NASA Technical Reports Server (NTRS) 20050041939: Navier-Stokes Computations of Longitudinal Forces and Moments for a Blended Wing Body

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by  NASA Technical Reports Server (NTRS)

AIAA-2005–0045
Navier-StokesComputationsofLongitudinalForcesandMomentsforaBlendedWingBody
S.PaulPao∗, RobertT.Biedron†, MichaelA.Park‡, C.MichaelFremaux§, and
DanD.Vicroy¶
NASALangleyResearchCenter,Hampton,VA23681
Abstract
TheobjectofthispaperistoinvestigatethefeasibilityofapplyingCFDmethodstoaerodynamicanalysesforaircraft
stability and control. The integrated aerodynamic parameters used in stability and control, however, are not necessarily
thoseextensivelyvalidatedinthestateoftheartCFDtechnology.Hence,anexploratorystudyofsuchapplicationsandthe
comparisonofthesolutionstoavailableexperimentaldatawillhelptoassessthevalidityofthecurrentcomputationmeth-
ods. Inaddition,thisstudywillalsoexamineissuesrelatedtowindtunnelmeasurementssuchasmeasurementuncertainty
andsupportinterferenceeffects. SeveralsetsofexperimentaldatafromtheNASALangley14x22-FootSubsonicTunnel
andtheNationalTransonicFacilityarepresented. TwoNavier-Stokesflowsolvers, oneusingstructuredmeshesandthe
other unstructured meshes, were used to compute longitudinal static stability derivatives for an advanced Blended Wing
Bodyconfigurationoverawiderangeofanglesofattack. ThecomputationswereperformedfortwodifferentReynolds
numbersandtheresultingforcesandmomentsarecomparedwiththeabovementionedwindtunneldata.
Introduction
Windtunneltestingisbecomingincreasinglyexpensive,andthenumberoffacilitiesavailablefortestingisdecreasing.
At the same time, the cost of computing has dropped dramatically. There is is a growing awareness that Computational
FluidDynamics(CFD)willneedtotobevalidatedforthetaskofreliablyanalyzethestaticanddynamicstabilitycharacter-
isticsoffutureaircraftsystems. However,manyoftheinnovativevehicleconceptsbeingconsideredhaveunconventional
vehicle geometry. The placement of control surfaces and the interactions between them may be very different from that
of traditional designs. The drive towards ultra high efficiency commercial transport systems requires precise knowledge
ofallaspectsofaerodynamics,propulsion,stabilityandcontrol(S&C),andcomponentflowphysics,includingnonlinear
effects.
ThisexpandingrequirementtouseCFDforS&CbringsformidablechallengestotheCFDcommunity. Currentappli-
cations of CFD are generally focused upon the mission performance aspects of the airplane such as lift and drag for the
cruisesegmentoftheflight,andhighliftdevicesfortheterminaloperationsegments. Intheseoperationalsegments,true
alsoathighliftconditions, attachedflowisoftenthenorm, withtheexceptionthatmildlyseparatedfloworshedvortex
dynamicsmaybeimportantinsomecases. Evenstillliftanddragcoefficientsareachallenge,otherflightconditions,such
assideslip,wouldnormallybestudiedwithmuchlessemphasis. Asaconsequence,mostofthecurrentCFDvalidation
analysishastodowithliftanddragcoefficients.
Foratypicalsixdegree-of-freedom(6-DOF)aircraftmotionsimulation,asmightbeusedforhandlingqualityassess-
ment,body-axisaerodynamicforcesandmomentsaremodeledusingTaylorseriesexpansionsbasedonforceandmoment
coefficients. Accurateassessmentoftheseforceandmomentcoefficients(magnitudesaswellastrends)iscritical. Data
at high angles of attack, side slip, or high angular rates may be required to model some extreme conditions. Moment
coefficients, in particular, are known to be difficult to accurately compute. Since a simulation model is only as good as
thedatasupplied,itisobviousthattheinput,whetheranalytical,experimental,orcomputational,musthavehighenough
fidelitytosatisfytheneedsoftheenduser.
AnaddedcomplicationisthedearthofexperimentaldataforbenchmarkingandvalidationofS&Cpredictions. Most
existingS&Cdataconsistsofintegratedforcesandmoments,withsurfacepressuresinafewcasesandflowvisualization
evenlessfrequently. AcriticalareaofneedforCFD-basedS&Cpredictionisthatofexperimentaldatawithadequatesup-
portinginformation(e.g.,on-andoff-bodyflowphysics,model-mountinterferenceinformation,boundarylayertransition
detection,andhigh-fidelitydataontunnelflowcharacteristics).
WithrecentadvancesofCFDtechnologyandtheavailabilityofaffordablecomputingpower,CFDpractitionersusing
Navier-Stokes solvers have begun to successfully address stability and control problems.1–3 Many experienced analysts
∗SeniorResearchEngineer,ConfigurationAerodynamicsBranch,AssociateFellowAIAA
†SeniorResearchScientist,ComputationalModelingAndSimulationBranch,MemberAIAA
‡ResearchScientist,ComputationalModelingAndSimulationBranch,MemberAIAA
§SeniorResearchEngineer,VehicleDynamicsBranch,SeniorMemberAIAA
¶SeniorResearchEngineer,VehicleDynamicsBranch,AssociateFellowAIAA
ThismaterialisdeclaredaworkoftheU.S.GovernmentandisnotsubjecttocopyrightprotectionintheUnitedStates.
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anddesignersofaircraftcontrolsystemsareskepticalforgoodreasons: fidelityofthedatabaseforflightpredictionisof
criticalimportance, andtheaccuracyandproductivityofCFDhaveyettobevalidatedespeciallyatmassivelyseparated
flow conditions. To help bridge the gap between CFD practitioners and the S&C community, NASA Langley Research
Center hosted the first of several planned COMSAC (Computational Methods for Stability And Control) symposia1 in
September2003. TheinauguralsymposiumsoughttoencouragediscussionofissuesthatcurrentlylimittheuseofCFD
forS&CapplicationsandtoformulateplansforexpandeduseofCFDinthisarea.
Subsequenttothesymposium,NASALangleyResearchCenterembarkedonamulti-yearprojecttoassessstate-of-the-
artCFDcodesforevaluationofbothstaticanddynamicstabilityderivatives. Tosupportaswellasleverageotherresearch
workintheVehicleSystemsProgram,thefocusoftheNASACOMSACeffortisaBlendedWingBody(BWB)configu-
ration. TheBWBisanadvanced-conceptvehiclethatshouldofferincreasedL/Dalongwithreducedtakeoffweightand
fuelburnoverconventionaldesigns.2 Foraircraftconfigurationsingeneral,accuratepredictionofthelongitudinalpitching
moment coefficient, C , is particularly important, since it would affect configuration design options, the design of the
M
controlsystem,andoverallvehicleperformancesinceminimumtrimdragisdependentuponaccuratepredictionofC .
M
ThispaperdescribestheinitialresultsforlongitudinalstaticforcesandmomentsobtainedfromtwooftheCFDcodes
underevaluation. ThesecomputedresultswerecomparedwithexperimentaldataforanearlyversionoftheBoeingBWB
configurationobtainedintwoNASALangleywindtunnelfacilitiesusingappropriatelyscaledmodelsforeachtunnel. The
data include body axis forces and moments, as well as lift and drag. Experimental data were obtained for a number of
differentslatandelevonconfigurations. ForthisinitialCFDstudy,thedatausedinthispapercorrespondtoconfigurations
withundeflectedelevonsandleadingedgeslats.
DescriptionofWindTunnelMeasurements
ModelDescriptions
Thewindtunneldatapresentedinthispaper arefromaseriesoftestsofasubsonictri-jetBWBconfiguration. Two
differentscalewindtunnelmodelsofanearlyBoeingblendedwingbodyconfigurationhavebeenusedintunneltests: a
2%scaletransonicmetalmodelanda3%scalecompositesubsonicmodel. Athree-viewoftheconfigurationgeometryis
showninFigure1. Themomentreferencecenterwas38.67%ofthemeanaerodynamicchord.Themodelreferencevalues
arelistedinTable1. Themodelshavethreepylon-mountedflow-throughnacelleslocatedontheuppersurfaceoftheaft
center-body. Thecontrolsurfacesconsistof18elevons,rudderoneachwingletandleadingedgeslats. Thetwooutboard
elevonssplittoserveasbothelevonsanddragrudders.
The2%-scalemodeloftheBWBwasbuiltforaseriesoftestsintheNASALangleyNationalTransonicFacility(NTF),
includingthoseperformedtosupportCFDcodebenchmarkingfortheCOMSACproject.Forthesemeasurements,allcon-
trolsurfacesandhigh-liftdevicesweresetattheirundeflectedpositions. Duetothelackofatraditionalfuselageandthe
desiretohavenoaft-enddistortion,the2%BWBmodelwasfixedtoasting/strutmountattachedontheundersideofthe
modelasshowninFigure2. Thestrutwasconsistedofasymmetricairfoiltominimizesupportinterferencewhileprovid-
ingsufficientstrengthtoaccommodatethelargeloadsassociatedwithtestingintheNTF.Themodelsupportsystemwas
actuatedinpitchbythetunnelcontrolsystemforangleofattackchanges.FortheCOMSACinvestigation,thetestwascon-
ductedintheNTFtunnelatMach=0.2andthreechordReynoldsnumbers: Re =2.47×106,3.7×106,and10×106.
c¯
The NTF data presented in this paper had post-test correction for tunnel flow angularity, but not been corrected for the
influenceofthesupportsystem.
The 3% low-speed model was designed for both static and dynamic testing and has been used in several tests to
date. ThedatausedinthisreportarefromaseriesoftestsintheNASALangley14x22-FootSubsonicTunnel(hereafter
referredtoas14x22-ST)investigatingthestaticanddynamicstabilityandcontrolcharacteristicsofthisconfigurationover
a large angle of attack and sideslip range. For the data reported in this study, the model was mounted in two different
configurations, as shown in Figures 3 and 4, intended for static force and moment measurements. Figure 3 shows the
relativelylarge,verticalpostmount,attachedtothebottomofthemodel. Thepostdiameteratthemodeljunctionwas3
inches.Thismountingarrangementwasusedtomeasurebodyaxesforcesandmomentsoveranangleofattackrangefrom
−10◦to+36◦atdynamicpressuresuptoq =60psf,correspondingtoaMachnumberofM =0.203andaReynolds
∞ ∞
numberbasedonthemeanchordofthemodel,Re =3.76×106.
c¯
The second 14x22-ST installation for static measurements had the model mounted through the bottom of the model
onasting/strutwithacircularcrosssectionthroughout. Thissupportsystemwillbereferredtoasthesmallpostmount
(SP),asshowninFigure4. Thestrutdiameterofoneinchwasrelativelysmallascomparedtothesizeofthemodeland
tothediameteroftheverticalpostmount. Thistestwasusedtomeasurethebodyaxesforcesandmomentsoveralarge
angleofattackandsidesliprange.3 Themaximumdynamicpressurewasq =26psf withM =0.134andresultedin
∞ ∞
Re =2.47×106.
c¯
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WindTunnelMeasurements
Supportinterferencewasamajorconcernforallofthesemeasurements. Theinfluenceofthewakeandthepressure
footprint of the support system on the surface of the model can potentially change the measured forces and moments to
a large extent, depending on the angle of attack. While standard tunnel corrections were applied to the measured data,
the data presented here were not corrected to account for the influence of the support system. In order to put the data
comparisonsinperspective, Table2showsthe95%confidenceleveluncertaintyforC andC forfour14x22-STand
N M
NTFtunnelconditions. Itshouldbenotedthatthereportedwindtunneldataaretheaveragevaluesofrepeatedsampling
duringthereal-timetunneloperation. Theactualmeasurementresolutionshouldbebetterthanthereferenceuncertainty
valuescitedinTable2.
Normalforcecoefficient,C ,andpitchingmomentcoefficient,C ,areplottedagainstangleofattackinFigures5and
N M
6,respectively.InFigure5,bothReynoldsnumbereffectsandinstallationeffectsarenoted.Acomparisonofthe14x22-ST
resultsonthelargepost(LP)atM =0.203and0.134,correspondingtoRe =3.7×106andRe =2.47×106shows
∞ c¯ c¯
aslightshiftofthenormalforcecurveforanglesofattackaboveabout22◦ duetothechangeinthetunnelMachnumber,
M andthecorrespondingRe . Likewise, asmallbutdiscernibledifferenceinthelocalslopesofthecurvesisevident
∞ c¯
betweentheblade-mountedNTFdataandthepost-mounted14x22-STdata,althoughitisdifficulttodistinguishbetween
thelargepostandsmallpost(SP)resultsatthescaleofthefigure.
While Reynolds number effects on C are clearly evident for the large post data in Figure 6, more dramatic is the
M
effectofmountingtype. TheNTFresultswillbeconsideredasa”baseline”inthisfigureforcomparisonpurposessince
the2%modelwasmountedonthestreamlinedstrutdescribedaboveandillustratedinFigure2. Thisfairedshapewould
beexpectedtoproducetherelativelysmallestwake, and, thus, thesmallestpressurefootprintontheundersurfaceofthe
model behind the strut. On the other hand, the faired strut would produce a flow acceleration on either side of the strut.
Whilethestrutpositionwasupstreamofthemodelmomentreferencecenter,thereducedpressureinthisforwardmodel
stationcouldhaveinducedanose-downpitchingmoment. Ingoingtothesmallpostmount,apositive(nose-up)shiftis
noted. Increasingthediameterofthepostneartheinterfacewiththemodeltothreeinchescausesamajorpositiveshift
relative to the blade mount (LP vs. NTF). The large post clearly produces a significant wake footprint on the lower, aft
surfaceofthemodelandhasamajorimpactonthepitchingmoment.
DescriptionofComputationalMethods
PAB3DCodeDescription
PAB3D4–7 isacell-based, finitevolume, structuredmeshNavier-Stokessolver. Complexgeometriesmaybeaccom-
modated using zonal decomposition with point-matched or flux-conservative patched interfaces. Upwind-biased spatial
differencingisusedfortheconvectivefluxes;fortheresultspresentedhere,Roe’sfluxdifferencesplitting8wasemployed.
Theviscousfluxesarecentrallydifferencedusingthin-layerapproximationsinthethreegeneralizedcoordinatedirections.
Anumberofturbulencemodelsareavailableinthecodeincludingthestandardk-(cid:15)two-equationmodel,explicitalgebraic
stress models as formulated by Girimaji9 and by Shih, Zhu, and Lumley.10 For all results presented in this paper, the
Girimajiexplicitalgebraicstressmodelwasused.
Toadvancethesolutionintime,PAB3Dusesanimplicit,backward-Eulertimeintegration. Localtimesteppingmay
beusedtoaccelerateconvergencetoasteadystate,orconstanttimesteppingmaybeusedtoobtainsecond-orderaccurate
solutions in time. The latter method was used exclusively for the results presented below. At each time step the linear
systemissolvedusinganapproximatefactorizationapproach. Fortime-accuratecomputations, subiterationsareusedto
reducetheerrorsarisingfromlinearizationandapproximatefactorization.
FUN3DCodeDescription
FUN3D11–13 isanode-based,finite-volume,unstructuredmeshNavier-Stokessolver. Withinthecode,theconvective
fluxesarecomputedwithoneofseveralavailableflux-splittingschemes,andforsecond-orderaccuracythevaluesatdual-
cell interfaces are reconstructed using gradients at mesh nodes computed via a least-squares technique. For all results
presented in this paper, Roe’s flux difference splitting was used for the convective fluxes. The full viscous fluxes are
discretized using a finite-volume formulation that is equivalent to a Galerkin-type approximation on tetrahedral meshes.
Fornon-tetrahedralmeshes,anedge-basedformulationisusedthatretainsthecompleteviscousstresses,withoutthin-layer
approximations. For turbulent flows, both the one-equation model of Spalart and Allmaras14 (SA) and the two-equation
SSTmodelofMenter15 areavailable. TheSAmodelmaybesolvedlooselycoupledtothemean-flowequationsortightly
coupledtothemean-flowequations.Eithermodelisintegratedtothewall,withouttheuseofwallfunctions.Forallresults
presentedinthispaper,theoneequationSAmodelisemployed,solvedinalooselycoupledfashion.
FUN3Dusesanimplicit,backward-Eulertimeintegrationalgorithmtoadvancethesolutionintime. Solutionsmaybe
obtainedinasecond-order, time-accuratemanner, usingsubiterationsonthenon-linearprobleminpseudotime, orwith
localtimesteppingtoaccelerateconvergencetoasteadystate; bothtechniqueswereusedtoobtaintheresultspresented
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below. At each time step, the linear system is solved using a point-implicit or line-implicit Gauss-Seidel method; the
formerwasusedforthesecomputations.
ComputationalModelandGrids
Theconfigurationmodeledinthecomputationscorrespondstothebaselinewindtunnelconfigurationwithoutslator
elevon deflection. The nacelles are flow through, as in the experiment. Because only longitudinal forces and moments
areconsideredhere,halfoftheconfigurationismodeled,withsymmetryassumed. Significantly,thecomputationalmodel
doesnotincludeanymountinghardwareortunnelgeometry. Inclusionofthesefeaturesinthecomputationisongoingand
willbereportedoninthefuture.
ThreedifferentstructuredgridswereusedforthePAB3Dcomputationspresentedbelow. Thefirstgrid, usedforthe
Re =2.47×106 computations,consistedofapproximately3.7millioncells. ThisgridisillustratedinFigure7,where
c¯
everyotherpointonthesymmetryplaneisshown, andisreferredtoasGrid1. Thisgridhadwallspacingsuchthatthe
average y+ for the Re =2.47×106 condition was approximately y+ = 0.2. Grid 2F, used for the Re =3.76×106
c¯ c¯
computations,thoughsimilarinlayouttoGrid1,wasofadifferentfamilyandcontainedapproximately5.3millioncells.
Thisgridhadwallspacingsuchthattheaveragey+ atRe =3.76×106 wasalsoapproximatelyy+ = 0.2. Inaddition,
c¯
thisgridwascoarsenedbyremovingeveryotherpointineachdirection,yieldingameshofapproximately670,000cells.
ThismediumgridisillustratedinFigure8,andisreferredtoasGrid2M.
ThesingleunstructuredgridusedfortheFUN3Dcomputationsconsistedofapproximately2.3millionnodes,withan
averagey+ attheRe =2.47×106 conditionofapproximatelyy+ = 0.3. Theunstructuredgridonthesymmetryplane
c¯
isshowninFigure9. Notethatwhencomparingrelativegridresolution,thenatureoftheflowsolvermustbeaccounted
for; it is appropriate to compare the number of cells in the meshes used for PAB3D (cell based) to the number of nodes
in the meshes used for FUN3D (node based). Thus the FUN3D mesh has roughly 60% of the resolution of Grid 1 and
roughly40%oftheresolutionofGrid2F.Ofcourse,howthecellsandnodesaredistributedisveryimportant,butisless
easilyquantifiable.
CFDResultsandDataComparison
CFDsolutionswerecomputedusingbothcodesfortwoReynoldsnumbers: Re =2.47×106andRe =3.76×106.
c¯ c¯
ThecorrespondingMachnumbersusedforthecomputationsforFUN3DwereM =0.13andM =0.20,eachthesame
∞ ∞
astheMachnumberatthecorrespondingexperimentaltestconditions. ForthePAB3Dcomputations, theMachnumber
wasM =0.23,alargerthantheexperimentalvaluestoavoidpotentialconvergencedegradationwhencompressibleflow
∞
solversareusedatlowMachnumbers. ThetotalpressureinthecomputationwasadjustedtomatchtheappropriateR for
c¯
eachcase.
FUN3Dsolutionswereobtainedoveranominalangleofattackrangeof−10◦ to+36◦. However,theexactangleof
attackrangevariedwiththeReynoldsnumber. Specifically,therangeswereα=−5◦toα=+35◦forRe =2.47×106,
c¯
andα=−8◦toα=+36◦forRe =3.76×106. Todetermineifasteadystatehadbeenattainedinthecomputations,the
c¯
pitchingmomentcoefficientwasmonitoredinadditiontodensityresidual. Pitchingmomentisamoresensitiveindicator
than either lift or drag, and is the quantity of primary interest from the computations. A steady state was defined as no
perceptible variation in pitching moment coefficient over several hundred iterations when plotted on a scale with ranges
±0.001 about the nominal value. At nearly all angles of attack, steady state solutions were obtained. However, within
approximatelyonedegreeofα = 15◦,forallReynoldsnumbers,steadystatesolutionscouldnotbeobtained. Forthese
angles of attack, the flow solver was restarted in time-accurate mode, and the unsteady solution was advanced in time
for approximately 8-10 cycles of solution oscillation. Time average values of the force and moment coefficients were
calculated over the last four cycles, along with the minimum and maximum values. In the figures, the mean values are
plottedassymbols,withverticalbarsindicatingthevariationfromthemean. Itshouldnotedthatallthefiguresshowing
FUN3Dresultshavethecomputedresultsplottedthiswayforanglesofattackaround15◦;howeverthevariationisreally
onlyperceptibleonthepitchingmomentplots,indicatinghowsensitiveanindicatorpitchingmomentis.
The PAB3D solutions were computed over a nominal angle of attack range of −12◦ to +36◦. As with the FUN3D
cases, the exact range varied with Reynolds number, and with mesh. On Grid 1, the ranges was α = 0◦ to α = +15◦
forRe = 2.47×106. OnGrid2M,therangewasα = −12◦ toα = +36◦ forRe = 3.76×106. Inaddition, afew
c¯ c¯
computationswerecarriedoutforRe =3.76×106onGrid2Foverarangeofα=−2◦toα=+16◦toassesstheeffect
c¯
ofmeshsizeontheresults. AllPAB3Dsolutionswereruninatime-accuratemanner. OnGrid1,forRe = 2.47×106,
c¯
mostsolutionswouldnotconvergetoacompletelysteadystate,withsmalloscillationsinforceandmomentcoefficients
beingobserved.ThedataobtainedonGrid1werethereforeaveragedoverthelast500timesteps(outoftypically4000time
steps),andtheseaveragevaluesareplottedinthefigures.SolutionsobtainedonGrid2FandGrid2MforRe =3.76×106
c¯
didconvergetoasteadystateinallcases,sothefinal,steady,forceandmomentvaluesareplotted.
Thenotationfortheexperimentaldatashowninthefiguresisasfollows: 14x22Expdenotesdatatakeninthe14x22-
ST, with SP used to denote data taken with the model on the small post mount (Figure 4), LP used to denote data taken
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withthemodelonthelargepostmount(Figure3);NTFExp,Run24XdenotesdatatakenintheNTFwiththemodelon
theblademount(Figure2), foraparticularrunnumber. Becauseoftheproprietarynatureofthedata, axesshowingthe
forceandmomentdatadonothavescales.
Figures 10 and 11 show the comparison between computed and measured normal force coefficients for these two
Reynoldsnumbers. Thereislittlevariationamongthevarioustunneldataandthecomputations. Theagreementisslightly
betterbetweenthecomputationsandtheNTFdatathanbetweenthecomputationsandthe14x22-STdata. The14x22-ST
data,especiallyforRe =2.47×106,showastrongbreakinslopenearα =22◦,followedbyacontinuationofpositive
c¯
slopebeyondα = 25◦. TheNTFdatawerenotobtainedbeyondα = 16◦, sothereisnowaytoknowifasimilartrend
would be observed in that data set. As for the lower Reynolds number, the computed results do not show this break in
slope. Although not evident in the plot, the PAB3D solutions computed for Re = 3.76×106 on the finer Grid 2F are
c¯
virtuallyidenticaltothosecomputedonthemediumGrid2MovertherangesofanglesofattacksuchthatthetwoPAB3D
datasetsoverlap.
Figures12and13showthecomparisonbetweentheaxialforcecoefficientsobtainedfromCFDandexperiment.Atthe
higherReynoldsnumbers,theaxialforcecoefficientmeasuredinthe14x22-STincreasesbetweenα=12◦ andα=25◦,
but decreases with increasing α after that. As with the normal force coefficients, the computed axial force coefficients
are in better agreement with the NTF data (limited to α < 16◦) than the 14x22-ST data. The PAB3D results computed
on the finer Grid 2F show slightly better agreement with the NTF data than the Grid 2M results, especially in the range
−2≤α≤8◦. Apartfromthehigheranglesofattack(beyond∼α=18◦),thereisasmuchvariationbetweenthevarious
setsoftunneldataasbetweenthecomputedresultsandthetunneldata.
Next,pitchingmomentcoefficientvariationwithangleofattackisshowninFigures14and15. Pitchingmomentisfar
moresensitivetodetailedflowphenomenonthaneithernormaloraxialforce,soitisnotsurprisingtofindmorevariation
inC betweenexperimentaldataandcomputationaldata,thanthedatavariationinC orC .
M A N
At Re = 2.47×106, quite a large difference is observed between the 14x22-ST large-post data and the small-post
c¯
data,particularlyforα < 10◦. TheNTFdata,thoughtakenoveramorelimitedrange,aremuchclosertothe14x22-ST
small-postdata. Ingeneral,theCFDresultsareingoodagreementwiththeNTFdata.
ForRe =3.76×106asimilardiscrepancybetweenthe14x22-STdata(largepostonly)andtheNTFdataisobserved.
c¯
Again the CFD results lie closer to the NTF data than the 14x22-ST data, with the FUN3D results in generally good
agreement with the NTF data. The PAB3D results computed on Grid 2F are nearly identical to those computed on the
coarserGrid2M,althoughthedropinC beyondα<14◦isslightlysteeperonthefinermesh.
M
The pitching moment curves from both the computation and the experiment show a marked variation with angle of
attack, suggesting a significant change in flow features over the BWB configuration as the incidence varies. No visual-
ization is available from the tunnel tests, but an indication of the changes that occur can be seen in the CFD solutions.
Figures16to18showtheprogressioninnear-surfacestreamlinesalongtheuppersurfaceastheangleofattackisraised
from5◦ to10◦ to15◦ atRe = 3.76×106. Atα = 5◦,theflowisattachedeverywhere,withflowpredominantlyinthe
c¯
axialdirection. Astheangleofattackisraisedto10◦,significantspanwiseflowappearsontheoutboardwingpanel. At
α = 15◦,flowseparationoccursneartheleadingedgebreak,asindicatedbythenodeinthestreamlinepattern. Virtually
theentireoutboardwingpanelhasreversed,spanwiseflowatα=15◦. Ofcourse,atsuchahighangleofattackinflight,
leadingedgeslatswouldbedeployedtominimizesuchundesirableflow.
ConcludingRemarks
TheresultspresentedhererepresentafirststeptowardassessingtheusefulnessofNavier-StokesCFDmethodsforthe
predictionofparametersrelevanttoaircraftlongitudinalstability. Fromastaticstabilitypointofview, pitchingmoment
coefficient is arguably the most important longitudinal data obtained from either CFD or experiment. This study has
brought to light that both CFD solutions and the experimental data have significant variations for any given value of the
angle of attack. Hence, not only the CFD solution accuracy should be improved, but the wind tunnel data uncertainties
mustalsobequantifiedsuchthatthecomputationalmethodscanbevalidatedtoahighlevelofconfidence.
Theauthorswouldliketoemphasisthatthescopeofthispaperislimitedandexploratoryinnature,muchmoreremains
tobedone. Thevariationsbetweenexperimentaldatasetssuggestthatmodelmountingsystemshaveasignificanteffect
ontheforcesandmomentsforaircraftconfigurationssuchastheblendedwingbody. ComparingtheresultsoftheCFD
simulations with and without model support may provide a means of correcting the tunnel data to free-flight conditions.
Additional areas of consideration are the effects of turbulence models and grid resolutions in the wake region on the
accuracy of computational predictions. The inclusion of these considerations in CFD simulations using Navier-Stokes
methodsisunderway.
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11Anderson,W.K.andBonhaus,D.L.: “AnImplicitUpwindAlgorithmforComputingTurbulentFlowsonUnstructuredGrid”.Computersand
Fluids,Vol.23,No.1.pp.1-21,1994.
12Anderson,W.K.,Rausch,R.D.,andBonhaus,D.L.:“ImplicitMultigridAlgorithmsforIncompressibleTurbulentFlowsonUnstructuredGrids”.
J.Comp.Phys.Vol.128,1996,pp.391-408.
13Nielsen,E.,Lu,J.,Park,M.,andDarmofal,D.:“AnImplicit,ExactDualAdjointSolutionMethodforTurbulentFlowsonUnstructuredGrids”.
ComputersandFluids,Vol.33,No.9,pp.1131-1155.
14Spalart,P.R.,andAllmaras,S.R.: “AOne-EquationTurbulenceModelforAerodynamicFlows”.LaRechercheAerospatialeNo.1,1994,pp.
5–21.
15Menter,F.:“ImprovedTwo-Equationk-ωTurbulenceModelforAerodynamicFlows”. NASATM103975,1992.
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Modelscale 2% 3%
Wingarea,ft2 S 5.5627 12.5161
Wingspan,ft b 4.800 7.200
Meanaerodynamicchord,in c¯ 21.364 32.046
Length,in l 39.564 59.346
Height,in h 9.660 14.490
Momentref. centerx-coord.,in x 20.927 31.391
mrc
Momentref. centerz-coord.,in z 2.683 4.024
mrc
Table1 Modelreferencevalues.
Balance M Re q ,psf C ,95%confidence,2σ C ,95%confidence,2σ
∞ c¯ ∞ N M
14x22VST-03 0.203 3.76×106 60. ±0.0076 ±0.00042
14x22VST-03 0.134 2.47×106 26. ±0.0175 ±0.00096
NTF-113B 0.20 3.7×106 93.5 ±0.0063 ±0.00039
NTF-113B 0.20 2.47×106 62.4 ±0.0095 ±0.00058
Table2 Balanceaccuracyatselectedtunnelconditions.
Fig.1 Three-viewofBoeingblendedwingbodyBWB-450Lconfiguration.
Fig.2 2%scaleBWBmodelonablade-mountedinstallation Fig. 3 3% scale BWB model mounted on the large-post
intheNationalTransonicFacility(NTF). modelsupportinthe14x22FootWindTunnel.
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Fig.4 3%scaleBWBmodelmountedonthesmall-postmodelsupportinthe14x22FootWindTunnel.
0.2
N M
C C
NTF, Rec=3.7M
14x22,LP,Rec=3.7M
14x22,LP,Rec=2.6M NTF, Rec=3.7M
14x22,SP,Rec=2.6M 14x22,LP,Rec=3.7M
14x22,LP,Rec=2.6M
14x22,SP,Rec=2.6M
-10 0 10 20 30 40 -10 0 10 20 30 40
a ,deg. a ,deg.
0.2
Fig.5 Measurednormalforcecoefficientcomparisonat Fig.6 Measuredpitchingmomentcoefficientcompari-
Re =2.6×106 and Re =3.7×106 with different sonatRe =2.6×106andRe =3.7×106withdif-
¯c ¯c ¯c ¯c
mountingarrangements. ferentmountingarrangements.
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Fig. 7 Structured grid used in PAB3D computations for Fig. 8 Structured grid used in PAB3D computations for
Re =2.47×106(“Grid1”);everyotherpointshown. Re =3.76×106 (“Grid 2F”); every other point shown,
¯c ¯c
correspondingtothemediummesh(“Grid2M”).
Fig.9 UnstructuredgridusedforFUN3Dcomputations.
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BWBNormalForceCoefficients BWBNormalForceCoefficients
N N
C C
Re =2.5x106
c Re =3.7x106
FUN3D c
PAB3D(Grid1) FUN3D
14x22Exp,SP PAB3D(Grid2F)
14x22Exp,LP PAB3D(Grid2M)
NTF Exp,Run242 14x22Exp,LP
NTF Exp,Run240
-10 0 10 20 30 40 -10 0 10 20 30 40
a ,deg. a ,deg.
Fig.10 NormalforcecoefficientcomparisonsbetweenCFD Fig.11 NormalforcecoefficientcomparisonsbetweenCFD
solutionsandwindtunneldataatRe =2.47×106. solutionsandwindtunneldataatRe =3.76×106.
¯c ¯c
BWBAxialForceCoefficients BWBAxialForceCoefficients
A A
C C
Rec=2.5x106 Re =3.7x106
FUN3D c FUN3D
PAB3D(Grid1) PAB3D(Grid2F)
14x22Exp,SP PAB3D(Grid2M)
14x22Exp,LP 14x22Exp,LP
NTFExp,Run242 NTFExp,Run240
-10 0 10 20 30 40 -10 0 10 20 30 40
a ,deg. a ,deg.
Fig.12 AxialforcecoefficientcomparisonsbetweenCFDso- Fig.13 AxialforcecoefficientcomparisonsbetweenCFDso-
lutionsandwindtunneldataatRe =2.47×106. lutionsandwindtunneldataatRe =3.76×106.
¯c ¯c
BWBPitchingMomentCoefficients BWBPitchingMomentCoefficients
M M
C C
Rec=2.5x106 Re =3.7x106
FUN3D c FUN3D
PAB3D(Grid1) PAB3D(Grid2F)
14x22Exp,SP PAB3D(Grid2M)
14x22Exp,LP 14x22Exp,LP
NTF Exp,Run242 NTF Exp,Run240
-10 0 10 20 30 40 -10 0 10 20 30 40
a ,deg. a ,deg.
Fig. 14 Pitching moment coefficient comparisons between Fig. 15 Pitching moment coefficient comparisons between
CFDsolutionsandwindtunneldataatRe =2.47×106. CFDsolutionsandwindtunneldataatRe =3.76×106.
¯c ¯c
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