),andexpansionwaves form off the lip, further increasingthe mixingbetweenthe two streams(seeFigure3). Figures8, 9,and10 show speciesmassfractionsfor nitrogen,hydro-gen, and water at the duct exit for the experimental,NASTD, andWIND results. The x-axis of theseplotsgoesfrom thetopwall to thebottomwall (left handsideof the plot representsthe boundarylayer region on the

lower viscouswall). Theoriginal NASTD10 (precursorto WIND) resultswerecomputedusing the PDT alge-braic turbulencemodel. The WIND resultsare com-puted(using the SST model); both the Chien k-ε andPDT algebraicmodelsfailed to developa turbulentvis-cosity profile in the mixing layer. Nevertheless,theWIND results (using the SST model) comparefairlywell with the experiment, although the experimentaldatapointsdo not extendinto theboundarylayer. Dif-ferencesbetweenthe WIND and NASTD results aremost apparentin the boundarylayer. In Figure 9, alower massfraction of hydrogenat the wall was pre-dicted by WIND compared with NASTD.

Case 2: Supersonic Jet Flow

Case2 representssubsonicair flowing throughanaxisymmetricconverging-diverging nozzleandacceler-ating supersonically, representing flow through agenericfighter jet enginenozzleexiting into the ambi-ent. This caseconsistsof a homogeneousoxygen/nitro-gen mixture (air) flowing through the nozzle. Twodifferentinflow temperaturesweretestedaspartof Case

2, representingcold (104o F, Subcase2A) air, and hot

(1550o F, Subcase2B) air acceleratedsupersonically,andexiting into ambientair (seeFigure11). For thesetwo temperatures,bothfrozenchemistryandperfectgasrunswerecompleted,for a total of four runs. This casewasrun in axisymmetricmode. The inflow conditionsfor thenozzleareshown in Table2. Theambientregionhas an inflow Mach number of 0.01.

The grid for Case2 (Figure 12) consistsof threezones. The first representsthe internal nozzle regionand is 121 x 81 points. Zone 2 is the inflow for theambientregion, consistingof 41 axial and 34 vertical

The freestreamflow enteringthe mixing sectionrepre-sentsvitiated air, whosemassfractionsare0.233H2O,0.001H2, and0.766N2. A 7-species,8-reactionchem-istry model is usedto capturemixing and diffusion ofspeciesspecified in the chemistry file h2air-7sp-std-15k.chm. The frozen BC was usedfor the freestreaminflow, arbitrary inflow frozen BC for the hydrogenstream,the lower wall is adiabaticandno-slip,andthe

static pressure is extrapolated at the exit.

A grid dependencestudywasconductedon Case1to assessthe effect of the computationalgrids on thesolutionaccuracy. An exit profileof H2O massfractionsis shown in Figure2 for differentgrid sizes,giving anindication that the solution is not changingmuch withsuccessive grid levels. The lowestvaluesof H2O occurto theleft of theplot nearthewall, wherethesensitivityof thedifferentgrid sizesis mostapparent.A grid sizeof 363x159wasusedfor thecalculationspresentedhere.

Case1 resultsareshown in Figures4 through10,and are comparedwith numerical and experimentalresultsfoundin Reference3. Figures5 through7 giveaqualitative overview of the boundarylayer and shearlayer developmentand thicknesses,highlightedby theH2O, Mach number and turbulent viscosity profiles.Thetwo inflow streams,alongwith theinflow boundarylayer and lip region, drive the mixing in this problem,andcontribute to theverticaldiffusionof both layersatthe exit of the combustor. Speciesmixing is illustratedin Figure 4, which shows H2, N2, and H2O axial con-tours throughthe duct in two differentdirections. Thesolid lines show cuts parallel with the wall, and thedashedlinesshow cutsstraightacrosstheduct(notslop-ing, but in the true x-direction). As indicatedin Figure3, the cuts start at the hydrogeninflow plane 0.0785inches off the bottom wall and traverse downstream.

Table 1: Case 1 Flow Conditions

FreestreamHydrogen

Stream

Mach No. 2.44 1.0

Temperature 2070 R (1150K) 540 R (300K)

Pressure 14.7 psi(101 kPa)

14.7 psi(101 kPa)

Turb. model SST SST

Viscosity Law Wilke Wilke

Species H2, H2O, N2 H2

Wall BC adiabatic adiabatic


points. Theambientexhaustregion representedaszone3 consistsof 121axial and121verticalpoints,andgoes25 nozzlediametersdownstream(thenozzlediameteris0.3 ft). Thelower inviscid wall is thenozzlecenterline.The grid sizing for Case2 wasdeterminedto be suffi-cient as indicated in Reference 11.

The frozen runs have an inflow consistingof air,representedas0.23massfractionoxygenand0.77massfraction nitrogen(to comparedirectly with the perfectgas case). The laminar viscosity was computedwithbothSutherlandandWilke laws. Thedefault 7-species,8-reactionchemistrymechanismwasused,specifiedbythechemistryfile h2air-7sp-std-15k.chm. Thearbitraryinflow BC wasusedat the nozzleandplenuminflows,the internalnozzleupperadiabaticwall is viscous,andtheotherwalls areinviscid (to representthenozzlecen-terline). The MenterSSTmodelwasusedto compute

theeddyviscosity. For all Case2 runs(frozenor perfectgas), temperatureand pressurewere specified in theWIND input file asstaticvalues. For Subcase2A, thetotal temperaturevalueslistedin Table1 werelowered8degreesin orderto force matchingof total temperatureat the nozzle entrance with the experiment.

Case2 resultsareshown in Figures13 through22for Subcases2A and2B, bothrunwith frozenchemistryandasa perfectgas. Figures13 through16 show con-toursof variousflow propertiesfor Subcase2B. Thesegive a qualitative view of how theflow expandsinto theexhaustregion. Figures15 and16 show turbulent vis-cosity contours(normalizedby freestreamlaminarvis-cosity) in thex-y planewhich canbecompareddirectlyto examinetheeffectsof theSutherlandandWilke vis-cositymodels. Similarly, radialprofilesof theturbulent


Internal NozzleSubcase2A:

(104 F)

Internal NozzleSubcase2B:

(1550 F)

Mach No. 0.2 0.2

Total Tempera-ture

104 F (564R) 1550 F (2010R)

Total Pressure 115.0 psi (793kPa)

115.0 psi (793kPa)

Turb. Model SST SST

Viscosity Law Sutherland Sutherland &Wilke

Species oxygen,nitrogen(air)

oxygen,nitrogen(air)

Chemistry model frozen& perfectgas

frozen& perfectgas

Wall BC adiabatic adiabatic

viscosity(normalizedby the freestreamlaminarviscos-ity) atzone3 exit areshown in Figure17. It canbeseenthatSutherlandhasamorepronouncedeffect in thesub-sonicportion of the flow away from the nozzlecenter-line. Close to the nozzlecenterline,the two modelsgive very similar results. Figures18 and19 show pro-files of Machnumberat thenozzlecenterlinestartingattheexit of thenozzleandgoingabout25 nozzlediame-tersdownstreamfor both subcases.This givesan indi-cationof how thehigh-speednozzleflow mixesinto thevery low Mach numberambient. The resultsshownhere(andin Reference11) indicatethat theSSTmodel,aswell astheChienk-ε modelusedin WIND, overpre-dict the mixing ratesof supersonicjets. This can beseenfrom Figures18 through 22 showing that Machnumber, static and total temperatureare not predictedcorrectlyespeciallyfar away from the nozzlepotentialcore. A total temperatureplot for Subcase2A is notshown becausenoexperimentaldatawasavailable. Thefrozensolution in Figure20 shows a higher total tem-peraturevalue(about50degrees)at thenozzleexit com-pared with the experiment, even though the totaltemperatureand pressurevalues at the nozzle inflowheld at the correctvalues. This is probablydue to apostprocessingissueintroducedwhen computingstag-nation temperature(for a mixture of gases)from thesolution file. The stagnationtemperatureis computedfrom Cpandstatictemperature,andCpvaluesusedmaybe incorrectbecausethey are not computedusing thethermodynamiccurve fit coefficients during postpro-cessing.Nevertheless,Case2 resultsshow that the fro-zen and perfect gas calculations are giving similarresultsfor Subcase2B (hot),but staticandtotal temper-atureprofilesfor theSubcase2A (cold) differ consider-ably.

SignificantCPU time differenceswere seenwhenemploying the chemistryequations. Subcase2B (per-fect gas) took 66.85 microsecondsper node iteration;thefrozencasetook justoverninetimesmoreCPUtimeat 610 microsecondsper node iteration. Use of theWilke viscositymodelboostedthe CPU time from 610to 710 microseconds per node iteration.Case 3: Convergent-Divergent Nozzle

Case3 representssubsonic,vitiated air exiting acombustor and acceleratingsupersonicallythrough aMach2 convergent-divergentnozzle. This casewasrun2-D. The frozenhomogeneousmixtureandperfectgasresultsare comparedto experimentand 1-D analysis.One frozen calculation(Subcase3A) and two perfectgas calculations (Subcases3B and 3C) were com-pleted. Flow conditionscanbeseenin Table3. For thefrozencase,massfractionsof thevitiatedair weresetto0.233for O2, 0.226H2O, and0.544N2. Theratioof theturbulent viscosity to the laminar viscosity was set to0.01at the inflow to matchconditionsusedin the CFDanalysisof the referencepaper. Two perfectgasSub-caseswerecompleted:Subcase3C with γ (ratio of spe-


show the accelerationof gas through the nozzle con-strictionto supersonicspeedsandsubsequentchangesinflow properties. Resultsfrom the three subcasesarecomparedin Figures28 through32 to seetheeffectsofthe different chemistry models on the homogeneousmixture. In addition, 1-D analysisusing area-Machnumberrelationand isentropicrelationsalongthe cen-terline of the duct is comparedalso. As seenin Figure28, the frozen subcase and perfect gas subcase(γ=1.256) are close to the Pitot rake data and corre-sponding numerical results from the CFD code

VULCAN5,12. Subcase3C slightly overpredicts thePitot pressuredistribution comparedwith the experi-mentaldata. The 1-D Pitot pressurevaluefor γ=1.256is closeto averagevaluesfound from CFD andexperi-mentin thecoreregion of theflow. The1-D Pitot pres-sure value for γ=1.4 shows a lower than expectedpressurecomparedwith the analogousWIND result(which slightly overpredictsthedata). Figure28 showsthat approximatingthe frozen chemistrywith constantvaluesof γ andR is averygoodapproximationfor prob-lems involving homogenousmixture of species. Thisstatementmaybe limited to caseswith exit Machnum-bersin the rangeof 2, andmay not be valid for higherMachnumberproblems. ThePitot pressureis normal-izedby thetotal pressurein theheaterof 7.62atm(112psi). Furthermore,plotsof staticpressure,temperature,Machandu-velocity alongtheductcenterlineshown inFigures 29 through 32 give some indication of theeffectsof the chemistrymodel. The WIND resultsarecomparedwith valuescomputedfrom the 1-D analysisusingboth γ=1.4 and1.256. The agreementwasfairlygood, highlighted by the static temperatureprofile inFigure29. Overall, the WIND perfectgascalculationswith γ=1.4 show the mostnotabledifferencesfrom thefrozenresultsespeciallytowardsthe exit of the nozzle.Lower initial turbulencelevels(or a laminarrun) tendtolower thepressureat theexit (lessoverall total pressurelosses). CPU time was about350 microsecondspernodeiterationfor thefrozencase,and260microsecondsper node iteration for the perfect gas case.

4. Conclusions

Threedifferentcaseswerethesubjectof CFD vali-dations examining the frozen chemistry capability inWIND in supportof future high-speed,high-tempera-ture propulsionapplications. The frozen calculationscanbeconsideredthebuilding block for themorephysi-cally intensiveandcomputationallydemandingcombus-tion cases.It hasbeenshown that the frozenchemistrymodel gives fairly good comparisonfor the mixingproblem(Case1). Thegrid refinementstudyfor Case1indicatesthat the 363 x 159 grid wassufficient to cap-turethemixing effects. As shown in theresultsfor Case2, theWilke andSutherlandviscositylaws gave similarresults,andthe availableturbulencemodelsfail to pre-

cific heats)setto 1.4andthegasconstantsetto 1716ft2/

sec2-R ( 287 m2/s2-K); Subcase3B with γ setto 1.256

andthe gasconstantsetto 1946ft2/sec2-R (326 m2/s2-

K), approximatingthe thermodynamicpropertiesof themixture in the frozencase. The γ=1.256valueusedinSubcase3B andin the1-D analysisis thevaluethatfallsout from thesolutionof Subcase3A in thecoreflow atthe inflow planeof thenozzle. Thearbitraryinflow BCwasusedfor the inflow, viscouswalls weresetat 900R(500K), and the backpressurewas forced at 14.7 psi.TheMenterSSTmodelwasusedto computethe turbu-lent viscosity, and Sutherland’s law was usedto com-pute the laminar viscosity for all subcases.

The2-D grid for Case3 (Figure23) consistsof onezonewith 197 points axially (distributed equally) and257 points vertically. Three grid levels were usedtodeterminegrid independence,andH2O massfractionsatthe exit planeare comparedin Figure 24 for the threesizes.Thefinegrid (197x257)wasusedfor calculationsin this paper.

Case3 resultsareshown in Figures25 through32.Threesubcaseswerecompletedaspart of Case3: fro-zen chemistry Subcase3A, perfect gas Subcase3B

(γ=1.256,R=1946ft2/sec2-R), andperfectgasSubcase

3C (γ=1.4,R=1716ft2/sec2-R). Figures25 through27


Subcase3A Subcase3B Subcase3C

Mach No. 0.14 0.14 0.14

Tempera-ture

3489 R(1940 K)

3489 R(1940 K)

3489 R(1940 K)

Pressure 111.5 psi(769 kPa)

111.5 psi(769 kPa)

111.5 psi(769 kPa)

Turb.Model

SST SST SST

ViscosityLaw

Sutherland Sutherland Sutherland

Species O2, H2O,

N2

air air

Chem.Model

frozen perfect gas perfect gas

Ratio ofSpecificHeats

f(T) 1.256 1.400

R (localgasconstant)

f(species) 1946 ft2/

sec2-R

1716 ft2/

sec2-R

Wall BC isothermal isothermal isothermal


519, 1950.

8) GRIDGEN Version 13,User Manual, Pointwise, Inc.1998, Bedford, Texas.

9) Menter, F.R., “Two-Equation Eddy-ViscosityTurbulence Models for EngineeringApplications,”AIAA Journal, Vol 32, No.8,1994, pp. 1598-1605.

10) Mani, M., Bush, R.H., & Vogel, P.G., “ImplicitEquilibrium and Finite-Rate Chemistry ModelsForHighSpeedFlowApplications,”AIAA Paper91-3299-CP, January 1991.

11) Dembowski, M.A., & Georgiadis, N.J., “AnEvaluationof ParametersInfluencingJetMixingUsing the WIND Navier-Stokes Code,” NASA/TM-2002-211727, August 2002.

12)White,J.A.,& Morrison,J.H.,“A Pseudo-TemporalMulti-Grid Relaxation Scheme for Solving theParabolized Navier-Stokes Equations,” AIAAPaper 99-3360, June 1999.

dict supersonicnozzleflows correctly. Someslight dif-ferencesbetweenperfect gas and chemistry are seenbetweenthe static and stagnationtemperatureplots.Fairly goodagreementwasseenbetweenexperimental,numericaland 1-D analysisfor Case3. Although theflow solution for Case3 tendsto be one-dimensional,the grid refinementstudy indicatesthat the 197 x 257grid was sufficient to capturethe 2-D effects near thenozzlewall. The resultsfor Case3 indicatethatmulti-speciesgas calculationsfor problemsinvolving homo-geneousmixtures can be approximatedby running inperfectgasmodewhile specifyingtheappropriatemix-turegasconstantandRatioof SpecificHeats. This con-clusion may not be valid for high Mach numberproblems. Futurestudiescould include the Chien k-εandSpalart-Allmarasmodelsandtheir effects,a possi-ble analysisof mixing problemslike Case1 involvinggreater temperatureand velocity differencesbetweenthe primary andsecondarystreams,a jet in a crossflow(wherethesecondaryflow is injectednormalto thepri-mary flow), as well as expansionof theseproblemstothree dimensions.

5. Acknowledgements

This work is funded by NASA Grant/CooperativeAgreementnumberNCC3-922. Help from the follow-ing individualsmadethis work possible:Nick Georgia-dis, John Slater, John Wolter, Dennis Yoder, JimDeBonis, Rickey Shyne, Dennis Lankford, and ChrisNelson.

References

1) TheWINDUser’sGuideVersion5,UserManual,TheNPARC Alliance, July 7 2000, Cleveland, OH.http://www.grc.nasa.gov/WWW/winddocsindex.html

2) Ebrahimi, H.B., Ryder R.C., Brankovic A., & LiuN.S.,“A MeasurementArchivefor Validationforthe National Combustion Code,” AIAA Paper2001-0811, January 2001.

3) Burrows, M.C., & Kurkov, A.P., “Analytical andExperimentalStudyof SupersonicCombustionofHydrogen in a Vitiated Airstream,” NASA-TM-X-2828, September 1973.

4) Seiner, J.M., Ponton, M.K., Jansen, B.J. & Lagen,N.T., “TheEffectsof TemperatureonSupersonicJet Noise Emission,” DGLR/AIAA 14thAeroacoustics Conference, Aachen, Germany,AIAA Paper 92-02-046, May 1992.

5) Springer, R.R., Cutler, A.D., Diskin, G.S., & Smith,M.W., “Conventional/Laser Diagnostics toAssess Flow Quality in a Combustion-HeatedFacility,” AIAA Paper 99-2170, June 1999.

6) White,F.M.,ViscousFluid Flow, McGraw-Hill, Inc.,New York, NY, 1974.

7)Wilke, C.R.,“A ViscousEquationfor GasMixtures,”Journal of Chemical Physics, Vol. 18, pp. 517-

Figure 1: 363x159 grid for mixing section of Case 1.

−2.0 3.0 8.0distance from top wall (cm)

0.00

0.10

0.20

H2O

mas

s fra

ctio

ns

Grid DependenceCase 1 − exit plane

coarse grid(181x80)medium grid (363x159)fine grid (434x190)

Figure 2: Case 1, H2O mass fractions at mixing sectionexit plane, revealing the grid sensitivity of thesolution.


0.0 5.0 10.0 15.00.00

0.10

0.20

0.30

0.40

0.50

N2 (parallel to the wall)H2O (parallel to the wall)

0.0

0.2

0.4

0.6

0.8

1.0

H2 (parallel to the wall)N2 (horizontal)H2O (horizontal)H2 (horizontal)

x (inches)

nitro

gen, w

ate

r m

ass fra

ctions

hydro

gen m

ass fra

ctions

Figure 4: Case 1, axial variation of H2O, N2, H2 massfractions following the wall (solid lines), andhorizontal or true x-direction (dashed lines).Both start at the hydrogen entrance 0.0785inches off the bottom wall.

Figure 5: Case 1, H2O mass fraction contours inthe x-y plane.

Figure 6: Case 1, Mach number contours in the x-yplane.

Figure 7: SST turbulent viscosity contours in the x-yplane, indicating the high viscosity being gen-erated in the mixing layer.

−0.110 −0.100 −0.090 −0.080 −0.070 −0.060distance from top wall (meters)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

N2

ma

ss f

ractio

ns

N2 mass fractionsexit plane − SST

Burrows&KurkovNASTDWIND

Figure 8: Case 1, nitrogen mass fractions at duct exit.

slug/ft-sec

Figure 3: Case 1, zoomed and unzoomed views of mix-ing section with hydrogen stream on bottomand freestream on top.


−0.12 −0.07 −0.02distance from top wall (meters)

0.0

0.2

0.4

0.6

0.8

1.0H

2 m

ass

fra

ctio

ns

H2 mass fractionsexit plane − SST


Figure 9: Case 1, hydrogen mass fractions at duct exit.

−0.12 −0.07 −0.02distance from top wall (meters)

0.00

0.10

0.20

H2O

mass

fra

ctio

ns

H2O mass fractionsexit plane − SST


Figure 10: Case 1, water mass fractions at duct exit.

Figure 11: Definition of geometry for Case 2, showinginflow planes and nozzle geometry. The gridstructure is colored by Mach number.

Figure 12: Three-zone grid for Case 2. The mixing sec-tion is 121x121 points.


Figure 13: Case 2, Mach number contours for Subcase2B (frozen).

Figure 14: Case 2, total temperature (R) contours forSubcase 2B (frozen).

Figure 15: Case 2, normalized turbulent viscosity con-tours (SST) for Subcase 2B (frozen) usingSutherland’s law to compute the laminar vis-cosity.

Figure 16: Case 2, normalized turbulent viscosity con-tours (SST) for Subcase 2B (frozen) usingWilke’s law to compute the laminar viscosity.

0.0 10.0 20.0 30.0x/D (D=0.3ft)

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Ma

ch

nu

mb

er

Seiner: experimentWIND: perfect gasWIND: frozen

Figure 18: Case 2, Mach number decay along the noz-zle centerline for Subcase 2B (1550F).

0.0 0.1 0.3 0.4 0.6r/R (R=101.6 cm)

−1.0e+03

1.9e+04

3.9e+04

5.9e+04

7.9e+04

no

rma

lize

d t

urb

ule

nt

vis

co

sity

WilkeSutherland

Figure 17: Case 2, normalized turbulent viscosity pro-files at the outflow of the computationaldomain for Subcase 2B (1550F, frozen) com-paring the effects of the Wilke and Sutherlandviscosity laws.


0.0 10.0 20.0 30.0x/D (D=0.3ft)

300.0

500.0

700.0

900.0

1100.0

1300.0

1500.0

1700.0

To

tal T

em

pe

ratu

re (

F)


Figure 20: Case 2, total temperature decay along thenozzle centerline for Subcase 2B (1550F).

0.0 5.0 10.0 15.0 20.0 25.0 30.0x/D (D=0.3ft)

−200.0

−150.0

−100.0

−50.0

0.0

50.0

100.0

sta

tic t

em

pe

ratu

re (

F)


Figure 21: Case 2, static temperature profiles along thenozzle centerline for Subcase 2A (104F).

0.0 10.0 20.0 30.0x/D (D=0.3ft)

250.0

350.0

450.0

550.0

650.0

750.0

Sta

tic T

em

pera

ture

(F

)


Figure 22: Case 2, static temperature decay along thenozzle centerline for Subcase 2B (1550F).

Figure 23: 197x257 grid for Case 3.

0.0 5.0 10.0 15.0 20.0 25.0 30.0x/D (D=0.3ft)

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0M

ach n

um

ber


Figure19: Case2, Mach numberdecayalongthe noz-zle centerline for Subcase 2A (104F).


Figure 25: Case 3, Mach number contours in thex-yplane for the frozen chemistry case.

Figure 26: Case 3, static pressure contours in thex-yplane for the frozen chemistry case.

0.0 1.0 2.0 3.0 4.0Y, exit diameter (cm)

0.62

0.65

0.67

0.70

0.72

norm

alized p

itot pre

ssure

pitot rake dataWIND: frozenWIND: perfect gas (gamma=1.256,R=1946)WIND: perfect gas (gamma=1.4,R=1716)1−D analysis (gamma=1.256,R=1946)1−D analysis (gamma=1.4,R=1716)VULCAN

Figure 28: Case 3, plot of pressure at the duct exit com-paringWIND frozenandperfectgasmodelstoexperiment, numerical results, and 1-D gasanalysis. The Pitot pressure is normalized by7.62 atm (112 psi).

Figure27:Case3, statictemperaturecontoursin thex-yplane for the frozen chemistry case.

−2.0 −1.0 0.0 1.0 2.0Y, exit diameter (cm)

0.22590

0.22595

0.22600

0.22605

0.22610

H2O

mas

s fr

actio

ns

Grid DependenceCase 3 − exit plane

coarse (50x64)medium (101x129)fine (202x257)

(streamwise x vertical)

Figure 24: Case 3, H2O mass fractions at exit plane,showing coarse, medium, and fine grid solu-tion results.

Y (cm)


−20.0 −15.0 −10.0 −5.0 0.0x (cm)

0.0

0.5

1.0

1.5

2.0

2.5

Ma

ch

nu

mb

er

Mach Numbercenterline cut − SST − case3

perfect gas (gamma=1.256, R=1946)perfect gas (gamma=1.4,R=1716)frozen1D gas equations (gamma=1.256,R=1946)1D gas equations (gamma=1.4,R=1716)

Figure 30: Case 3, plot of Mach number along the ductcenterline comparing WIND frozen, and per-fect gas models with 1-D analysis.

−20.0 −15.0 −10.0 −5.0 0.0x (cm)

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

axia

l vel

ocity

(ft/

sec)

Axial Velocitycenterline cut − SST − case3

perfect gas (gamma=1.256,R=1946)perfect gas (gamma=1.4,R=1716)frozen1D gas equations (gamma=1.256,R=1946)1D gas equations (gamma=1.4,R=1716)

Figure 31: Case 3, plot of the axial velocity along theduct centerline comparing WIND frozen, andperfect gas models with 1-D analysis.

−20.0 −15.0 −10.0 −5.0 0.0x (cm)

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

stat

ic p

ress

ure

(psi

)

Static Pressurecenterline cut − SSt − case3

perfect gas (gamma=1.256,R=1946)perfect gas (gamma=1.4, R=1716)frozen1D gas equations (gamma=1.256,R=1946)1D gas equations (gamma=1.4,R=1716)

Figure 32: Case 3, plot of the static pressure along theduct centerline comparing WIND frozen, andperfect gas models with 1-D analysis.

−20.0 −15.0 −10.0 −5.0 0.0x (cm)

1500.0

2000.0

2500.0

3000.0

3500.0

stat

ic te

mpe

ratu

re (R

)

Static Temperaturecenterline cut − SST − case3

perfect gas (gamma=1.256, R= 1946)perfect gas (gamma=1.4,R=1716)frozen1D gas equations (gamma=1.256,R=1946)1D gas equations (gamma=1.4,R=1716)

Figure 29: Case 3, plot of static temperature along theduct centerline comparing WIND frozen, andperfect gas models with 1-D analysis.

wind validation cases: computational study of thermally

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