NASA Technical Reports Server (NTRS) 20170001424: Approach to Modeling Boundary Layer Ingestion Using a Fully Coupled Propulsion-RANS Model Approach to Modeling Boundary Layer Ingestion Using a Fully Coupled Propulsion-RANS Model

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by  NASA Technical Reports Server (NTRS)

Approach to Modeling Boundary Layer Ingestion using a Fully
Coupled Propulsion-RANS Model
JustinS.Gray,*
NASAGlennResearchCenter,PropulsionSystemsAnalysisBranch,ClevelandOH
CharlesA.Mader†,GaetanK.W.Kenway†,JoaquimR.R.A.Martins†‡
UniversityofMichigan,DepartmentofAerospaceEngineering,AnnArborMI
Airframe-propulsion integration concepts that use boundary layer ingestion have the potential to reduce aircraft
fuel burn. One concept that has been recently explored is NASA’s Starc-ABL aircraft configuration, which offers
the potential for 12% mission fuel burn reduction by using a turbo-electric propulsion system with an aft-mounted
electrically driven boundary layer ingestion propulsor. This large potential for improved performance motivates a
moredetailedstudyoftheboundarylayeringestionpropulsordesign,buttodate,analysesofboundarylayeringestion
have used uncoupled methods. These methods account for only aerodynamic effects on the propulsion system or
propulsion system effects on the aerodynamics, but not both simultaneously. This work presents a new approach
for building fully coupled propulsive-aerodynamic models of boundary layer ingestion propulsion systems. A 1D
thermodynamic cycle analysis is coupled to a RANS simulation to model the Starc-ABL aft propulsor at a cruise
conditionandtheeffectsvariationinpropulsordesignonperformanceareexamined. Theresultsindicatesthatboth
propulsion and aerodynamic effects contribute equally toward the overall performance and that the fully coupled
modelyieldssubstantiallydifferentresultscomparedtouncoupled.Themostsignificantfindingisthatboundarylayer
ingestion,whileofferingsubstantialfuelburnsavings,introducesthrottledependentaerodynamicseffectsthatneedto
beaccountedfor. Thisworkrepresentsafirststeptowardthemultidisciplinarydesignoptimizationofboundarylayer
ingestionpropulsionsystems.
Nomenclature
()fe quantitycomputedatthefan-exitboundary
()ff quantitycomputedatthefan-faceboundary
()prop quantitycomputedfromthepropulsionmodel
() freestreamquantity
∞
δ boundarylayerheight
m˙ massflowrate
η adiabaticefficiency
a
η propulsiveefficiency
p
residualfunction
R
ρ airdensity
A referencewingarea
ref
C forcecoefficientforforcesgeneratedbythefuselage
F-fuse
C forcecoefficientforforcesgeneratedbythepropulsor
F-prop
C netforcecoefficient
F-x
d nacelleouterdiameter
nac
*AerospaceEngineer,NASAGlennResearchCenter,PropulsionSystemsAnalysisBranch,AIAAMember
†ResearchInvestigator,DepartmentofAerospaceEngineering,AIAASeniorMember
‡Professor,UniversityofMichigan,DepartmentofAerospaceEngineering,AIAAAssociateFellow
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F forceintegratedoverthefuselage
fuse
F forceintegratedoverthepropulsor
prop
F netforceintegratedoverthebody
x
P staticpressure
s
P totalpressure
t
T totaltemperature
t
V airspeed
FPR fanpressureratio
I. Introduction
Althoughboundarylayeringestion(BLI),orwakeingestion,hasbeenwellstudiedformarineapplicationssince
the 1960s [1, 2, 3] it has not yet seen wide-spread adoption in aircraft applications. However, recent studies have
consideredseveralnewBLI-basedaircraftconfigurationsthatcouldofferareductioninaircraftfuelburnbetween5%
and 12% [4, 5, 6]. This dramatic reduction in fuel burn is achieved via tight integration of the propulsion system
andairframeaerodynamics,butactuallyrealizingsuchlargeperformancegainsrequiresmodifyingtheaircraftdesign
process to account for this integration. Traditionally, in aircraft design, the airframe and the propulsion system are
designedseparatelyandthentheenginesizingismanagedusingsimplethrustscaling.Thisworkswhenthepropulsion
systemisplacedinfree-streamair,awayfromtheaerodynamicinfluenceoftheairframe,anditisreasonabletoassume
thatsmallchangestoeithersystemdonotaffecttheother.
BLIsystemsinvalidatethisassumptionbydesign. In1947, thefirsttheoreticalstudyofBLInotedthatitwould
introduceasignificantdependencebetweenaircraftdragandengineairflow[7]. DecadeslaterSmithandRobers[8]
quantifiedthisinteractionfromthepropulsionsystemperspective,byrelatingthepropulsiveefficiencytoasetofnon-
dimensionalviscouswakeparameters. Theyfoundthattheoverallpropulsiveefficiencycanriseaboveoneinsome
cases.TheseeffortshighlightstheprimarychallengeofmodelingaircraftmissionperformanceinthepresenceofBLI:
theaerodynamicmodelsmustbeafunctionofpropulsionmassflow,andthepropulsionmodelsmustbeafunctionof
the the boundary layer profile. Drela [9] proposed a control volume approach to the aerodynamic bookkeeping as a
waytoside-stepthisissue. Anotherapproachforamoreunifiedbookkeepingistousetheexergyconcepttoquantify
theoverallefficiency[10,11].
Despiteaddressingthethrustanddragaccountingproblem,thesemethodsrequirethatsomelevelofpropulsion-
aerodynamiccouplingismodeledtocapturethemultidisciplinaryinteractionsthatimpactonaircraftperformance. A
number of studies considered the effects of BLI from a quasi-single disciplinary perspective that only captures part
ofthecoupling. Hardinetal.[12]analyzedtheeffectoftheboundarylayervelocityprofileonfanperformancefor
atraditionalturbofanpropulsionsystem, butdidnotpassthepropulsiondatabackintotheaerodynamicstocapture
the drag effects. Kim and Liou [13, 14] performed a series of aerodynamic shape optimizations on NASA’s Hybrid
WingBody(HWB)withBLIpropulsionsystemsusingpoweredboundaryconditions,butdidnotconsiderpropulsion
designvariables. Blumenthaletal.[15]analyzedatailconethrusterontheCommonResearchModelgeometryusing
anactuatordiskapproachandfoundthatshapeoptimizationofthetailconeofferedperformanceimprovementsover
thebaselinedesign,buttheirworkkeptthediameterofandpressurechangeacrosstheactuatordiskconstant,which
amountedtoafixedpropulsionmodel.Therehavealsobeenanumberofpropulsion-centricstudiesonBLIpropulsion
systems,butthesedidnotconsiderthechangestotheflowfieldduetothepresenceoftheengine[5,16,17,4]. All
thesestudiesaremotivatedbytheBLIbenefitsarisingfrominterdisciplinaryinteractions,buttheymakeassumptions
topartiallydecoupletheanalysestomakethemodelingeasier.
Fully coupling the propulsion and aerodynamic analyses presents significant implementation challenges. The
propulsion system can be modeled using relatively inexpensive 1D thermodynamic analyses that work with scalar
values to represent bulk fluid properties. To capture viscous affects on complex 3D geometries, the aerodynamics
modeling requires a RANS simulation. Therefore, a coupling method must be developed to exchange data between
thepropulsiveandaerodynamicmodels. TheneedtoincludeRANSmodelsinthedesignprocessstronglysuggests
theneedtoincludeshapeoptimizationaspartofthedesignprocess,sincetheaerodynamicperformanceissensitiveto
smallgeometrychanges. RANSshapeoptimizationwithrespecttolargenumbersofgeometryvariablesrequiresthe
useofgradient-basedoptimizationwithadjointanalyticderivatives,soaCFDtoolthatprovidesanadjointisrequired.
Duetothepropulsive-aerodynamiccoupling,theaerodynamicadjointaloneisnotsufficient. Afullycoupledanalysis
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requires a coupled-adjoint in order to consider both propulsion and airframe shape design variables. This means
that the propulsion model must also have a correspondent adjoint solver. The coupled adjoint approach, originally
developedbyMartinsetal.[18,19],iswellestablishedforaerostructuralapplications[20,21],buthasnotyetbeen
extendedtoaero-propulsiveapplications.
The above challenges have prevented prior work on propulsion-airframe integration from considering the fully
coupledsystem. TheultimategoalofthisresearchistoaddressthesedifficultiesandperformaMultidisciplinaryDe-
signOptimization(MDO)onNASA’sStarc-ABLconfigurationusingafullycoupledpropulsive-aerodynamicmodel.
However,beforeweperformdesignoptimization,wemustdevelopthecoupledmodel. Thus,thispaperpresentsthe
necessaryfirststep:thedevelopmentofanewcouplingapproachforpropulsive-aerodynamicapplicationsandanasso-
ciatedimplementationbuiltintheOpenMDAOframework[22]. Adesignstudywasperformedtoquantifytheeffects
offanpressureratio(FPR)ontheoverallperformanceofthesystem.Theresultsshowthatthereisastronginteraction
betweenthepropulsionandaerodynamicsdisciplinesthatstronglyimpactsthedesignofBLIpropulsionsystems. By
analyzingthecoupledperformance,wedemonstratethatbothaerodynamicandpropulsiveeffectsareequallysignif-
icant. Furthermore,weshowthatanuncoupledanalysismethodmisseskeymultidisciplinaryinteractionsthatcould
causeaerodynamiceffectssuchasthrottledependentlift,drag,andpitchingmoment.
II. TheStarc-ABLAircraftConfiguration
In2016,NASAdevelopedanewaircraftconfigurationcalledtheStarc-ABL—single-aisleturbo-electricaircraft
withanaftboundarylayerpropulsor—thatincorporatedBLIintoanotherwisetraditionalairframelayoutbyadding
anaft-mountedpropulsor. ThisaircraftisdesignedtocruiseatMach0.72and37,000ftwithawingareaof1400ft2.
ArenderingoftheaircraftconfigurationisshowninFigure1. Starc-ABLusesaturbo-electricpropulsionsystemwith
wing-mountedturbofanenginesthatalsoincludeelectricgeneratorstoprovidepowertoanelectricmotorpowering
theBLIpropulsor.
Figure1: NASA’sStarc-ABLaircraftconcept,incorporatingahybridelectricpropulsionsystemandaft-mountedBLI
propulsor[4]
In their initial design study, Welstead and Felder [4] conclude that this configuration could offer up to a 12%
reductioninfuelburncomparedthesameconfigurationwithamoretraditionalpropulsionsystem. Forthatstudy,the
authorsassumethattheBLIpropulsorwouldalwaysrunwithafixedpowerinputof3,500hp,regardlessoftheflight
speed,altitude,orthrottlesettingoftheengine(exceptatverylowthrottlesettings,wherethepowerrequirementwas
relaxed). TheirpropulsorhadaFPRof1.2,andanadiabaticefficiencyof95.6%.
Theuniqueturbo-electricpropulsionsystemlapsesdifferentlycomparedtoatraditionalunder-wingenginecon-
figuration. ThefixedshaftpowerinputtotheBLIpropulsorcausesittolapsemuchlessthanifitwerepoweredby
a traditional gas turbine. The power for the aft propulsor is produced by generators integrated into the under-wing
engines. Thegeneratorsaddanadditionalloadtothethelowspeedspoolandcausetheenginestolapsemorequickly
thannormal. Thismeansthatatlowaltitudesandspeeds—suchastake-off—theBLIpropulsordoesnotprovideas
significantaportionoftheoverallthrust. However,astheaircraftclimbsandincreasesspeed,BLIpropulsorbegins
to contribute a larger share of the overall thrust. According to Welstead and Felder [4], the BLI propulsor provides
only20%oftheoverallthrustduringtake-off,buttowardstheendoftheclimbitprovides44%. Thismeansthatthe
performanceofthepropulsorismuchmoreimportantatcruisethanitisduringtake-offandclimb.
ThelargeshareofthrustgeneratedbytheBLIpropulsoratcruiseisultimatelywhatenablesthesignificantmission
fuel burn reductions of this configuration. Hence the design of that propulsor is vitally important to the overall
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performanceandviabilityoftheconcept,butaspreviouslyexplained,itisalsooneofthemostchallengingaspectsto
addressbecauseofthecouplingbetweenthepropulsionandaerodynamicsanalyses.
Inthiswork,webeginafullycoupleddetailedstudyoftheBLIpropulsorbyconsideringasimplifiedgeometryof
anisolatedaxisymmetricfuselageatzeroangleofattack. Althoughthissimplifiedgeometrycannotbeconsideredan
aircraftconfigurationsinceitdoesnotprovideanyliftandisnotstable,thisrepresentsthesimplestcasewherewecan
capturetheprimaryinterdisciplinaryinteractionsforaBLIpropulsorontheStarc-ABLconfiguration. Aprofileview
ofthesimplifiedconfiguration,alongwithkeydimensionsareshowninFigure2.
Figure 2: Axisymmetric fuselage with aft mounted BLI propulsor representing a simplified Starc-ABL configuration.
Forforceaccounting,thebluesectionisconsideredtobefuselageandtheorangesectionisconsideredtobepropulsor.
III. Modeling
A. PropulsionModel
TheBLIpropulsorismodeledusingthe1DthermodynamiccycleanalysistoolpyCycle[23,24]. pyCycle,whichis
developedusingOpenMDAO,allowsforflexiblemodelingofpropulsionsystemsbyprovidingalibraryofdifferent
cycle elements (inlet, compressor, combustor, nozzle, duct) that can be combined to model a specific propulsion
system. pyCyclealsoprovidesadjointanalyticderivativesforitscomputations,whichwillenableoptimizationwitha
fullycoupledpropulsive-aerodynamicadjointinfuturework.
The propulsor model in the present work is comprised of a single compressor representing the fan. The model
inputsareFPR,andtotaltemperatureandpressureatthefan-face. Theoutputsarethetotaltemperatureandpressure
at the fan exit, and the mass flow rate the fan can sustain for a fixed shaft power of 3,500 hp. Welstead and Felder
selected 3,500 hp in their original work by sizing their propulsor to capture about 70% of reduced speed air. Their
motivationbehindthischoicewasbasedonananalysisindicatingthatthatincreasingthepropulsordiameterbeyond
thatlevelwasgeneratingonlymarginalgains. Forthisworkthatassumptionwasretained,althoughfutureworkwill
allowshaftpowertovary.
Thefanadiabaticefficiency(η )iscomputedasafunctionofFPR.AtalowerFPRlessflowturningisrequired
a
andhenceahigheradiabaticefficiencycanbeachieved. Weassumethefollowinglinearrelationshipbetweenη and
a
FPR,
η =1.066 0.0866FPR, (1)
a
−
whichmatchestheassumptionsmadeinWelsteadandFelder’swork.
B. BLIAerodynamicModel
TheaerodynamicmodelusestheRANSsolverADflow[20,25], whichprovidesanefficientviscousadjointandan
in-memoryinterfacetoPythonthatgreatlysimplifiestheintegrationwithOpenMDAO.Theaxisymmetricgeometry
allows for a small structured, multiblock mesh with 170,000 cells. On a desktop computer with 3.6GHz, 4 core,
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Intelcore-I7processorand8GBofmemorythismeshcanbeconverged10ordersofmagnitudeinapproximately2
minutes.
Figure3:FFDblocklayoutdefiningthegeometryparametrization. BluenodesdefinetheFFDboxesthatmovetoallow
propulsorscaling.Rednodesareheldfixedtomaintainthefuselageandnozzlepluggeometry.
The initial geometry for this model was designed to be similar to a Boeing 737-900 in fuselage length and di-
ameter. Free-formdeformation(FFD)wasusedtoparameterizetheBLIpropulsordiameter. Thiswasaccomplished
by defining an FFD that rigidly translates the top of the nacelle up or down to scale the propulsor. Figure 3 shows
the layout of the FFD boxes that parameterize the geometry, where the blue nodes are the corners of the boxes that
translateupanddowntoscalethenacellediameter. Therednodeswereheldfixedtomaintainthefuselageandnozzle
pluggeometry. Infuturework,additionalcontrolpointscanbeadded,andbothredandbluenodescouldbevariedto
achievemoredetailedshapecontrol.
Thepropulsionrelatedinputsarethediameterofthenacelle(d )andthetwoboundaryconditionsthataccount
nac
forthefan: fan-faceandfan-exit,asshowninFigure2. Thefan-faceisanoutflowboundarycondition(flowleaving
theCFDdomain)wherethestaticpressureisspecified. Thefan-exitisaninflowboundarycondition,wherethetotal
pressureandtemperaturearespecified. Themodeloutputsintegratedforcesonthewholebody,F . Themodelalso
x
outputsforcesbrokendownintofuselage(F )andpropulsor(F )components. F iscomputedasthenetforce
fuse prop fuse
integrated over the blue surfaces in Figure 2. F is computed as the net force integrated over the orange surfaces
prop
in Figure 2. Traditionally, F would be called “drag” and F would be called “thrust”. However, for a BLI
fuse prop
configuration,thrustanddragarenolongerindependentquantitiesandthereforecannotbeneatlyseparated. Thus,we
usethisforcenamingapproachtodrawacleardistinctionandhighlightthecouplednatureoftheforces.
Theaerodynamicmodelalsooutputstheintegratedmassflowratesacrossboththefan-faceandfan-exitboundary
conditionsandthemass-averagedtotalpropertiesatthefan-faceboundaryconditions. Takingamass-averageofthe
total properties, as apposed to an arithmetic-average or area-average, is important for keeping a conservative data
transferbetweentheaerodynamicandpropulsionanalyses.
C. PoddedConfigurationAerodynamicModel
To provide a consistent point of reference modeled with the same tools and assumptions as the BLI configuration,
we constructed an aerodynamic model emulating a conventional podded configuration. This model consists of two
separatesimulations: oneforthecleanfuselageandoneforthepoddedpropulsor,asshowninFigure4.
Inthisdecoupledconfigurationwecanassumethattheaerodynamicperformanceofthefuselageandthepropulsor
areindependentofeachother. UsingthecleanfuselagewecancomputeabaselineF andthentheF ofthepodded
fuse x
configurationcanbefoundbysummingF withtheF fromaconvergedsimulationoftheindependentpropulsor.
fuse prop
Other than replacing the fuselage with a rounded spinner in the podded propulsor model, the geometry of the
nacelle and boundary conditions are identical between the BLI and podded aerodynamic models. This allows the
sameFFDparameterizationtobeusedforbothmodels,andalsomeansthesamecouplingschemeisusedforboththe
BLIandpoddedconfigurations.
D. FullyCoupledModel
Before describing the coupling method used in this work, we clarify what we mean by “coupled” and “uncoupled”.
Wedefineacoupledmodeltobeonewheredataispassedbetweentwoormoreanalysesinareciprocalmanner,so
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Figure4:Poddedpropulsorconfigurationwithcleanfuselage(top)anddetailedviewofthepropulsor(bottom).
that some form of iteration (manual or automatic) between the analyses is required to reach physical compatibility.
Wedefineuncoupledanalysistobeoneinwhichdataispassedthroughsequentiallyfromonemodeltoanother,and
thusitcanbesolvedwithasinglepassthroughthemultidisciplinaryanalysis.
Therehasbeensomerecentworkdevelopingcoupledpropulsion-aerodynamicmodelsforsupersonicapplications.
Heath et al. [26] manually coupled a RANS analysis to a propulsion model by matching the flow areas and states
between the two and using the propulsion model to predict the static pressure for the fan-face boundary condition.
Thisworkcomparedtheinstalledperformanceandsonicboomfortwodiscreteinletdesigns,andthelimitednumber
of configurations made manual coupling a reasonable approach. Connolly et al. [27] developed a transient coupled
modelusinganEuleraerodynamicmodelwith1Dgas-dynamicspropulsionmodelforaero-propulso-servo-elasticity
applications.Theyiteratebypassingboundaryconditionvaluesattheinterfacesbetweenthetwomodelsateverytime
steptocomputestatederivativesforthetimeintegration. Theworkhereusesasimilarschemetotheonedeveloped
byConnollyetal.,wherethermodynamicstatesareexchangedbythetwomodels. However,themethodsdifferinkey
implementation details. Their implementation integrates the propulsion model directly into the aerodynamic solver,
includingthecouplingtermsasadditionalstatevariablestobeconvergedwiththerestofthesimulation. Themethod
used in this work relies on the OpenMDAO framework to manage the multidisciplinary analysis and converge the
simulation[22]. Thisapproachislessintrusive,requiringnomodificationstoeitheranalysiscodeandallowingfora
morecomplexsolverstructure.
ff , ff pyCycle m˙ prop,Pfe,Tfe
RPt RTt t t
Broyden d ,Pff
nac s
Rpm˙rop Ptff,Ttff Rdnac,RffPs ADflow
Figure5:XDSM[28]forthecoupledpropulsion-aerodynamicanalysis.
Thefullycoupledpropulsion-aerodynamicsimulationwasbuiltwithatwo-levelsolverschemeshowninFigure5,
that was used for both the podded and BLI configurations. The top level is converged by a nonlinear Gauss–Seidel
solver that manages three residuals defined by the coupling variables: fan-face total pressure (Pff), fan-face total
t
temperature (Tff), and propulsor mass flow rate (m˙prop). The inner level is converged using a Broyden solver that
t
handles two additional residuals: ff and . The mass flow rate between the fan-face and fan-exit boundary
RPs Rdnac
conditionsisbalancedbyvaryingfan-facestaticpressure(Pff)toconvergethe ff :
s RPs
ff =m˙ff m˙fe. (2)
RPs −
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Themassflowratebetweentheaerodynamicandpropulsionsimulationsisbalancedbyvaryingthenacellediameter
(d )toconverge ff :
nac Rdnac
=m˙prop m˙fe. (3)
Rdnac −
This last residual is formulated based on the assumption of a fixed input shaft power of 3,500hp. This provides a
convenient way to compare different propulsor designs. Since they all have the same amount of input power, the
configurationthatprovidesthehighestoverallF isthemostefficient.
x
Notethatanalternatereferencepointisalsopossiblewherethepower(andhencem˙prop)wouldbevariedtodrive
F =0. Inthiscase,thedesignwiththelowestpowerinputtothepropulsorwouldbethemostefficient. Ultimately,
x
thisapproachwasdiscardedbecausetheStarc-ABLreliesonmorethanjusttheaftBLIpropulsorforitsthrust,asit
alsoreliesonapairofunder-wingengines. Itsnotyetclearwhatthebestthrustsplitbetweentheunder-wingengines
andBLIpropulsorwouldbe,andthefixed-powerschemelendsitselfmorenaturallytoaproblemformulationwitha
variablethrustsplit.
IV. Results
We conducted a trade study by performing a parameter sweep of FPR from 1.2 to 1.35 and then comparing the
performance of the podded configuration to that of the BLI configuration. For the podded configuration we assume
thatchangestothefuselageonlyaffectF ,andchangestothepropulsionsystemonlyaffectF . WithBLI,this
fuse prop
assumptionis nolonger validand themetric ofperformance isbasedon thenet-force inthe axialdirection (F ) on
x
thecombinedfuselage-propulsorsystem. HoweveritisstillusefultoexamineF andF tounderstandhowthese
prop fuse
quantitiesvaryacrossthepropulsordesignspaceandhowthenetperformanceisachieved.
Allresultsarepresentedasforcecoefficientsnon-dimensionalizedasfollows:
2f
C = . (4)
F ρ V2A
∞ ∞ ref
Inourconventionthesignoftheforce,andofthenon-dimensionalcoefficientaswell,indicatesthedirectionofaction.
Positivevaluesrepresentforwardforcethatcauseacceleration. Negativevaluesrepresentbackwardforcethatcause
deceleration. Thephysicalvaluesusedtonon-dimensionalizetheforcesarelistedinTable1. Itisimportanttonote
thatweretainthisconventionevenwhenbreakingF intoF andF ,soitisexpectedthattheF bepositive
x prop fuse prop
andF benegative.
fuse
Table1:Referencevaluesforforcenon-dimensionalization.
ρ 0.0008slug/ft3
∞
V 707.3ft/sec
∞
A 1400ft2
ref
Whenworkingwithforcecoefficientsitiscommonreferto“countsofforce”, whichare104 C . Theresults
f
×
presented below show that the BLI system outperforms the conventional podded configuration by at least 5 force
countsacrosstherangeofFPRdesignsconsidered,andthattheaerodynamicsandthepropulsiveimprovementsboth
contributeequallytothegains. Thus,afullycoupledanalysisisnecessarytoaccuratelycapturethefullBLIeffect.
TheaerodynamicbenefitoftheBLIconfigurationisshownqualitativelyinFigure6,whichplotscontoursofMach
number. Thebottomimagerepresentsthecleanfuselage,themiddleoneisaBLIconfigurationwithaFPRof1.35,
and the top one is a BLI configuration with a FPR of 1.2. As the FPR is reduced, for the same input power to the
fan,themassflowrateincreases,requiringalargernacelle. Thediameterofthenacellehasastronginfluenceonthe
heightoftheboundarylayerontheaftfuselage. Thelargestnacelle,fortheFPRof1.2,alsohasthethickestboundary
layer. Theboundarylayerheights(δ)measuredatthenacellelipforthethreeconfigurationsarelistedinTable2. The
boundarylayergrows15%betweenthepoddedconfigurationandtheBLIconfigurationwithaFPRof1.35,whilefor
theFPR1.2designitgrowsby25%. Thisvariationintheboundarylayerprofileasafunctionofthenacelledesign
demonstratesasensitivityoftheaerodynamicstothepropulsiondesignvariable(FPR).
A. NetforceasafunctionofFPR
The clean fuselage produces a net force of F = F 2,331lbs. For the BLI configuration, the net force was
x prop
−
computedviaintegrationofthepressure,viscous, andmomentumforcesonthewholebody. ThecomparisonofF
x
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Figure6:ConvergedflowsolutionsforFPR=1.2(top),FPR=1.35(middle),andthecleanfuselage(bottom)designs
Table2:BoundarylayerheightatthenacellelipforpoddedandBLIconfigurations.
configuration δ(ft) %change
podded 4.0
BLI,FPR1.35 4.6 15%
BLI,FPR1.2 5.0 25%
between the podded and BLI configurations is show in Figure 7. The primary conclusion from Figure 7 is that BLI
offers an additional 5 to 6 of net force counts. That represents a 33% improvement in performance relative to the
conventionalpoddedconfiguration. Thedataalsoshowstwokeytrends:first,forthepoddedconfigurationnetforceis
insensitivetoFPR;second,theBLIconfigurationclearlyperformsbetterforlowerFPRdesigns. Wecangainfurther
insightintothesetrendsbybreakingC downintoC andC componentstolookatthecontributionsfrom
F-x F-fuse F-prop
eachdiscipline.
B. PropulsorforceasafunctionofFPR
Figure8showsthevariationofthepropulsorforcewithFPRforbothpoddedandBLIconfigurations. Forthepodded
configuration, where F is constant, all the variation in C is due to changes in F at different FPR designs.
fuse F-x prop
Figure8showsthatthereisonlya.2forcecountvariationinF asafunctionofFPRforthepoddedconfiguration.
prop
Thisresultmightbesurprisingifviewedfromapurelythermodynamicperspective. Thermodynamicswouldpredict
F increasingasFPRisloweredduetohigherpropulsiveefficiencyandahigheradiabaticefficiency—definedby
prop
Eqn. (1). However, the coupled analysis accounts for both thermodynamic and aerodynamics effects, and while the
netthrustdoesgoup,thenacelledragalsoincreasesbynearlyasmuch. Hence,theneteffectisafairlyflatresponse,
withslightlybetterperformancetowardsanFPRof1.25. ThedragincreasesforlowerFPRdesignsbecausethereisa
strongershockontheoutersurfaceofthenacelleforthelargernacelles,asseeninFigure9.
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Figure7:Netforceonthebody(fuselageandpropulsor)asafunctionofdesignFPR.
Figure8:Forceintegratedoverpropulsor(C )asafunctionofdesignFPR.
F-prop
Thepresenceofthatshockinbothconfigurationsindicatesthatthenacellegeometryisnotideal. Infact,wecan
seethatthesameeffectispresentfortheBLIconfigurationbylookingatFigure6,wheretheareaofhighspeedflow
islargerfortheFPR1.2configurationontop. Althoughwewouldnormallyexpectthelargernacelleforalargerfan
tohavemoredrag,itispossiblethatsomeoftheadverseaffectwouldbemitigatedbyabettergeometry. Futurework
willuseshapeoptimizationtoallowforoptimalinletnacelleshapingforeachdesign.However,sincethissub-optimal
inletdesignisusedforallthecasespresentedherein,ourperformancecomparisonisvalid.
ThepropulsorforcetrendfortheBLIconfigurationinFigure8showsadifferentresultthanthetrendinFigure7.
For FPR=1.35, the BLI configuration outperforms the podded configuration by 3.9 force counts. For FPR=1.2, the
difference is 3.3 force counts. Although this variation is small, it is still opposite of the variation of C with FPR.
Fx
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Figure9: ContoursofMachforthepropulsorsimulationontheFPR = 1.2(top)andFPR = 1.35(bottom)designsof
thepoddedconfiguration.
ThisBLItrendoccursbecauseasthenacellegrows,theBLIbenefitbeginstofalloff,sincemoreoftheenginemass
flowisingestedfromhighervelocityair.Hence,theBLIbenefittothepropulsionsystembecomeslesspronouncedfor
lowerFPRdesigns. Additionally,bycomparingFigure7withFigure8,weseethatonlyconsideringtheBLIeffecton
thepropulsionanalysiswouldbothunder-predictthebenefitbyapproximately40%,andresultinadifferentoptimal
FPRvalue.
ThedifferenceinmagnitudeandtrendbetweenC andC highlightstheimportanceofusingafullycoupled
F-prop FX
analysistostudyBLI.Anotherimportantdifferencebetweenuncoupledandcoupledmodelingapproachescanbeseen
by examining the calculation for mass-averaged fan-face total pressure (Pff). For an uncoupled scheme, where we
t
assumethattheaerodynamicsareunchangedfromthepoddedconfiguration,Pffiscomputedasfollows:
t
(cid:82)dnacP (y)m˙(y)dy
Pff(d )= 0 t , (5)
t nac (cid:82)dnacm˙(y)dy
0
where P (y) is extracted from the boundary layer profile of the clean fuselage in the podded configuration and is
t
independentfromanypropulsiondesignvariables. ThismethodwasusedbyWelsteadandFelder[4]intheirstudy
of the Starc-ABL configuration, and by Liu et. al [16] and Laskaridis et al. [17] in their studies of a hybrid wing
bodyturbo-electricdistributedpropulsionconfiguration. WiththefullycoupledanalysisP (FPR,y)andm˙(FPR,y)
t
arenowafunctionofbothpropulsordesignanddiameter,andhencePffbecomes
t
(cid:82)dnacP (FPR,y)m˙(FPR,y)dy
Pff(FPR,d )= 0 t . (6)
t nac (cid:82)dnacm˙(FPR,y)dy
0
Figure10comparesmass-averagedPff asafunctionofFPRbetweenpoddedconfigurationandtheBLIconfigu-
t
ration. TheBLIresultsarecomputedusingbothuncoupled—Eqn.(5)—andcoupled—Eqn.(6)—methods. Forthe
poddedconfiguration,PffisindependentofFPRsincetheinletingestsfreestreamair.TheBLIconfigurationanalyzed
t
using the uncoupled method (dashed blue line), does capture the inverse relationship of Pff with FPR. However, it
t
over-predicts Pff by about 5% compared to the coupled method (solid blue line). Pff has a meaningful impact on
t t
propulsor performance. For an electrically driven propulsor, a 5% lower Pff means 5% lower nozzle pressure ratio,
t
andhencenearly5%lowerthrust. TheeffectwouldbeevenmorepronouncedforaBLIdesignusingaconventional
turbofan,wheretheadditionaltotalpressurelosswouldhaveadirectimpactontheoveralpressureratioandthermal
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