A rod-linear cascade model for emulating rotor-stator interaction noise in turbofans
A numerical study
Teruna, Christopher; Ragni, Daniele; Avallone, Francesco; Casalino, Damiano
DOI
10.1016/j.ast.2019.04.047
Publication date
2019
Document Version
Final published version
Published in
Aerospace Science and Technology
Citation (APA)
Teruna, C., Ragni, D., Avallone, F., & Casalino, D. (2019). A rod-linear cascade model for emulating
rotor-stator interaction noise in turbofans: A numerical study. Aerospace Science and Technology, 90, 275-288.
https://doi.org/10.1016/j.ast.2019.04.047
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Contents lists available atScienceDirect
Aerospace
Science
and
Technology
www.elsevier.com/locate/aescteA
rod-linear
cascade
model
for
emulating
rotor-stator
interaction
noise
in
turbofans:
A
numerical
study
Christopher Teruna
∗
,
Daniele Ragni,
Francesco Avallone,
Damiano Casalino
DelftUniversityofTechnology,Kluyverweg1,Delft,theNetherlands
a
r
t
i
c
l
e
i
n
f
o
a
b
s
t
r
a
c
t
Articlehistory:
Received27December2018 Receivedinrevisedform4April2019 Accepted26April2019
Availableonline2May2019 Keywords:
Rod-airfoil
Rotor/statorinteraction Linearcascade
Turbulenceimpingementnoise
Thismanuscript presents arod-linearcascade model for emulating rotor-statorinteraction noise.The modelisintendedas atestplatformforstudyingnoisemitigationtechniquesforaturbofanfanstage, while it also extendsthe classical rod-airfoil configuration by consideringa row of blades basedon realistic geometricaldetails. Therod-linearcascade model consists ofarodpositionedupstream ofa 7-bladelinearcascade, suchthatthe rodwake impinges ontothecentral blade.The rodisscaled to obtainafundamentalsheddingfrequencyequaltothefirstbladepassingfrequencyoftheNASA-Glenn Source DiagnosticsTest(SDT) fanstageat
approach condition.
Thecascade bladeprofile isalsobased on the OGV ofthe SDT sampled at90% of the radial span. Subsequently, numerical simulations are performedusing lattice-BoltzmannMethodon acomputationalsetup comprised ofacontractionand atestsectionenclosingtherod-linearcascademodel.Theintegrallengthscalesoftherodwakeandthe meanloadingofthecentralbladehavebeenfoundtobeingoodagreementwiththetrendsobserved intheSDTfanstage.Theprimarynoisesourcesarelocalizedatthecentralbladeleadingedge,although noisepropagationtothefar-fieldisinfluencedbyadditionaldiffractionbytheotherblades.Furthermore, the acoustic-bladerowinteraction causesintense pressurefluctuationwithinthe inter-bladechannels, includinginthosethatarenotdirectlyaffectedbytherodwake.©2019PublishedbyElsevierMassonSAS.
1. Introduction
One of the noise generation mechanisms in an aeroengine is the rotor-stator interaction [1], which involves periodic impinge-mentoftherotorwakeonthestator.Theprocesscausesunsteady loadingonthestatorsurfacefollowedbynoiseradiationwithboth tonalandbroadbandcomponents[2].Rotor-statorinteractionina modern high-bypass turbofan can be found, for instance, in the fanstage,wheretheturbulentfan(rotor)wakeinteractswiththe outletguidevanes(OGV/stator).Theinteractionprocessisalso ex-pectedto become moresignificant asfuture designs are heading towards higher bypass ratio [3], since the increased engine di-ameterwould be accompanied with reducedaxial length dueto weightandstructuralconstraints.Thiscausesthefan waketo be more coherent when impinging the OGV, resulting in increased tonalnoiseproduction.Consideringthistrend,itisofpractical in-tereststo gain further insights on the aeroacoustics of the noise generation mechanism and to explore potential noise mitigation strategies. Nonetheless, investigating a complex system, such as a complete fan stage, may become quite challenging and
expen-*
Correspondingauthor.E-mailaddress:c.teruna@tudelft.nl(C. Teruna).
sive,especiallyinearlystagesofdesign.Instead,itwouldbemore feasible to first examine models based on simplified geometrical elementsthatstillpreservetheflowfeaturesofinterest.Anumber ofmodelshavebeenproposed forstudyingvariousaviationnoise sources,suchasthetandemcylinderconfigurationforlandinggear noise [4–6], therod-airfoil configurationforblade-vortex interac-tioninhelicopterandrotor-statorinteractioninturbofan[7,8],and squarecylinder-wedgeconfigurationforhigh-liftdevicesnoise[9]. Therod-airfoilconfiguration(RAC)hasbeenquotedtobe suit-able foremulating therotor-stator interaction mechanismdueto thequasi-tonalandbroadbandexcitationinducedbytherodwake ontotheairfoil[7,8,10–12].TheclassicalRACconsistsofarod po-sitionedupstream ofan airfoil,anditwasintroduced asa bench-markconfiguration forcomputationalaeroacoustics (CAA)studies onturbulentwake-body interaction[7,13–16].However,thereare various features inherent of the rotor-stator aeroacoustics which areabsentintheRACduetotheusageoftheisolated, symmetri-calairfoil;twoamongwhichwillbeaddressedinthismanuscript. Firstly, typicalstatorvanes inafan stageare designedwithlarge camber, installed athighincidence angle,andarranged ina cas-cade to achieve significant flow deflection. Secondly, the high-solidity environment typical of a fan stage results in significant acousticinteractionsbetweenonebladeanditsneighbors [17,18].
https://doi.org/10.1016/j.ast.2019.04.047
Collectively,theseaerodynamicsandaeroacousticsimplicationsare oftenreferredtoascascadeeffects.
Todemonstratethesignificance ofcascadeeffects,Finez et al. [19] previouslyperformedexperimentalmeasurementonthe trail-ing edge noise of a linear cascade. They observed that Amiet’s isolatedairfoilmodel[20] underpredicted theirmeasurements by 5–20 dB atlowtomidfrequencyranges.Theauthorsobtained bet-terresultsusing themodified Glegg’s cascadetrailingedge noise model[17] withadditionalcorrectionsto compensateforthe im-perfectperiodicityoftheexperimentalsetup.Theyalsodiscovered that the cascadeeffects are moreprominentat frequencyranges where the acoustic wavelength is larger than the blade-to-blade separation.
Meanwhile,other studies haveshownhowgeometrical details mayinfluencethecascadeacousticsresponse,particularlyforthe tonal noise component[21–25]. In a recentstudy, DeLaborderie et al.haveinvestigatedthecambereffectstocascadeacoustics re-sponse [25]. Theyextended theflat-plate-cascade acousticmodel ofPossonet al. [26] byincludingthecambereffects,andapplied the model on a single-stage axial compressor. The results were also compared to CAA (Computational Aero-Acoustics) computa-tionsbasedon3D compressibleNavier-Stokesequations[27].The inclusion of camber effects to the acoustic model was shown to improve the agreement of the analytical model against the CAA results.
Consequently, replacing the isolated airfoil ofthe RAC witha linear cascade is beneficial for obtaining a more representative setup foremulating the fan wake-OGV impingement mechanism, hencetherod-linearcascademodel(RLC).Thecascadeprofileand the forcing period of the rod wake are also derived from those of the NASA-GlennSource Diagnostic Test (SDT) fan stage. How-ever, theRLC only considers one blade that undergoes rodwake impingementforthefollowingreasons:1) it wouldbe difficultto synchronizethephase ofthevortexshedding frommultiplerods to match the phase relation between the wake impingement on one blade and the others,as inthe case of a realturbofan, and 2) toavoidunwantedfeedbackmechanismduetothepresenceof multiplevortexstreetsclosetoeachother[28].Tothisscope,this manuscript aims at characterizing the aerodynamics and aeroa-coustics features of the rod-linear cascade model. The study is performedusingcommerciallattice-Boltzmannsolver,PowerFLOW, toreproducetheRLCsetupascloselyaspossibletoan experimen-tal setting.Moreover, the outlook ofthis studyis to employ the RLCforstudyingtheeffectsofvariousnoisemitigationtechniques inaturbomachinery-likeflowfield,includingpotentialimpactson theaerodynamicperformance.
Thispaperis organized asfollows.Section 2 provides the de-scriptionofthemethodologiesusedinthispaper,includingabrief overview of lattice-Boltzmann method in PowerFLOW, the rod-linear cascadeconfiguration, anddetails of the simulation setup. Section 3 discusses the computational results on the rod-linear cascadetest rig,includingagrid independencestudy.Asummary ofthispaperisreportedinsection4.
2. Methodology 2.1. Numericaltechnique
Thissectiondescribesthenumericaltechniqueofthe commer-cial solver SIMULIA PowerFLOW 5.4b, a solver based on lattice-Boltzmann Method (LBM). The same methodology has alsobeen usedpreviouslyforstudyingtheRAC[14] andthetandemcylinder configuration[6].Furtherdetailsonthemethodologycanbefound in[29].
The LBM is derived from the Boltzmann’s kinetic theory of gaseswhichdescribesthemotionoffluidparticlesonmicroscopic
level,such asrandommovement (i.e.,Brownianmotion)and par-ticlecollision.Thesephenomenacanbemathematicallyexpressed astheBoltzmanntransport equation(BTE),inwhichthestatesof eachparticle(e.g.,positionandmomentum)aregivenas probabil-itydistributionfunctions.Afterneglectingthebodyforces,theBTE ismathematicallyexpressedasfollows.
∂
F∂
t+
V· ∇
F=
C (1)where F
(
x,
t)
istheparticledistributionfunctioninspatial(x)and temporal dimension (t), V is the particle velocity vector, and C is thecollision operator. Withthe LBM approach,the BTEis dis-cretized onto a Cartesian grid (i.e., lattice) where fluid particles areconfinedwithinthenodes,andthevelocityvectorofthefluid particles are limitedto a number of directions.PowerFLOW em-ploys D3Q19 model,which considers 19discrete velocity vectors in 3dimensions, forsolving low Machnumberproblems [14,30]. Themathematicalexpressionforthelattice-Boltzmannequationis givenasfollows.Fn
(
x+
Vnt
,
t+
t)
−
Fn(
x,
t)
=
Cn(
x,
t)
(2) where Fn is the particle distribution function in nth direction withinthelattice, Vnisthediscreteparticlevelocityvectorinnth direction. The left handsideof Eq. (2) isan expression for time-explicit advection with the increment of Vnt (spatial) and
t (temporal).ThecollisiontermCnfollowsthatof Bhatnagar-Gross-Krookmodel[31]: Cn
= −
t
τ
[F
n(
x,
t)
−
F eq n(
x,
t)
]
(3)where
τ
istherelaxationtime whichisafunctionoffluid viscos-ityandtemperature,andFneqwhichistheequilibriumdistribution function. The single relaxationtime isalsorelatedto the dimen-sionlesskinematicviscosityasfollows[32].ν
=
a2sτ
−
t 2 (4) Moreover, forlow Mach number, Feqn is approximated with a second-orderexpansionasfollows[30].
Feqn
=
ρω
n 1+
Vn·
u a2s+
(
Vn·
u)
2 2a4s−
|
u|2 2a2s (5) whereω
naretheweightingfunctionsbasedontheD3Q19model, and as=
√13 is non-dimensional speed of sound in lattice unit. Eventually,macroscopicflowquantities,suchasdensityρ
and ve-locityu,canberecoveredafterobtaining Fn.ρ
(
x,
t)
=
n Fn(
x,
t)
(6)ρ
u(
x,
t)
=
n VnFn(
x,
t)
(7) For highReynolds number flows which are commonin aero-space applications,theVery LargeEddy Simulation (VLES)model based ontwo-equations k−
Renormalization Group (RNG) [33] isemployedfortakingintoaccountthesub-gridunresolved turbu-lencescales.Thek
−
RNG isusedtolocallyadjusttheturbulent relaxationtime
τ
effasfollows.τ
eff=
τ
+
Cμk2
/
where Cμ
=
0.
09 andη
is based on a local strain parameter (k|
S/
|
), a local vorticity parameter (k|
ω
/
|
), and local helicity parameters. Furthermore, a wall function is applied on the first wall-adjacent grid on a no-slipwall. It is based on the general-izedlaw-of-the-wall model[34], extendedto considerthe effects ofpressure gradient andsurface roughness. The wall function is expressedasfollows. u+=
1 kln y+ A+
B,
(9) where A=
1+
f dp dx,
B=
5.
0,
k=
0.
41,
y+=
uτyν
(10a-d)andwhereA isafunctionofthepressuregradient.
TheLBM scheme iscarriedout on a lattice ofcubic elements which are referred to asvoxels (i.e., volumetric pixel). The voxel resolution ina certain region can be adjusted depending on the requireddetail,such that the resolutionofvoxels in adjacent re-gionsisallowedtovarybyafactorof2.Theresolutionisspecified asa numberofvoxels assignedfora certain characteristiclength (e.g.,roddiameterD inthismanuscript).Meanwhile,solidbodies arediscretizedwithplanarsurfaces,referredto assurfels (surface elements),atlocationswhereavoxelintersectswiththesurfaceof thebody.Furthermore,thefluidparticleinteractionwiththesolid surface isgoverned bythe wall boundarycondition, such as par-ticlebounce-backprocess forno-slipwall andspecularreflection for slipwall[32] respectively.
The numericalscheme within LBM isinherently compressible and unsteady. Furthermore, the low dispersion and dissipation propertiesofLBMallowstheacousticfieldto beresolveddirectly within the computational domain (i.e., direct acoustics computa-tion),withacutofffrequencythatcorrespondstoapproximately15 voxelsperwavelength.Duetothisrequirement,usinganacoustic analogyremainsamorefeasibleoptionforfar-fieldnoise compu-tation. For thispurpose, PowerFLOW employs Ffowcs-Williams & Hawkings(FW-H)analogy[35] basedonFarrasat’sformulation1A [36] withforward-timesolution[37],extendedforpermeable sur-faceintegration.
2.2.Therod-linearcascademodel
Thepresentstudyconsidersa setupasshowninFig.1,which consistsofacontractionandatestsectionhousingtherodandthe linearcascade. The setup is alsointended to be an experimental rig for the Anechoic Vertical Tunnel atDelft University of Tech-nology.Thecontraction is1 m longandhasa circularinletwith adiameter of0.6 m anda rectangular outletof 0.4 m wide and 0.25 m high. Consequently, thetest section isdesigned withthe samedimensionsasthecontractionoutlet,withitswidthequalto thespanoftherodandthecascadeblades(i.e.,0.4 m).For com-pensatingthe flow deflection induced by the linear cascade(i.e., 40◦ [38]),thetestsectionincludesacurvedsegmentupstreamof the RLC, where the inflow is turned of the opposite of the flow deflectionangle. Thistreatment also preventsthe outflow ofthe test section frompotentially damaging thewalls ofthe anechoic chamber whenan experimentis performed. The curvedsegment startsat50 mmdownstreamofthetest sectioninletandendsat 180 mmupstreamoftherodcenter.Theradius ofcurvature(i.e., 650 mm)hasbeencarefullychosentoavoidflowseparationwithin thetestsection.
ThecascadeprofilehasbeenderivedfromtheOGVoftheNASA Glenn - Source Diagnostics Test (SDT) rig [39], sampled at 90% of the outer radius. This represents the location where the fan wake-OGVinteraction isstrongerduetotherelatively highmean
Fig. 1. Technicaldrawingofrod-linearcascadeexperimentsetup,dimensionsarein mm.
velocity,yettheinterferencefromthebladetipremainsnegligible [38].The SDTOGV profileisscaledat1:1andextrudedtoobtain ablade thatspans400 mm withconstant chord.The solidity(
σ
) ofthe OGV inthe SDT rigat theselected radial location is1.
22, which corresponds to the blade-to-blade separation of 32.5 mm. With the given cascade solidity, 7 blades can be accommodated withinthetestsection.Thebladesareinstalledatanincidenceof 1◦ to achieve the blade outlet angleas measured from previous numerical studies on the SDT rig [38,40]. 29◦ stagger angle has beenchosentoensurethatthebladeleadingedgesarepositioned attheidenticalstreamwisedistancefromtherod.Thisstagger an-gleisdifferentthantheoneappliedontheSDT(i.e.,11◦),however itwillbeshownlaterthattheloadingontheOGVoftheRLCand theSDTremaincomparable.Additionally,zig-zagtrippingelements [40] havebeeninstalledonboththepressureandsuctionsidesof the blades at10% chordlength toforce laminar-turbulent transi-tion.The rod is mounted upstream of the cascade with 41 mm separation in between the rod base and the central blade lead-ing edge. The rodhas a diameter of D
=
5.
2 mm such that the mean vortex shedding frequency matches with the first blade-passage-frequency (BPF-1)ofthe SDTfan stage(≈
2.
87 kHz [39]) at the freestream velocity U∞ of 75 m/s. The U∞ is chosen to be slightly lower than that measured in the SDT fan stage [38] at approach condition (i.e., 61.7% of maximum RPM) due to the limitation of the wind tunnel facility where the experiment is planned.The resulting Reynoldsnumber basedon therod diam-eter is ReD=
26600), which fallsinto the shear layer transition regime [41]. Thus, a vortex shedding Strouhal number based on theroddiameterStD ofaround0.
19−
0.
2 isexpected[41,42].A close-up schematic of the rod-linear cascademodel is pro-vided in Fig. 2, in which the coordinates have been normalized withtheroddiameterD.Thefigurealsodescribestwocoordinate systems.Thefirstisthelocalcoordinatesystem( X andY ),whose X axisisalignedwiththeinflowvector.Thelocalcoordinate sys-tem is inclined at
γ
=
40◦ against the global coordinate system ( XG andYG) whose XG is alignedwiththe cascadeoutletangle. Thus,γ
isequaltothe flowdeflectionangleinduced bythe cas-cade. The Z axis forboth coordinate systems are coinciding and thusdoesnotrequireseparatenomenclature.Thelocalcoordinate systemshouldbetakenasthedefaultthroughoutthismanuscript unlessotherwisespecified.Fig. 2. Detailsonpositioningoftherod-linearcascadecomponentswith3outof the7bladesareshown.
It is also convenient to define a blade nomenclature system sincethere are anumberofblades to bereferred to. Thecentral bladereferstotheonewhoseleadingedgeislocatedatY
/
D=
0, whiletheother bladesaregivenletters(T - top,B- bottom)and numbers(1,2,and3- thehigherthenumberthefurtherawaythe bladeisfromthecentralblade).2.3. Numericalsetup
A lateral cutaway of the computational domain is shown in Fig. 3. The simulation domain is a box that is 3.85 m long in the XG direction, and2.6 m in both YG and ZG directions. The RLC setup is placed inside the domain such that the contrac-tion inlet coincides withthe upstream boundary. The mass flow boundaryconditionisspecifiedatthecontractioninlettoachieve U∞
=
75 m/s atthe contractionexit (i.e.,test section inlet). The downstream boundary is an outlet where atmospheric pressure (i.e.,p∞=
1 atm)isspecified.Alloftheotherboundariesare spec-ifiedasinletwithzerovelocity.Solidbodies,includingthe contrac-tion,testsection,rod,cascadeblades,andzig-zagtrips,areno-slip walls.Anacousticbufferzoneisdefinedbeyondtheouterradiusof 100D (i.e.,thebufferzoneboundaryisshowninFig.3),wherethe centerislocatedat60D downstream ofthecentralblade trailingFig. 4. Acutplaneshowingthegridarrangementatthedomainmidspan.Theinset showsaclose-upviewontheregionboundedbytheredbox.(Forinterpretationof thecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.) edge. The bufferzone dampens outward-traveling acoustic waves aswellasinward-reflectedwavesfromthedomainboundaries.
Thedomaincontainsatotalof12gridrefinementregionswith thesmallestcellsizebeing0
.
016D.Consequently,theaverage y+ ofthefirstwall-adjacentcellis8 ontherodandtheleadingedges ofthecentralblade,blade T1,andbladeB1;the y+ ontheother bladesistwiceasmuchduetocoarsergridresolution.Grid refine-mentisalsoperformedsurroundingthecontractiontoresolvethe boundarylayerdevelopmentupstreamofthetestsection.The dis-cretization strategy results ina total of 645×
106 voxels forthe finest grid resolution, and an example of the voxel arrangement surroundingtheRLCisshowninFig.4.Agridindependencestudy has beenperformedto verify theconvergence trendof the solu-tions,anditwillbediscussedinthesubsequentsection.Far-field noise computation is performed using a FW-H inte-gration surface that encloses the exterior of the test section, as shown in Fig. 5. Parts of the FW-H surface that intersects with nonquiescent flow field should be removed to eliminate the ef-fects of pseudo-sound (e.g., hydrodynamic fluctuations) [43,44]. These parts are located at1) upstream ofthe rod-linear cascade model where the FW-H surface intersects with the test section,
Fig. 5. FfowcsWilliams–Hawkingspermeablesurfacesetupwith7capsareshown. Thecontractionishiddenfromtheview.ThemainFW-Hsurfaceisshownas wire-framewithtransparentsurface.
and2) downstreamofthetest sectionoutletwherethe jetshear layerfromthetestsection permeatestheFW-H surface. Unfortu-nately, removalof the latter would reduce the measurement ac-curacy at shallowangles closeto the test section outlet [45,46]. Consequently,theFW-Hcaps areappliedontopofthemain per-meablesurfacetofilterpseudo-soundcontamination.Thecapsare planarsurfacesthat are stacked inthestreamwise directionwith asmall separation(i.e., 20 mmor3
.
85D) inbetween. The sepa-rationwouldcausethehydrodynamicfluctuationsto berecorded byeachcapwithtemporallag.Thislagissignificantlyshorterfor thepassingacousticwavessincethespeedofsoundismuchfaster thantheconvectionvelocityofthehydrodynamicfluctuations.This resultsinthepseudo-sound signal tobe averagedout during the FW-Hcomputation,whiletheacousticonesarepreserved.Subsequently,far-fieldnoiseisevaluatedon31probesthatare placedonan arclocatedatthe midplaneofthe testsection. The radiusof the arcis1 m withthe originlocated atthe centerof therod. Thearc’szero-anglereferenceisalignedwithpositive XG axis.Theprobesarespreadacrosstherangeof
[−
150◦,
150◦]
and an increment of 10 degree. The permeable surface records2800 samplesat56.5 kHzfor 160vortexshedding cycles (i.e.,56 ms). AFourieranalysisoftheacoustics timeseriesis performedusing Welch’spowerspectraldensityestimatewith50%overlapbetween FFTbins, resultingin soundspectra withfrequency resolutionof 51.4 Hz.Unlessspecified,thepowerspectraldensityisnormalized inlogarithmic scalewith referencepressureof20 μPa, whilethe frequencyisexpressedasStrouhalnumberbasedontherod diam-eter(StD).After an initial transient, the simulation is carried out for 56.7 ms,which isequivalent to162vortex shedding cycleofthe rodwake.Thetotalsimulationtimewouldallowreliableacoustics measurementforfrequenciesaslowas300 Hz.Allsimulationsare carried out on a parallel computing facility running 200-core of Intel-SandybridgeXeonE5-2660.
2.4.Gridindependencestudyandverification
Agridindependencestudyhasbeenconductedwiththree dif-ferentgrid resolutions, namely coarse, medium, andfine with re-finementratioof
√
2 inbetween.Asummaryofthetestmatrixis providedin Table1.The convergence trendofthe computational domain will be examined based on two aspects of the solution, aerodynamicsandfar-field acoustics.Unless specified,the results shownhasbeenobtainedusingthefinestgridconfiguration. 2.4.1. AerodynamicsoftherodandthecentralbladeThespanwisecorrelationofsurfacepressurefluctuationsonthe rodhasbeenobservedtoaffectthestatisticalbehavioroftherod wake [7,42,47], and therefore,should be well-resolved to obtain
Fig. 6. Spanwisecorrelation ofrodsurfacepressure fluctuation. Therod ReD is
26600 inthepresentsimulation.
Table 1
Domainspecificationsforgridconvergencestudy.
Type Resolution (voxels/D) Voxel count (106) CPU hours (103)
Coarse 62.5 107 7.4
Medium 88.4 300 29.4
Fine 125 645 118
accuratethree-dimensionalcharacteristicsofthevortexstreet.The cross-correlation of the surface pressure fluctuation (Rp p ) at a locationshiftedby
Z relativetoareferencelocation Zrefis math-ematicallyexpressedasfollows.
Rp p
(
Zref+
Z)
=
p(
Zref+ Z
)
p(
Zref)
p(
Zref)
p(
Zref)
(11) wherep
(
Z,
t)
=
p(
Z,
t)
−
p(
Z)
(i.e.,pressurefluctuation surround-ingatime-averagedvalue),and·
istheensembleaverage opera-tor.The referencepoint Zref islocated atthemidspanoftherod, 90◦awayfromthemeanstagnationpoint.The results are shown in Fig. 6,in which the spanwise coor-dinate has been non-dimensionalized with rod diameter D. The fine caseis shownto produce good agreement against other ex-perimental measurements on isolated rodat subcritical Reynolds numberrange[42,47].Thediscrepanciesthatarepresentmightbe attributed to the weak feedback from the airfoil downstream as observedbyJianget al.[15].
The interaction betweentheturbulent rodwake andthe cen-tral blade is reflected by the surface pressure statistics. The grid convergencetrendsofthemeanandroot-mean-square(RMS) fluc-tuations of the surface pressure on the central blade are shown in Fig. 7. The mean pressure coefficient is defined as Cp,mean
=
(
p−
p∞)/(
0.
5ρ
∞U2∞
)
,whiletheRMSofthepressurefluctuationsis normalized as p RMS
/(
0.
5ρ
∞U2∞
)
. In general, the trend showsconsistent results among the three resolution levels, except for the p RMS of the coarse case that overpredicts the other results. Thismightbecausedbytheinsufficientresolutiontoproperly re-solvetheturbulentstructuresshedbythetrippingelements,since Fig. 7(ii) showsthat the p RMS ofthe coarse simulationmatches theothersquitewellupto X
/
C=
0.
1 wherethe trippingelement islocated.Thisis alsoevidentinFig. 8(i)inwhich acontinuous streakof highvorticity region can be observedto originate from thetrippingelements.Thisstreakappearsto besimilarinnature to a shear layer, however, itis not present in both medium andFig. 7. MeanandfluctuationRMSofsurfacepressureonthecentralblade.The distri-butiononthepressuresideisindicatedwith×,whilethesuctionsideisunmarked. finesimulations,resultingina moresimilar p RMS distributionfor bothcases.
2.4.2. Far-fieldacousticswithFW-Hanalogy
The presentstudy employs FW-H caps to filterpseudo-sound duetothe jetshearlayer fromthetest sectionoutletinteracting with the FW-H permeable surface. The FW-H results have been shownto converge asthe numberof caps is increased[46]. The convergencetrendfortheRLCsetupisshowninFig.9intermof overallsoundpressurelevel(OSPL).Whennocapisused,theOSPL isunderpredictedinthedirectionsthatareclosetothenormalof themissingcap (e.g.,
[−
30◦,
30◦]
). Conversely,using asingle cap results inoverprediction dueto the additional contribution from thepseudo-sound associatedwiththe jet shearlayercoming out fromthetestsection.Nonetheless,thefigureshowsthat7capsare sufficientforobtainingconvergedOSPLatallobservationangles.The soundpowerlevel (PWL)can be usedto evaluate the ef-fect of varying grid resolution on the overall characteristics of thesoundsources.ThePWL isevaluated throughasummationof
Fig. 9. EffectofthenumberofFW-Hcapsonthefar-fieldoverallsoundpressure level(OSPL).
sound intensityovera spherical domeenclosing the test section. The dome has a radius of 1 m relative to the rodcenter and it sweeps afullcircleintheazimuthal directionbutislimitedfrom 0◦to150◦inthemeridiandirection.Thedomesurfaceisthen dis-cretizedintoarectangulargridwithaprobelocatedateachvertex with10◦increment.Thisdiscretizationstrategyresultsinatotalof 491probes.
The PWL spectra in Fig. 10 exhibits good convergence trend, especiallybetweenmediumandfinecases.The fundamentaltone levelandthefirstharmonicsareidenticalacrossthethreegrid res-olutions. The coarse case, however,shows lower broadband level across thespectraasthecorresponding gridresolutionisless ca-pable at resolving fine turbulent structuresin therod wake that areresponsibleforbroadbandnoisegeneration;thisisalsoclearly showninFig.8.ThePWLspectraoftheRLCischaracterizedby a broadbandbaseataround60 dB,andnarrowbandpeaks surround-ing StD
=
0.
2, 0.
4, and 0.
6 thatcorrespond to the fundamental frequencyandtheharmonicsoftherodwakeshedding.The reliabilityoftheFW-H resultsisalsoassessed by compar-ing withacousticinformationextracteddirectlyfromthe compu-tationaldomain(i.e.,directacousticscomputation–DAC).TheDAC probesareplacedataradiusof0.6 mfromtherodcenter,which isstill locatedoutsideoftheacousticbufferzone.Theprobes ac-quire 1400 samples ata samplingrateof 28.3 kHzforthe same sampling length as the FW-H permeablesurface. The results are showninFig.11wheregenerallygoodagreementcanbeobserved forvariousmeasurementangles.Thediscrepancyathighfrequency rangesiscausedby thelowercutofffrequencyoftheDACprobes,
Fig. 8. Comparisonofspanwisevorticity(ωZ)contourbetweenvariousvoxelresolutionsettings.These instantaneoussnapshotsweretaken atapproximatelythesame
Fig. 10. Theconvergencetrendoftheacousticssourcepowerlevel(PWL)against variousgridresolutions.
sincetheyarelocatedatregionwithcoarsergridresolution com-paredtothatwhichenclosestheFW-Hpermeablesurface. 3. Resultsanddiscussions
3.1.Velocityfieldstatisticsandintegrallengthscalesintherodwake
ThemeanandRMS statisticsofthevelocityprofilewithin the test section are shown in Fig.13. The mean streamwise velocity u and the RMS of the velocity fluctuations u RMS are normalized against freestream velocity U∞
=
75 m/s, andthe tangential co-ordinatewith theroddiameter D.Meanwhile, Fig. 15showsthe velocity fluctuationsspectra in selected locationswithin the test section.TheselocationsarealsodepictedinFig.12.The velocity profile in the test section upstream of the rod ( X
/
D= −
7) is shown to be uniform, aside froma small region in proximity of the boundary layer edge at Y/
D=
20, where the mean velocity is 3% higher than U∞. The turbulence inten-sity along the height ofthe test section also remains below 1%. The velocity fluctuation spectra at a further upstream location ( X/
D= −
10,
Y/
D=
0) in Fig.15showsthepeaks corresponding totherodsheddingfrequencyanditsharmonics.Thisislikelydue toacousticwavesfromthecentralbladesince theturbulent fluc-tuationsintheareaisrelativelylow.InFig.13(ii),the rodwakecan beidentified asthedeficitin the mean streamwise velocity, and the increased turbulent fluc-tuation. An inset in the u RMS profile visualizes a pair of peaks that corresponds to the shear layer from the upper and lower sidesoftherod. Thevelocity fluctuationspectra intherodwake (Y
/
D=
0) is dominated by the broadband components although thetonal peaksare still distinguishable.Outside ofthe rodwake ( X/
D=
4,
Y/
D=
15), thebroadband levelismuch lower, similar tothat upstream oftherod( X/
D= −
10,
Y/
D=
0). Thisalso in-dicatesthatthepeaksinthespectraattheselocationsarecaused byacousticwaves.Thevelocityprofileinsidethecascadechannelsispresentedin Fig.13(iii). TheRMSvelocityplotclearlyshowsthatonlythe in-ner channelsadjacent to the central blade are influenced by the rodwake;theotherchannelshaveverysimilarmeanvelocityand turbulentfluctuationprofiles(seeFig.14).Thisobservationis con-sistent with the spectra in Fig. 15 where the PSD level within thecentralblade - blade T1channel( X
/
D=
10,
Y/
D=
3) is sig-nificantly higher than that in the blade T2 - blade T3 channel ( X/
D=
10,
Y/
D=
15).Moreover, thePSD level upstream of theblade T2 - blade T3 channel( X
/
D=
4,
Y/
D=
15)above StD>
0.
5 isalsohigherthanFig. 11. ComparisonbetweenresultsofFW-Handdirectacousticscomputationfor the“fine”gridconfigurationatvariousmicrophoneanglesandradialdistanceof 0.6 m.
thatinside thechannel( X
/
D=
10,
Y/
D=
15).Thediscrepancyis likelytobeduetothecompactnessoftheacousticwavesrelative tothebladechordlength.Sincethebladechordcorrespondstothe wavelengthatthefrequencyofStD=
0.
58,acousticwavescloseto or higherthan thisfrequency wouldbe diffracted less efficiently bythecascadeblades.Plot(iv)ofFig.13depictstheflowfieldatthetestsection out-let. Due to the cascade stagger angle setting, the height of the test sectiondownstream ofthecascadeisnarrowerby 30%. Con-sequently, the mean velocity at the test section outlet becomes significantly higher than U∞.The influence ofthe rod wakecan stillbeobservedatthislocationasthebumpsurroundingY
/
D=
0 in the RMS velocity plot. The velocity fluctuation spectra at the centeroftheoutletisshowntobebroadbandinFig.15,implying that the coherence ofthe large scalevortices in the rodwake is lostafterimpingingthecentralblade.Spanwise vorticity (
ω
z) contour andλ
2 [48] iso-surface are showninFig.16toillustratetheinstantaneousflowfieldin prox-imity ofthe rodand the central blade. The rod sheds turbulentFig. 12. Sampling locations of velocity statistics shown in Fig.13and15.
Fig. 13. Profilesofmeanaxialvelocity(U/U∞)androot-mean-squareofvelocity fluctuations(u RMS/U∞)measuredatvariousstations throughoutthemidspanof
thetestsection( Z/D=0).
Fig. 14. AcloserlookatthevelocityprofilesofFig.13(iii).Thelocationsofeach bladearealsoindicated.
Fig. 15. Powerspectraldensityofstreamwisevelocityfluctuationatthemidspanof thetestsection.
Fig. 16. Instantaneous contour of spanwise vorticity (ωz) at the midspan and
lambda-2iso-surface(λ2= −3×109s−2)withy=0 planeincludedfor
highlight-ingthewakepattern.Theiso-surfaceisshownupto±5D inthespanwisedirection. Bothcontourscorrespondtothesametimeinstance.
Fig. 17. Cross-correlationcoefficientsRm
i j(x)ofthethreevelocityfluctuation
compo-nentsandthecumulativelengthat2D upstreamofthecentralblade.
Table 2
Theintegrallengthscalesofwithintherodwakeat D distanceupstreamofthe centralbladeleadingedge.
Present Podboy et al. [52]* Casalino et al. [51]+ LX uu 4.78 mm 4.65 mm 6.50 mm LY v v 3.78 mm – 4.50 mm LZ w w 3.64 mm – 6.80 mm
* HotwiremeasurementinsidetheNASASDTrig. +
LBM/VLESsimulationoftheNASASDTrig.
vortices which are then impinging the leading edge of the cen-tral blade. The vortices are severely deformed andbroken down intosmalleddiesastheyinteractwiththeleadingedge,producing soundintheprocessasdescribedbyPowell’sanalogy[49].Fig.16 alsoshowsthattheunsteadyrodwakedoesnotappearto contam-inatetheflowfieldinthecascadechannelsexceptthetwonextto thecentralblade.
Theturbulentwakeimpingingonthecentralbladeleadingedge canbecharacterizedusingtheintegrallengthscales Lm inmth di-rection,usingtheestimationprocedurebasedoncross-correlation proposed by Gea Aguillera et al. [50]. The integral length scales areexpressedasinEq. (12).Thesamemethodwasalsoappliedin similarstudies[40,51,46]. Lmi j
(
x)
=
∞0 Rmi j
(
x)
dx=
∞0 u i
(
x+
sem)
u j(
x)
u i
(
x)
u j(
x)
dx (12)
whereRmi j
(
x)
isthecorrelationcoefficientbetweenthetimeseries atlocationsalong x, u i and u j are the turbulent velocity fluctu-ationcomponents inith and jth directionsrespectively, em isthe unitaryvectorinmthdirection,s istheseparationfromareference locationx,and·
istheensemble-averagingoperator.The cross-correlation is computed based on a reference posi-tionlocatedatD distanceupstreamofcentralbladeleadingedge. Fromthereferenceposition,50 pointsare spreadalongthe posi-tivestreamwise ( X ),tangential (Y ),andradial ( Z )directions.The separationbetweeneach pointis 0
.
02D in thestreamwisedirec-Fig. 18. Meansurfacepressuredistributionatthemidspanoftherodandthe cas-cadeblades.
tion and0
.
1D in both the tangential andradial directions. After-ward,1600samplesofthecorresponding velocityfluctuationsare retrievedat28.6 kHzfromeachpoint.The results of Eq. (12) are shown in Fig. 17 and the length scalesaresummarizedinTable2.Theresultsarealsocomparedto other studies conductedwiththe NASA-GlennSDT fanstage [51, 52]. It is importantto note, however, that the length scale esti-mate of Podboyet al. [52] is based onthe averaging ofvelocity fluctuationspectraatagivenlocation(i.e.,autocorrelation)inthe limitofzerofrequency.Thisestimatewasconsideredtobe unsuit-ableinthepresentstudyduetothefactthatthesamplingtimeof asimulationistypicallymuchshorterthanthatofanexperiment, whichwouldlead tounreliablespectralaveraging atthelow fre-quencyranges.Casalinoet al. [51] also usedthecross-correlation procedureandfoundthattheirresultsoverestimatethatofPodboy et al.Nevertheless,allresultsshowsimilarorderofmagnitudeand trend,e.g.,thelengthscaleintheaxialdirectionislongerthanin theotherdirections.Thisinformationwouldbeusefulfor design-ing relevantnoise mitigation technique,such asthe leadingedge serrations[50,51,53].
Fig. 19. Comparisonofthedistributionofthesurfacepressuredifferencebetween pressuresideandsuctionsideoftheRLCcentralbladeandtheNASASDTOGV.
Fig. 20. RMSsurfacepressuredistributiononthecentralblade,bladeT1,andblade B1.
3.2. Surfacepressurestatistics
Themeansurfacepressurecoefficientonboththerodandthe airfoil are shown in Fig. 18. Jiang et al. [15] has previously ob-servedthatastheseparationbetweentherodandthedownstream body becomes larger than 6D, the rod pressure distribution ap-proachesthatofanisolatedrod.Thisisconsistentwiththepresent resultinFig.18(i)sincetherod-centralbladeseparationis8D in presentcase. Therodof theRLCalsoshow very similarpressure distributioncompared tothat oftheRAC[15,54], whichmay im-plythatthecascadeoftheRLCdoesnotaffecttheroddifferently thanthatoftheRAC.
Themeanpressurecoefficientofthecentralbladeiscompared withtheadjacentblades(i.e.,bladeT1andB1)inFig.18(ii).The freestream velocity used for normalizing the surface pressure of the central blade, however, is 0
.
9U∞. This is obtained by time-averaging thestreamwise velocity componentat 2D upstream of thecentralbladeleading edge.Theresultingscaledpressure coef-ficientresemblesthat oftheT1andB1blade,whichisconsistent withtheobservationsinprevioussectionthattherodwakecauses momentumdeficitintheflowfieldsurroundingthecentralblade.It is alsointeresting to compare the loading characteristics of thecentralbladetotheOGVoftheSDTfanstagesincethepurpose of usinga detailed geometry isto approach therealistic operat-ingcondition ascloseaspossible.Thiscomparisonisprovidedin Fig. 19 in term of
Cp,mean, which is the difference of pressure coefficient between the pressure and suction sides of the blade (Eq. (13)).
Cp,mean is thennormalizedwiththe maximumvalue foreachrespectivecase(i.e.,max
(
Cp,mean)
).Fig. 21. Far-field soundspectraand OSPLdirectivitypattern measuredat anarc alongthemidplaneofthetestsection.
Table 3
MeanandfluctuationstatisticsofliftanddragcoefficientsoftheRLCcomponents. CL,mean CD,mean C L,RMS C D,RMS Rod ≈0 1.22 0.16 0.019 Central blade 1.18 0.52 0.16 0.066 Blade T1 1.53 0.64 0.11 0.051 Blade B1 1.54 0.64 0.12 0.069 Blade T2 1.52 0.65 0.07 0.035 Blade B2 1.54 0.66 0.10 0.059
Cp,mean
=
Cp,mean|
pressure−
Cp,mean|
suction (13) The comparisonshowsacceptableagreement exceptat X/
C=
0.
2 andatdownstreamof X/
C=
0.
4.Theformermayhavebeen caused due to the tripping element used in the RLC, while the latter could be associatedwith the discrepancyin the flow field characteristicsdownstreamoftheblademid-chordduetodifferent staggeranglesettings.Fig. 22. Far-field sound spectra at selected directions. Plots (ii) to (v) provide zoomed view at frequency bands as specified in Fig.21. The surface pressure fluctuations distribution is illustrated in
Fig.20,where p RMS hasbeennormalized with0
.
5ρ
∞U2∞.As ex-pected,the rodwakecauses highlevel ofpressure fluctuation at thecentralbladeleading edge.Nonetheless,thefluctuation inten-sity decreases immediately further downstream, which indicates thattheunsteady loadingassociatedwiththerodwake impinge-mentislocalizedattheleadingedgeregion.Anotherspikeisalso observed nearby the central blade trailing edge which might be caused by the turbulent structures over the central blade inter-actingwiththetrailingedge.Meanwhile, thepressurefluctuation level on the blade T1/B1 is significantly lower, although closer comparisonrevealsthatthesidesofthebladesthatarefacingthe central blade (e.g.,pressure side of blade T1and suction side of bladeB1)experience slightlyhigherlevelcompared tothe oppo-sitesides.A summary on the aerodynamic forces statistics of the RLC componentsare provided inTable 3.The forcesare expressed as liftanddrag coefficientswithrespect tothelocalcoordinate sys-tem.The rodCD,mean is withintheexpectationofan isolatedrod [41,47] and the rod in the RAC [15]. The mean lift anddrag on allbladesarealmostidentical,exceptforthecentralbladethatis undertherodwakeinfluence.Ontheother hand,theRMSforces ontheinner blades(i.e.,T1/B1)isslightlyhigherthanthatofthe outer ones(i.e., T2/B2). Consistentwiththe observationon p RMS distributions in Fig. 20, this implies that the aerodynamic influ-enceofthe rodwake islimitedonlytothechannelsneighboring thecentralblade.
3.3.Acousticsanalyses
Unlikethe RAC,the soundpropagationfromthecentral blade intheRLC isheavily influenced bythe usage ofthecascadeand thetest section. Thisis elaborated further by the far-fieldsound spectrainFig.21(i)andFig.22,andbandwidth-filtereddirectivity patterninFig.21(ii).Furthermore,thedilatationfield (
∇ ·
u)and RMSpressurefluctuation (p RMS) contoursin Fig.23and24 pro-videacousticfieldvisualizationsurroundingtheRLC.Thedilatationfieldisexpressedintermoftime derivativeofpressureasshown inEq. (14) [55].
∇ ·
u= −
1ρ
∞c2 ∞∂
p∂
t (14)where
ρ
∞ andc∞ arefreestreamdensityandspeedofsound re-spectively.Afterward, ∂∂pt isnormalizedusingfreestream dynamic pressure(i.e.,0.
5ρ
∞U2∞)andthecharacteristictime(i.e.,D
/
U∞). The lowest frequencyband (i.e., 0.
02<
StD<
0.
05) is mainly associatedwiththe fluctuationsinside theshearlayer atthetest section outlet, which can be clearly observed in Fig. 23 (i) and Fig.24 (i).Nevertheless,the fluctuationsarenot presentinother higher frequencybands, implying that the soundfrom the shear layerisrestrictedtothelowfrequencyranges.Thefrequencybandsurroundingthefundamentalshedding fre-quency(i.e.,0
.
15<
StD<
0.
25)isshowntodominatethespectra. Thesoundsourceofthisbandcorrespondstotheperiodic upwash-downwashfluctuationsintherodvortexstreetasshowninFig.23 (ii),whicharescatteredbythecentralbladeleading edge. Subse-quently, sound wavesare propagated intothe adjacent channels, diffracted by theneighboring bladesbefore impinging theceiling and the floor of the test section. The acoustic-blade interaction ofthisfrequencybandisalsoresponsible forthehigh p RMS level withintheinter-bladechannelsasshowninFig.24(ii).This phe-nomenonmaybesimilarinnaturetothecascaderesonancewithin theinter-bladechannelsasobserved byParker[56] andmore re-centlybyYokoyamaet al.[57].Nevertheless,thep RMSinthe chan-nels furtheraway fromthe centralbladeis lowerthan thecloser onessincethe aerodynamic excitationislimitedonly tothe cen-tral blade,unlike thecase ofParker andYokoyama in whichthe entirecascadeisexcitedduetovortexsheddingfromeachblade.The smaller eddies within the rod wake are responsible for thenoisegenerationathigherStrouhalbands(i.e.,StD
>
0.
25),as depicted in Fig. 23 (iii). These frequency bands exhibit stronger radiation toward the upper arc in contrast with the lower and midfrequencybands.While thereasonforthisbehaviorremainsFig. 23. Bandpass-filteredcontourofinstantaneousdilatationfieldintermoftime derivativeofpressure.
unclear, it might be associated with the cascade stagger setting andtheinfluenceoftheacousticwavecompactnessrelativetothe blade-to-bladeseparation,whichinturnaffectstheductmode ra-diation from each cascade channel [23]. The high p RMS regions remain present in the frequency band of 0
.
5>
StD>
0.
75 (i.e., Fig.24(iii)),althoughtheextentoftheregionsissmaller,i.e., lim-itedtothechannelsadjacenttothecentralblade.Thedirectivityofthesoundcomingoutofthetestsection out-letisrelativelyuniformatlowfrequencyrangesuptoStD
=
0.
05. Abovethisfrequency, thedirectivity starts totake cardioidshape with the preference towards the lower arc for0.
05>
StD>
0.
5. ThisisclearlyshowninFig.22(iv)inwhichthepeakatStD=
0.
19 isaround 5 dBhigher at−
50◦ comparedto at50◦.Nonetheless, this trend reverses for frequency ranges above StD>
0.
5 where thebroadband sounddistributionis generallyhigher towardsthe upper arc(i.e., in Fig. 22(vi)). Theseasymmetrical radiation be-haviorsmightberelatedtothegeometricalaspectsofthecascade itself(e.g., bladecamber andstaggerangle) [22,23,58], andthese arealsointerestingaspects oftheRLCtobeverifiedinthefuture experimentalstudy.Fig. 24. Bandpass-filtered contour of RMS of pressure fluctuation in decibel scale.
4. Conclusionandoutlook
Thismanuscripthaspresentedanumericalstudyonthe aero-dynamics and aeroacoustics characteristics of the rod-linear cas-cade model(RLC). The flow field was solved using unsteady, ex-plicit solver based on lattice-Boltzmann method, while the far-fieldnoisewascomputedusingtheFfowcs-WilliamsandHawkings analogy.Agridindependencestudyhasbeenperformedtoensure therobustnessofthepresentnumericalsolutions.
Therodhasbeendesignedtoshedturbulentvortexstreetwith a fundamental frequencythat equal to the 1st BPF of the NASA-GlennSDTfanstageatapproach condition.Thecascadeprofileand solidityare alsoderivedfromtheSDT,whichallowed7blades to beusedinsidearectangulartestsection.Thetestsectionhasbeen equippedwithacurvedsegmentupstreamoftheRLCto compen-satetheflowdeflectionproducedbythecascade.Nonetheless,flow fieldassessmentrevealedthatthevelocitydistributionhasbecome sufficiently uniformwithrelatively low turbulentintensity atthe rodlocation.
The rod shed turbulent wake that impinged onto the central bladeleadingedge.Theintegrallengthscaleswithintherodwake were measured and found to follow the trend observed in the SDT fan stage, despite the streamwise length scale being signifi-cantlyunderpredicted.Therodwakeimpingementprocessinduced
strongunsteadypressurefluctuationsonthecentralbladeleading edge,whicharesubsequentlyscatteredassoundwaves.
Surface pressure measurements on the rod revealed that the centralblade didnotcausesignificant feedbackbetweenthe two bodies.However,themeanloadingonthecentralbladewaslower compared to the other blades due to the momentum deficit in-ducedbytherodwake.Nevertheless,byusingnormalizationbased onthelowermeanvelocityintherodwake,thecentralbladeand theadjacentbladeswerefoundtohavesimilarloading characteris-tics.Consistently,themeanforcesactingontheblades,exceptthe central blade,were identical,while the forcesRMS were slightly higherforthoselocatednexttothecentralblade.
Acousticanalyseshaveshownthattheinstallationandcascade effectshaveasignificantinfluenceonthefar-fieldsound character-istics.Thefrequencyband surroundingthefundamental shedding frequencydominatedthesoundspectrainallmeasureddirections, whereastheinstallation effectassociatedwiththejet shearlayer atthetestsection outletwaslimitedtothelowfrequencyranges. Furthermore,thecascadeeffectscausedhighpressure fluctuation inside the inter-blade channels, including those that are not di-rectly perturbed by the rod wake. The pressure fluctuation level wasobservedtobelowerinchannelsfurtheraway fromthe cen-tralblade,aswellasathigherfrequencyranges.
Toconclude,theRLCisasystemthatcouplestwoaeroacoustics phenomena, namely the leading edge noise generation by inter-actionwithoncomingturbulence,andtheacoustics-blade interac-tions dueto theusage of highsoliditycascade. Since these phe-nomenaareinherentinfanwake-OGVinteractionmechanism,the RLCpresentstheopportunityasatestrigforexploringnovelnoise mitigationtechniquesforapplicationsinfutureturbofans.Itisalso conjecturedthatnoisereductionwithintheRLCcouldbeachieved withthe following mechanisms: 1) dampening the surface pres-surefluctuation at the leading edge (e.g., withporous materials [59]),2) enhancing decorrelation or phase interferenceeffects of theturbulenceimpingementprocess(e.g.,withleadingedge serra-tions[53]),and3)reducingthecascadeeffects(e.g.,withacoustic treatmenton theblade surface [60]).Furthermore,future studies usingtheRLCwouldalsoallowelucidating theimpact ofvarious noisemitigationstrategiesontheOGVperformancesincethe geo-metricaldetailsarepreserved.
DeclarationofCompetingInterest
Theauthor(s)declare(s)that thereisnoconflictofinterest re-gardingthepublicationofthisarticle.
Acknowledgement
Thisstudyissupported by theproject SMARTANSWER(Smart Mitigation of flow-induced Acoustic Radiation and Transmission forreducedAircraft, surface traNSport,Workplaces andwind en-ERgynoise)whichhasreceivedfundingfromtheEuropeanUnion’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curiegrant agreementNo. 722401. Moreinformation canbefoundonhttps://www.h2020-smartanswer.eu/.
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