BLAYER User Guide - NASA

NASA/TM—2018-219749

BLAYER User Guide David A. Saunders and Dinesh K. Prabhu Analytical Mechanics Associates, Inc. Aerothermodynamics Branch National Aeronautics and Space Administration Ames Research Center Moffett Field, CA

January2018

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TableofContents

PageAbstract……………………………………………………………………………………………………………………..….…..4Nomenclature……………………………………………………………………………………………………..……..….….4I.Introduction…………………………………………………………………………………………………………..……..…..5II.InputsandOutputs…………………………………………………………………………………………………………...5III.Background…………………………………………………………………………………………………………………..…..9IV.Methodology……………………………………………………………………………………………………………………10V.Validation……………………………………………………………………………………………………………..………...17VI.AnomalousBehaviors………..……………………………………………………………………………………..…….23VII.Acknowledgments……………………………………………………………………………………………………..……28VIII.References………………………………………………………………………………………………………………..…...28

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BLAYER User Guide

David Saunders* and Dinesh Prabhu*

Asoftwareutilityemployedforpost-processingcomputationalfluiddynamicssolutionsaboutatmosphericentryvehiclesisdescribedasasupplementtothedocumentationwithinthesourcecode. This BLAYER application and its ancillary utilities are in the public domain athttps://sourceforge.net/projects/cfdutilities/. BLAYER was developed at NASA Ames ResearchCenterinsupportoftheDPLR(DataParallelLineRelaxation)flowsolver.Itsunderlyingalgorithmhassincebeen incorporatedbyothers intotheLAURAandUS3DflowsolversatNASALangleyResearchCenterandtheUniversityofMinnesotarespectively.Theessenceofthealgorithmisto locate theboundary layer edgeby seeking thepeak curvature in a total enthalpyprofile.Turningthatinsightintoapracticaltoolsuitedtoawiderangeofpossibleprofileshasledtoahybridtwo-stagemethod.Thetraditionalmethod—locationof(say)99.5%offree-streamtotalenthalpy—remainsanoption,thoughitmaybelessrobust.

NomenclatureCH =filmcoefficientorheattransfercoefficient,Wm-2K-1f(t) =normalizedtotalenthalpyratio,nondimensionalH =totalenthalpy,Jkg-1i,j,k =gridpointindexk =averagesurfaceroughnessheight,mK =degreesKelvinm =metersM =MachnumberPa =Pascalsqw =heatfluxatthewall,Wm-2qvw =catalyticheatfluxatthewall,Wm-2,for2-temperatureflowsolutionsReq =ReynoldsnumberbasedonmomentumthicknessqRekk =Reynoldsnumberbasedonroughnessheightk(butviscosityatthewall)Reue =unitReynoldsnumberbasedonedgeconditionst =arclengthfromthewallalonga(possiblynormalized)flowprofile,mornondimensionalT =translationaltemperature,KTv =vibrationaltemperature,Kv =velocity,ms-1x,y,z =Cartesiancoordinates,mg =ratioofspecificheats,Cp/Cv(heatcapacitiesatconstantpressureandconstantvolume) d =boundarylayerthickness,md* =displacementthickness,mdu =velocitythickness,me =emissivity,nondimensionalq =momentumthickness,mr =density,kgm-3s =Stefan-Boltzmannconstant,Wm-2K-4t =shearstress,Paorforce/unitarea k =curvatureofa(normalized)profile,t-1,ortotalthermalconductivity,Wm-1K-1µ =viscosity,Pas

*SeniorResearchScientist,AMA,Inc.atNASAAmesResearchCenter,MoffettField,CA94035

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Subscriptsc =compressiblee,edge =boundarylayeredgevalueinc =incompressiblemod =moderatedtan =tangentialcomponent(paralleltothewall)w,wall =wallsurfacevalue∞ =free-streamvalue

I.Introduction

BLAYERisoneofmanysoftwareutilitiesdevelopedbytheAerothermodynamcsBranchatNASAAmesResearchCenterinsupportofflowcalculationsperformedonmultiblockstructuredcomputationalgrids.Itreadsavolumedatasetextractedfromaflowsolution,ineitherTECPLOT[1]orPLOT3D[2]format,andwritesa surface dataset in TECPLOT format containing either two or three sets of values: (1) wall data, (2)boundary layer edge-related data, and (optionally) a third set of values either at a specified surfaceroughnessheightkorattheestimatedmomentumthicknessheight,q.Post-processingof2-Dand3-Dlaminar solutions is commonlyperformedwithBLAYER topredict likely transition to turbulent flowviacorrelationsinvolvingReq orRekk.

Section II reproduces control inputdescriptions from theBLAYER source code, anddocuments thevariousoutputslikewise.Theinitialimplementationdatesfrom2004,andSectionIIIprovidessomeofthehistory and other background information. Details of the edge detection procedure (with a choicebetweenatwo-stagehybridmethodandthetraditional99.5%methodplustwochoicesofboundarylayerprofile)areprovidedintheMethodologySectionIV.ComputedresultsarecomparedwiththosefromflatplatetheoryinValidationSectionValongwithastudyofaxisymmetricresultsforahemisphereinairandillustrationsof3-DresultsinairandintheMartianatmosphere.AfinalSectionVIpresentsexamplesofbehavioronless-than-idealboundarylayerprofilesobservedbytheauthors.Theutilityisrobustenoughthatplottableresultscanbeexpectedfromanylikelyflowsolution,eveninseparatedflowregions,withtheprovisothatmeaningfulresultswillbeconfinedtosteady,attachedflow.

II.InputsandOutputs

Themainassumptionsmade inBLAYERareappropriateforhypersonicflowsolutionsonstructuredmultiblockgrids,asfollows:

• ThegridconsistsofasinglelayerofstructuredblocksinPLOT3DorTECPLOTformat.• Theradialgridlinesaresufficientlynormaltothesurface(atleastintheboundarylayerregion)

forthe1-Dedgedetectionmethodtotreatgridarclengthsaswalldistances.• TheflowquantitiesaregiveninSIunitsatthegridpoints,notatcellcenters.• Theflowmaybe2-Dor3-D.Thisisdeterminedautomatically.Internally,2-Darraysaretreatedas

iftheyaredimensioned(1:ni,1,1:nk).• TheflowsolutionBCatthewallisexpectedtoberadiativeequilibrium.Ifnot,theoutputsurface

heatfluxwillbeinvalid.Forexample,coldwallcases(constantTw)willproduceconstantqw.• Theflowisnotadiabaticatthewall,becauseenthalpyprofilesshouldhavezerogradientthere.Notethatthewallsurfaceisexpectedtobeatk=1,orj=1forthe2-Dcase.Bydefault,theutility

findsthefaceoredgeofeachgridblockwiththesmallestaverageinitialincrementoffit,andifnecessarypermutestheblocktoputthewallatthek=1position.Overridingthiswalldetectionispossibleandmaybenecessary—seetheoptionalcontrolfileblayer.inp.2below.Thisfilecanalsobeusedtosuppress

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processingofcertainblocks.Forblankedblocks,thesurfacecoordinatesareoutputandallfunctionvaluesaresetto1.Suchblocksareretainedintheoutputzonessoasnottoaltertheirnumbering.

BLAYERprocessesonegridblockatatime,andeachradiallineisprocessedindependently.Theinputvolume dataset may be TECPLOT ASCII with variable names as shown in two forms below, or PLOT3Dformattedorunformatted(forwhichameansofenteringvariablenamesisanoption—seecontrolfileblayer.inp.3below).Forlargemeshes,thePLOT3D/unformattedoptionishighlyrecommended.Suchfilesarerecognizedbyrequiringuseofgridfilenamesendingin.gor.gu.Thenthesamenamesareexpectedforthecorresponding*.for*.fufiles.

TheoutputresultsareinTECPLOTASCIIorbinaryformat,onesurfacezonepergridblockintwoorthreegroups:wallvalues,boundarylayeredgevalues,and(ifk>0isspecified)roughnessheightkvalues.An optional additional output,blayer_edge_surface.dat, containing boundary layer edge coord-inatesandthicknessesmayoccasionallyberequestedtovisualizethecomputededgesurface.SeeFig.1.

Integralquantitiesdisplacementthickness(d*),momentumthickness(q),andvelocitythicknessarecomputedviaquadratureofnonmonotonic (plainHermite) local splinesvs. radial grid linearc length,using tangential components of velocity (parallel to the wall) at the boundary layer edge d. Theformulationsappearonpage14.

BLAYERControlFile(StandardInput):TITLE INPUT VOLUME DATASET volume.gu ! Tecplot ASCII or ***.g|***.gu PLOT3D ASCII|binary OUTPUT TECPLOT FILE blayer.dat ! Wall and boundary layer edge results 2 ! 1 = DATAPACKING=POINT; 2 = DATAPACKING=BLOCK MISCELLANEOUS CONTROLS 0 ! Edge method: three choices are explained below 0.85 ! Emissivity (0.89 = RCG everywhere) 0.001524 ! Roughness ht. k, m (=0.060" for Orion) |0|-1|-2 0 1 1 ! Block #, i, j for sample H/Hinf & Re-kk profiles 5 ! # species [5 if omitted] 1 ! # temperatures [1 if these numbers are omitted] 0 ! # extra items [0 " " " " " ] 0. ! Optional input for Hinf > 0. | blk. 1 1,1,nk value 98. ! Optional %H/Hinf > 0. value for Hignore | 95% 0. ! Optional Hshift if > 0. (e.g., Hform(0K) for CO2) Seebelowfortheextendeduseofthedatapackingcontroltoinvokeanoptionalsecondoutputfile.

Edgemethod(EM)ExtendedUsage: EM >= 0. means use the enthalpy ratio (H + Hshift) / (Hinf + Hshift) EM < 0. means use the enthalpy ratio (H - Hwall) / (Hinf - Hwall) |EM| < 90. means use the hybrid curvature-based method |EM| = 99.5 means use the traditional 99.5% method (or 99. or whatever) Thus EM = 99.5 means hybrid with Hshift profile (H/Hinf for air/Hshift=0.) EM = -1. means hybrid with Hwall profile EM = -99. means traditional 99% method with Hwall profile

Roughnessheightcontrolkhasmultipleusesasfollows:k = 0. means suppress the third set of results k > 0. means normal usage for a height in meters k + 20. means replace d* (displacement thickness) with velocity thickness

while also outputting results for roughness height k k = -1. means output results at height q (momentum thickness) and Req instead

of Rekk k = -2. means the same as -1. but output Req/Medge instead (use if Medge > 1?) k = -21. means the same as -1. but replaces q with velocity thickness k = -22. means the same as -2. but replaces q with velocity thickness

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NotethatReqcanalsobeobtainedwithinTECPLOTbymultiplyingunitReynoldsnumberReuewithq.ReueistheunitReynoldsnumberbasedonedgeconditions.RekkisReynoldsnumberbasedonroughnessheightkandconditionsatthatheightbutusingviscosityatthewallratherthanatk.

Hinfcontrolshowthetotalenthalpyratioineachprofileisnormalizedasfollows: Hinf > 0. ⇒ use that value to normalize all profiles Hinf = 0. ⇒ use the value from block 1, point (1,1,nk) [default] Hinf = -1. ⇒ use the (i,j,nk) value for profile (i,j) of each block Hinf = -2. ⇒ use the peak value along each profile (for arc-jet solutions?)

Hignoreistheenthalpyratiovaluebelowwhichprofiledataareignored—i.e.,thepointatwhichtostartthesearchfortheboundary layeredge.Thedefault is95%,butforOrionthishasbeenfoundtoencounter another heuristic affecting theupper endof the search region. Therefore, 98% is now therecommendedchoice.(FortheShuttleOMSpod,even95%missesthemuchmorelikelyedgeestimatethat50%willfind.)Notethatthiscontrolmayaffectanotherheuristicthatdetermineswheretostopshortofpossibleshock-relatedanomaliesinthefarendofaprofile.

Hshiftisdiscussedonp.11.Itshouldbezeroforsolutionsinair,butwaspromptedbycalculationsforMars.Itisignorediftheedgemethodisnegative,meaningusetheprofile(H–Hwall)/(H∞–Hwall).

OptionAncillaryControlFile,blayer.inp.2

Line1maybeusedtosuppressprocessingofsomeblocks;ablanklinemeansprocessallblocks.

Lines2+maybeusedtooverridetheautomatedwalldetectionscheme,oneblockperline.

Forexample:

10 12 14:18 meansblankblocks10,12,14,15,16,17,18(anyintelligibleintegerlistworks) 2 5 guaranteesthatforblocks2,3,4,face5(k=1)isthewall3 5 4 5

OptionAncillaryControlFile,blayer.inp.3

Thisoptionwaspromptedby theneed forhandling inputvolumedatasets inPLOT3D form.Line1shouldcontainallspeciesnames.Ifextraflowvariablesarepresent,theirnamesshouldappearonline2.Forexample:

n2 o2 no no+ n2+ o2+ n o n+ o+ e Cp N_tot

Ifeitherlineisempty(orthiscontrolfileismissing),thevariablenamesaredefaultedasfollows:

sp_1 sp_2 sp_3 ... sp_11 xtra_1 xtra_2

InputVolumeFileFormat(1):TECPLOTASCII TITLE = "" VARIABLES = "x, m" "y, m" ["z, m" for the 3-D case] "rho, kg/m^3" density "p, Pa" pressure "T, K" translational temperature ["Tv, K" vibrational temperature; the default is 1 temp.] "c_N_2" 1 or more species densities "c_O_2"

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"c_N_O" "c_N" "c_O" [“::: more species if specified; the default is 5 species] "u, m/s" velocity components "v, m/s" ["w, m/s"] for the 3-D case "H0, J/kg" total enthalpy "M" Mach number "mu, Pa.s" viscosity ["kappa, W/m.K" total thermal conductivity if # temperatures > 1] [“::: miscellaneous extras; the default is 0 extras] ZONE T="Zone 1" I=17, J=25, [K=81, ]ZONETYPE=Ordered DATAPACKING=BLOCK DT=(DOUBLE DOUBLE .................... DOUBLE DOUBLE ) 6.64733315E+00 6.57563824E+00 6.48970469E+00 6.39077472E+00 6. ... : : : : : Also,theformatwrittenbytheDPLR[3]postprocessorishandledasinthefollowingexample: [Optional title] variables=x,y,[z,]rho,p,T,C_n2,C_o2,C_no,C_n,C_o,u,v,[w,]h,M,mu zone t="flow2|3d" F=point, i= 161 j= 157 k= 1|81 6.64733315E+00 6.57563824E+00 6.48970469E+00 6.39077472E+00 6. ... : : : : : InputVolumeFileFormat(2):PLOT3DFormattedorUnformatted

Asmentionedabove,theunformattedoptionhereproducessignificantlybetterI/Operformanceforlargegrids.Theinputvolumegridfilenameshouldendin.gu.ForDPLRusers,thePOSTFLOWcontrolfileshoulduseoutputformat3,andthefollowingflowvariablecodes

ivarp = 0 100 110 120 1000 10 151 [152] 132 154 50 [extras] orivarp = 0 100 110 120 125 1000 150 151 [152] 132 154 50 52 [extras]

for single-temperature and two-temperature solutions, respectively, analogous to the above TECPLOTformat.

OutputResults(TECPLOTASCIIorBinary):OneZonePerGridBlock

Thecolumnsbelowrepresentsurfacedatasetsofresultsatthewall, resultsattheboundary layeredge, and (unlessk = 0 is specified) results at roughnessheightk or (ifk < 0 is specified) atheightq(momentumthickness).Wall Boundary layer edge Roughness height (k =/ 0) x density height k y pressure density s | z temperature |velocity| density total enthalpy viscosity pressure u Re-kk temperature v [ Tvw ] [ w ] or (if k = -1. or -2.): total enthalpy Mach number viscosity viscosity Theta height values N2 species density N2 species density O2 " " O2 " " k (= theta) NO " " NO " " density at theta N " " N " " |velocity| at theta O " " O " " viscosity at theta [ ?? " " ] [ ?? " " ] Re-theta (k = -1.) | heat flux delta Re-theta/Medge (= -2.) tau_x delta* or vel-thickness, depending on input k tau_y theta (see more on k above) [ tau_z ] Re-ue [ kappaw ] CH [ extras ] [ kappae ] [ extras ]

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Notethatthe2-Dcasewritesrunninglengths(alongthewallfromtheupstreamedgeofthecurrentblock)inplaceofcoordinatez.Thisstartsatzeroforeachblock,though.Also,aSORT_SURFACE_SLICEutilityisavailablefromthepresentauthortodeterminecumulativesurfacearclengthsacrossblockboundariesfroma3-Dsolutionsliced(withinTECPLOT)at(say)y=0.001mforasymmetryplanecut.

OptionalAdditionalOutputFile(TECPLOTASCII):blayer_edge_surface.dat

A user request led to retrofitting of optional output of a plottable file containing boundary layersurfacecoordinatesandthicknessesviatheoutputdatapackingcontrol: 21or22producesstructuredzones(inpointorderforthisformattedfile)whilefunctioningasfor1or2otherwise(pointorblockorderforthemainoutputfile).Figure1showsanexample.

Figure1. Thesurfaceformedbytheboundarylayer edge coordinates for a half-body MarsInSightcaseataMach24condition,0°angleofattack,isshownwithcontoursofedgethicknessfromBLAYERalongwiththeinnerandoutergridboundary surfaces. While the hybridmethodhasproducedaresultforallbodypoints(mostlyred), only forebody/attached-flow results arelikelytobemeaningful.

III.Background

Theboundarylayeratthesurfaceofanatmosphericentryvehicleistheregionwheretheenthalpyof

the freestreamflow isbeingdissipatedbyviscosity, transferringenergy in the formofheat.RealgasNavier-Stokes flow solvers routinely model this phenomenon as part of predicting the aerothermo-dynamicenvironmentsthatentryvehiclesmustbedesignedtowithstand.Theimportanceofknowingboundary layer properties and their relation to possible transition from laminar to turbulent flow isillustratedbySpaceShuttleDiscoverymissionSTS-114,whentheappearanceoftilegapfillerprotrusionsontheundersideofthenosewasdeemedseriousenoughthatacrewmemberwascalledupontoexitthevehicleandremovethepotentialthreatpriortodescentfromorbit.[4]

Hypersonicentryvehiclestendtobefairlysimpleshapessuchassphere-conesthatlendthemselvestouseofstructuredcomputationalgridsconsistingofasinglelayerofgridblocks.EventheSpaceShuttleOrbitercanbegriddedthisway.Sincethegridlinesoffthebodyshouldbeperpendiculartothewall,atleastintheboundarylayer,theyinturnlendthemselvestodirectuseforprofilesoftheappropriateflowsolutionquantity—totalenthalpy(whichisconservedacrossashockas longastheinviscidpartoftheshocklayerisadiabatic).Thus,entiresurfacedistributionsofboundarylayerpropertiescanbecalculatedone surface grid point at a time, either within the flow solver or as a post-processing utility. Suchcalculationsaremeaningfulforattachedflow,yetseparatedflowregionsneedtobehandledgracefully,ifonlyforplottingpurposes.

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Boundarylayer“edge”locationscanbeaffectedbytheparticularchoiceofboundarylayerprofileandthe associatednormalizations. There are at least two choicesof total enthalpyprofile, and these canproduce different calculated edge locations. Derived quantities such as displacement thickness andmomentum thickness, on the other hand, should be insensitive to the profile choice, as will bedemonstratedinSectionIV.Thismaynotbetrue,though,forprofileswithovershootsorundershoots,evenontheforebody,aswillbeillustratedinSectionVI.

The BLAYER utility used as part of post-processing flow solutions forOrion/MPCV and other entryvehiclesisageneralizationoftheearlierBLAYER_RESULTSutilitydevelopedatNASAAmesResearchCenterfollowingtheSTS-107Columbiaaccident.BLAYERhandles3-Dand2-D/axi-symmetricflowsandavariablenumberofgasspeciesforanyatmosphere.Itallowsformorethanonetemperatureandforoptionalextraflow quantities, and omits optional handling of Orbiter tile datasets. It produces a surface datasetcontainingcomputedvaluesofnumerousquantitiesatthewallandattheboundarylayeredgeheight,and(optionally)certainquantitiesataspecifiedsurfaceroughnessheightk.

IV.Methodology

Thetraditionalapproachofdefiningtheboundarylayeredgeatagivenbodypointasthelocationnearest to thebodyof99%or99.5%of the free-stream total enthalpynormally suffices for the two-dimensional flowsuponwhich that choice isbased. Three-dimensional flowhowever can, inpractice,presentboundarylayerprofilesthatmaydiffersignificantlyfromtheir2-Dcounterpartsbyundershootingorovershootingthefree-streamreferencevalueintheregionofinterest.ThetotalenthalpyratioH/H∞doesn’tnecessarilyasymptoteto1nearthebody.Indeed,enoughofanundershootcanmeanthatthetraditionalmethodfailscompletely.Locatingthepeakcurvaturealongeachprofileinsteadasa“kneeinthecurve”istheapproachthathasbeenappliedhereinpursuitofamorerobustedgemethod.Itturnsout, though, thatcurvaturecanbeavexingquantity toworkwith, so this ideaalsopresentspracticaldifficultiesdemandingheuristicsthatriskbeingthwartedbyoddprofilescommonlyseeninthewake—notthatresultsfromseparatedflowregionsareexpectedtobemeaningfulasalreadyindicated.

Theschemepresentlyimplementedisahybridmethod:useacurvature-basedschemetolocatethelikelyneighborhoodoftheedgeinthetotalenthalpyratioprofile,thenapplythe99.5%ruletothepeakratiointhatneighborhood.Forwell-behavedprofiles,thisisconsistentwiththetraditionaledgemethod(which remains a user option). In the presence of overshoots or undershoots, the hybrid methodinevitablyproducesedgethicknessesdifferingfromtraditionalmethodresults,butplausibleresultsforirregularprofilescanbeobtainedwhenthetraditionalmethodfails.

Whiletotalenthalpyistheappropriateprofilechoiceforedgedetectioninhypersonicflow(andlowerspeeds),acomputedboundarylayeredgelocationisaffectedbytheparticularchoiceofprofile.Theunitsneedtobenondimensionalized,specially ifprofilecurvaturesarebeingused.Thearc lengthchoice inBLAYERistonormalizedistancesalongwall-normalgridlinesbythetotalarclengthoftherelevantgridline. (Use of a common reference lengthwould have been another reasonable choice.) Initially, totalenthalpywasnormalizedbythefree-streamvalue,asH/H∞,whichissuitableinairwiththeDPLRenergyreferencevaluechoicesbutnotinotheratmospheressuchasatMars,whereenthalpiescanbenegative.Onechoiceistoshiftalltotalenthalpies,ifnecessary,toavoidpossiblenegativevalues,givingtheratio(H+Hshift)/(H∞+Hshift).AtMars,therecommendedadditiveshiftis8,932,880.0J/kg,basedontheenthalpyofformationofCO2at0K.Another(widelypreferred)choiceistousetheratio(H–Hwall)/(H∞–Hwall),andthiswouldaffectresultseveninair.BLAYERsupportsthisoption,butitisnotinuseforOrion/MPCV.

ArepresentativenormalizedtotalenthalpyratioprofilefromanouterwinggridblockonthewindsideofaShuttleOrbitergridforaMach17.88conditionisshownbelow(Figs.2and3).Thehybridedgemethodsuppressestheouterquarterofpointsonawall-normalgridlinetoavoidshockeffects.Fortheremaininggridpoints,itfirstlocatestheneighborhoodofthepeakcurvaturebyworkingwithasmoothed

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andmoderated form of raw curvature. Raw curvature values are estimated with three-point finitedifferencefirstandsecondderivativesoftotalenthalpyratiof(t)vs.normalizeddistancetas:curvaturek=-f(t)"(1+f(t)'2)-1.5.Therawcurvaturedistributionstendtobespikyandintractable(Fig.4,left).Theyarethereforesmoothedwithonepassofalocalaveragingmethod,thenmoderatedasfollows:kmod=(1+|k|)-0.1;ifk<0,kmod¬2–kmod.A1-Dminimizationdeterminesthe(preliminary)edgelocationbetweendatapoints(Fig.4,right),butthat isnowjustpartofdefininganeighborhoodforthehybridschemeasitappliesthe99.5%ruletothepeakratiointhatneighborhood.Thepeakexceeds1.0intheexampleshown,thusproducinganedgeheightofabout0.04(normalizedunits).

Onereasonfornolongeremployingthepurepeak-curvaturelocationisthatcurvaturecansometimesbeessentiallyconstantorflatintheedgeregion.Theprecisepeakmayliebetweenindicesjandj+1foroneprofilethenbetweenj+1andj+2(say)foraneighboringprofile,possiblyproducinganunlikelyjumpinthepeak-curvature-basededgethicknessd.Eventhoughditselfisseldomthequantityofinterest,itscontours should vary more continuously/smoothly than has been observed in the presence of thisphenomenon.Thus,thehybridmethodderivesalargerindexrangefromthecarefullycomputedpeakcurvaturelocation,thenlocateswhere99.5%ofthepeakratio inthatindexrangeliesviainverselocalsplineinterpolationasasecondstep.

Figure2.BodypointlocationfortheboundarylayerprofileshowninFig.3.

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Figure3.RepresentativeShuttlenormalizedboundarylayerprofileandedgelocationcomputedbyBLAYER’shybridmethodasthepointwherethetotalenthalpyratioisat99.5%ofthepeakratiointheregionofinterest.Thisneighborhoodisinitiallylocatedviaacurvature-basedscheme(seeFig.4).

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Figure4.PartoftherawcurvaturedistributionfortheprofileofFig.3isshownontheleft,withaspikypeakthathasbeenmoderatedasarelatedfunctionontheright,whereanextremumhasbeenestimatedpreciselybetweengridpoints.Originally,thedenormalizedformofthis locationwastakentobetheboundary layeredge.However,thislocationisnotindependentofthechoiceofprofileoritsnormalizations,sothehybridmethodemploysonlythegridpointindexnearesttothecurvaturepeaktodefineanedgeneighborhood.

Derived Quantity Formulations: Various wall and edge-related quantities are derived from the

underlying flow solution as follows.[5] Partial derivatives with respect to wall-normal distance areapproximatedby2-pointfinitedifferencingofprofiledatapointsk=1(wall)andk=2.Forexample,theunitwallnormalvectorcomponentsareapproximatedas(x2–x1)/(t2–0),(y2–y1)/t2,and(z2–z1)/t2wheret2 is thewall-normal gridpoint 2 distance from thewall. Note that to avoidpossibledifficulties at astagnationpoint,velocitiesaresafeguardedbyadding10-10tothembeforetheyareusedinthefollowingcalculations.

Surfaceconvectiveheatflux,qw:IncludingheatfluxintheinputvolumedatasetisnotanoptionwithDPLR.ThechoicethatallowsBLAYERto includesurfaceheatflux intheoutputdataset istoassumetheradiativeequilibriumboundaryconditionqw=esTw4,whereeistheemissivity,sistheStefan-Boltzmannconstant (originallyhard-codedas5.66097x10-8,althoughthe2014value[6] is5.670367x10-8W.m-2.K-4),andTwisthewalltemperature,K.Fortypicalarc-jetflowsolutions,useofdifferentboundaryconditionscanmeanthatBLAYER’sqwoutputismeaningless.Also,Orionstandardpracticeisforapost-processingscripttoreplacethisBLAYERoutputwiththesurfaceheatfluxfromDPLR.Inretrospect,two-pointfinitedifferencingatthewallwouldhavebeenamoregeneralwaytoprovidethesurfaceheatflux.

Catalyticheatflux,qvw:Two-temperaturesolutionsareexpectedtoincludevibrationaltemperatureTvandtotalthermalconductivityk(Wm-1K-1)intheinputvolumedataset.Acatalyticsurfaceheatfluxisdefinedasqvw=qw(totalheatflux)-kw(∂T/∂t)w,wheretisarc-lengthalongthebody-normalgridline.

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SurfaceShearStress,t:Theshearstressvectoratthewallisdefinedasthewallviscositytimesthewall-normalderivativeofthetangentialvelocity:tw=µw∂𝑣tan/∂twhere𝑣tan=𝑣–𝑣·𝑛isthetangentialcomponentofvelocityatgridpoint2offthewall,𝑛isthewall-normalvectortogridpoint2,and𝑣isthevelocityvectoratgridpoint2.

Displacement thickness, d*: BLAYER computes several integral quantities with local cubic splinequadraturebetweenthewallandtheboundarylayeredgeusingprofiledatafromthewalltothegridpointbeyondandnearesttotheedgelocation.Displacementthickness(“delstar”)isdefinedfrommassflowrateas:

𝛿∗ = 1 −𝜌 𝑡 |𝑣,-. 𝑡 |𝜌/01/|𝑣,-.|/01/

𝑑𝑡3

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Momentumthickness,q:Thisisalsobasedonmassflowrate:

𝜃 =𝜌 𝑡 |𝑣,-. 𝑡 |𝜌/01/|𝑣,-.|/01/

1 −𝑣,-.(𝑡)|𝑣,-.|/01/

3

4𝑑𝑡

Velocitythickness,du:Thisquantitymaybesubstitutedfordisplacementthicknessviatheroughness

heightcontrolinput,q.v.:

d8 = 1 −|𝑣𝑡𝑎𝑛 𝑡 ||𝑣𝑡𝑎𝑛|𝑒𝑑𝑔𝑒

𝑑𝑡3

4

UnitReynoldsNumber,Reue:TheunitReynoldsnumberbasedonedgeconditionsis:

𝑅𝑒8/ = =>?@>|A|>?@>

B>?@>𝑅𝑒CC =

=D|A|DBEFGG

NotethatthecommonlyrequiredReqcouldbeobtainedfrommultiplyingReueandqateachsurfacepoint(withinTECPLOT),butalternativesareavailable.Ifroughnessheightk>0isspecified,Rekk iscomputedusingconditionsatheightk,exceptthatviscosityistakentobethewallvalue.[7]Ifkisenteredas-1.or-2.,RekkisreplacedbyReq orReq/Medgerespectively.ThelattermaybeappropriateifMedge>1.

Filmcoefficient:Thisquantityistypicallyrequiredbymaterialresponsesolvers:

𝐶I =𝑞K

𝐻/01/ − 𝐻K-MM

RepresentativeprofilesandtheireffectsonsomeofthesederivedquantitiesareplottedinFigs.5-8.Figure5illustratesthesomewhatdifferentedgeresultsproducedbydifferentchoicesoftotalenthalpyratioprofilewithanexamplefromacalculationforIRVE-2(InflatableReentryVehicleExperiment)ataMach2condition(axisymmetric).Similardifferencesareunavoidablewithdifferentformsofnormalizingthewalldistances(suchasbyaconstantreferencelengthforallradialgridlinesratherthanbytheradialgridlinearclengthsashere).Thus,thecomputededgelocationisnotunique,butastheensuingfiguresshow,thisisnotnecessarilycriticaltotheintegratedquantities,whicharebarelyaffectedbythechoiceofprofile.TheprofileinFig.5isati=64,wherex~0.35andr~0.72,alittlelessthanhalfwayalongtheforebodycone.

15

Figure5.TwoformsofthetotalenthalpyratioprofilearecomparedforanIRVE-2bodypointatMach2inair.Theplottedwalldistancehasbeendenormalized,andtheright-handplotisazoomoftheleft-handplot.Thescalesamplifytheprofiledifferences.Thesetwoformsofthehybridmethodproduceedgeheightsthatareabout1.3mmapart on a vehicle that is 3meters in diameter (0.00784 and 0.00913m). Database calculations forOrion/MPCVemploytheformshowninred.

Figure6illustratestheintegrandsfortheprofileofFig.5thatproducenegligiblydifferentvaluesfordisplacementthicknessd*andformomentumthicknessq.Notehowtheyasymptotetowardszerointhevicinityofthedifferentedgeestimates.

Figure6.Theintegrandsfordisplacementthicknessd*andmomentumthicknessqfromthetwoprofilesinFig.5 are shown to asymptote towards zero and to differ only imperceptibly in spite of the visible difference incomputedboundarylayerthicknessesatthisbodypoint.

16

Thefullforebodydistributionsforedgethicknessdanddisplacementthicknessd*arecomparedinFig.7.Notehowinsensitivethelatteristothechoiceoftotalenthalpyratio.

Figure 7. While different choices of total enthalpy profile can affect calculated boundary layer thicknessesnoticeably,derivedquantitiesofinterestareprobablymuchlesssensitive,asseeninthisIRVE-2example.SeealsoFig.8.Edgethicknessdisontheleft;displacementthicknessd*isontheright.

ForebodydistributionsformomentumthicknessqandheattransfercoefficientCHarecomparedin

Fig.8.Aswithd*,thesearehardlyaffectedbythedifferentchoicesoftotalenthalpyratio.Notethatatthestagnationpoint(xw=0.),thetangentialvelocitycomponentiszerofortheentireprofile,producingzerosford* andq.BLAYERnowtrapssuchafindingandreplacesthezeroswithextrapolations.

Figure8.Theminimaleffectoftotalenthalpyprofileonforebodymomentumthicknessqisshownontheleftforthe forebody of IRVE-2 at the sameMach 2 condition as in Figs. 6-7. Another BLAYER output, heat transfercoefficientCH,isunaffectedbyboundarylayeredgecalculations,andessentiallyconstantonthisforebody(right).

xw (m)

delta

(m)

yw (m

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60.000

0.005

0.010

0.015

0.020

0.025

0.030

0

0.2

0.4

0.6

0.8

1

1.2

1.4

H / Hinf(H - Hw) / (Hinf - Hw)Not to scale

Full-body IRVE-2 Mach 2 Solution, 5-species airBL edge detection comparison

17

V.Validation

Surprisingly,untilthepresentsoftwarewasinitiatedfollowingtheColumbiaaccident,nosimilarutilityisknowntohavebeeninroutineuseatNASA.Thisissurelyasymptomofwriting“research”codeswithoutwidespreaduseinmindandnotduetoanylackofunderstandingofboundarylayertheoryandpractice.The original motivation here was to facilitate estimation of Req and Rekk for application to laminar-turbulent transitioncorrelations,and toexplore thepeak-curvature idea for itspotential in improvingbehavioron3-Dconfigurations.Asindicatedabove,acomputedboundarylayeredgeisnotunique,asitcandependonthechoiceofprofile(theenthalpy-relatedquantityandthewalldistance,bothofwhichare normalized in some way). Initial BLAYER studies simply compared the pure curvature-based edgedetectionwith the traditional 99.5%method, revealing the need for various refinements in order toproducesmoothlyvaryingresultsalongthesurface,eventuallyleadingtothecurrenthybridmethod.Afewstandardcasesarepresentedhere.

FlatPlateCase(2-Dplanarflow,idealgas):Steady2-Dincompressiblelaminarflowwithconstantviscosity, density and free-stream velocity over a flat plate lends itself to analysis with the Blasiusequations, which have been validated against experiment.[5, 8] Corrections to the equations forcompressible flow have also been established.[9] For a comparison between flat plate theory andcomputationsbyDPLRandBLAYER,anexampleisdetailedasfollows.

FlatPlateFreestreamConditions&Modeling:𝑀O = 4,𝑇O = 217.8K,𝑇K = 2𝑇O,𝜌O = 0.029 YZ[\.

Anideal-gasmodel(𝛾 = 1.4)isusedalongwithSutherland’slawforviscosity(𝜇 = 1.458×10ab c\

dd4.efc)

and a constant Prandtl number (Pr) of 0.71. Note that for𝑇 ≫ 110.3𝐾, 𝜇~𝑇4.k. Consequently, anexponentof0.5isusedinapower-lawapproximationtoSutherland’slawintheempiricalrelationsfordisplacementandmomentumthicknessesofacompressibleboundarylayer.

FlatPlateGrid:129(streamwise)´257(wallnormal).

FlatPlateMethodology:(i)apointwiseboundaryconditionisimposedatthewall—aninviscid(tangency)boundaryconditionatthefirst15pointsalongthestreamwisedirection,andano-slipboundaryconditionattheremainingpoints;(ii)thepointsalongeachverticalgridlineareredistributedusingOUTBOUND[10](off-lineprecursorofDPLR’sshockalignmentscheme)afteraninitialflowfieldcomputationsuchthat(a)thecellReynoldsnumberatthewallisunity,and(b)betterresolutionoftheobliqueshockisachievedaswell;(iii)theflowfieldcomputedonthereclusteredgridispost-processedusingBLAYERtoextractedgeandintegralquantities—displacementandmomentumthicknesses.

Foranincompressiblelaminarboundarylayeronaflatplatewithnostreamwisepressuregradient,thedisplacementandmomentumthicknessesare:[5,8]

𝛿lmn∗ = d.op4qr/s

𝑥and𝜃lmn =4.bbxdr/s

𝑥where𝑅𝑒} ==>8>}B>

(1)

Theseexpressionsforanincompressibleboundarylayerhavetobescaledforacompressibleboundarylayer.Tothisend,werelyonthereferencetemperaturemethoddevelopedbyEckert.[9]

The reference temperature, 𝑇∗, is defined as a weighted sum of the edge, wall, and recoverytemperatures:

𝑇∗ = 0.5𝑇/ + 0.5𝑇K + 0.22𝑟�adp

𝑀/p𝑇/ (2)

wheretherecoveryfactor,𝑟,foralaminarboundarylayeris:

𝑟 = 𝑃𝑟 (3)

18

Scaling involvessimplyreplacingtheReynoldsnumber,𝑅𝑒},withanewvaluebasedonthereferencetemperature,i.e.,𝑅𝑒}evaluatedwithdensityandviscosityevaluatedatthereferencetemperature.ThetextbookofHirschel[11]providesthefollowingexpressions(attributedtotheworkofSimeonides[12]):

𝛿n∗ = 𝛿lmn∗ −0.122 + 1.122 cEc>+ 0.0666𝑀/

p c∗

c>

4.k �ad (4)

and

𝜃n = 𝜃lmnc∗

c>

4.k �ad (5)

wheretheexponent,𝜔,is0.5forSutherland’slaw.

Flat PlateResults: The angleof theoblique shockwavewasdetermined froma straight-line fit (notshown)tofourshocklocations(peakpressures)atthestationsx=2,4,6,8m.as14.63°,whichcomparesfavorablywiththetheoreticalvalueof14.48°(sin-1(1/𝑀O).Figure9showspartoftheflowfieldasH/H∞contoursalongwiththedistributionsofd,d*andqproducedbyDPLRandthehybridmethodofBLAYER.

Figure9.Totalenthalpynormalizedbyfreestreamtotalenthalpy,alongwithresultsfromBLAYERusingthehybridmethodonaflatplateDPLRsolution(compressible).Theedgeordinatesrangefrom0to0.015m—roughly two orders of magnitude smaller than the physical distance of the outer boundary of thecomputationaldomain.Theoretically,theedgecurveisparabolicfortheincompressiblecase.

19

Figure10comparesBLAYERresultswiththecompressiblecorrectionstotheBlasiusequations,showingquitegoodagreement.

Hemisphere Case (2-D axisymmetric, air): An early study compared the pure curvature-based

methodwiththeplain99.5%methodforaunit-radiushemisphereatMach~22in7-speciesair,asinFig.11.Theright-handplotshowsthatthetwoedgedetectionmethodsareindistinguishablehere,withtheexpectedsmoothnessinedge-relatedquantities.Notethatzerosareinitiallycomputedford*andqatthestagnationpoint (because tangential velocitiesareall zeroalong the stagnation line). These zerosaretrappedandreplacedwithextrapolationsalongthesurfacebythecurrentversionofBLAYER.Thefree-streamconditionshereare:V∞=7.708km/s,r∞=5.3169E-3kg/m3,T∞=300K,Re=2.101million/m,M∞=22.15.

Figure11.ForahemispheresolutionatMach~22(left),thecurvature-basededgemethodisindistinguishablefromtheplain99.5%methodintheright-handplot.Thisisahot-wall/radiativeequilibriumlaminarcase.

Figure 10. Axial variations of computed flat plate displacement and momentum thicknesses (solid lines)comparedwith thecompressibleBlasius forms (dashed lines).The±5%errorbarsshownonthecomputedresultsareintendedtoconveythelevelofdisagreement.Themoreimportantthickness,q,iswidelyusedtopredicttransitionoftheflowfromlaminartoturbulent.

20

Laminar cold wall (Twall = 300 K) and fully turbulent (Baldwin-Lomax) cold-wall variations of thishemisphere case are also presented. The different wall boundary conditions have less effect on thevariousthicknessescomputedbyBLAYERthanmightbeexpected(Twall=2000-3000Kforthehotwallcase),probablybecausetheboundarylayerthicknessesarerelativelysmallatthisReynoldsno.SeeFig.12.

Figure12.Bothlaminarandfullyturbulenthemispheresolutionsforthisfreestreamareinsensitivetothewallboundary condition (radiative equilibrium, solid lines, and cold wall/300 K, dashed lines). DisplacementthicknessiscommonlynegativeathighReynoldsnumbers.

The laminar derived quantities Req and Rekk commonly used to predict turbulent transition arecomparedforcoldandhotwallvariationsinFig.13.ThesepredictionsarenotnecessarilyinconsistentbecauseReqisusedtopredicttransitiononasmoothsurfacewhileRekkpredictstransitionduetosurfaceroughness.Weseethatthehotwallcasewithroughnessheightk=0.1mmisunlikelytobecometurbulentatall(Rekk<200everywhere)whilethecoldwallcaseshouldtransition.

Figure13.Rekk(ontheright)issignificantlymoreaffectedthanReq(ontheleft)bythewallboundarycondition,becauseRekkusesviscosityatthewall,notattheedge,andviscosityissensitivetotemperature.Seepp.6-7forextendeduseofBLAYER’sroughnessheightinputtoobtainReqorReq/MedgeinplaceofRekk.Alternatively,useTECPLOTequations.

21

OrionCase(3-Dflowinair):A3-DexampleofboundarylayeredgeresultsisshowninFig.14,withpleasinglysmoothcontoursintheattachedaftbodyregion.Thelesssmoothcontoursappearingontheforebodywouldundoubtedlybeimprovedbyafurthergridalignmentwiththebowshock.

Figure14. RepresentativeBLAYERbehavior is shown fora turbulent (Baldwin-Lomax)OrioncaseatahighMachcondition.Theminorforebodycontourirregularities(upperimage)aremorelikelytoindicateimperfectgridalignmentwiththebowshockthannon-smoothvariationoftheboundarylayeredgedetectionscheme.Edgeheightvariationisadmirablysmoothontheattachedregionoftheaftbodyinthelowerimage.

22

Mars InSight Case (3-D flow in CO2): Figure 15 illustrates another 3-D application, to laminar-turbulenttransitionpredictionsatMars.

Figure15.ArepresentativeexampleofBLAYERapplicationtoturbulenttransitionpredictionisshowninthisforebodycontourplotofReqandRekktoalaminarMarsInSightsolutionataMach25peakheatingconditionand10°angleofattack.

23

VI.AnomalousBehaviors

Underordinarycircumstances,totalenthalpyprofilesshouldnotexhibitovershootsorundershootsintheboundarylayerregion.Inpractice,anomalousprofilesareinevitable,andBLAYERisanattempttocopewith thembetter than the traditional edge detectionmethoddoes. Establishing a single set ofheuristicstoaccommodateeverypossibility,however,remainsanidealyettobeachieved.Apartfromtheseparatedflowsthatarelikelywithinanyfull-bodysolution,alongwiththeirwakeflows,theremaybeshock-shockinteractionssuchasthoseproducedbythenoseoftheShuttleOrbiteratthewingleadingedge.TheShuttleOMSpods(OrbitalManeuveringSystem)provideamoretractableexample.Evenatthehighentryanglesofattack,theyexperiencetheirownstagnationspointsandboundarylayersthatarenotproperlycapturedbyBLAYER’sdefaultsettings.Indeed,the“Hignore”controlwasintroducedwiththissituationinmind:avalueof50%wasfoundtoenablesensibleresultsduringSTS-120whensometiledamagewasobservedonthestarboardpod,asshowninFig.16.Implausiblythickboundarylayersarepredictedinthisregionwiththestandardheuristics,andasampleprofileillustratesthereason.ForOrionapplications, this95%defaultcut-offheuristichasprovedvulnerable;98% isnowthe“Hignore” inputemployedinOrionpost-processingscripts.

Figure16.TheBLAYERdefaultof95%forthestartoftheboundarylayeredgesearchmissesthemoreplausiblethicknessinaDPLRsolutionnearthestagnationregionoftheShuttleOMSpodatanSTS-120missioncondition(Mach9,a=38.71°).Thisrepresentativetotalenthalpyprofilenearwhereatilecavityappearedshowswhy.

Mars InSight Anomaly: A second example shows anomalous results on a perfectly ordinary

configurationthatcanbetracedtounexpectedtravelofshock-relateddisturbancestotheboundarylayerregion towards the lee-side shoulder of the heat shield. This was first noticed in a plot of the Reqdistributionfora70°sphere/coneatangleofattackduringaMarsentry. Switchingtothetraditional99.5%edgemethodproducedamuch cleanerdistribution. The simplermethod is unaffectedby theprofileovershootsthatturnedouttobepresent(Fig.17).TheoddReqdistributionisreflectedbysimilarbehavior in the edge thickness and in themomentum thickness (Fig. 18). The contour plot of totalenthalpyratio(shiftedform)inFig.19suggeststhatshock-relatedeffectsbeginoppositethesphere-cone

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.10.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Enthalpy ratio

Wal

l dis

tanc

e, m

Boundary layer edge is at ( 0.70242, 0.04520 )

Block: 41 i: 9 j: 12Boundary Layer Profile

File name: CFD12.OMS.blayer.70.qplot Plot date: 2007-11-05 @ 12:59

24

tangencypointandtraveltothelee-sideshoulder.Figure20confirmsthatintheregionaroundr=0.95m,thedisturbancedoes indeedentertheboundary layer.Thus, inthisexample,thehybridmethodisrevealingwhatarereallyflowsolutionimperfectionsratherthansufferingfromalgorithmweaknesses.Notethatgridlineorthogonalityatthewall,gridalignmentwiththeshock,andflowsolverconvergencewerealleliminatedaspossiblesources.Afourthgridalignmentmadenoperceptibledifference,whiletheradialgridlinefortheillustratedprofilewasshowntobejust0.5°offbody-normalforitsfulllength(seetheredgridlineinFig.19).

Figure17.AnomalousbehaviorofthecenterlineReqdistributionforaMarsInSightsolutionatMach24.5,a=10°,ontheleeside.Thetotalenthalpyprofileshownisforthebodypointwheretheanomalyisgreatestnearradius=0.95m,anditcontainsanovershootthatmovestheedgehigherforthehybridmethod.

Figure18.Evidenceofprofileundershootsandovershootsappearsintheedgethicknessdistribution(left)forthecaseofFig.17.Themomentumthicknessdistribution(right)fromthehybridmethodissimilarlyanomalous.Notethattheflat-plate-inspiredassumptionsinthedefinitionofqbreakdowntowardsthestagnationpointinspiteofsafeguardingagainstzerotangentialvelocity.SeeFigs.19and20forevidencethattheovershootregionextendsintotheboundarylayertowardsthelee-sideshoulder.

Radius (m)

Re-

thet

a

xw (m

)

-1 -0.5 0 0.5 1

0.0

50.0

100.0

150.0

200.0

250.0

300.0

-1.5

-1

-0.5

0

0.5

Total enthalpy ratio

Wal

l dis

tanc

e, m

0.8 0.85 0.9 0.95 10

0.02

0.04

0.06

0.08 Mars InSight Calculation (DPLR, laminar flow)Peak heat flux point on peak heat flux trajectoryAoA = 10° , Mach = 24.48, t = 674.4 s

Centerline profile at r/R ~ 0.71 on lee side

Curvature-based edge

Traditional 0.995 edge

Radius (m)

delta

(m)

xw (m

)

-1 -0.5 0 0.5 10.000

0.002

0.004

0.006

0.008

0.010

0.012

-1.5

-1

-0.5

0

0.5

Radius (m)

thet

a (m

)

xw (m

)

-1 -0.5 0 0.5 10.0000

0.0005

0.0010

0.0015

0.0020

0.0025-1.5

-1

-0.5

0

0.5

25

Figure19.ContoursoftheshiftedformoftotalenthalpyratiofortheMarsInSightcaseofFigs.17and18showayellowbandslightlyhigherthan1.0thatemanatesfromtheshockoppositethesphere/conejunctureandtravelstotheboundarylayerregionofthelee-sideshoulder.Theredlinemid-leftisthelocationofthetotalenthalpyprofileshowninFig.17.SeealsoFig.20.

26

Figure20.VelocityvectorsaddedtothecontoursofFig.19confirmthattheyellowbandslightlyexceeding1.0doesentertheboundarylayerintheregionnearradius=0.95m.Theflowsolutioniscell-centered.Theredlinecorrespondstothevertex-centeredgridlineoftheprofileshowninFig.17.

27

EdgeDetectionFailures: Eitheroftheedgedetectionmethodscanfailcompletelyforanomalousprofilesatwhatareboundtobeaftbodypointsbarringsomeinputerror.(Amongotherpossibilities,longoff-body grid lines in thewake tend to violate someof theBLAYER assumptions.) BLAYER reports edgedetection failuresbywriting the firstoffendingprofile (x,y,z,t,hratio) to standardoutput foreachgridblock,andreportingthetotalcountoftroublesomeprofilesforthatblock.Resultsforsomeuncertain“kedge”indexwillstillbeproducedandtherunproceedssothatplottingcanstillbeperformed.Figure21showsaprofileforwhichthehybridalgorithmfailedwiththe95%defaultfor“Hignore”becausethetotalenthalpyratioislessthanthecut-offvalueeverywhere.

Figure21.ThisH/H∞profile is forasurfacegridpointon thebaseof theOrion smoothOMLataMach26condition,inthewake.Withthedefaultsettings,including0.95astheratioforthestartoftheedgesearch,thehybridalgorithmfails,asofcoursedoesthetraditional0.995method.

N.B.: Extremely tight grid spacing occasionally explains BLAYER misbehavior. This is because, by

default,theutilitydetermineswhichfaceofeachgridblockhasthesmallestaverageoff-facegridspacingandpermutesindicesifnecessarytomakethatfacebethek=1faceasassumedbytheensuingsteps.(Verytightresolutionoftheshock,forinstance,hasbeenobservedtotripthistest.)Thework-aroundistouseancillarycontrolfileblayer.inp.2tospecifythecorrectfaceforeachblock.Seepage7.Notethatevenfor2-Dsolutions,face5shouldbespecifiedforthej=1face,becausesuchsolutionsaretreatedasbeingdimensioned(ni,1,nj),not(ni,nj).

28

Finally,anexcerptfromtheBLAYERsourcecodehistorysectionillustratesthetypeofpracticaldifficultyencounteredbythecurvature-basedapproachintheedgeregionwheregradientsarehighest:

! 06/24/08 Discontinuities towards the Shuttle wing tip were ! traced to profiles that straighten up short of 1.0 ! before achieving 1.0. This means the heuristic ! size of the neighborhood of the peak curvature ! can include ~1.0 for one profile but not for a ! neighboring profile. Stage 2 of the edge method ! then seeks 99.5% of quite different peaks in those ! neighborhoods. Use of 99.5% means even small ! changes lead to large differences in edge thickness ! when the profile is so steep. Mike Olsen suggested ! using 95% to reduce the effect greatly, but then ! all edge-related quantities would be significantly ! lower everywhere. After much pondering, we stay ! with 99.5%, and accept that wing tip regions are of ! limited interest anyway, even on the wind side.

TheinterestedreaderisremindedthattheBLAYERsourcecode[13] isthoroughlydocumentedin-line,

andshouldbeconsultedwhenquestionsarise.

VII.Acknowledgments

The BLAYER software was implemented at NASA Ames Research Center under TSA Aerothermo-

dynamicsBranchcontractswithELORETCorporation(NNA04BC25C)andERC, Inc. (NNA10DE12C),andfundedmostlybytheShuttleRTF(ReturntoFlight)program.AtthetimeofwritingthisUserGuide,theauthorsarecontractorswithAMA,Inc.atNASAARC(ContractNNA15BB15C).HelpfulreviewcommentsfromRyanMcDaniel,MichaelOlsen,MichaelWilder(NASAARC)andBrettCruden(AMA,Inc.atNASAARC)aregratefullyacknowledged.

VIII.References

[1].TECPLOT(morepreciselyTECPLOT360)isoneofafamilyofdatavisualizationandanalysistoolsdevelopedbyTecplot,Inc.,Bellevue,WA.TECPLOTisadefactostandardatNASA.

[2].https://en.wikipedia.org/wiki/PLOT3D_file_format[3].Wright,MichaelJ.,White,ToddR.,Mangini,Nancy,“DataParallelLineRelaxation(DPLR)Code

UserManual:Acadia–Version4.01.1.”[4].https://en.wikipedia.org/wiki/STS-114#In-flight_repair[5].White, Frank M., Viscous Fluid Flow, 3rd Edition, McGraw-Hill, 2005.[6]. Committee on Data for Science and Technology (CODATA); https://www.nist.gov/programs-

projects/codata-values-fundamental-physical-constants[7]. Reda, Daniel C., “Review and Synthesis of Roughness-Dominated Transition Correlations for

ReentryApplications,”JournalofSpacecraftandRockets,Vol.39,No.2,Mar-Apr2002.[8].Schlichting,H.,Boundary-layerTheory.Springer2004.[9].Eckert,E.R.G.,“EngineeringRelationsofFrictionandHeatTransfertoSurfacesinHigh-Velocity

Flow,”J.Aero.Sci.,Vol.22,No.8,1955,pp.585-587.[10].DavidA.SaundersandSeokkwanYoon,“AnApproachtoShockEnvelopeGridTailoringandIts

EffectonReentryVehicleSolutions,”AIAAPaper2007-207,2007.[11]. Hirschel, E. H., Basics of Aerothermodynamics. Vol. 204 of Progress in Astronautics and

Aeronautics,AIAA,2005.[12]. Simeonides, G., “Hypersonic Shock Wave Boundary Layer Interactions over Compression

Corners,”DoctoralThesis,UniversityofBristol,U.K.,1992.[13].https://sourceforge.net/projects/cfdutilities

29