NASA Technical Reports Server (NTRS) 20160007736: Isolated Open Rotor Noise Prediction Assessment Using the F31A31 Historical Blade Set

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by  NASA Technical Reports Server (NTRS)

Isolated Open Rotor Noise Prediction Assessment Using the
F31A31 Historical Blade Set
DouglasM.Nark∗,WilliamT.Jones†,D.DouglasBoyd,Jr.‡,andNikolasS.Zawodny§
NASALangleyResearchCenter,Hampton,VA23681-2199
In an effort to mitigate next-generation fuel efficiency and environmental impact concerns for aviation, open ro-
tor propulsion systems have received renewed interest. However, maintaining the high propulsive efficiency while
simultaneouslymeetingnoisegoalshasbeenoneofthechallengesinmakingopenrotorpropulsionaviableoption.
Improvements in prediction tools and design methodologies have opened the design space for next generation open
rotor designs that satisfy these challenging objectives. As such, validation of aerodynamic and acoustic prediction
toolshasbeenanimportantaspectofopenrotorresearchefforts.Thispaperdescribesvalidationeffortsofacombined
computationalfluiddynamicsandFfowcsWilliamsandHawkingsequationmethodologyforopenrotoraeroacoustic
modeling. Performanceandacousticpredictionsweremadeforabenchmarkopenrotorbladesetandcomparedwith
measurements over a range of rotor speeds and observer angles. Overall, the results indicate that the computational
approachisacceptableforassessinglow-noiseopenrotordesigns. Additionally,thisapproachmaybeusedtoprovide
realisticincidentsourcefieldsforacousticshielding/scatteringstudiesonvariousaircraftconfigurations.
I. Introduction
Inanefforttomitigatenext-generationfuelefficiencyandenvironmentalimpactconcernsforaviation,alternatives
to today’s commonly-used turbofan propulsion systems have received renewed interest. Open rotors are one option
thathavethepotentialtosignificantlyreducefuelburnrelativetoconventionalturbofanengines. Thisadvantagewas
demonstrated as part of a comprehensive study of open rotors in the 1980s by NASA and the U.S. aircraft engine
industry.1,2 However,maintainingthehighpropulsiveefficiencywhilesimultaneouslymeetingnoisegoalshasbeen
oneofthechallengesinmakingopenrotorpropulsionaviableoption.
Improvements in prediction tools and design methodologies have opened the design space for next generation
open rotor designs that satisfy these challenging objectives. As such, NASA and General Electric Aviation recently
embarked on a joint effort to investigate modern blade designs. Validation of aerodynamic and acoustic prediction
toolswasanimportantaspectoftheeffortandabaselinebladesetrepresentativeofearly1990sdesignswasincluded
intesting. Thispaperdescribesacombinedcomputationalfluiddynamics(CFD)andFfowcsWilliamsandHawkings
(FW-H) equation methodology for open rotor aeroacoustic modeling. Specifically, two separate (one structured and
one unstructured) CFD codes were used to predict the aerodynamic performance of the baseline F31A31 blade set.
Resultant blade surface pressure from the aerodynamic predictions were then used as input to two separate FW-H
solvers to predict the open rotor noise source. Predicted and measured performance and acoustic results were then
comparedoverarangeofrotorspeedsandobserverangles(atasingleMachnumberandzeroangleofattack).
Theremainderofthepaperdetailstheaerodynamicandacousticpredictions,aswellastheresultantcomparison
withmeasureddata.TheselectedtestconfigurationandoperatingconditionsofinterestarefirstpresentedinSectionII.
ThisisfollowedbyadiscussionoftheaerodynamiccalculationsinSectionIII.Generationoftheacousticpredictions
andcomparisonwithmeasurementsarethenpresentedinSectionIV.Finally,concludingremarksregardingsomeof
themoresignificantresultsandfurtherareasofinterestarepresentedinSectionV.
∗SeniorResearchScientist,ResearchDirectorate,StructuralAcousticsBranch,AIAAAssociateFellow
†SeniorResearchScientist,ResearchDirectorate,ComputationalAerosciencesBranch,AIAAAssociateFellow
‡SeniorResearchEngineer,ResearchDirectorate,AeroacousticsBranch,AIAASeniorMember
§ResearchAerospaceEngineer,ResearchDirectorate,AeroacousticsBranch,AIAAMember
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II. TestConfiguration
Abladedesigncalledthehistoricalbladeset(alsoknownasF31/A31)waschosentoserveasthebaselineforthis
validationstudy. Thisselectionwasdueinlargeparttothewealthofgeometric,aerodynamic,andacousticdatasets
available. A sub-scale model of this blade set having 12 front rotor blades and 10 aft rotor blades with a diameter
ofapproximately25.6 inches(0.65m)wastestedin NASAwindtunnels.3–5 Thisincludedlow speedtestinginthe
NASA9-ft. x15-ft. (2.7mx4.6m)windtunneltoinvestigateaerodynamicandacousticperformance,aswellashigh
speedtestingintheNASA8-ft. x6-ft. (2.4mx1.8m)windtunnel. Thisworkfocusesontheisolated,zeroangleof
attack low speed configuration as tested in the NASA 9-ft. x 15-ft. wind tunnel (see Figure 1). During this testing,
acousticdatawasacquiredat18microphonepositionsalongalineartraverseoffset5ft. (1.52m)fromthecenterline
of the model. The measurements cover geometric observer angles between 17.6◦(upstream) and 140◦(downstream)
fromtheopenrotoraxis(seeFigure1andTable1).
This study focuses on comparison between the predicted and measured tonal components since these dominate
theacousticspectraforthisbladeset. Inordertomakeadirectcomparisonbetweenthetonalacousticamplitudesof
theexperimentalandcomputationaldatasets,anextractiontechniquewasperformedontheexperimentalnarrowband
acoustic spectra. Following approaches employed by Envia6 and Rizzi et al.,7 a peak-finding algorithm was imple-
mentedtoidentifytonesintheacousticnarrowbandspectra,usingathresholdvalueof2dB.Specifically,thespectral
valueatafrequencybinwasflaggedasa“tone”ifitwasatleast2dBaboveoneofitsneighboringbins. Toaccount
fortheeffectsofspectralleakage,thetotalenergyoftheflagged“tone”wasestimatedasthesumoftheenergyinthe
frequencybinsspanningtwofrequencybinsoneithersideoftheflaggedfrequencybin.
III. AerodynamicPredictions
Bothstructured(OVERFLOW2)andunstructured(FUN3D)computationalfluiddynamics(CFD)codesareused
inthisstudytopredictopenrotoraerodynamicperformanceandobtainbladeloadinginformation.
A. OVERFLOW2
OVERFLOW28–11isathree-dimensionaltime-marchingimplicitNavier-Stokescodethatusesstructuredoversetgrid
systems. Several different inviscid flux algorithms and implicit solution algorithms are included and the code has
optionsforthinlayerorfullviscousterms. Awidevarietyofboundaryconditionsareavailable,aswellasalgebraic,
one-equation, and two-equation turbulence models. Low speed preconditioning is also available for several of the
inviscid flux algorithms and solution algorithms in the code. The code also supports bodies in relative motion, and
includesbothasix-degree-of-freedom(6-DOF)modelandagridassemblycode.
In the current study, OVERFLOW 2 simulations were performed using a dual time-stepping scheme. The opti-
mizedsecondorderbackwarddifferencingformulation(BDF2OPT)wasutilizedwithafixednumberof60Newtonian
sub-iterationsperphysicaltime-step. Asaresultofthisfixednumberofsub-iterations,theL −norm(RHS)orders
∞
of convergence varied between 4 and 7 depending on the simulation case. A local CFL number was determined by
usingthesumofmaximumeigenvalueineachcoordinatedirection,withanupperlimitCFLnumber(CFL )of5.
max
Spatialdifferencingwascarriedoutusingafourthordercentraldifferencingschemeforinviscidterms,andasecond
ordercentraldifferencingschemefortheviscousterms. Theone-equationturbulencemodelofSpalartandAllmaras
alongwithaDetachedEddySimulation(DES)andtherotation/curvaturecorrection(SARC)wasutilized.
Overset grid generation was performed using the Chimera Grid Tools v2.1 software package12,13 and the open
rotor computational grid consists of ten levels, one overset near-body grid level (per surface component) and nine
Cartesianoff-bodygridlevels,totalingapproximately160milliongridpoints. Theoversetnear-bodygridsmakeup
approximately41%ofthetotalnumberofgridpoints.Furthermore,thenear-bodygridsextendoutwardfromtherotor
bladesapproximately30%ofthemeanbladechord(basedontheF31blade),andoutwardfromtherotorcenterbody
approximately1.2meanbladechords. ThefirstlevelCartesianoff-bodygridhasauniformspacingofapproximately
4%ofthemeanbladechord. TheremainingCartesianoff-bodygridsweregeneratedautomaticallybyOVERFLOW
2andextendapproximately30rotortipradiioutwardinalldirections.
Theaerodynamicsimulationsutilized600computercoresontheNASPleiadessupercomputerforallcases.Acon-
vergedsolutionwasfoundtobeconservativelyobtainedinfivefullrotorrevolutionsusingthetime-steppingscheme
discussedabove, regardlessofthephysicaltimestepused. Eachphysicaltimestepinthesolutionrequiredapprox-
imately 60 seconds (one second per sub-iteration) using the BDF2OPT scheme. This resulted in a total simulation
timeof24hoursperrevolutionusinga0.25◦azimuthalresolution,andsixhoursperrevolutionusinga1.0◦azimuthal
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resolution.
B. FUN3D
The FUN3D flow solver14–18 has an extensive set of options and solution mechanisms for spatial and temporal dis-
cretizations on general static or dynamic mixed-element unstructured meshes that may or may not contain overset
meshtopologies. Inthecurrentstudy,thespatialdiscretizationusesafinite-volumeapproachinwhichthedependent
variablesarestoredattheverticesofmixedelementmeshes. Inviscidfluxesatcellinterfacesarecomputedbyusing
theupwindschemeofRoe,19andviscousfluxesareformedbyusinganapproachthatisequivalenttoacentraldiffer-
enceGalerkinprocedure.Theeddyviscosityismodeledbyusingtheone-equationapproachofSpalartandAllmaras20
with the source term modification proposed by Dacles-Mariani et al.21 Scalable parallelization is achieved through
domaindecompositionandmessage-passingcommunication.
Anapproximatesolutionofthelinearsystemofequationsthatisformedwithineachtimestepisobtainedthrough
severaliterationsofamulticolorGauss-Seidelpoint-iterativescheme. Theturbulencemodelisintegratedalltheway
tothewallwithouttheuseofwallfunctions. Theturbulencemodelissolvedseparatelyfromthemeanflowequations
ateachtimestepwithatimeintegrationandalinearsystemsolutionschemethatisidenticaltothatemployedforthe
meanflowequations.
A dual time-stepping algorithm with sub-iterations is used to converge the solution within each physical time-
step. For these simulations, a maximum of 20 sub-iterations per time-step was used. However, a temporal error
controller was used to monitor the sub-iteration convergence history advancing to the next physical time-step when
theflowresidualsdroppedbelowtenpercentoftheestimatedtemporalerror. Avarietyoftimemarchingschemesare
availableinFUN3D,includingasecond-orderbackward-differencingformulation(BDF2),andanoptimizedsecond
orderbackwarddifferencingformulation(BDF2OPT).TheBDF2OPTscheme22waschosenforthecurrentapplication
as it produces lower truncation error compared to the standard BDF2 scheme at nominally the same computational
costbutwithslightlyincreasedmemoryusage.
The generation of the individual components used to define the overset mesh system were performed with the
GridEx meshing framework.23 Surface meshes were generated directly on the Computer Aided Design (CAD) ge-
ometrythroughtheCAPRIinterface24 andleveragingtheVGRIDalgorithm.25 Thevolumemeshesweregenerated
viatheAdvancingFrontwithLocalReconnectionin3D(AFLR3)software.26 Thecompleteunstructuredcomposite
meshconsistedofapproximately103millionmeshverticeswith30%representingthemeshintheimmediatevicinity
oftheforeandaftbladerows. Themaximummeshspacingonallsolidsurfaceswaslimitedto2%ofthemeanblade
chord. Thegeometrymodelincludedthestingaftofthenacellecenterbody,butdidnotconsiderthebladeattachment
tothetunnelfloor. Thus,thecomputationaldomainwasdefinedbyacylinderaboutthecenterbodycenterlinewitha
radiusof40timestheradiusoftheforwardbladerow,extending80F31meanbladechordsupstreamofthenacelle
and160chordsdownstreamofthesting.
TheoversetmeshsystemwasassembledwithSUGGAR++27establishingdomainconnectivityinformationforthe
components. Duetotheperiodicmotionofthegeometryandtheassumptionofrigidblades,thedomainconnectivity
information for the component positions at each time step was pre-computed as a pre-processing step to flow simu-
lation. The domain connectivity information was then loaded from disk at each time-step of the simulation thereby
increasingtheefficiencyofthesimulation.
The aerodynamic simulations utilized 2048 computer cores on the NAS Pleiades supercomputer for all cases
and were run fully dense on Intel Sandybridge processors. A periodic solution was conservatively considered to be
obtained after six full rotor revolutions using the time-stepping scheme discussed above. FW-H data was extracted
onaseventhrevolution. Aphysicaltimestepinthesolutionrequiredapproximately50secondsonaverageusingthe
BDF2OPTschemewithavariablenumberofsub-iterationsdeterminedbythetemporalerrorcontroller. Thisresulted
inasimulationtimeoffivehoursperrevolutionusinga1.0◦azimuthalresolution.
C. AerodynamicResults
Threerotorspeeds,showninTable2,wereconsideredrangingfromtheapproachRPMtothenominaltakeoffRPM.
AsalsopresentedinTable2,thefrontandaftrotorswereoperatedatthesameRPMandwithidenticalbladesetting
angles. The tunnel Mach number (i.e., open rotor “forward flight speed”) was held fixed at 0.2. Rigid blade shapes
correspondingtothoseatthemaximumclimbconditionwerealsousedatalltipspeeds. Therefore,anysmallchange
in“hot”bladeshapeasafunctionofRPMwerenotincluded. Initialaerodynamicpredictionsforbothcodesutilizeda
timeresolutionequivalenttoanazimuthalangleof1.0◦. However,decisionsrelatedtogridgenerationledtodifferent
treatments of the aft portion of the nacelle centerbody as shown in Figure 3. In the OVERFLOW2 predictions, the
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choicewasmadetotruncateandroundtheaftportionofthecenterbodytominimizedownstreamboundaryinfluences.
Incontrast,theFUN3Dpredictionsincludedthefullextentofthedownstreamportionofthecenterbody. Asindicated
insubsequentdiscussionontheacousticprediction(SectionIV),thisdoesnotaffectthegeometryoftheacousticdata
surfaces. Inaddition,becauseonlyisolatedrotorsareconsidered,anyeffectsonscattering/shieldingsurfacesarenot
included. However,itshouldbenotedthatthisdifferenceinaftcenterbodymayeffectthepredictedloadingvalueson
theacousticdatasurfaces.
Comparisonofpredictedandmeasuredtotalthrustandtorqueratio,presentedinFigure4,showthetwocodesto
provideconsistentperformancepredictions.Goodagreementisachievedfortotalthrustwithaslightdiscrepancyatthe
highestRPM.However,lessfavorablecomparisonisachievedforthetorqueratio,particularlyatlowerRPM.Thismay
perhapsbeexpected,asthebladeanglessettingsdigressfromdesignpointastheRPMisreduced.Thismighttherefore
leadtoincreasedflowseparationrequiringenhancedgridresolutiontoproperlycapture. Inlightofthisandstandard
practice,atemporalandspatialgridrefinementstudyisinorder.Suchafullstudyisnotincludedinthiswork,however,
aninitialOVERFLOW2temporalresolutionstudywasundertaken.Assuch,additionalaerodynamicpredictionswere
performedusingtemporalresolutionscorrespondingtoazimuthalanglesof0.5◦and0.25◦.Theresultantperformance
parameter predictions are presented in Table 3. A clear trend is difficult to discern, indicating the need for a fuller
(temporalandspatial)gridrefinementstudy. However,basedonthereasonablecomparisonofperformancemetrics,
theavailableloadingvalueswereusedinsubsequentacousticcalculations.
IV. AcousticPredictions
TheacousticpredictionmethodsusedinthisstudyarebasedontheFW-Hequation,28whichisarearrangementof
theexactcontinuityandNavier-Stokesequationsintoawaveequationforthedensitywithanonlinearforcingterm.
ThroughtheapplicationofgeneralizedfunctionsandaGreen’sfunctiontechnique,thesolutiontotheequationcanbe
reducedtoasurfaceandavolumeintegral. However,thesolutionisoftenwellapproximatedbythesurfaceintegral
alone,asthevolumeintegralincludesphysicaleffectssuchasrefractionandnonlinearsteepening. Whentheseeffects
aresmall,theFW-Hsurfacecancoincidewiththesolidbodygeneratingtheunsteadyflow. Thisisoftenreferredto
asanimpermeabledatasurface. Wheneffectssuchasrefractionareimportant,theFW-Hsurfacecanbepushedout
intotheflowtoencompassimportantflowgradients. Inthiscase, thedatasurfaceisreferredtoasbeingpermeable
(also, penetrable or porous). Hence, the time history of the density, which is directly related to the pressure in the
far-field,canbeobtainedatlocationsfarfromthebodyfromasurfaceintegralthatiseitherclosetoorontheactual
body.Forpermeablesurfacesthatareoffthebody,thetimehistoriesofalltheflowvariablesareneeded,butnospatial
derivativesareexplicitlyrequired. Forsurfacescoincidingwiththebody,onlythepressuretimehistoryisneeded.
ThePSU-WOPWOP(PSW)code29 andtheF1AmoduleofNASA’ssecondgenerationAircraftNOisePrediction
Program(ANOPP2),30 bothimplementingFarassat’sretarded-timeformulation1AoftheFW-Hequation,wereused
aspartoftheacousticpredictionprocess. Inparticular,boththePSWandANOPP2solverswereusedfortheacoustic
predictions based on the structured code (i.e., OVERFLOW 2) loading and the two codes provided nearly identical
results.Therefore,onlyasinglesetofresultsbasedontheOVERFLOW2loadingarepresentedandmaybeconsidered
indicativeofbothacousticpredictioncodes. Conversely,comparisonsoftheacousticpredictionsfortheunstructured
(i.e.,FUN3D)loadingareongoingandonlythoseusingthePSWcodearepresentedherein.
All acoustic predictions were based on impermeable data surfaces. As seen in Figure 5, only the rotor blade
surfaces were included for which the required surface pressure values were provided by the aforementioned CFD
solvers. Inadditiontotherotorsurfaces,theOVERFLOW2datasurfacescontainedaportionofthecollargridsfor
eachblade. Thiswasnecessarytoaccountforthebladerootandtheinclusionofthesmallportionofnacellesurface
had a negligible effect on the acoustic results. In specifying the geometry and loading values for the acoustic data
surfaces,theinformationmaybeconsidered‘constant’,‘periodic’,or‘aperiodic’. Informationspecifiedas‘constant’
isassumedtoremainunchangedforallsourcetimes. Intermsofgeometry,thismeansthatthebladeshapesremain
unchanged as they rotate. For loading specification, the surface pressure values would remain unchanged as the
bladesrotate(aswouldbethecaseifthemeanloadingvalueswerespecified). For‘periodic’data, valuesaretaken
to change as a function of azimuthal angle. Finally, for ‘aperiodic’ data, values are taken to change arbitrarily as a
function of time. As mentioned previously, the blades were assumed rigid, with shapes taken to be the same at all
speeds. Therefore, within the acoustic calculations, the geometry of the acoustic data surfaces could be considered
‘constant’androtatingatthespecifiedRPM.ThismeantthatsurfacegeometryforonlyasingleCFDtimestepwould
beneededasinput. Alternatively,thedatasurfacescouldbespecifiedas‘periodic’andthegeometryforalltimesteps
would be needed. Predictions were performed using both approaches to verify input specification and, as expected,
essentiallyidenticalresultswereobtained.Therefore,theacousticdatasurfacegeometrywasspecifiedas‘constant’in
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subsequentpredictionsduetothereductionininputfilesize. Conversely,thesurfacepressureloadingwastakentobe
‘periodic’(i.e.,changingasafunctionofazimuthalangleandrepeatingonaonce-per-revolutionbasis). Specifically,
time dependent surface pressure loading values for one full rotor revolution were extracted from the CFD solutions
(after suitable convergence was reached) and used as input. Initially, baseline acoustic predictions were performed
using CFD values at 1.0◦azimuthal resolution. Additional predictions were then performed using higher temporal
resolutionCFDresults.
A. BaselineResults
Acoustic predictions were obtained at observer locations corresponding to the 9’x15’ wind tunnel microphone ar-
rangement shown in Figure 2. While the separate thickness (monopole) and loading (dipole) acoustic contributions
areobtainedinthepredictions,onlythetotalvaluesarepresentedforcomparisonwithmeasuredvalues. Inanattempt
to cover a range of possible metrics for prediction assessment, comparisons include the directivity for a number of
dominanttones, tonalamplitudesforasubsetofshaftorders, andoverallsoundpressurelevels. Figure6showsthe
predictedandmeasuredtonesoundpressurelevel(SPL)asafunctionofsidelineangleatthehighesttipspeed(6436
RPM)foranumberofnotabletonesofinterest.Comparisonsbeginwiththebladepassagefrequencyoftheaft(BPF )
2
and forward (BPF ) blade rows and continues through various interaction tones (additive combinations of BPF and
1 1
BPF ).Includedinthecaptionsarethecorrespondingmultiplesoftheopenrotorshaftfrequency(i.e.,shaftorder).For
2
thiscase,theshaftfrequencyis107.3HzandBPF ,forexample,correspondstoashaftorderof10.Ascanbeseen,the
2
individualrotortonescorrespondingtoshaftorder10and12arecapturedquitewell,particularlyaroundthebroadside
angles.Resultsforthefirstinteractiontone,BPF +BPF ,arelessfavorable.However,thetrendsinthedataappearto
1 2
bereasonablywellpredictedovertherangeofinteractiontonesconsidered.Inanefforttoinvestigatethisfurther,com-
parisonofmeasuredandpredictedSPLforshaftordersupto50atupstream(45◦),broadside(90◦),anddownstream
(135◦)observersarepresentedinFigure7. Notethatonlyevenshaftordersarepresentedasthereareanevennum-
berofbladesintheforwardandaftbladerows. Conclusionsconsistentwiththosefromthedirectivityplotsmaybe
drawnfortheindividualrotortones. Theloworderinteractiontones(BPF +BPF ,BPF +2BPF ,2BPF +BPF )
1 2 1 2 1 2
corresponding to shaft orders 22, 32, and 34 are fairly well captured with some over-prediction at select observer
angles. The higher order interaction tones (BPF +3BPF ,2BPF +2BPF ,3BPF +BPF ) corresponding to shaft
1 2 1 2 1 2
orders 42, 44, and 46 are also captured fairly well. However, there appears to be under-prediction of the measured
levelsastheshaftorderincreases. Asimilareffectappearstooccurwiththehigherharmonicsoftheindividualrotor
tones (i.e., nBPF and nBPF ) . While they are captured, there is a generally consistent under-prediction over the
1 2
variousobserverangles. Asthehigherorderinteractiontonesandhigherharmonicsoftheindividualrotortonesare
drivenbytheharmonicsoftheunsteadybladeloading,thesecomparisonswouldlikelyimprovewithincreasedspatial
gridresolution.
Inadditiontospatialgridresolutionmentionedabove,asdiscussedbyEnvia,6aportionofthediscrepanciesnoted
above may also be due in part to blade-to-blade variations within the test hardware. The experimental data shows
tonesatall(bothoddandeven)shaftorders. However,sincethebladecountsareeven,thepredictionscontainonly
evenordertones(whethersumordifference). Thepredictionsassumeidentical(‘constant’)bladeshapes. Incontrast,
theactualtesthardwarelikelyincludessomeblade-to-bladeshapeandanglesettingvariation. Therefore,theprecise
phasingcontainedinthepredictionsdoesnotoccurandacousticenergymaybedistributedacrossallshaftorders.
As shown in Figures 8 and 9 similar observations may be made for the 5551 RPM case. Directivity plots show
individual rotor tones are well captured and the measured data trends appear to be well predicted. Comparison of
tonalSPLalsoshowsimilartrendsoverthevariousobserverlocations. Resultsofextractedlevelsforthe4620RPM
case are similar and therefore are not included. However, to provide further insight, Figure 10 shows comparisons
of the overall sound pressure level (OASPL) in the shaft order range from 8 to 100 for all three rotor speeds. It
shouldalsobenotedthatsincethemeasuredlevelsincludebothtoneandbroadbandcontent,itisnecessarytosubtract
the broadband levels from the measured data before calculating the OASPL. Thus, the presented measured levels
are based on the tone levels obtained from the aforementioned tonal extraction technique (Section II). As seen in
previous comparisons, the measured data trends are captured reasonably well for the two higher rotor speeds. The
two predictions follow very similar trends over these two speeds as well. However, at the lowest RPM case, the
comparisonsdeteriorate,particularlyattheupstreamobserverangles. Itisinterestingtonotethatatthisrotorspeed,
thefirstinteractiontone(BPF +BPF )isastrongcontributortotheOASPLatforwardobserverangles. Asthisisa
1 2
toneforwhichcomparisonsbetweenmeasurementandpredictionwereleastfavorable,thismaybeapossiblecause
forthelargerdiscrepancy. Overall,thepredictedOASPLlevelsgenerallydecreasewithdecreasingrotorspeedasseen
inthemeasuredlevels. However,therateatwhichthemeasuredlevelsdecreasedoesnotmatchthemeasuredvalues,
particularlyattheupstreamobserverangles.
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B. TemporalResolutionRefinement
Previous discussions pointed to the need for a temporal and spatial grid refinement study. While a full study is not
includedinthiswork,aninitialOVERFLOW2temporalresolutionstudywasundertakentobegintheinvestigation.
Thisentailedperformingadditionalaerodynamicpredictionsforthe6436RPMcaseusingtemporalresolutionscor-
respondingtoazimuthalanglesof0.5◦ and0.25◦.Acousticpredictionsusingtheseextractedbladesurfacepressures
werethenperformedfollowingthesameapproachasdescribedabove. Directivityplotscorrespondingtothesepre-
dictions are presented in Figure 11. Here, the measured and baseline 1.0◦ resolution results are again plotted for
comparisonwiththehighertemporalresolutionresults. Ingeneral,theincreasedtemporalresolutiondoesnotappear
tohavealargeeffectonthepredictedresults. Thetrendsinthepredictedvaluesaremaintainedandlargedeviations
inabsolutelevelsaregenerallynotapparent. Oneexceptionisthefirstloworderinteractiontone(BPF +BPF ),for
1 2
whichalargedeviationisevidentatseveraldownstreamobserverangles. Thismay, inpart, betheresultoftheob-
serverangleresolution,asthefeaturemayappearatlowertemporalresolutionsatslightlydifferentobserversangles.
However,astheoveralldirectivityofthistoneisnotwellcaptured,itmayalsobeevidenceoftheneedforincreased
spatialresolution.FurthertonelevelandOASPLcomparisonsarepresentedinFigures12and13,respectively.Again,
similartrendstothosefoundinpreviouscomparisonsareobserved. Thus,asmightbeexpectedfromtheperformance
parametercomparisons,theinitialtemporalgridrefinementdidnotyieldmajorchangesinthegeneralpredictionqual-
ity. However, sincethe initialtemporal resolution waslikely acceptable forthe frequencies considered, future work
onspatialgridrefinementmayyieldmoresignificantmodificationtothepredictions.
V. ConcludingRemarks
In this study, the OVERFLOW 2 and FUN3D codes were used to predict the aerodynamic performance of the
baseline F31A31 blade set. Blade surface pressure results from the aerodynamic predictions were then used with
PSU-WOPWOPandtheF1AmoduleofNASA’ssecondgenerationAircraftNOisePredictionProgramtopredictthe
openrotornoisesource. Althoughpredictionofabsolutelevelsmaybedifficult,comparisonsbetweenmeasurement
andpredictionsindicatethatgeneraltrendswerecapturedfairlywell. Evidenceoftheneedforincreasedspatialgrid
resolution was observed and a more complete grid refinement study will be pursued in future work. Overall, the
resultsindicatethatthecomputationalapproachisacceptableforassessinglow-noiserotordesigns. Additionally,this
approach may be used to provide realistic incident source fields for acoustic shielding/scattering studies on various
aircraftconfigurations.
Acknowledgments
ThisresearchwasfundedbytheAdvancedAirTransportTechnologyProjectofNASA’sAdvancedAirVehicles
Program.
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Figure1: F31A31testhardwareinstalledintheNASA9-ft. x15-ft. windtunnel.
Figure2: F31A31testhardwareinstalledintheNASA9-ft. x15-ft. windtunnel.
(a)OVERFLOW2. (b)FUN3D.
Figure3: Computationalsurfacesforaerodynamiccalculations.
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ObserverAngle[deg] x[m] y[m] z[m]
17.8 -3.907 1.524 0.0
22.5 -2.840 1.524 0.0
30.0 -1.800 1.524 0.0
37.5 -1.146 1.524 0.0
45.0 -0.684 1.524 0.0
52.5 -0.330 1.524 0.0
60.0 -0.040 1.524 0.0
67.7 0.208 1.524 0.0
75.0 0.431 1.524 0.0
82.5 0.639 1.524 0.0
90.0 0.840 1.524 0.0
97.5 1.040 1.524 0.0
105.0 1.248 1.524 0.0
112.5 1.471 1.524 0.0
120.0 1.720 1.524 0.0
127.5 2.009 1.524 0.0
135.0 2.364 1.524 0.0
140.6 2.695 1.524 0.0
Table1: Sidelinemicrophonelocationsinthe9-ft. x15-ft. windtunnel.
FrontRotor AftRotor
Case
NumberofBlades BladeAngle RPM NumberofBlades BladeAngle RPM
1 12 40.1◦ 4620 10 40.8◦ 4620
2 12 40.1◦ 5551 10 40.8◦ 5551
3 12 40.1◦ 6436 10 40.8◦ 6436
Table2: Rotorparametersandflightconditionsconsidered.
Thrust[N] Torque[Nm]
TemporalResolution[deg.]
Rotor1 Rotor2 Rotor1 Rotor2
1.00 1383.7 1401.0 262.8 247.8
0.50 1378.2 1403.2 261.8 248.2
0.25 1379.5 1400.5 262.8 248.9
Table3:PredictedOVERFLOW2performanceparametersforvarioustemporalresolutions(RPM =RPM =6436).
1 2
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(a)Totalthrustproducedbybothrotors. (b)Torqueratio.
Figure4:Measured(9x15)andpredictedF31A31performanceparametersasafunctionofRPM(M=0.2). Predicted
valuesarebasedonOVERFLOW2(OVF)andFUN3D(F3D)loadingobtainedatatemporalresolutioncorresponding
toa1.0degreeazimuthalangle.
(a)Overflow2. (b)FUN3D.
Figure5: Impermeabledatasurfacesusedinacousticpredictions.
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