Numerical investigation of leading edge noise reduction on a rod-airfoil configuration using porous materials and serrations

Delft University of Technology

Numerical investigation of leading edge noise reduction on a rod-airfoil configuration using

porous materials and serrations

Teruna, Christopher; Avallone, Francesco; Casalino, Damiano; Ragni, Daniele

DOI

10.1016/j.jsv.2020.115880

Publication date

2021

Document Version

Final published version

Published in

Journal of Sound and Vibration

Citation (APA)

Teruna, C., Avallone, F., Casalino, D., & Ragni, D. (2021). Numerical investigation of leading edge noise

reduction on a rod-airfoil configuration using porous materials and serrations. Journal of Sound and

Vibration, 494, [115880]. https://doi.org/10.1016/j.jsv.2020.115880

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ContentslistsavailableatScienceDirect

Journal

of

Sound

and

Vibration

journalhomepage:www.elsevier.com/locate/jsv

Numerical

investigation

of

leading

edge

noise

reduction

on

a

rod-airfoil

configuration

using

porous

materials

and

serrations

Christopher

Teruna

∗

,

Francesco

Avallone

,

Damiano

Casalino

,

Daniele

Ragni

Delft University of Technology, Kluyverweg 1, Delft, the Netherlands

a

r

t

i

c

l

e

i

n

f

o

Article history:

Received 7 February 2020 Revised 23 November 2020 Accepted 25 November 2020 Available online 25 November 2020

Keywords: Rod-airfoil Turbulence-impingement noise Porous material Serrations

a

b

s

t

r

a

c

t

A lattice-Boltzmann method has been employed to study the aeroacoustics and aerody- namics of airfoils equipped with leading edge treatments, namely the porous leading edge and leading edge serrations. The present study aims to identify the differences in noise re- duction mechanisms between the two treatments. Within the context of turbomachinery applications, the airfoils undergo aerodynamic excitation due to the impingement of tur- bulent wake shed by an upstream rod. Two airfoil profiles are considered: NACA 0012 and NACA 5406; the latter mimics geometrical features and aerodynamic loading distribution of the outlet-guide vane in a turbofan test rig. Simulations are carried out at a freestream Mach number of 0.22, corresponding to Reynolds number based on the rod diameter of 48 0 0 0. The serrations are designed to follow a sinusoidal planform shape, whereas the porous leading edge is based on a Ni-Cr-Al metal-foam with homogeneous and isotropic properties. It is found that the porous leading edge attenuates noise by dampening sur- face pressure fluctuations due to the reduced blockage effect compared to the solid one. Differently, the leading edge serrations promote destructive interference of noise sources along the span. When applied against turbulent inflow with tonal characteristic, such as that induced by the impingement of Kàrmàn vortex street in the rod wake, the latter is more effective. On the other hand, both treatments are found to produce similar broad- band noise reduction. When comparing aerodynamic performances, it is found that under a lifting condition, cross-flow is present through the porous material which results in lift reduction and drag increase. A serrated porous leading edge is then proposed to com- bine the benefits of the two leading edge treatments. This results in optimal noise reduc- tion performances and lower aerodynamic penalty with respect to the fully porous leading edge.

© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/)

1. Introduction

Turbulence-impingementnoise,alsoreferredtoasleadingedge(LE)noise,isarelevantnoisegenerationmechanismin aircraftpropulsionsystems,such asturbofansandhelicopterrotors. LEnoiseis generatedbythe aerodynamicinteraction betweenasolidbodyandaturbulentinflow[1,2].Inaturbofan,thisprocessoccursastheturbulentfanwakeperiodically

∗_{Corresponding author.}

E-mail address: c.teruna@tudelft.nl (C. Teruna).

https://doi.org/10.1016/j.jsv.2020.115880

0022-460X/© 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

impingesontheoutlet-guide-vane(OGV)[3,4].Asfutureturbofansaredesignedwithhigherbypassratioinordertoachieve better propulsive efficiency, the fan wake-OGV interaction is becoming more crucial considering that the axial distance betweenthe fanandtheOGV isreduced[5].As aconsequence,differenttypesofnovel noisemitigation techniquesmay become necessary, andit isdesirable tounderstandtheir acousticandaerodynamicimplications inearly stageof design. Nevertheless,examiningacompleteturbofansystemislikelytobeexpensiveandchallenginggivenitsinherentcomplexity. Instead, it ismore attractive toconsider a simplified setup that focuseson thespecific noise generation mechanisms. In particular,therod-airfoilconfigurationhasbeenproposedforthepurposeofmimickingtheaeroacousticoffanwake-OGV interaction [6,7]. As a matter of fact, the turbulent Kármán vortex street in therod wake impingeson the downstream airfoil,generatingsoundwithbothquasi-tonalandbroadbandcomponents,similartothatinafanstage[8].

Several passiveLE noise mitigation techniques havebeen proposed in literature, such asLE serrations [9–11].LE ser-rations were inspired by the tuberclesofwhale [12]and they were found to improve aerodynamicperformance at stall conditions[9,13,14].Interestingly,serrationswerealsofoundtomitigateLEnoise[13,15].Gea-Aguileraetal.[16]used com-putational aeroacoustics to predict the acoustics response of an airfoil equipped with LE serrations interacting with an anisotropicturbulentinflow.TheydiscoveredthatLEserrationsbreakthecoherentscatteringprocessattheLE.Theauthors concludedthattheserrationamplitudeandwavelengtharerequiredtobeatleasttwicethestreamwiseandspanwise inte-grallengthscalesoftheinflowturbulencetoachievesignificantnoisereduction.Chaitanyaetal.[17]performedaparametric studyusingaflatplateandaNACA65(12)10airfoiltoretrievetheoptimumserrationdesignparameters.Theauthors ob-servedthatnoisereductionwasthehighestwhentheserrationwavelengthwas4timesthespanwiseintegrallengthscale oftheinflowturbulence.AgrawalandSharma[18]studiedtheeffectofleadingedgeserrationsonarod-airfoilconfiguration usinga high-orderLES.Theserrationamplitudeandwavelengthwere 6%and30% ofthe airfoilchord lengthrespectively. The serratedairfoilwasfoundtoreduce noisemainlyathigherfrequencies.Morerecently,Casalinoetal.[4]performeda numericalstudyusinglattice-Boltzmannmethodtoassessthenoisereductionwhenaleadingedgeundulationisappliedto statorbladesinarealisticaero-enginefanstage.Theyconfirmedthatthenoisereductionscaleswiththeratioofturbulence length scale totheserrationamplitude. However, themaximum predictednoise reduction wasintheorderof 1.5dBand theyarguedthatadesignofserratedOGVshouldaccountfortheradialvariationoftheturbulencelengthscalesinthefan wake.

TheapplicationsofpermeablematerialstoreduceLEnoisehavealsoreceivedtheattentionofaeroacousticcommunity. Sarradj andGeyer [19] investigatedthe effects of varying the flow transport propertiesof porous materials on LEnoise attenuation.TheymanufacturedfiveporousSD7003airfoilsusingseveralmaterialswithdifferentpermeabilityand poros-ityvalues.Ina turbulentflow-field, theporous airfoilsgeneratedlessnoisecompared tothesolid ones. Theauthors also reportedthat porousmaterialwithhigherpermeabilitygenerallyincreasedthe noiseattenuation.Roger etal.[20] manu-facturedaporousNACA0012airfoilbycoveringanaluminumflat-platewithsteelwool,beforewrappingitinawiremesh. Whentheairfoilissubjectedtohomogeneousturbulentinflow,themaximumnoisereductionwasfoundtobearound6dB. Thiswasconsideredpromisingsincetheporousmaterialwasappliedwithnoprioroptimizationguideline. Morerecently, Geyer et al. [21]studied the LE noise reduction for a thick camberedairfoil withperforated LE.The holediameter and inclination anglewerevariedandtheir effectsonfar-fieldnoise intensitywere examined.Substantialnoise reductionwas achievedinlow tomedium frequencyrange,whiletheaerodynamicperformance atlowangle-of-attackwasrelatively un-affected.There wasalsoaslightnoise increaseathigherfrequencywhichwasattributedtothehighersurfaceroughness duetothepresenceoftheholes.

Both LE serrations and porous LE are considered to be promising solutions for LE noise mitigation in the literature. Nevertheless, a better understanding of the different noise reduction mechanisms will allow for improved leadingedge treatments tobe realized. Forthisreason, LE serrations,forwhich a descriptionof thenoise reduction mechanisms and optimization approaches are known [16,17], are compared with porous LE under the same inflow conditions. The main objectiveofthismanuscriptis,therefore,toidentifythedifferencesinaeroacousticeffectsbetweenthetwoLEtreatments. Inthiscontext,therod-airfoilconfigurationisselectedasithasbeenpreviouslyproposedasasimplifiedmodelthatmimics severalaeroacousticsaspectsofafanstage[6].Moreover,athincamberedairfoilisconsideredsinceitbetterrepresentsthe geometrical featuresofan turbomachinerybladecompared totheNACA0012oftheclassical rod-airfoilconfiguration[6]. The usage of a more realistic airfoil profile will also provide usefulinsights regarding the impact ofthe differentnoise mitigationtechniquesonaerodynamicperformance,whichhasalsonotbeenfullydiscussedinliterature.

Thispaperisorganizedasfollows.Section2providesthedescriptionofthelattice-Boltzmanntechniquethat hasbeen used inthisstudy.Section 3presentsthenumericalsetup oftherod-airfoil configuration,followedbythe validationand verificationofthemethodology.Section4discussesthecomputationalresultsontheapplicationsofvariousnoisemitigation techniquesontherod-airfoilconfiguration.TheconclusionandoutlookofthismanuscriptarereportedinSection5.

2. Methodology

2.1. Flowsolver

The commercialsoftware3DSSimuliaPowerFLOW5.4bhasbeenusedto computetheflow-field inthesimulation do-main.Thesoftwarehasbeenpreviouslyusedtoinvestigateotherwake-bodyinteractioncases[4,7,22].Thenumerical tech-nique isbasedon lattice-Boltzmannmethod(LBM), whichcomputestheadvectionandcollision offluidparticles usinga

Fig. 1. The isometric view of the rod-airfoil simulation setup. One of the side plate has been hidden from view. The sponge zone boundary is drawn as the outer black circle.

statisticalgaskineticmodel.ThediscretizationusedforthisparticularLBMapplicationconsistsof19discretevelocitiesin threedimensions(D3Q19),involvingathird-ordertruncationoftheChapman-Enskogexpansion[23].Anexplicittime inte-gration andacollisionmodelbasedonBhatnagar-Gross-Krook(BGK)[24]areused.TheBGKmodelintroducesarelaxation oftheparticledistributionfunctiontowardsthatofMaxwell-Boltzmanndistributionthatdescribesgasparticlesatrest.Flow variables,(i.e.,densityandmomentum)arerecoveredbyintegratingtheparticledistributionfunctionsoverthe19discrete statedirections.TurbulentfluctuationsaremodelledbyextendingtheLBMtoincludeaneffectiveturbulentrelaxationtime

[25],whichreplacestherelaxationtimeintheBGKmodel.Theeffectiverelaxationtimeiscomputedusingthetwo-equation

k−



renormalizationgroup[26]model.AspointedoutinChenetal.[27],thisapproachallowsfortakingintoaccountthe non-linearityoftheReynoldsstresses,anditissubsequentlyreferredtoasvery-largeeddysimulation(VLES).

The unit lattice on which the lattice-Boltzmann scheme is applied, is referred to asvoxel (i.e., volumetric element). The voxeldimension inthe simulation domain can be adjusted on a region-by-region basis, such that the voxel size in adjacent regions isallowed tovary by afactor of2. Solidbodies are discretized asplanar surfaces,referred to assurfels

(surfaceelements).Surfelsaregeneratedatplaceswhereavoxelintersectswiththesurfaceofthebody.Furthermore,the fluid particle interaction withthe solid surfaceis governedby the wall boundary condition, such asparticlebounce-back process forno-slipwall andspecularreflection forslipwall [28].A wallfunction isapplied onthe firstwall-adjacent grid to approximate the wall shear stress. The function is based on the generalized law-of-the-wall model [29], extended to considertheeffectsofpressuregradientandsurfaceroughness.

The LBM scheme isinherently compressibleand unsteady. Combined withthelow dispersion anddissipation charac-teristics ofthesolution,LBM allowsforresolvingtheacousticfield withinthecomputationaldomain (i.e.,directacoustics computation)withacutoff frequencythatcorrespondstoapproximately15voxelsperwavelength[30].Thiswouldrequire a relatively highvoxelresolution atthefar-fieldregion that wouldcausea tremendously highcomputational cost.As an alternative,an acousticanalogybasedonthatofFfowcs-Williams& Hawkings(FW-H)[31]hasbeenutilized.Inparticular, the formulation1Aof Farrasat[32] withforward-timesolution [33]is employed. Thesoundsource integrationis carried outonapermeablesurfaceenclosingthenear-fieldregionandasaresult,thecontributionofdipolesourcesatthesurface ofsolidobjectsandthatofquadrupolesourcesintheturbulentflow-fieldareincluded.

2.2. Simulationsetup

An isometric view showingthe arrangementof the rod-airfoilsetup is shownin Fig. 1.The simulation replicates the rod-airfoil setupofJacobetal.[6]whichconsistsofan airfoilwithchord lengthc=100mm positioneddownstreamofa rodwithdiameterD₌10mm.The airfoilleadingedgeisseparatedfromtherodbaseby100 mm(i.e.,10D orc).Therod centerislocated at15Dor1.5c downstreamofa rectangularopen-jetnozzle.Boththerodandtheairfoilhaveaspanof 300mm(i.e.,30D or3c)andaremountedbetweensideplates.Consequently,aspanwisecorrelationcorrection(e.g.,Kato’s

[34]),whichiscommonlyemployedforsimulations withnarrowerspanmodels,isnot requiredforacousticcomputation. Moreover,ithasbeenreportedpreviously[18]thatthespanwisecorrectionmodelsstillhavelimitations,anditremainsan argumentofwhetherthoseareapplicableforairfoilswithdifferentLEtreatments.

A totalof threeairfoil profilesare considered asshown inFig.2 (i.e.,NACA 0012,0006,and5406), although the ap-plication of LEtreatments is investigatedonly forNACA 0012and5406 airfoils.Forthe sake ofbrevity, the NACAprefix will not be mentioned hereafter.The 0012 isused forvalidating thesimulation setup andto examine theeffects of the differentLEtreatmentsforareferenceairfoil.The5406profilehasbeenchosensinceitsharessimilargeometricalfeatures

Fig. 2. The types of airfoil and noise reduction techniques considered in this numerical study; SLE (straight-LE), PLE (porous-LE), SPLE (streamlined porous- LE), BLE (blocked porous-LE), WLE (serrated/wavy-LE), WPLE (serrations-porous-LE). The porous section of the airfoil is shown with lower opacity. Insets provide the zoomed-in lateral view at the LE. Note that for the insets of WLE/WPLE configurations, the top-down view is shown instead.

Fig. 3. The nomenclature for the rod-serrated airfoil (WLE) configuration.

typicallyfoundinturbomachineryblades,such asarelativelysmallthicknessandpronouncedcamber.Moreover,the cam-beredprofilealsoallowsexaminingtheeffectsoftheLEtreatments onaerodynamicperformance.The0006profile,which hasanidenticalLEradiusasthe5406,isconsideredtoverifythatthecamberinthelatterdoesnotsignificantlyaffectthe far-fieldnoise[35,36].Both0012and0006areinstalled atzeroangleofattack. The5406hasan incidenceof8degrees to approximatethemeanloadingdistributionona statorvaneintheNASA-GlennSourceDiagnostics Test(SDT)rig[8,37]at 90%oftheouterspanwhentheengineisatapproachsettings.The5406isalsoshiftedupwardby4mm(0_.4D)toaccount fortherodwakedeflectioninducedbytheaerodynamicloadingoftheairfoil.

SeveraltypesofLEtreatments fornoise reductionare consideredin thisstudy,including:(1)LEserrations,whichare alsoreferred toaswavyLE(WLE)[17,38,39],(2)poroustreatments(PLE,BLE,andSPLE),and(3)acombinationoftheLE serrations andtheporousmaterial (WPLE).Thedescriptionofacronyms foreach LEtreatmentis providedinthe caption ofFig.2.Asketchofthetop-downviewforanairfoilwithLEserrationsisshowninFig.3.LEserrationsarecharacterized by amplitude H (i.e., thechordwise distancebetween theserrationtip androot) andwavelength (i.e.,spanwise distance betweenadjacentserrationtips)



.Bothparameterscanbetuned toachievedmaximumnoisereductionaccordingtothe integrallengthscalesofinflowturbulenceL[16,17,40]suchthat



/L4andH/L>2.Tomeettheserequirements,H and



are chosentobe3D (0.3c),afterfollowingtheestimationprocedurethatwillbediscussedinSection 3.3.Thus,theentire airfoilspanequalsto10serrationwavelengths.

The LEserrations are applied by modifying the chord length of airfoilsection cWLE along the spanwise direction(z).

FollowingtheprocedureusedbyChenetal.[11],thechordlengthofthemodifiedairfoilcWLEatagivenspanwiseposition

z isdefinedas: cWLE

(

z

)

=c+ H 2cos



₂

_π

_z





(1)

Table 1

The properties of the Ni-Cr-Al metal foam with d c = 800 μm.

dc (μ m) φ(%) RV (N s/m 4 ) RI (m −1 )

800 91.65 6728 2613

Fig. 4. The arrangement of the porous medium model for the 0012-BLE.

LEserrationsareintegratedintotherestoftheairfoilbymodifyingitssurfacecoordinates(xWLE)upstreamofachordwise

extent(xlim);coordinatesdownstreamofxlimremainunchanged.

xWLE=



_x

SLE

xlim



[cWLE

(

z

)

− c+xlim]−

(

cWLE

(

z

)

− c

)

(2)

TheporousLEismodeledusinganequivalentfluidregionapproach[41,42].Formaterialswhoseporesaremuchsmaller than thecharacteristiclengthofthebody,thisapproach requireslesscomputational resourcesasopposedtofully-resolve the internaltopology oftheporous medium.Inthe simulation,theporousLEis modeledasa combinationoftwolayers of porous medium models, namely the “Acoustic Porous Medium” (APM) and the “Porous Medium” (PM). Both models introduce additionalmomentum loss intothe flow-field inside theporous medium accordingtoDarcy’s law.The APM is slightlydifferentthanthePMmodelsuchthattheformerconsidersaporositythatgovernsthetranspirationattheporous mediuminterface.Theporosity

φ

isdefinedasfollows:

φ

=1−

ρ

p

ρ

s

(3)

where

ρ

pand

ρ

saredensityoftheporousmaterialsampleandthatoftheskeletalportion(matrix)ofthesample, respec-tively.TheflowresistivityisdescribedbytheHazen-Dupuit-Darcyequation[43,44]asfollows:

1

ρ

Δph =

μ

K

ρ

v

d+C

v

2 d (4)

where the left handside refers to a pressuredrop Δp across a porous materialsample ofthicknessh,

μ

and

ρ

are the dynamicviscosityanddensityofthe fluidrespectively, and

v

d is the Darcy velocityrefers to the fluid velocityinside the porousmedium.TheHazen-Dupuit-DarcyequationformsasecondorderpolynomialintermoftheDarcyvelocity.Thefirst coefficient is associatedwiththe viscous lossesintheporous medium, whichcan be expressedasthe viscousresistivity

RV =

μ

/

(

K

ρ

)

.TheformcoefficientC inthesecondtermreferstotheinertialresistivityRI=C duetolocalflowacceleration insidethepores.Thisnon-lineartermbecomesmoresignificantwhentheReynoldsnumberinsidetheporousmediaislarge

[44].Equation(4)isvalidforporousmediawhoseporesizeismuchsmallerthanthecharacteristiclength(e.g.,thickness) ofthe sample[43,44].Inthisstudy,the porousmedium isbasedon anopen-cellNi-Cr-Al metal-foamwitha meanpore diameterdc=800μ m,assummarizedinTable1[45].

AsreportedbyDukhanetal.[46]andBariletal.[47],theresistivityofaporousmaterialconsistsoftwocomponents:(1) thethickness-dependentresistivityassociatedwiththeentrance/exiteffect(i.e.,flowunsteadinessneartheporousmedium surface), and(2) the bulk resistivity that is independent ofthe sample thickness(i.e., asymptoticresistivity). The values listedinTable1refertotheasymptoticresistivity,whicharevalidforh>hcrit,wherehcritisacriticalthickness.Tosimplify

the definitionoftheresistivityforpresentapplication, atwo-layer APM-PMapproachisemployed [48].Suchapproach is intendedtoisolateregionsthataredominatedbytheentrance/exiteffectfromtherestoftheporousmedium.Naaktgeboren etal.[49]havereportedthattheentrance/exiteffectislimitedtoanentrancelength,whichisaboutoneporediameterfor metal-foams.Followingthis,theAPMlayeroftheporousLEhasaconstantthicknessof1mm,whiletheremainingvolume underneathistreatedasPMregion.TheAPM-PMapproachhasbeenpreviouslyverifiedbytheauthors[48],inwhichatest rigforcharacterizingtheporousmaterialresistivity[50]hasbeennumericallyreplicated.

ForairfoilswithporousLE, theporousmediumregion isappliedtothefirst 15%ofthechord length.Thus,the extent of airfoilplanformthat is modifiedwitheither LEserrations orporous LEisidentical. Asidefrom theregular porous LE application(0012-PLEand5406-PLE),therearetwootherconfigurationswithadditionalmodifications.The0012-BLE,which isshowninFig.4,hasasolid corealong thesymmetryplane oftheairfoilstartingfromx/c=0.05(i.e.,5percentofthe chord).Thisisintendedtostudytheeffectofpartiallyblockingtheporousmedium,suchthattheflowfromonesideofthe airfoilispreventedfromreachingtheotherside.Differently,the5406-SPLEinFig.2(c2)isconsideredinordertoinvestigate theeffectofstreamliningtheshapeofsolid-porousjunction.Theporousmediumisalsoappliedasanextensionattheroot region ofthe LEserrationsforthe 5406-WPLE (serration-porous-LE),asshowninFig. 2(c4).The porousextension covers

Fig. 5. ( a ) Side view of the simulation domain for the rod-airfoil configuration; the outer boundaries are not drawn to scale. Blue crosses indicate micro- phone locations for far-field noise computation. A closer view on the baseline rod-NACA 0012 configuration (0012-SLE) is provided on the right ( b). Vertical dashed lines indicate the locations where the velocity statistics are sampled and shown in Fig. 6 . Red dots (F and G) indicate the location where velocity fluctuation spectra are computed and shown in Fig. 7 . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

25%oftheserrationamplitude(i.e.,0_.075_<x_/c<0_.15)anditssurfacecontourfollowsthatofthebaseline5406airfoil.This treatment isconsideredinorderto furthersuppressthe soundsource intensityattheserrationroot[11,39],whichmight resultinimprovednoisereductioncomparedtotheregularserrations.

Asketch ofthesimulationdomainwiththeboundaryconditionsisprovided inFig.5.Theentiresimulationdomainis acubewhosesidesare4m(400Dor40c)long,whichiscenteredatthemidspanoftheairfoilleadingedge.Amassflow isprescribedatthenozzleinlettoobtainthemeanfreestreamvelocityof72m/sacrosstheoutlet. Domainboundariesare specified withzero-velocityinletasidefromthedownstream face,wherean outletwithastaticpressureof 100000Pa is prescribed.Allsolidsurfacesareno-slipwallswiththeexceptionofthenozzlewhichisspecifiedasaslipwall.Anacoustic buffer zoneisdefinedoutsideasphericalboundarythat enclosesthenear-fieldregion suchthatoutward-travellingsound waves are preventedfrombeingreflected by the domain boundaries.The simulation domain issubdividedinto 13 voxel refinement regions.Thefinestvoxelresolutionisappliednext totherodandairfoilsurfaces.Thefinestgriddimension is 8× 10−3_{D suchthat atotalof125voxels areassignedacrossthediameteroftherod. Thiscorrespondstothe averagey}+

of thefirst wall-adjacent cellof 25on therodand 15on theairfoil. On average,domaindiscretization resultsin a total of approximately200_{× 10}6 _{voxels forthe finestvoxelresolution. Airfoilswithporoustreatments would requirealarger}

number of voxels dueto the discretization of the porous medium region. More details of the domain statistics will be providedinSection3.2.

Forfar-fieldnoisecomputation,theFW-Hanalogyisemployedonapermeablesurfaceenclosingtherod-airfoil configu-ration.Inordertomitigatetheinfluenceofpseudo-sound(i.e.,non-radiatingaerodynamicfluctuations)atthedownstream terminationoftheFW-H permeablesurface,an additionalstackof6planarsurfacesis addeddownstreamoftheexisting facewithaseparationof2D.Thesestacked surfacesallow foraveraging-outthepseudo-sound contribution(e.g.,fromthe airfoilwakeandtheopen-jetshearlayer)whilepreservingtheacousticones.Thisstrategyhasalsobeenappliedina sim-ilarstudyofwakeinteractionnoise[22].The permeableFW-Hsurfacerecordsacousticpressureatarateof29.5kHz.The powerspectral densityoftheacousticspressureisobtainedusingWelch’smethod[51],inwhichaHanningwindowwith 50%hasbeenappliedtoobtainafrequencyresolutionof100Hz.

Thesimulationsarecarriedoutwithaphysicaltimestepof1.33× 10−7_{sfor67flowpassesalongtheairfoilchord(i.e.,}

total physicaltime of 0.108s),excluding the initialtransientof 10flow passes. The simulation time isalsoequal to 150 vortexsheddingcyclesproducedbytherod.TherequiredcomputationalhoursvarieswithdifferentLEtreatment,whichis reportedinSection3.2.

3. Validationofmethodologyandgridindependencestudy

3.1. Validationoftherod-airfoilconfiguration

A validation study is carried out for the baseline rod-airfoil configuration (0012-SLE) [6], in which aerodynamic and acoustic resultsarecomparedto referencedatafromliterature. Plot (b)inFig.5illustrates theside viewofthe 0012-SLE configurationwiththecoordinatesystem,inwhichvelocitystatisticsareextractedalongthelinesAtoEandatpointsFand G.Ateach location,thevelocitytime historyissampledat15kHzfor130vortexsheddingcycles.Thevelocityprofilesfor

Fig. 6. Profiles of mean and root-mean-square (RMS) of fluctuations of the axial velocity component at different locations along the rod-airfoil configura- tion. Note that reference data from Jiang et al. [52] are only available for plots B and C.

linesAtoEarepresentedinFig.6,wherepresentresultsarecomparedagainstpreviousnumerical[7,52]andexperimental

[6]data.The overallagreementissatisfactory,althoughvelocity profilesatC, D,andE(i.e.,asideanddownstream ofthe airfoil) showa y/c shiftwithrespecttotheexperimental ones. Thismightbeattributedtothefact thatthe verticalshift of the airfoil position is not considered in the simulation. Additionally, it has beenreported [53] that the airfoil in the experimenthassurfaceimperfectionsatthesuctionside,whichmightresultinlowermeanvelocityandhigherfluctuations incomparisontosimulationresults.

The streamwisevelocity fluctuationspectra

φ

uu atpointsFandG are plottedin Fig.7.

φ

uu hasbeennormalizedwith areferencevelocityof1m/sandthefrequencyaxisisexpressedastheStrouhalnumberbasedontheroddiameterStD=

f D/U∞.Thesimulationresultsareinlinewithprevious LESworksofChenetal.[11],Giretetal.[53],andEltaweeletal.

[54],althoughminordiscrepancieswiththeexperimentarestillpresent.Forinstance,thepeakofthetonefromthepresent simulation is located atStD=0.195, which is higher that of the experiment, i.e, StD=0.19. This frequency shiftusually arisesfromasmalldifferenceintheboundarylayerseparationpointontherod[11]thatisofteninfluencedbyturbulence modeling[55].

ThesurfacepressurestatisticsontherodandtheairfoilsurfacesareshowninFig.8.Thetime-averagedsurfacepressure isexpressedaspressurecoefficientCp,mean,whiletheroot-mean-square(RMS)ofsurfacepressurefluctuationspRMSis

nor-malized withthefreestream dynamicpressure q_∞=0.5

ρ

_∞U2

∞.The rodCp,mean isplottedincylindricalcoordinatesystem

withthezeroanglereferencetowards theupstreamdirection.The surfacepressuredistributionon therodisinlinewith experimental measurements,although theregionsurroundingtherodbaseagrees betterwithApeltandWest[56] rather thanthatofSzepessyandBearman[57].TheCp,mean distributionisalsofoundtobe comparabletotheLESresultsofGiret

Fig. 7. Power spectral density of streamwise velocity fluctuations φuu at points (F) ( x/c = −0 . 87 , y/c = 0 . 05 ) and (G) ( x/c = 0 . 25 , y/c = 0 . 08 ). The S uu is

normalized with a reference velocity of 1 m/s.

Fig. 8. Surface pressure statistics on the rod and the 0012-SLE airfoil.

airfoilCp,meandistribution.This behaviorhas beenreportedtobeduetothesurfaceimperfectionoftheairfoilmodelinthe

experiment[53].Nonetheless,theairfoilCp,mean distributionsofthepresentresultsareingoodagreementwithotherLES

resultsfromliterature.TheCp,RMSdistributionontheairfoil isalsofound tobesimilartothatofJiangetal.[52],although

itslightlyunderpredictsthatofGiretetal.[53].

Forevaluatingtheacousticresponse oftherod-airfoilconfiguration,the far-fieldnoise iscomputedatseveralobserver pointsalonganarcinthex− yplanewitharadiusof185Dcenteredattheairfoilleadingedge[6].Thepointsareseparated with5-degreeincrement, rangingfrom0to ±160degreeswiththezeroreferenceinthedownstream(i.e.,x/c>0) direc-tion;theyareshownasbluecrossesinFig.5.Theresultingsoundpressurespectraandoverallsoundpressurelevel(OSPL) directivity patternare shownin Fig.9. Thesound pressurelevel (SPL)hasbeen normalizedwitha referencepressure of 20μPa.Spectraobtainedfromthesimulationshow goodpredictionofbothspectral broadeningandamplitudeofthe fun-damentaltone. Moreover,currentresultiscomparabletothoseofSattietal.[7]andGiretetal.[53].TheOSPLdirectivity patterninplot(b)clearlyshowsdipole-like lobescorresponding totheliftfluctuation inducedby therodwake impinge-ment. The overall trendofpresentsimulation is still inlinewiththose of Jacob etal.[6]andGiret etal. [53], although there is anoticeable discrepancytowards theshallow anglein thedownstream direction. Thisis dueto theomission of thedownstreamfaceoftheFW-HpermeablesurfaceinthesimulationofGiretetal.[53]whereasinthepresentcase,the FW-Hpermeablesurfacecompletelyenclosestherod-airfoilsetup.

Tofurther assessthereliability ofthesimulation,Fig. 10compares thesoundspectraobtainedusingthe solid-surface FW-H approach and that using the permeable surface enclosing the near-field region. In the figure, the spectra labeled “Total(FW-H Permeable)” aretakenfromthat labeled“Present(LBM-VLES)” inFig.9whichhavebeenobtainedusingthe

Fig. 9. ( a ) Sound spectra in the far-field, computed at a location directly above the airfoil LE ( θ= 90 ◦_{, i.e., x/c = 0 and y/c = 9 . 25 ) and ( b) OSPL directivity} pattern with zero degree reference towards the downstream direction.

Fig. 10. Comparisons of far-field noise contributions between the rod, the airfoil, and both combined. Sound spectra are computed at x/c = 0 , and y/c = 9 . 25 .

permeable-surfaceFW-Happroach.Differently,noisespectraobtainedusingthesolid-surfaceFW-Happroachonlyconsiders adistributionofequivalentdipolesatawall.Consequently,othernoisecontributions,includingquadrupoles(e.g.,the open-jet shearlayer) andinstallationeffects,are neglected.Nevertheless,itis possibletoseparately quantifythefar-fieldnoise contribution ofdifferentobjects inthesimulation domainusingthe solid-surfaceFW-H approach.Fig.10 showsthatthe sumoftheindividualnoise contributionofbothrodandairfoil(i.e.,redsolidline)isverysimilartothetotalnoiseofthe setup (i.e.,blacksolid line),exceptatveryhighfrequencies(Stc>0.7).Thisimpliesthatovermostofthefrequencyrange of interest,other noisesource contributionsandinstallation effectsare relatively small.The figure alsoindicates thatthe noisecontributionoftherodismuchsmallerthantheairfoil;notethatthenoisefromtheairfoilincludestheeffectsofthe aerodynamicperturbationresultingfromtherodwakeimpingingtheairfoilLE.Consequently,thefigureevidencesthatthe far-fieldnoiseisdominatedbythatproducedbytheaerodynamicinteractionbetweentherod-wakeandtheairfoil.

Thissubsection hasshownthatthe methodologyandsimulationsetup allowsforan accurate predictionofthe aeroa-coustics ofthe rod-airfoil configuration.However, giventhe widerange ofairfoiltypes andLEtreatments that are being considered, agrid independencestudyisalso performedto ascertainthatthe gridresolutionissufficient toachieve con-vergedsolutions.

3.2. Gridindependencestudy

Grid independence studies havebeen performed for each airfoil type (i.e., 0012,0006, and 5406) and LE treatment, however,forthe sakeofbrevity, onlythefollowing casesarereportedinthissubsection: 5406-SLE,5406-PLE,and 5406-WLE.Foreachcase,threedifferentgridresolutionsareconsideredwithrefinementratioof√2_,namelycoarse,medium,and

fine.Theconvergencetrendsofthesimulationresultsareevaluatedbasedonthemeanliftanddragcoefficients(C_l,meanand

Cd,mean) oftheairfoil,andtheacousticsourcepowerlevel(PWL).Thesimulationconfigurationsforthegridindependence

Table 2

Comparison of the domain statistics for rod-5406 configurations.

Type Resolution (voxels/ D ) Voxel count ( 10 6 ) CPU hours ( 10 3 ) 5406-SLE Coarse 62.5 43.5 6.6 Medium 88.4 89.5 19.2 Fine 125 200.5 60.8 5406-PLE Coarse 62.5 44.1 7.4 Medium 88.4 91.1 21.1 Fine 125 205.1 67.1 5406-WLE Coarse 62.5 45.7 6.9 Medium 88.4 91.9 19.9 Fine 125 205.8 62.3

Fig. 11. The trend of the time-averaged lift C l,mean and drag C d,mean with the number of voxels in the simulation domain ( N voxel ).

voxels are larger forPLE andWLE cases since extra voxels are required to discretize the porousmedium region andto resolvethemorecomplexedgecurvatureoftheLEserrations.

Fig.11showstheconvergencetrendsofCl,mean andCd,mean.Theabscissashowsthevoxelcountcorresponding toeach

resolutionsettinginlogarithmicscale.Thegridresolutionlevelisindicatedasnumbersnexttothedatapoints.Straightlines areusedtoconnectdatapointsbetweenresolutionlevel3(coarse)to1(fine),whileRichardsonextrapolationsatresolution level0areplottedusingdashedlines.Althoughtheaerodynamicforcesappeartoapproachconvergencequalitatively,they are also examined quantitatively by computingthe grid convergenceindex (GCI). Forinstance, the GCI1,2=0.0298% and

GCI0,1=0.0009%forCl,mean oftheSLEcasewiththeGCI ratioequalsto1.0099≈ 1.ThesmallGCI valueandtheGCI ratio

beingclosetounityindicatethatthecomputationalgridsarewithintheasymptoticrangeofconvergence[58].Ithasbeen verifiedthattheGCI valuesandratiosfortheothercasesexhibitsimilartrend.

Theeffectofvaryingthegridresolutiontothefar-fieldnoiseisdepictedinFig.12.Inthegraph,thesoundpowerlevel forthethree5406configurationsareplottedfor0.05<StD<1.Comparingtheresultsfordifferentgridresolutions,thelow (i.e,StD<0.1)andhighfrequency(StD>0.6)regionsappeartobemoresensitivethantherest.Thelattercanbeassociated withthecut-off frequencyassociatedwiththevoxelsizeatthepermeableFW-Hsurface.Thediscrepancyatlowfrequency mightbe relatedtotheinstallation effect(e.g.,thescatteringoftheshearlayerby thenozzlelip).Nonetheless,thefigure shows that the results haveconverged for the finestgrid resolution at thefrequency range where LEnoise is the most relevant(i.e.,0_.08_<StD<0.8).

3.3. Integrallengthscalesintherodwake

The turbulent integral length scales in the rod wake are estimated in order to obtain an optimal design for the LE serrations[17].FollowingtheprocedureoutlinedinPope[59],theintegrallengthscalesareestimatedasfollows:

Lm i j

(

x,l

)

= _∞ 0 Rm i j

(

x

)

dl= _∞ 0



ui

(

x+lem

)

uj

(

x

)





ui

(

x

)

uj

(

x

)



dl (5)

Fig. 12. The influence of the grid resolution on the sound power level (PWL) of different LE treatments on the 5406 airfoils.

Table 3

The integral length scales L m

i j in the rod

wake at 2 . 5 D upstream of the airfoil LE. Airfoil Lx

uu /D Lyvv /D Lzww /D

NACA 0012 1.50 1.10 0.73 NACA 5406 1.42 1.09 0.73

where Rm

i j

(

x

)

isthe correlation coefficientevaluated based ona referencelocation x ,ui anduj arethe turbulentvelocity fluctuationscomponentsinithandjthdirectionsrespectively, e mtheunitaryvectorinthemthdirection,andl=l · emisthe separationlengthfromthereferencelocation.

·

isthetemporal-averagingoperatorwiththeassumptionthattheturbulent fluctuationsintherodwakeareergodic.ThisestimationprocedurewasalsoemployedintheLEserrationsinvestigationby GeaAguilleraetal.[16].

Table3summarizestheintegral lengthcomputedusingEq.(5)forthe0012-SLEand5406-SLEcasesata reference lo-cation2_.5DupstreamoftheairfoilLEinthemid-sectionplane.ThediscreteintegrationinEq.5isperformedforaspatial separationequals 0.1Dalong thestreamwise(x),vertical(y), andspanwise(z)directions,forwhichthecorresponding ve-locitycomponentsaredenotedu,

v

,andwrespectively.Thespatialseparationismuchlargerthanthelocalvoxelsizeand it hasbeenverifiedthat usingsmallervalue doesnot changetheobserved trends.Thelength scales intherodwakeare longerinthestreamwisedirectionratherthanthespanwise,whichissimilartothosefoundintheNASASDTturbofanrig

[4,60].Thelengthscalesareslightlyreducedinstreamwiseandtangentialdirectionsfortherod-airfoilconfigurationusing the 5406profile.Nevertheless,theserrationamplitudeandwavelengthof3D(0.3c)satisfy therequirementsofH/Lx

uu≥ 2 and



_/Lz

ww4forbothairfoilprofiles[16,17].

4. Analysesofresults

4.1. AcousticsresponseofdifferentLEtreatments

Far-field noisecomputations forthe baselineairfoils (SLE)areillustrated inFig.13.Inplot (a), thePWL spectraofthe 0012,0006,and 5406 airfoilsare compared. The 0006 and5406 airfoilsshow an increase atthe fundamental tone fre-quency by≈ 3dBover that ofthe0012.Furthermore,thetoneharmonics andhigh-frequencybroadband componentsare alsoincreasedsignificantlyforthethinnerairfoils.Thisbehaviorcanbeattributedtothestrongervorticaldistortiondueto ahighervelocitygradientnearaLEwithsmallradius(i.e.,thinLE)[36].Thenoiseincreasecausedbythethinnerairfoilsis alsoevident inthefar-fielddirectivityplotin(b), wheretheir averageOSPLis2.5dBhighercomparedtothatofthe0012. Sinceboth5406and0006airfoilsshowsimilarPWLvaluesanddirectivitypatterns,itisimpliedthattheLEnoiseisweakly influenced by smallmodifications of angleof attack andcamber, whichhas alsobeen reportedby Devenportetal.[35]. Hence,thisjustifiesusingthe5406profileinsteadofthe0006forthisstudyastheformeralsoallowsforinvestigatingthe effectsoftheLEtreatmentsonaerodynamicperformanceofanairfoilprofileusedinturbomachinery.

The effectsofthedifferentLEtreatmentsonthe PWLaredepictedinFig.14,wheretheplotsforthe0012airfoilsare givenin (a).The 0012-WLEreducesthetonal peakintensityby ≈ 9dBrelative tothat oftheSLE. Whilethisreduction is significant,itisstillsmallerthanthedifferencebetweentheindividualnoisecontributionfromtheairfoilandtherodthatis previouslyshowninFig.10.IncontrasttotheWLE,thetonalpeakoftheporoustreatments(PLEandBLE)remainsatsimilar levelastheSLEone.Broadbandnoisecomponentsnearthefundamentaltoneandathigherfrequenciesarealsoattenuated bytheWLEtreatment,withanaveragereductionbetween4to5dB.ThePLEshowsnoticeablebroadbandattenuationonly for StD>0.25, whereas theBLE onlyaffectsthe high-frequency tonalpeaks.The PWL valuesforthethree LEtreatments

Fig. 13. The comparison of the sound power level (PWL) ( a ) and the far-field directivity pattern ( b) of the baseline airfoils.

Fig. 14. The comparison of the sound power level (PWL) for the different LE treatments.

are similar forStD>0.65.Nevertheless,it isclearthat the WLEexhibitsthe highestnoise reductionamongthe different LEtreatments. ThePWLfor5406airfoilsareprovided inFig.14(b). The5406-WLEreducesthefundamentaltonelevelby ≈ 8dB, whichis the largestamong allof theLE treatments. Both5406-PLE andSPLEshow smaller noise reductionthan the WLEone, although thelatteris abletofurther reduce theintensityofthe firstharmonic (i.e.,StD=0.39).The WPLE configurationalsoperformsslightlyworsecomparedtoitsWLEcounterpart,indicatingthatcoveringtheserrationrootwith theporousmediumdoesnotnecessarilyimprovesthenoisereduction.

The overall PWL (OAPWL)difference betweenthe baseline airfoilandthose withtheLE treatments issummarized in

Fig.15.ThefigureshowstwomaincomponentsofthePWLspectra;thetonalcomponent(0.15<StD<0.25)andthe broad-band one(StD>0.25).Only0012-WLEand5406-WLEarefoundtoexhibitsubstantial reductionoftonalnoisecomponent. In contrast, poroustreatments (PLE,BLE, andSPLE) produce higherattenuation of the broadband noise componentthan thetonalone.The5406-WPLE showssmallernoisereductioncomparedtothe5406-WLE,inparticularforthetonalnoise component. Thissuggeststhattheporousextension hasan adverseeffectonthenoisereductionmechanismofserrations

[38,39],whichwillbediscussedfurtherinSection4.3.FollowingtheanalyticalmodelproposedbyLyuetal.[61],thenoise reduction levelof theserrationsata particularfrequency increaseswithStH=

ω

H/U∞,where

ω

=2

π

f .For instance,the

StH forWLEequals 3.68 for the fundamentaltone frequency,butStH=2.76 for WPLEassuming that theporous extension decreases theeffectiveamplitudeoftheserrations.Inlogarithmicscale,thedifferenceinStH betweentheWLEandWPLE leadsto 1.3dB lowernoise reduction forthelatter,which iscomparableto thedifference betweenthetwo asshownin

Fig.15.

Thefar-fielddirectivitypatternsfordifferentLEtreatmentsareplottedinFig.16.Inaddition,therelativeOSPLdifferences betweenmodifiedairfoilsandbaseline onesare showninFig.17.TheOSPLisobtainedbyintegratingthesoundpressure

Fig. 15. The OAPWL difference between the LE treatments (LET) cases and the baseline (SLE) for tonal ( 0 . 15 < St D < 0 . 25 ) and broadband noise components

( St D > 0 . 25 ).

Fig. 16. The comparison of the far-field noise directivity pattern for the different LE treatments.

Fig. 18. Comparison of source power level reduction ( ΔPWL SLE ,LET = PWL SLE − PWL LET ) between the simulation results and the corresponding analytical

prediction for LE serrations [17,61] .

spectrainthefrequencyrangeof0_.08_<StD<0.8.Inbothfigures,plot(a)showsthevaluesforthe0012airfoilsand(b)for the5406ones. ItisevidentthattheLEtreatmentsonthe0012donotcauseasignificantchangeinthedirectivitypattern. Nevertheless,the0012-WLEshowstwomainlobes,i.e.at±115◦ and±60◦,whichindicatesanon-compactsourcebehavior. The 0012-PLE shows a slightnoise increase atshallow angles,i.e. between_±30◦_, butnoise reduction is achievedin the otherdirectionswithanaverageof1.5dB.The0012-BLEshowshighernoiselevelthanthePLEvariant,particularlytowards theupstream direction,althoughits noiselevelatshallowanglesissimilartotheSLEone. Inplot(b),the5406-WLEalso showstwo mainlobes,similar toits 0012counterpart,which impliesthat thenon-compactness aspectof thesourceson the serrationsispresentforbothairfoilprofiles.Unlikethe0012-PLE, the5406-PLE exhibitsanasymmetric directivity,in whichnoise increasecanbe observedat20◦<

θ

<30◦ anda noisedecreaseat−40◦_<

_θ

_<0◦_{.Theasymmetricdirectivity}

isalsofoundfortheSPLEandWPLEconfigurations,whichmightbeattributedtothemeanloadingeffect,whichenhances thesurfacepressurefluctuationsattheairfoilsuctionside.

4.2. Noisereductioncomparisonagainstanalyticalmodels

Thereareseveralanalyticalmodelsthathavebeenproposed topredictthenoisereductionlevelforLEserrations,such asthosedescribedbyLyu andAzarpeyvand[61],Chaintanyaetal.[17],andmorerecentlybyTurnerandKim[62].These analyticalmodelsdescribeaself-similartrendofnoisereductionwithrespecttotheStrouhalnumberbasedontheserration amplitudeStH.TheformerproposedalinearfunctionwhereasthelatteraBesselfunctionofthefirstkind.Thecomparisons betweenthenoisereductionpredictionfromtheanalyticalmodelswiththesimulationresultsarepresentedinFig.18. Re-sultsfromanalyticalmodelsareplottedassolidlines,withtheblackonecorrespondingtothatofChaintanyaetal.[17]and theredonetoLyuandAzarpeyvand[61].TheanalyticalmodelofChaintanyaetal.isplottedforserrationswith“optimum” wavelength,whichis4timestheinflowturbulencelengthscale;thesamedesignappliedfortheserrationsinpresentstudy. Themodelalsoassumesthefollowing:1)sourcesalongtheserrationshavesimilarintensityandfullycorrelated,and2)the phase relation oftheaerodynamicresponse on theairfoilis identicalto thatof theinflow turbulence.Bothassumptions are rarelysatisfiedinactualserrationssincethesourceintensitycouldvarysignificantlybetweenserrationpeak androot, and theinflow turbulenceis distortedasit approachesthe LE[63,64].Nevertheless,both analytical models consider the spanwisephaseinterferenceofnoisesourcesalongtheserrationspanastheprimarynoisemitigationmechanism.

InFig.18,thefrequencyaxisispresentedasStrouhalnumberbasedontheroddiameterStD;anappropriatescalingfrom

StH toStD fortheanalytical modelshasbeentakenintoaccount.FortheWLEairfoils,thesimulationresultsshowdecent agreementwiththeBesselfunctionuptothefundamentaltonefrequency.Sincethistonecorrespondstothequasi-periodic upwash/downwashinducedbytheimpingingvortexstreet,itispossibletoconsidertheprocesstobeharmonic,forwhich the spanwise phase interferenceeffect is more influential. However, the agreement becomes worse at higherfrequency, which can be relatedto the smaller spanwise correlation length (i.e., lower coherence betweensources at the serration peak androot).Nevertheless,thepeakΔPWLSLE,LET atthe secondtonestill coincideswiththeuniversal trend.Thismight

beduetothefactthattheanalyticalmodelsrepresentthetheoreticallimitofnoisereductionwhentheinflowturbulence isdominatedbyasinglegustcomponent,whichishardlythecaseforthevortexstreetintherodwake.

For PLE airfoils,the agreement is generallypoor astheir noise reduction is severaldB lower than the trends of the analyticalmodels.Interestingly,thegradientoftheΔPWLSLE,LETfortheporousairfoilappearstogenerallyfollowthelinear

function, althoughthisisalsolimitedatlower frequencies.Whiletheanalytical modelsarenot expectedto beapplicable for the porous treatments, thiscomparison also suggeststhat the spanwisephase interferenceeffect plays a minorrole in term ofnoise reduction mechanism forporous LE cases.In fact, as alluded earlierin thismanuscript, porousLE and LE serrations have different effects on the airfoil aeroacoustics. A detaileddiscussion on thisaspect is presented inthe subsequentsubsections.

Fig. 19. Root-mean-square of surface pressure fluctuations C p,RMS = p RMS / 0 . 5 ρ∞ U ∞ distribution along the airfoil chord. For the 5406 airfoils, the values on 2 the pressure side are plotted using lighter colour.

4.3. Theeffectsofleadingedgetreatmentsonnoisesourcecharacteristics

Intheprevioussubsections,itisobservedthatthenoisereductionoftheporousLEisgenerallysmallerthanthatofthe LEserrations.Tobetterunderstandthereasonforthisbehavior, noisesourcecharacteristicsondifferentLEtreatmentsare investigatedinthissubsection.FollowingCurle’sacousticanalogy[65]andAmiet’sLEnoisemodel[1],noiseisproducedas theconsequenceoffluctuatingaerodynamicforcesonasolidbodythateffectivelyserveasequivalentdipolesources.Hence, far-fieldnoiselevelisproportional totheintensityandspatialcoherence ofthedipolesourcesattheairfoilsurface.Based onthese,noiseattenuationcanbeachievedby:(1)mitigatingthesurfacepressurefluctuationstoreducethesoundsource intensityand(2)reducing the coherencelevel orinducingdestructive interferencebetweenthesoundsources. Theseare referredtoassourcereductionandspanwiseinterferenceeffectsrespectivelyandbothwillbediscussedinthefollowing.

TheinfluenceoftheLEtreatmentsonunsteadyaerodynamicforcesontheairfoilisexaminedusingtheRMSofsurface pressurefluctuations(pRMS) plotsinFig.19.Inthefigure,the pRMSisnormalizedwithfreestreamdynamicpressureq∞=

0_.5

ρ

_∞U2

∞and expressed asCp,RMS.Results for the 0012 seriesare provided in plots (a) and (b),whilethose for 5406 series

are in plots (c) to (e). Compared to the 0012-SLE, the PLE andBLE variants are shown to reduce the peakCp,RMS level

at the LE.This indicates a smaller blockage effect imposed by the permeableleading edge on theimpinging turbulence comparedtothesolidone [20,64].However,whiletheintensityofpressurefluctuationsfortheSLEdecaysrapidlyfurther downstream, itremainshigherforboth PLEandBLE.Infact,thesumofCp,RMSintherangeof0<x/c<0.15 forthePLE

is 6% lower than thatof theSLE, whilethere isalmost no difference inthe caseofBLE. Suchminor reductioninCp,RMS

can belinked totherelatively smallnoiseattenuationforthe0012airfoilswithporoustreatments. The0012-WLEshows that theCp,RMS at the serrationroot is slightly higherthan the SLE one, but the intensityat the serration mid andtip

is significantly lower.Asa result, thespanwise averageof theCp,RMSon theWLE issmaller than thaton theSLE, which

contributesto asubstantial noisereduction.TheC_p,RMS decreasesatserrationmidsincethelocaledge contourisskewed

against theimpingingvortex street[1,38,66].Differently, theCp,RMS reductionattheserrationtipcanbe attributedto the

secondaryvortexsystemgeneratedbytheserrations[39].ThisisshownusingtheflowvisualizationinFig.20;notethatthe vorticity signfollowstheright-handrule.The figuredepictsaclockwise-rotatingvorteximpingingtheserrationtip,which inducesdownwashattheLE.However,thisalsoleadstotheproductionofclockwise-rotatingstreamwisevorticityalongthe serrationmid,such thatthe serrationtip experiences additionalupwashwhileatthe serrationroot, adownwash. Dueto theinfluenceofthissecondaryvortexsystem,theaerodynamicfluctuationsattheserrationtiparepartiallycancelledout, whiletheyareenhancedattheserrationroot.

Fig. 20. Instantaneous flow visualization for the 5406-WLE, bandpassed at 0 . 19 < St D < 0 . 21 . The cut plane shows the contour of spanwise vorticity z .

The iso-surface corresponds to λ2 = −3 × 10 7 s −2 , colored with streamwise vorticity _{x values. Vorticity is normalized against the characteristic time scale}

D/U ∞ .

The5406airfoilsshowverysimilar trendsasthe0012ones. ThepeakCp,RMS levelatx/c=0ofthePLEandSPLE

con-figurations is approximately85% lower thanthat ofthe SLE,butthe pressurefluctuationson thesuction side are higher atdownstreampositions(seetheinsetinFig.19(c)).Furthermore,highCp,RMSlevelisfoundclosetothelocationof

solid-porousjunctionsforeachporoustreatment(i.e.,x/c=0.15forPLE andx/c=0.1forSPLE).Sincethesolid-porousjunction representsanimpedancediscontinuity(i.e.,asuddenchangeinpermeability),itisexpectedthatacousticscatteringwould alsooccuratthislocation[67].FortheWLE,theCp,RMSattheserrationtipandmidissubstantiallysmallerthanthatofthe

SLEalthoughtheintensityattherootishigher.PressurefluctuationsdownstreamoftheLEserration(i.e.,x/c>0.15)decays rapidlyandmatchestheleveloftheSLE,implyingthatnoisesourcesareconcentratedalongtheserrationsthemselves.The WPLEtreatmentshowssimilardistributionofpressurefluctuationsastheWLEattheserrationtipandmid.However,the sharppeakpreviously foundattheserrationrootoftheWLEhasbeensubstitutedbyawideronewithlowerpeak inten-sity. Nevertheless,thesumoftheCp,RMS intherange0.08<x/c<0.3(i.e.,betweentheedgeoftheporousextensionand

thelocationwheretheWPLEtrendconvergestotheSLEone)fortheWPLEis≈ 10%highercomparedtothatoftheWLE, which canbe relatedtothesmaller noisereduction oftheWPLE.Moreover, sincetheC_p,RMSdistribution ontheWPLE is

thehighestattheedgeoftheporousextension insteadoftheserrationroot, thiscorroboratestheassumptioninprevious subectionthatporousextensiondecreasestheeffectiveserrationsamplitudeasperceivedbytheimpingingturbulentinflow. Thiswouldeventuallyreducetheefficacyoftheserrations,andresultinsmallernoisereduction[61].

Based onFig.19,theporousLEtreatments areabletosubstantiallymitigatethesurfacepressurefluctuations,whereas ontheLEserrations,thisisobservedonlyattheserrationtipandmid.Nonetheless,theLEserrationsareabletoproduce highernoisereductionthantheporoustreatments,whichhavebeenpreviouslyreportedduetophaseinterferenceamong noisesourcesalongtheserrationspan[38,39].Toverifythis,two-pointcross-correlationcoefficientsofthesurfacepressure fluctuationsarecomputedatdifferentspanwisepositions,asdefinedinthefollowing:

Rpp

(

z,Δz

)

=





p

(

z

)

p

(

z+Δz

)



p2

(

_z

)





_p2

(

_z+Δz

)

(6)

wherep

(

z

)

isthetimeseriesofsurfacepressurefluctuationsatareferencespanwiselocation z _,

·

isthetemporal-average operator, andΔz is the spanwise separationfrom the z .For computing Rpp,surface pressurefluctuationsare sampledfor 135 vortexshedding cyclesat15 kHz. The spanwiseseparation equals 0.375D such that there are 9samplingpointsper serrationwavelength.The referencespanwiselocation isattheairfoilmidspan(z/D=0), whilethechordwise coordinate variesfordifferentLEtreatmentsdependingonwhereCp,RMSisthehighest(seeFig.19).

TheRpp plotsareshowninFig.21wherethespanwisecoordinateisnormalizedwiththeroddiameter.Thecalculation isperformedintherangeof0<z/D<9,whichisequivalentto3serrationwavelengthsforWLEandWPLEconfigurations; the correlationcoefficientsforthe SLEairfoilsapproacheszeroatz_{/D≈ 8}.Inplot(a),the Rpp forporoustreatments (PLE andBLE)showamonotonousRppdecaythatisinitiallyfasterthantheSLEone,butbecomesslowerforz/D>4.This sug-geststhattheporousLEenhancesthebreakdownofthesmallereddieswhereasthelargeronesstillpersist.Differently,the WLEproducesan alternatingRpptrend,whichdecreases tonegativevaluesneartheserrationroot(e.g.,z/D=1.5,4.5,7.5) and recovers to positive values at locations near the neighbouring serration tip (e.g., z/D=3.0,6.0,9.0). The stark con-trastincorrelationvalueattheserrationtipandrootimpliesasubstantialdestructiveinterferencebetweensourcesatthe two locations.Thiscanbeattributedtothephasedelaybetweenturbulenceimpingementatserrationtipandrootdueto their chordwiseseparation.Correspondingly,theserrationtipsshowpositiveRpp valuessincethey arelocatedatthesame streamwise position.However, theirpeak Rpp along thespanalsofollowsthedownwardtrendthatcanbe foundinother typesofLEtreatments.

Fig. 21. The spanwise correlation R pp of the surface pressure fluctuations for the different LE treatments. The locations of serration tips and roots for the

WLE are indicated in the plots.

The correlation plots for5406 airfoilsin plot(b)are alsoexhibiting similar behaviorsasthe 0012ones. Forinstance, both PLE andSPLE also show a decreasing trend that initially outpaces that of the SLE, but further away this trend is reversed.The quasi-periodiccorrelationbehaviorcanalsobe observedforbothWLE andWPLE.However,unliketheWLE, theWPLEexhibitsminorvariationsatlocationswheretheporousextensionisapplied(e.g.,1_<z_/D<2).Attheselocations, theRpp oftheWPLEdoesnotreachvaluesthatareaslow astheWLEones.Sincethenegativecorrelationvalueislinked tothestreamwiseseparationbetweenthenoisesourcesattheserrationtipandroot,thissupportsthehypothesisthatthe serrationamplitudeoftheWPLEis effectivelysmallerthanthat oftheWLE,whichhasthe consequenceofimpedingthe noisereductionmechanismoftheserrationplanform[61].

Thecorrelation analysisisextendedintofrequencydomaininordertolookintothespanwisephaseinterferenceeffect fordifferent LEtreatments.The cross-spectral densityofthesurfacepressurefluctuationsGpp

(

f

)

isdefinedasinEq.(7), where rpp

(

z ,Δz,t

)

isthe temporal cross-correlation function betweena referencelocation z andanother one located Δz away,j=√−1,T equalsthesamplinglength,andApp isthephaseangle.

Gpp

(

z,Δz,f

)

=

 T

0

rpp

(

z,Δz,t

)

e−j2πf tdt

=

|

Gpp

(

z,Δz,f

)

|

[cosApp

(

z,Δz,f

)

+jsinApp

(

z,Δz,f

)

] (7) The cross-spectral density plots are illustrated in Fig. 22. The

|

Gpp

(

f

)

|

is computed withthe reference at the airfoil midspan against two other locations (a) Δz/D=0_.75 and(b) Δz/D=1_.5_, which correspond to the location of serration midandrootrespectivelyfortheWLEandWPLEairfoils.Inallplots,thepeakofthecross-spectraldensitycoincideswith the fundamentaltonefrequencyandits harmonics.This isexpectedsince theturbulent fluctuationsinthe rodwakeare dominatedbythecoherentlargespanwisevorticespreviouslyshowninFig.20andFig.21.Thecross-spectraldensityplots forthe0012 airfoilsareshownatthefirstrowofFig.22.Itisapparent thatthe spanwisesourcecoherenceis weakened forairfoils withLEtreatments, whichcorresponds to lowernoise radiation.The

|

Gpp

(

f

)

|

reduction is moreprominentat theserrationmidlocation(z_/D=0_.75)forthe0012-WLE,duetotheCp,RMSbeinglowerattheserrationmidcomparedto

theroot. Atthebottomrowofthefigure,5406airfoilsarealsoshowingsimilarphenomena.Nevertheless,inplot(b), the

|

Gpp

(

f

)

|

levelofairfoilswithLEserrations(WLEandWPLE)ishigherthanthatofporousones(PLEandSPLE)despitethe former producinglarger noise reduction.This isdueto the differencein thesource phase relationalong the airfoilspan whichwillbediscussedinthefollowing.

Previously,Fig.21suggeststhatthenoisesourcesonLEserrationshavealargespanwisephasevariation,whichpromotes destructive interference that resultsin noiseattenuation. Toverifythis, the cross-spectrumphase angleApp isplotted in

Fig. 23. The App has been averaged along a serrationwavelength (0<z/D<3) asthe spanwise correlation level is still relatively high(Rpp>0.5) within this distanceas shownin Fig. 21; phase interferencebetween sources at regions with lowercorrelationlevelwouldhavelessinfluenceonfar-fieldnoise.Thephaseangleisexpressedusingitscosinevalue(−1<

cos

(

App

)

<1), wherehigher number indicates stronger in-phase relation. Forsolid airfoils (0012-SLE and 5406-SLE),the phaseanglegenerallydecreasesinthehighfrequencyrangeassmallereddieslosecoherenceatafasterratethanthelarger ones (e.g.,the large vortices corresponding to StD=0.2). Among the different LEtreatments, only airfoils equippedwith LE serrations(0012-WLE, 5406-WLE, and5406-WPLE)are able tosignificantly decrease thephase angleat StD=0.2that corresponds tolargetonalnoisereduction. Conversely,thephaseangleoftheairfoilswithporoustreatments surrounding the fundamentaltonefrequencyiscomparableto that oftheSLE.Giventhat the poroustreatments slightlydecreasethe coherence levelatthethisfrequency,thisleadstoarelativelysmalltonalnoisereduction.Howeverathigherfrequencies,

Fig. 22. The magnitude of cross-spectral density | G pp| at two locations separated by ( a ) Δz/D = 0 . 75 and ( b) Δz/D = 1 . 5 from the airfoil midspan. The top

row corresponds to 0012 airfoils, while the 5406 ones are at the bottom.

Fig. 23. The spanwise-averaged ( 0 < z/D < 3 ) phase angle of the cross-power-spectra of surface pressure fluctuations A pp for the different LE treatments.

their phaseanglevaluestendtobe lowerthantheSLEone. ThisisinlinewiththeinformationinFigs.14and15where thenoisereductionoftheporoustreatmentsismoresubstantialforthebroadbandnoisecomponentathigherfrequencies. Bothsourcereduction andspanwiseinterferenceeffectsofdifferentLEtreatments havebeenevaluated inthis subsec-tion.Subsequently,inordertodeterminewhichmechanismplaysamoredominantroleinnoiseattenuation,acomparison betweenthenoise(OSPL)attenuationagainsttheliftfluctuations(Cl,RMS)reductionisprovidedinTable4.Thiscomparison

followstheapplicationofCurle’sanalogyforacompactdipolesource(i.e.,wherethecharacteristiclengthofthesourceis muchsmallerthantheacousticwavelengths),whichrelatesthefar-fieldsoundpressure pawiththeunsteadyforceF

(

t

)

on abody,asthefollowing:



p2 a



=



1 4

π

a_∞



2_cos2

₍

θ

₎

r2



∂

F

(

t

)

∂

t

2



(8)

Table 4

The comparison between the reduction in lift fluctu- ations and noise mitigation for airfoils with LE treat- ments relative to the solid ones; LET: leading edge treatment.

20 log (Cl,RMS,LET

Cl,RMS,SLE) OSPL LET ,SLE (dB)

0012-WLE −3 . 71 −10 . 25 0012-PLE −1 . 38 −1 . 17 0012-BLE −0 . 94 −0 . 80 5406-WLE −3 . 69 −7 . 78 5406-PLE −1 . 45 −1 . 10 5406-SPLE −2 . 06 −2 . 42 5406-WPLE −3 . 43 −4 . 43

wherea_∞ isthefreestreamspeedofsound,

θ

andr aretheobserverangleanddistancerelativetothesourcerespectively, and



· isthetemporalaverageoperator.

In Table4,theOSPLattenuationvaluesarebased onthoseinFig.16 averagedalong theobservationangles60◦<

θ

<

130◦ (i.e.,alongthemaindipolelobe).TheCl,RMSisfirstcomputedonsectionalbasisandspanwise-averagingisperformed

afterward.TheC_l,RMSratiointhetableisexpressedinlogarithmicscaletoallowforcomparisonwiththenoiseattenuation. The tableevidencesthat bothvaluesarecomparableforairfoilswithporousLE(0012-PLE/BLEand5406-PLE/SPLE),which impliesthatsuchtreatmentreducesnoisemainlybyattenuatingthesoundsourceintensity.Incontrast,theCl,RMSreduction

underpredicts the



OSPLfor0012-WLE and5406-WLEby a significant amount.Thus, itis possible toconcludethat the spanwise interference effect is the more dominant noise reduction mechanism for LEserrations. The 5406-WPLE shows a slightly smallerCl,RMS reduction asits WLE counterpart butwithsubstantially lower noise reduction.This impliesthat

the porous extension atthe serrationrootdecreases the efficacyofthe spanwise interferenceeffect ofthe serrations,as demonstratedearlierinthissubsection.

4.4. Theaerodynamiceffectsoftheleadingedgetreatments

TheLEtreatmentshavebeenshownintheprevioussubsectiontoattenuate far-fieldnoisetovariousextents.However, thisbenefitmightalsobeaccompaniedbyflow-fieldalterationsthataffectaerodynamicperformance.Thus,thissubsection assesses theeffectsoftheLEtreatmentsontheaerodynamicsofdifferentairfoilprofiles.Firstly,Fig.24displaysthe distri-butionoftime-averagedsurfacepressurecoefficientsCp,mean.Toassisttheinterpretationoftheplots,particularlyforairfoils

withporoustreatments (0012-PLE/BLEand5406-PLE/SPLE),velocity magnitudecontours attheairfoilmidspanare shown inFig.25.

Thecomparisonsbetween0012airfoilsareprovidedinFig.24plots(a)and(b)whilethosefor5406onesarein(c)to (f ).Inplot(a),0012-PLEandBLEexhibitlowerCp,mean atx/c<0.15whichcanbeattributedtotheflowtranspirationinto

theporousmedium[68].InFig.25,althoughpathlinesareshowntobedeflectedoutsideoftheporousLE,someeventually penetrate intotheporous mediumbefore beingejectedfurtherdownstream, nearthesolid-porous junction.Downstream of thesolid-porous junction(i.e.,x/c>0.15), theCp,mean ofthe porousairfoilsmatches that ofthebaseline airfoil, which

indicatesthatmajorflow-fieldalterationsarelocalizedneartheporousmediumregion.Nevertheless,asshowninFig.26(a) theporoustreatmentscauseanoticeablevelocitydeficitintheboundarylayer,whichindicatesanincrease inmomentum thickness whichleadstoa higherpressure drag.This process isalsoevidenced by Fig.25(c) and(e) astheflow ejection fromtheporousmediumregionleadstoafasterboundarylayergrowth.

TheC_p,meandistributiononthe0012-WLEvariesdependingonthespanwisepositionasdepictedinFig.24(b).Thesuction

peaksatthe serrationtipandmidare similartothat ofSLE,butthey arespreadacross largerchordwise distancewhich indicatesamilderflowacceleration.Differently,thesuctionpeakattheserrationrootismoreprominentthantheSLEone, followedbyahigheradversepressuregradientasthepressuredistributionapproachesthatoftheSLEatx/c>0.4.However, theadverse pressuregradieninfluenceontheairfoilperformance appearstobe minorsince theboundarylayerprofileat thetrailingedgeofthe0012-WLEstillmatcheswellwiththatofSLE(Fig.26(a)).

Plot(c)ofFig.24comparesthepressuredistributionofthe5406-SLEandthosewithporoustreatments(PLEandSPLE). TheC_p,meanpeakatthesuctionsideoftheairfoildisappears,whileontheotherside,thesurfacepressureislowercompared

tothatoftheSLE.ThesmallerCp,meandifferencebetweenbothsidesoftheporousLEimpliesapressurebalanceprocessthat

alsoleadstoliftreduction.Thisbehavior isalsodepictedinFig.25,inwhichpathlinesareshowntopenetratetheporous medium fromthepressuresideandlaterejectedatthesuctionside.Downstreamofthesolid-porousjunction,theC_p,mean

distributionofthe5406-PLEandSPLEisstillnoticeablydifferentcomparedtotheSLEone,particularlyonthesuctionside. ThisbehaviorisalsoreflectedintheboundarylayerprofileinFig.26(b),wherealargevelocitydeficitcausedbytheporous treatments canbefound.ThisisalsopresentinFig.25(d)and(f )wherethemeancross-flowthroughtheporousmedium resultsinarapidboundarylayergrowthonthesuctionside.Conversely,duetotheflowsuctionatthepressuresideofthe PLE andSPLEtreatments,theboundarylayerbecomesmoreenergeticasevidencedinFig.26,wherethemeanvelocityin thelowerpartoftheboundarylayerbecomeshigherthanthatintheSLEcase.

0.0 0.2 0.4 0.6 0.8 1.0 -0.5 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 -0.5 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 -2 -1 0 1 0.0 0.2 0.4 0.6 0.8 1.0 -2 -1 0 1 0.0 0.2 0.4 0.6 0.8 1.0 -2 -1 0 1

C

p, mean

x/c

SLE PLE BLE (surface) BLE (core) (b) 0012-WLE

C

p, mean

x/c

SLE WLE (tip) WLE (mid) WLE (root)

(a) 0012-PLE and BLE

(e) 5406-WPLE

C

p, mean

x/c

SLE PLE SPLE

(c) 5406-PLE and SPLE

C

p, mean

x/c

SLE WLE (tip) WLE (mid)) WLE (root) (d) 5406-WLE

C

p, mean

x/c

SLE WPLE (tip) WPLE (mid) WPLE (root)

Fig. 24. Time-averaged surface pressure distribution C p,mean for the different LE treatments. For the 5406 airfoils, the trends for the pressure side are plotted using lighter colour.

TheCp,meanforthe5406-WLEisplottedinFig.24(d).Thesuctionpeaksatbothserrationtipandmidarelowerthanthe

SLEone, andconsequently theycontribute lesstothetotal liftoftheairfoil. Incontrast,thesuction peakattheserration rootissignificantlyhigherthanthatoftheSLE,whichpartiallycompensatestheliftreductionattheserrationtipandmid. At x/c>0.4,theCp,mean distributions atthethreespanwise locationsbecomealmost identicaltothat oftheSLE.Plot (e)

showstheCp,mean forthe5406-WPLE.Alongtheserrationtipandmid,thesurfacepressuredistributionofthe5406-WPLE

resembles that of the WLE. However, the serration rootshows a significantly lower suction peak, which is similar that observedinPLEandSPLEcases.Becauseofthis,theWPLEisexpectedtoproducesmallerliftcomparedtotheWLEvariant. In addition, Fig. 26 evidences that the WPLE configuration causes a more noticeable velocity deficit at the suction side compared totheWLEone.Thisindicatesthat theporousextensionoftheWPLEisalsoresponsibleforamoresignificant dragincrease.

The effectsoftheLEtreatments onaerodynamicforcesare summarizedinFig.27.The time-averagedlift(Cl,mean)and

drag(Cd,mean)coefficientsinthetablearepresentedintermofrelativedifferencetothatoftheSLEcaseforeachrespective

airfoiltype.Althoughnotshowninthefigure,ithasbeenverifiedthattheC_d,mean oftherodinallcasesis≈ 1,similarto thatofanisolatedrod[69,70]atsubcriticalReynoldsnumber.Theresultsforthe0012airfoilsarelistedinplot(a).Among thedifferentLEtreatments,theporousones(PLEandBLE)causeadrasticdragincreasebyalmost30%,whichimpliesthat thesolidcoreintheBLEdoesnothaveasignificantinfluenceontheairfoildrag.ThisisreflectedinFig.26(a)asthereisno noticeabledifference betweentheboundarylayerprofilesoftheBLEandPLE.The dragincrease oftheporoustreatments canbeattributedtotheunsteadyflowtranspirationattheporousmediumsurfacethatenhancestheboundarylayergrowth

[48,71,72].Unliketheporoustreatments,theWLEconfigurationproducesaminordragincrease,whichcanbeattributedto thehigherAPGdownstreamoftheserrationroot[11].

Fig.27(b)liststheaerodynamicforcesofthe5406airfoils.Both5406-PLEandSPLEcauseasubstantialdragincreaseby morethan55%.Thisisduetothepressurebalanceprocessacrosstheporousmediumthatgreatlyenhancesflowinstability intheboundarylayeronthesuctionside,resultinginamassiveincreaseinmomentumthickness(Fig.26(b)).Nevertheless, theSPLEvariantshowsslightlyloweraerodynamicpenaltycomparedtothePLE,whichsuggeststhatstreamliningthe solid-porousjunctionisbeneficialformaintainingaerodynamicperformance.AmongthedifferentLEtreatments,theWLEshows

Fig. 25. Pathline plots and contours of time-averaged velocity magnitude | U| /U ∞ at the midspan of airfoils with porous LE ( c to f ) in comparison to the SLE ( a to b). Note that some pathlines may enter or leave the sampling plane in the direction normal to this page.

Fig. 26. The time-averaged streamwise velocity profile at x/c = 1 for each LE treatment. The plots are sampled at the midspan ( z/c = 0 ), except for WLE and WPLE configurations, where the values are averaged for one serration wavelength.