Definition of a benchmark for low Reynolds number propeller aeroacoustics

Definition of a benchmark for low Reynolds number propeller aeroacoustics

Casalino, Damiano; Grande, Edoardo; Romani, Gianluca; Ragni, Daniele; Avallone, Francesco

DOI

10.1016/j.ast.2021.106707

Publication date

2021

Document Version

Final published version

Published in

Aerospace Science and Technology

Citation (APA)

Casalino, D., Grande, E., Romani, G., Ragni, D., & Avallone, F. (2021). Definition of a benchmark for low

Reynolds number propeller aeroacoustics. Aerospace Science and Technology, 113, [106707].

https://doi.org/10.1016/j.ast.2021.106707

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Contents lists available atScienceDirect

Aerospace

Science

and

Technology

www.elsevier.com/locate/aescte

Definition

of

a

benchmark

for

low

Reynolds

number

propeller

aeroacoustics

Damiano Casalino

a

,

Edoardo Grande

b,

∗

,

Gianluca Romani

b

,

Daniele Ragni

b

,

Francesco Avallone

b

a_{SIMULIA,DassaultSystèmes,Germany}

b_{Aerodynamics,WindEnergy,FlightPerformanceandPropulsionDepartment,DelftUniversityofTechnology,theNetherlands}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received25November2020

Receivedinrevisedform16March2021 Accepted29March2021

Availableonline9April2021 CommunicatedbyQiulinQu Keywords:

Propellernoise

LowReynoldsnumberpropeller BEMT

LBM PowerFLOW

Aeroacousticbenchmark

Experimental and numerical results of a propeller of 0.3 m diameter operated at 5000 RPM and axialvelocityranging from0 to 20 m/sand advance ratioranging from0 to 0.8 are presented as a preliminarysteptowardsthedefinitionofabenchmarkconfigurationforlowReynoldsnumberpropeller aeroacoustics.ThecorrespondingrotationaltipMachnumberis0.23 andtheReynoldsnumberbasedon thebladesectionalchordandflowvelocityvariesfromabout46000 to106000 intheoperationaldomain andinthe30% to 100% bladeradialrange. Forceand noisemeasurementscarriedoutinalow-speed semi-anechoicwind-tunnelarecomparedtoscale-resolvedCFDandlow-fidelitynumericalpredictions. Results identify the experimental and numerical challenges of the benchmark and the relevance of fundamentalresearchquestionsrelatedtotransitionandotherlowReynoldsnumbereffects.

©2021TheAuthor(s).PublishedbyElsevierMassonSAS.ThisisanopenaccessarticleundertheCCBY license(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

The development of tools forthe design and optimization of

propellers employed in multi-copter unmanned air vehicles and

droneshastofacetwomajordifficulties.Thefirstoneisthe avail-abilityofreliableforce,flowandnoisedataacquiredforthesame experiment in controlled conditions. The second difficulty is re-latedto theintrinsic limitationof scale-resolved CFDmethods to

capture low Reynoldsnumber phenomena like laminarto

turbu-lentflowtransitionandtheoccurrenceoflaminarseparation bub-bles.

Recent attempts to validate Lattice-Boltzmann Method / Very Large Eddy Simulation (LBM/VLES) results [1] revealed that the flowrecirculationinducedby arotoroperatedina confined envi-ronment,andtheconsequentinteractionbetweenbladesand tur-bulenteddies,generateshigh-orderBlade-PassingFrequency(BPF) loadingnoise harmonics.Similarobservations havebeenmadein other experiments [2]. Other sources of experimental uncertain-ties are: (i) the vibration of the test rig resulting in additional sources relatedtothe randomblademotion[3],(ii)the presence of electricmotornoise, whichis affected by therotor torque [4]

*

Correspondingauthor.

E-mailaddress:e.grande@tudelft.nl(E. Grande).

andthus not easily separable fromthe rotor aerodynamic noise, ortreatableasabackgroundnoisecontribution,and(iii)theflow regimeatseveralradialstations(laminar/turbulent, attached/sepa-rated)andthepresenceoflaminarseparationbubbles.Inthecase ofnon-axialflowconditions,additionalcomplicationsarisedueto theperiodicinflowvariationandthenecessitytocharacterizeflow hysteresis mechanisms, while mitigating the higher vibrations of therig.Onthenumericalside,themain challengesare relatedto thecapabilityoftheCFDsolvertopredictthecorrecttransitional flow behaviour.Scale-resolved methodslike LBM/VLES[5] or De-tached Eddy Simulation [6] (DES), ordifferent variants ofhybrid ReynoldsAveraged Navier-Stokes(RANS) / LargeEddy Simulation (LES) methods are typically used for aeroacoustic purposes as a faster alternative to LES. However, hybrid methods have to deal with the “grey-area” related problem of finding the balance

be-tween eddy viscosity in the scale-modelled flow region and the

need of not anticipating separation on smooth surfaces,and not preventingtransition in boundarylayers andwakes [7,8]. Broad-bandnoiseisgeneratedbytheinteractionbetweenboundarylayer

turbulence and the trailing edge, by the impingement of inflow

turbulence on the leading edge, and by Blade-Vortex Interaction (BVI) at very low or negative advance ratios. Trailing edge noise prediction,inparticular,reliesonthe capabilitytopredict

transi-https://doi.org/10.1016/j.ast.2021.106707

tion with low-intrusive trippingdevices like zig-zagstrips [9,10] orsyntheticturbulencegenerators[11].

CapturingthecorrectboundarylayerpropertiesoflowReynolds number propellers is also crucial for the sake of accurate thrust andtorquepredictions.Typical turbulenceclosuremodelsusedin RANS solvers sufferto predict thecorrect near-wallbehaviour of turbulent flowsanddonotprovidereliable predictivecapabilities oftransitionalflows[12].Low-fidelitymethodsbasedontheBlade

Element Momentum Theory (BEMT) and two-dimensional airfoil

lift and drag coefficients computed via coupled

panel/boundary-layer modelslikeXfoil [13] canprovidesatisfactory accuracy, be-yond thecommonexpectation, atsufficientlyhighadvance ratios [14]. Unfortunately, BEMT methods suffer for the inaccurate 2D predictionofstallandpost-stallbehaviour ofhighlyloaded blade sectionsclosetothehubatlowadvanceratios[15,16],andforthe inaccurate modellingofthe near-wakeinductioneffects,again, at lowadvanceratios[14].

The main goalof the presentwork is toprovide an overview ofall the aforementionedexperimental, numericalandmodelling challengesby comparingpreliminary experimental,scale-resolved

LBM/VLES and low-fidelity BEMT results, and thus progress

to-wards the definition of a benchmark problem for low Reynolds

numberpropelleraeroacoustics.Thisispartofaresearchinitiative aimed at investigating the different broadband noise generation mechanisms and the properties of transitional flows at different radial stations and for different operating conditions, including non-axial flow conditions that are typical ofeVTOL vehicles and drones. More detailed descriptions of the experimental, numeri-calandmodellingpillarsofthepresentbenchmarkactivitywillbe providedinfuturepublicationsfollowingtheoverviewgiveninthe presentwork.

The paper is organized asfollows. The physical test environ-mentandthepropellergeometryaredescribedinsection2.

Infor-mation aboutthe employed acoustic measurement techniques is

provided insection 3.TheLBM/VLESsimulationframework based

on the commercialCFD software SIMULIA PowerFLOW® _by

Das-saultSystèmes(3DS)isdescribedinsection4.Inthesamesection, the Ffowcs-Williams & Hawkings (FW-H) tools available in the

SIMULIA PowerACOUSTICS® _{software used to compute the noise}

fromthetransientnear-fieldflowsolutionarealso presented. The BEMT-basedpropeller noise formulationavailable intheOpty

∂

B®

aeroacoustic toolkit by the firstauthor ispresented in section 5. Uncertaintiesandchallengescharacterizingthepresentbenchmark arediscussedinsection6.Experimental,low- andhigh-fidelity nu-mericalresultsarereported,comparedanddiscussedinsection7. Noisesourceanalysesarepresentedinsection8.Themainfindings ofthepresentworkarefinallydrawnintheconclusivesection. 2. Testrigandphysical/digitalenvironment

The test rig installed in the semi-anechoic aeroacoustic wind tunnel of Delft University of Technology (TU-Delft A-Tunnel) is showninFig.1.Inthepresentexperiment,aconvergentnozzleof contractionratio15

:

1 andexhaustdiameterof0

.

6 misused.The maximumflowspeedthattheA-Tunnelisabletoprovidewiththis nozzleis35 m/s,themeanstreamwisevelocityisuniformwithin 0

.

6%, the turbulenceintensity is 0

.

14% at 2

.

5 m/sanddecreases below0

.

1% with aflow velocity above10 m/s.The height ofthe test chamber is 3

.

2 m,andthe other two dimensionsare 6

.

4 m and4

.

4 m.Thecut-offfrequencyofthechamberisapproximately 200 Hz. Adescriptionof thetunnel,withdetails oftheflow and acousticcharacterizations,canbefoundinRef. [17].

The propeller isconnectedto aprofiled aluminiumcylindrical nacelleof5 cmdiameterforminimuminterferencewiththe pro-peller flow, within which the motor, an encoder, a loadcell and atorque cellareembedded.The nacelleissupported bystiffened

Fig. 1. Test rig in TU-Delft A-Tunnel.

hollowaluminiumNACA0012profilesof6 cmchord,insidewhich thecablingishousedandremotelyconnectedtothe instrumenta-tion.Theentirestructureisheldupabovethenozzleofthetunnel byfourwiretubes of2 cmdiameterfixedtothetunnel.The en-tirerigisverystiffandsubmittedtoalmostnovibrationwhenthe rotorisoperatedinaxialflowconditions,asinthepresent prelim-inarycampaign. Thenacelle hoststhe propeller drivetrain,which consistsof:

•

anelectricalbrushlessmotorLeopardHobby3536-5T1520KV

withadiameterof27

.

8 mmandmaximumpowerof550 W;

•

a USDigital EM1optical encoder to measurethe shaft rota-tionalspeed,which consistsofa rotatingdisk,alight source andaphotodetector;

•

a load cell Futek LSB200 excited with 5 VDC forthe thrust

measurement, and characterized by a maximum capacity of

22

.

2 N, non-linearity and hysteresis of

±

0

.

1% of RO and an operatingtemperaturerangeof223–365K;

•

a Transducer Techniques RTS-25 torque sensor excited with

10 VDC, characterized by a maximum capacity of 0

.

18 Nm,

non-linearityandhysteresisof

±

0

.

1% of ROandanoperating temperaturerangeof219–366K.

The motor is powered by a Delta Elektronika DC power supply

witha voltagerange of0–15V anda currentrange of0–100 A. Thedistancebetweentherotorplaneandthejetexhaustplaneis about0

.

5 m.Thethrust andtorquesignalsareacquiredbya Na-tionalInstrumentacquisition boardwithasamplingfrequencyof 5 KHz andan acquisition time of15 s. Anexploded view ofthe propellerdrivetrainisshowninFig.2.

ThepresenttestrighasbeendesignedtohostaPIVacquisition systemforrotor phase-lockedacquisition,andtoenable non-axial flowaeroacousticstudiesbypivotingthewholesystem.These as-pectswillbethesubjectoffuturepublications.

Thepropeller employedfor thisexperimentis derived froma

two-bladed APC-96 model,by reshaping each single profile with

a NACA4412 airfoil and rescaling the size to D

=

0

.

3 m rotor diameter (tip radius RT

=

0

.

15 m). An elliptical root section is merged withthe profiled section starting from a radius of1 cm (r

/

RT

=

6%).Thehubradiusis1

.

25 cm.Animageofthepropeller together withthe employed referencesystemis shownin Fig. 3. The chordandtwist radial distribution are plottedin Fig. 4. The propeller,madeofaluminiumalloys,wasmanufacturedusingCNC machiningwithRasurface finishbetween0

.

4 to0

.

8 μm.The

in-Fig. 2. Exploded view of the propeller drivetrain.

Fig. 3. Propeller geometry and reference system.

Fig. 4. Propellerchordandtwistdistributions.(Forinterpretationofthecoloursin thefigure(s),thereaderisreferredtothewebversionofthisarticle.)

terestofusingthismodelinsteadoftheoriginaloff-the-shelfone residesin: (i) thepossibilityto delivera CADmodelandthe an-alytical description ofthe constructive parameters aspart of the benchmarkdefinition,(ii)thepossibilitytocontrolmanufacturing tolerances, (iii)andthe highstiffness ofthe model,thus guaran-teeingnegligibleelasticdeformationsinoperation.

The propeller is located about 1

.

2 nozzle diameter from the nozzle, thus well inside the potential core of the jet. This pre-ventstheoccurrenceofnoisegeneratedbytheinteractionbetween therotorbladesandjetshear-layerinstabilities,aswellasspectral broadeningofnoisetonesduetorandomvariationsoftheacoustic traveltimeacrosstheunsteadyjetshearlayer.Asdiscussedin sec-tion6.4,flowsimulationsareconductedbyconsideringapropeller in free-stream conditions. The finite extension of the jet, whose crosssectionalareaisonlyfourtimeslargerthantherotorarea,is expectedtohaveaninfluenceontherotorsteadyloading,andthus onthenoiseBPFtone.Thiseffectwillbequantifiedinfuture stud-ies by comparing free-stream andjet-stream simulations results, inparticularforcasesatnon-zeroinflowangle.Indeed,whenthe rotor plane istilted, the jet deflection anddistortion induced by the propeller areexpectedto havea non negligibleeffecton the

Table 1

Propelleroperatingconditions.

V0(m/s) J Remin Remax 0 0 46400 96700 6 0.24 52100 98200 10 0.4 56300 99700 15 0.6 63000 102800 20 0.8 68400 105600

Fig. 5. Linear microphone array configuration.

periodicbladeloading,andthusontonalnoiseBPFharmonic com-ponents.

The propeller is operated by varying the jet wind tunnel

ve-locity and the motor RPM to obtain a range of advance ratio

J

=

V0

/(

nD

)

from0 to0

.

8,V0denotingthefree-streamaxialflow velocityandn the numberofrotorrevolutions persecond.Inthe presentwork, only results for five valuesof the jet exit velocity of0,6, 10,15 and20 m/s, 5000 RPM(rotational tipMach num-berof0

.

23)andzeroflowincidenceareconsidered,corresponding to J

=

0, 0

.

24, 0

.

4, 0

.

6, and 0

.

8, respectively. Notice that BEMT computationsare performedwithastepof2 m/softheaxial ve-locity(11 conditions), thereforethe advanceratiovalue of 0

.

6 is replacedbyavalueof0

.

64 (V0

=

16 m/s).Acousticresultsarenot reportedfor J

=

0

.

8,sincethepropellerthrustandthusthetonal noisevanish,whilethewind-tunnelbackgroundnoiseoverwhelms thebroadbandrotornoise.

Asummaryoftheoperatingconditionsandcorresponding

min-imum and maximum Reynolds number based on the sectional

chordandtotalvelocitycomputedbyBEMTisreportedinTable1. Itisworth mentioning that,dueto verylow valuesofthe jet Mach number (0

.

06 at J

=

0

.

8), no shear-layer corrections are neededto take intoaccount the effects ofthe mean-flow refrac-tionontheradiatednoiselevelsanddirectivity.

3. Noisemeasurements

Noisemeasurements are performedthrough 13G.R.A.S. 40PH

analog free-fieldmicrophones(frequency response:

±

1 dB inthe

frequencyrange of 10 Hzto 20 kHz, maximum output: 135 dB)

mountedonalinearmicrophonearray,sketchedinFig.5,located inaplaneperpendiculartothepropellerplane.Thearrayisat1

.

2 m(4D)inthe y directionwithrespecttothe propelleraxis.The distancebetween each microphoneis 0

.

15 m(0

.

5D), the micro-phone#7 islocatedatthepropeller plane,themicrophone#1 is 0

.

9 m(3D)abovethepropeller planeandthemicrophone#13 is 0

.

9 mbelow.Themicrophonemountingsupportsandarrayframe

are covered by a layerof acousticabsorbing material inorder to mitigatetheacousticreflections.

The data acquisition system consists of two National

Instru-ment modules NI9234. Asampling frequency of 51

.

2 kHz and a

recordingtimeof30 sareusedforeachmeasurement.The acous-ticsignalsareseparatedinto1197 Hanning-widowedWelchblocks with50% overlap,correspondingtoabandwidthof20 Hz.

Aftereverychangeoftheinflowvelocity,noiseacquisitionsare startedafterasufficientlylongtimetoachievestabilizedpressure conditionsinthechamber.Flowrecirculationaroundthepropeller ismonitoredwithahot-wirescanningatdifferentaxialandradial locations. Spuriouseffectsrelatedtotheflowrecirculationwillbe addressedinfuturestudies.

4. LBM/VLESflowsolverandFW-Htools

TheSIMULIAPowerFLOWsolver,version6-2019,hasbeenused inthe presentwork.The propertiesofthissoftware andits suit-ability for aeroacoustic applications are widely discussed in the literature, covering both aerospace, automotive and wind-energy applications. Referringto noisefrom rotatingparts,the following benchmark workscan be quoted: smallUAV rotors[1], car cool-ing fans[18],aircraft propellers[19], aero-engine fan/OGVstages [10,9,20], and helicopter rotors [21]. PowerFLOW is based on a

Cartesian mesh LBM with automatic mesh generation, with no

restriction on the geometric complexity of the models that can be treated. Fully automatic workflows, from case preparation to results post-processing, can be easily developed, as for complex thrust-vectoringmulti-coptereVTOLvehicles[5],forwhichan en-tireflightenvelopcanbeexploredinreasonabletimesbyrunning multiplejobsonaHPCcloudsystem.

LBM is intrinsically unsteady and compressible. It is based on the idea of statistically tracking the advection and collisions of fluid particles by an integer number of distribution functions alignedwithpredefineddiscretedirections.Flowvariablessuchas densityandvelocityarecomputedby takingtheappropriate mo-ments, i.e., summations over the setof discrete directionsof the particle distribution function [22]. The relaxation time andother parameters oftheequilibriumdistributionfunction arecomputed by considering scales related to the turbulent motion of the re-solvedflowfield,computedusingatwo-equationtransportmodel based on the k

−



re-normalization group theory [23,24]. Con-verselytoRANSmodels,Reynoldsstressesarenotexplicitlyadded totheflowgoverningequations,butareaconsequenceofan alter-nationofthegasrelaxationpropertiesthatleadtheflowtowardsa stateofdynamicequilibrium.ThisistheessenceoftheLBM/VLES model: anextension ofthe kinetic theoryfroma gasofparticles to a gas of eddies, which can be also interpreted as the appli-cation of a Boussinesq model at lattice Boltzmann level. It can be demonstratedthat theeffectiveReynoldsstresses havea non-linearstructureandarebettersuitedtorepresentturbulenceina state farfrom equilibrium, such as inthe presence of distortion, shearandrotation[25].

Thenoiseradiatedatthemicrophonepositionsiscomputedin a post-processing stage by using three softwares, twoare based on a standard FW-H Formulation 1A by Farassat [26], solved in forward-time[27] andperformingtheintegrationonthesolid sur-facesofthepropeller,andoneisbasedonthefrequency formula-tionfornon-movingsourcesbyLockard[28] extendedtothree di-mensions.ThefirstsoftwareisPowerACOUSTICS,anditisusedto compute thereferencesignalsandspectracompared tothe

mea-surements and low-fidelity predictions, whereas the second and

thirdsoftwarearepartoftheOpty

∂

B toolkitembeddedinthe

au-tomatic eVTOLaeroacousticPowerFLOW workflow.Thetwo

time-domain FW-H software compute identical noise signals, but the

second one, Opty

∂

B-PFNOISESCAN, gives access to additional noise

Fig. 6. Digital propeller model with wall partitioning and trip on the suction side.

sourceinformationthroughthe followinglistoffeaturesused for thepresentwork:

•

beam-forming analysis in the rotating reference system for broadbandnoisesourceanalysis;

•

visualization ofthe surface noise contribution at a given in-stantandmicrophone.

The frequency-domainFW-H softwareOpty

∂

B-FWHFREQ isused to

compute noise spectra in the reference system of the blade at

hundredsofmicrophoneonadigital beam-formingarray usedto perform beam-forming visualization of broadband noise sources. TheCLAEN-SC[29] algorithmavailableinOpty

∂

B-BF,benchmarked againstotherCLEAN-SCimplementations[30].

The3DSautomaticeVTOLnoisePowerFLOWworkflowhasbeen

used for the presentstudy. The workflow is fed with one blade

STLfile, a hub STLfile, and, ifpresent, an airframeSTL file.This guarantees a user-friendly access to a multi-fidelity approach in

3DSmodel-basedsystemengineeringframework foreVTOL flight

mechanics and community noise assessment. In the PowerFLOW

workflow,theuserprescribes ambientandflightconditions,rotor settings(centre,axis,RPM)and,ifrequired,referencethrustvalue foranautomaticcollective/cyclicpitchtrimoftherotor.Theblade geometryfile is processed by the Opty

∂

B-PFROTOR that generates: a blade portion for the setting of laminar/turbulent patches and thegeneration of meshrefinement regions, a zig-zagtrip onthe suctionand/or pressure side oftheblade, andastructured mesh for advanced force/noise post-processing. Interestingly, the same tool Opty

∂

B-PFROTOR used to process the blade geometry is also usedto generate all theinput filesrequiredby the fully

analyti-cal BEMT-basedforce/noisepredictionworkflow.The PowerFLOW

workflow creates a simulation setup from scratch, following an

established best practice in terms of mesh resolution and solu-tion sampling properties. Once the simulation is completed, the workflowexecutesthetoolOpty

∂

B-PFPROPtoperformstandardand advancedforce/noiseanalyses, communitynoise assessmentfora userdefinedtrajectory,andsoundauralization.Forthesakeofthe present analysis, a zig-zag trip of 0

.

17 mm height is located at 25% ofthe chordon thesuction side only. As depictedin Fig. 6, thetripseparatesawall-modelledlaminar-to-turbulentautomatic transitionpatchfromawall-modelledfully-turbulentpatch.An au-tomaticlaminar-to-turbulenttransitionmodelisusedontheother partitions. The finest mesh resolution of 5200 voxels/D is used aroundtheleading- andtrailing-edgeandthetrip,whereasatwice coarsermesh resolutionisused elsewherearound the blade.The griddependenceofbothforcesandfar-fieldnoise isdiscussedin section6.4.Thetripheightisresolvedwithabout3 voxels.Based ontheempiricalcriteriaofa height-basedcriticalReynolds num-berof200 [31],thetrip isabout6 timeshigherthanthecritical one forthe hover caseand a radial section r

/

RT

=

85%. Forthe samecondition, thetrip height inviscous units( y+) variesfrom about15 atr

/

RT

=

30% toabout50 atthetip.Therefore,a bound-arylayer transitionsimulation wouldbe over-tripped,but inthe presentcasethetripisonlyexpectedtodrivetheVLESmodel

to-wardsascale-resolvingbehaviour,andinthisrespectitisnotvery intrusive.Tosupportthisargument,asensitivitystudyofthe radi-atedacousticfieldtothetripheightisreportedinsection6.4.

Severalsimulationshavebeencarriedout withthegoalof in-vestigating the effect of the trip location on aerodynamic forces and noise, which will be extensively described in future publi-cations. More specifically, simulations for all the aforementioned valuesofthe advanceratiohavebeenalsoconductedwitha trip following thetransition linepredictedby the BEMTmethod.The resultsshowonlyasmallreductionofthebroadbandnoiselevels, asaconsequenceofadelayedunforcedtransitionatincreasing ad-vanceratios.Anexampleofnoisespectrumpredictedwiththetwo triplocationsisalsoreportedinsection6.4.

To concludethis section, some information aboutthe simula-tionsetupis provided.Afree-streamrepresentationoftheproblem is considered, thereforethe wind-tunnelnozzle, thejet flow and the different components of the test rig are not included in the simulation.Afullyanechoicenvironment issimulated,by consid-eringasphericalsimulationdomainof325D radius,withtherotor located in the centre, and by applying acoustic sponges starting

from a distance of 15D from the rotor. The overall number of

finest-equivalent voxels is 15

.

2 millionand every run, consisting of8 and 10 rotorrevolutionsforsettling andacquisition, respec-tively,requiresabout27 h on430 IntelXeonCPUE5-26972.6GHz processors.

5. BEMT-basedmodel

A conventional BEMT formulation with uniform inflow and

Prandtltip-lossescorrection isemployed. Therequiredblade

sec-tional forces are computed using the boundary layer model by

Drela&Giles[32,13] implementedintheBEMTtool.Aerodynamic polarsarepre-computedwithanangularstepof1 deginthe an-gle of attack range from

−

16◦ to 16◦,and at five values of the Reynoldsnumbercoveringthewholerangeofradialvariation.For thesakeofnumericalrobustnessandefficiency,allquantities

em-ployed by the iterative BEMT algorithm (sectional aerodynamic

coefficient and stall angles) and by the broadband noise model

(boundary layer properties atthe trailing edge)are polynomially fittedwithrespecttotheradialcoordinateandtheangleofattack. Post-stallliftanddragcoefficientsarecomputedusingtheViterna &Corriganapproach[33].

AcrucialelementofthedevelopedBEMTprocedureconsistsin

the way the iterativeaxial and azimuthal momentum balance is

applied. Following the classical BEMT procedure, the equilibrium foracircularradialstripofsize



r reads:



T

=

4

π

r

ρ

_∞V_∞2

(

1

+

a

)

a



r

=

1 2

ρ

∞V 2 1c

(

clcos

φ

−

cdsin

φ)

B



r (1)



Q

=

4

π

r3

ρ

∞V_∞

(

1

+

a

)

b



r

=

1 2

ρ

∞V 2 1c

(

cdcos

φ

+

clsin

φ)

Br



r

,

(2) where c istheblade sectional chord, B is the numberof blades,

a is the axial velocity induction coefficient

(

Vx

=

V∞

(

1

+

a

))

, b

is the azimuthal velocity induction coefficient (Vt

= 

r

(

1

−

b

)

),

V1

=



V2

x

+

Vt2 isthetotal velocityseen byevery radial section, and

φ

=

tan−1

(

Vx

/

Vt

)

istheflow inductionangle.Thelocalflow incidenceasaresultofthegeometricalbladesection pitch

θ

and wake induction is

α

= θ − φ

. The sectional lift and drag coeffi-cients cl and cd are function ofthe local

α

, Reynolds and Mach number,andarecomputedfromstoredlook-uptablesof polyno-mial fitting coefficients. By introducing the radial solidity coeffi-cient

σ

=

c B

/(

2

π

r

)

, the sectional thrust and torque coefficients

cT

=

clcos

φ

−

cdsin

φ

andcQ

=

cdcos

φ

+

clsin

φ

andsimplifying, itispossibletoobtainthefollowingtwoequations:

(

1

−

σ

4cT

)

a 2

_{+ (}

₁

₋

σ

2cT

)

a

−

σ

4cT1

+



r V_∞ 2

(

1

−

b

)

2

=

0 (3) b

=

σ

4 V_∞2

(

1

+

a

)

2

+ 

2r2

(

1

−

b

)

2 V_∞



r cQ 1

+

a

.

(4)

Thissystem ofalgebraic equationsis solved iteratively, b de-motingthe valueofb atthe previousiteration,withinitial guess valuesof0

.

2 and 0

.

1 fora and b,respectively,usinga relaxation coefficient of 0

.

3, andby considering the largest positive rootof thesecondorderequationfora.Thisprocedureallowsa toexceed theunitaryvalueatlowadvanceratios.

Integrationofthesectional thrustandtorquecoefficient along theradialextensionoftheblade,fromaminimumradiustothetip radiusRT providestheoverallthrustandtorquewhichare subse-quentiallytranslatedintothrustandtorquecoefficientsCT andCQ bydividingby

ρ

_∞



2

π

R4_T and

ρ

_∞



2

π

R5_T,respectively.Results re-portedin section 7have beenobtainedby integrating theforces fromr

/

RT

=

0

.

3 to1.

The radial distribution of the blade sectional force and the sectional airfoil surface are used to define the input of a

time-domain FW-H noise computation based on the compact dipole

and monopoleformulation by Casalino et al. [34]. This provides

the tonal noise contribution, whereas broadband noise is

com-puted using the trailing edge noise model by Roger & Moreau [35], extended to a rotating blade [36] and by using seven dif-ferentsemi-empiricalWallPressureSpectrum(WPS)modelsbased on boundary layer quantities extracted at95% of the chord. The

employedWPSmodelsare:

•

Schlinker&Amiet[37],basedonboundarylayeredgevelocity anddisplacementthickness;

•

correctedSchlinker & Amiet,wherethe exponentofthe cor-rectionfunction(equationA6inRef. [38])hasbeenmultiplied byanarbitraryfactor5;

•

Goody [39], based on boundary layer edge velocity, thick-nesses,andskinshearstress;

•

Rozenberg-07 [40], derived from Goody model, based on

boundarylayeredgevelocity,thickness,displacementand mo-mentum thicknesses, skin shear stress andstreamwise pres-suregradient;

•

Rozenberg-12[41],derivedfromRozenberg-07model;

•

Kamruzzaman et al. [42], derived from Goody model, based onboundarylayeredgevelocity,displacementandmomentum thicknesses,skin shearstress andstreamwisepressure gradi-ent;

•

Lee[43],derivedfromRozenberg-12model.

Asimilarbroadbandnoisepredictionprocedureforrotor/propeller

assessment andoptimization has been used by other authors in

thepast[44,45]. 6. Sanitychecks

In this section, possible causes of discrepancy between the

three approaches involved in the current benchmark are

inves-tigated with the goal of assessing the level of maturity of the currentbenchmarkbeforefurthersteps.Amutualcomparison be-tween predictions andmeasurements repeated atdifferenttimes isindeedthebestwaytoprogressivelyincreasethequalityofthe datasetpriorrealisingittothecommunity.

Fig. 7. Background,electricmotorandpropellernoiseinhoverconditionsat micro-phone#7,withverticallinesmarkingBPFharmonics.

6.1. Experimentalchallengesanduncertainties

The reportedexperimentconstitutesarepetition ofaprevious one described inRef. [46], afterwhich an amplitude modulation in the noisespectra was observed, dueto reflections onthe mi-crophone array. In the current experiment, the previous circular array hasbeenreplaced by alineararray,andacousticabsorbing materialhasbeen appliedaroundthemicrophonestomitigate re-flections. This new experiment offers the occasion to investigate theeffectsoffree-/fixed-transitionpointonthebladeby perform-ing noise measurements with/without a transition strip applied to 25% of the chord on the blade suction side. Although acous-tic reflections have been significantly removed, other previously identified sources ofuncertaintyremain andare currently scruti-nizedinpreparationoffuturemeasurementcampaigns.Theseare reportedinthefollowingparagraphs.

•

InstantaneousvariationofthepropellerRPM.Astatistical anal-ysisoftheBPFtonallevelwasconductedandledtothe obser-vationthatavarianceofabout1 dBcanbeexpectedoverthe wholeoperationalrangeandradiationarc,anduptoabout2 dBintwocases:(i)hover,duetothehigherforces,and(ii)at

J

=

0

.

8,duetothehigherimpact oftheinflowvelocity fluc-tuations.

•

Presence of rotor motor noise, which has been identified

through motor-alone noise measurements in high-frequency

tonalpeaksintherangeof1 to6 kHz,asevidentinthenoise spectrumPSDplottedinFig.7.

•

Presenceofashaftfrequencypeak(BPF

=

0

.

5)andharmonics duetoanimperfectbalanceoftheblades inhighload condi-tions, asalsoevident inFig. 7.It shouldbe pointedout that motor-alonenoisemeasurementsinloadedconditionscanalso reveal the presence of intense harmonics of the shaft fre-quency.

•

Presence ofbackground wind-tunnel noise below thecut-off frequency (

∼

200 Hz). As discussed in Ref. [46], the wind-tunnel noisemasksthe BPFtonalpeak at J

=

0

.

8.Therefore, noise resultsforthiscondition arenot reportedinthiswork. Atloweradvanceratiosasufficientsignal-to-noiseratioexists, butthenoiselevelatthefirstBPF(167 Hz)issubmitted toa certainuncertainty.

•

Locationoftheboundarylayertransitionatdifferentoperating conditions,especiallyfortheuntrippedcases.

Amoredetaileddescriptionoftheexperimentalfacilityand uncer-taintycharacterizationisthesubjectoffuturepublications.

6.2.Verificationofairfoilboundarylayeranalyticalsolution

The main challenge in a BEMT analytical approach consists

in computingthe correct aerodynamic polarand boundary layer

properties,includingtransition, laminarandturbulentseparation. InthisworkwehaveadoptedtheboundarylayermodelbyDrela& Giles[32],coupledwitha2ndorderpanelmethodthroughan iter-ativeprocessbasedontheboundarylayertranspirationvelocity.A specificfeatureoftheimplementedalgorithmisthemanagement oftheLighthill’ssingularityclosetolaminarseparation,which con-sists in assuming a vanishing streamwise gradient of the kinetic energy shape parameter, providing a value of the edge velocity gradient, and making use of de l’Höpital theorem. Performing a validationofthemodelisbeyondthescope ofthepresentwork, but it is interesting to perform a verification of the implemen-tation by using Xfoil results as a reference. A NACA4412 profile discretized with 160 panels clustered atthe leading edge and a blunt trailing edge of thickness t

/

c

=

2

.

52

·

10−3 is used. Polar computationshavebeenperformedforaMachnumberof0

.

1 and two values ofthe Reynolds number, 106 and 8

·

104, the second onebeingintheaveragerangeofthepresentpropelleranalysis.

Fig. 8 shows the aerodynamic lift and drag coefficients com-puted with Xfoil and withOpty

∂

B-BEMT. At highnegative angles ofattack, the Xfoil resultshave not reachedconvergence andno

attempt was done to prevent this. At the higher value of the

Reynolds number the agreement between the two codes is fair,

whereas, at the lower Reynolds number, a significant difference canbeobserved,inparticularinthedragcoefficient.

Boundary layer properties for the Reynolds number equal to 106 are plotted in Figs. 9 and 10 for an angle of attack of 4◦ and 12◦, respectively. At

α

=

4◦, the most significant difference betweenthetworesultsisthelocationofthetransition,whichis anticipatedby about10% by Opty

∂

B-BEMT. AtthisReynolds num-ber,bothsolutionsrevealthepresenceofatrailing-edgeturbulent separationonthesuctionsideatthehigherangleofattack,butthe displacementthicknessafterseparationundergoesaslowergrowth inthe Opty

∂

B-BEMT solution.Consequently, the displacement and momentumthicknessfollowadifferentdevelopmentinthewake. Thesedifferences are relatedto the underestimated drag at high positiveangleofattackobservedinFig.8.

Boundary layer propertiesforthe Reynolds numberof 8

·

104 areplottedinFigs.11and12foranangleofattackof4◦ and12◦, respectively. At

α

=

4◦, a laminar separation bubble on the suc-tionsidetakesplaceinbothsolutions,butitsextensionissmaller fortheOpty

∂

B-BEMT solution.Furthermore,theOpty

∂

B-BEMT solu-tionexhibitsasignificantlylower growthrateofthedisplacement thicknessinthebubble.Similartrendscanbeobservedat12◦ inci-dence,althoughtheinfluenceofthelaminarbubbleonthe differ-entevolutionofthe boundarylayerafter reattachmentissmaller than atlower incidence.A trailing-edgeturbulent separation can be observed also for this Reynolds number, and it is character-izedbya fastergrowthofthemomentumthicknesspredictedby

Opty

∂

B-BEMT. At this angle of attack, the trends in the wake are alsoverydifferentanddeservemoreattentioninthefuture.

Itisimportanttomentionthattheexistenceoflaminar separa-tionbubbleshasbeen observedalsoforthepresentpropellercase

through phase-locked PIV measurements and oil flow

visualiza-tions,whichwillbedescribedinfuturepublications.Anhypothesis istherefore underexamination, accordingto whichthe high fre-quencyhumps observedin the noise spectraare associated with thenearwakesheddingoriginatedfromalaminarseparation bub-ble[47,48].Asdiscussedinsection7,thecomparisonbetweenthe noisespectrameasuredforacleanandatrippedpropellerisvery usefultoshedsomelightonthisflowmechanism.

Fig. 8. Aerodynamic coefficients for Reynolds number of 106_{(top) and 8·10}4_(bottom).

Fig. 9. Boundary layer edge velocity, displacement thickness, momentum thickness and skin friction coefficient for Reynolds number of 106_andα=4◦_. 6.3. Selectionofthetrailing-edgenoisemodel

Apre-comparisonbetweenmeasurednoise spectraand

BEMT-based trailing-edge noise prediction carried out using the tool

Opty

∂

B-PNOISEisperformedwiththegoalofselectingthebestWPS modelforthepresentpropeller.Allcomputationshavebeen per-formedbyconsideringaconvectionvelocitycoefficientof0

.

65 and aspanwisecorrelationcoefficient ofbc

=

1

.

5 inRoger&Moreau’s formulation, without any further tuning. Fig. 13 shows

compari-sonbetweentheaforementionedsevenmodelsandthemeasured

noise spectra.Unfortunately, partoftherelevant frequencyrange iscontaminatedbytheelectricmotornoise.Moreover,asitwillbe discussedinsection7,themeasurednoisespectraat J

=

0

.

4 and

J

=

0

.

6 reveal thepresence ofa high-frequency hump, which is likelyduetoa laminarseparationbubble.Itisthereforenoteasy to perform a method assessment. For all advance ratios, all the Goody-likemodelsprovide similartrends,butsignificantly differ-entlevels, inlinewithprevious calculations[43].Inhover

condi-tions, the Rozenberg-07 model overestimatesthe noise levels by morethan20 dB,andthisislikelyduetoastrongersensitivityto thewallpressuregradient.Basedontheseresults,itcanbeargued thatthecorrectedSchinkler&Amiet’smodelprovidesslightly bet-terspectral trends, andsignificantly better noise levelprediction forallconditions.Insection7,onlythecorrectedSchinkler& Ami-et’sWPSmodelresultswillbecomparedtotheLBM/VLESresults. It is worth pointing out that the employed trailing-edge noise modelincludesaleading-edgebackscatteringcorrectionbasedon theleadingtermoftheSchwarzschild’ssolution.Nevertheless,itis expectedto be lessreliable inthe low Helmholtznumber range, sayforacousticwavelengthsmuchlargerthantheairfoilchord.

6.4.LBM-VLESsimulationgridindependenceandtripeffects

ThePowerFLOWsetupusedinthisstudyhasbeenalreadyused fora wide class ofpropeller/rotor aerodynamic andaeroacoustic simulations. Based on the acquiredexperience, the main sources

Fig. 10. Boundary layer edge velocity, displacement thickness, momentum thickness and skin friction coefficient for Reynolds number of 106_andα=12◦_.

Fig. 11. Boundary layer edge velocity, displacement thickness, momentum thickness and skin friction coefficient for Reynolds number of 8·104_andα=4◦_. ofnumericaluncertaintyarethemeshresolutionandthetrip

lo-cation.

Concerningthe firstone, abest practicehasbeen established, whichisbasedontheReynoldsnumber,butitisalwaysusefulto perform a mesh resolutionstudy. Fig.14 showsthe grid conver-gence trendofthe force coefficientsforan intermediate value of the advance value, andnoise spectraat a microphonelocated in the rotor plane. The employed grid refinement ratiois

√

2,with 1 and2 correspondingtothecoarseandfineresolutionlevel, re-spectively. Grid independence offorces is clearly reachedwith a medium resolution,thefineonebeingthebestpracticevalue for the present Reynolds number. In terms of noise, the tonal con-tributions arealsoconvergedatmediumlevel,whereasa conver-gencemarginofabout2 dBcanbeobservedinthehigh-frequency broadbandlevels.Theresults,however,exhibitanasymptotic con-vergencetowardslowerSPLvalues.

Inordertoinvestigatetheeffectsduetothetriplocation,also inconnectionwiththetransitionalregimeoftheuntripped/tripped

propeller measurements,simulations havebeenperformedforall advance ratios considering two trip locations: 25% of the chord, anda transition linepredicted by the BEMT tool. Fig. 15 shows

the comparison of the SPL spectrum at microphone #7 for two

valuesofthe advanceratioandthetwo differentlocationsofthe trip.TheBEMT-predictedtransitionlinesarealsoplotted.Forboth values ofthe advance ratio,the influence of the transition loca-tionontheBPFtonallevelisnegligible.Forthecase J

=

0

.

24 the transitionlocation along the blade span variesbetween45% and 60% ofthechordandtheeffectofthetriplocationisintheorder of1 dB.Conversely,forthecase J

=

0

.

6 thetransitionlocationis above75% ofthechordandthebroadbandnoisespectrumexhibits a leveldifferenceuptoabout10 dB,whichisofcourseduetothe largedifferenceinthetriplocation.Veryinterestingly,at J

=

0

.

6, dueto thenoisehumpinducedbythe laminarseparationbubble in the untripped blade tests, simulations and measurements ex-hibitanoppositetrend.

Fig. 12. Boundary layer edge velocity, displacement thickness, momentum thickness and skin friction coefficient for Reynolds number of 8·104_andα=12◦_. 7. Benchmarkresults

Inthissubsectionasubsetoflow- andhigh-fidelityresultsare comparedtoavailableexperimental data.Unlessotherwisestated, both low- and high-fidelity results are obtained by tripping the bladesat25% ofthechord.

Prior to the differentcomparisons, it is interesting to present some qualitative PowerFLOW solution.Fig. 16 showsiso-surfaces of

λ

2 (value

−

1

.

5

·

106 1/s2), coloured by vorticity magnitudein the rangefrom0 to 104 _s−1_{,forthe case J}

₌

₀

_.

_{4. Awell} devel-oped turbulent boundarylayer triggedby thezig-zagtrip canbe observedonthebladesuctionside.

Contour plots of the time-average velocity magnitude in a

meridianplaneareshowninFig.17forthreevaluesoftheadvance ratio.Interestingly,forthehighestvalue J

=

0

.

8,theslipstream ve-locityisveryclosetothefree-streamvalue,whichcorrespondsto a condition of zero thrust. Instantaneous vorticity magnitude on thesameplaneisshowninFig.18.Thetypicaltip-vortexpattern withtrailing andblade junctionvortices isvisible.For thehover condition ( J

=

0), therotor wakeislessorganizedandthe occur-renceofweakBVIcanbeobserved.

Results of thrust and torquecoefficients are shownin Fig. 19

and20.Comparedtoexperiments,thrustispredictedina satisfac-torywayover thewholeadvance ratiorange,andthe agreement between low- and high-fidelity results is quite satisfactory, even close to hover conditions, for which BEMT is typically not very accurate.Thezero-thrustconditionaround J

=

0

.

8 isalsowell pre-dicted by both LBM/VLESand BEMT. Overall, the three datasets exhibitthrust andtorquevaluesinfairlygoodagreement.Ina fu-turedeploymentofthepresentaeroacousticbenchmark,itwillbe interesting to measureforceswitha differentapparatusandina differentwindtunnel,andtocomparethecurrentpredictionswith otherCFDandlow-ordermethods.

Noise spectra attwo referencemicrophones #1 (ground) and #7 (rotorplane)areshowninFig.21.Low- andhigh-fidelity pre-dictionsarecomparedtountrippedblademeasurements.

Tonal noise is initially inspected. Consistently with the force prediction,theBEMT-basednoisemodelinOpty

∂

B-PNOISEisableto predictaccurateBPFtonepeaksthatcomparefairlywellwiththe LBM/VLESpredictionforthefourvaluesoftheadvanceratio.Both numerical predictions systematically underestimate the BPF tone peak, but, aspointedout insection 6.1,the test chamber cut-off

frequencyisintheorderof200 Hz,anditisthereforereasonable toexpect a non negligible acousticconfinement effect.The mea-suredspectra in hover exhibit higher tones atBPF harmonics. A similar behaviour was reported inpast studies [1]; it was corre-latedtotheoccurrenceof bladeloadingunsteadiness induced by theinteractionbetweenthebladeladingedgeandinflow perturba-tionsrecirculatedinthetestchamber.Likely,asimilarmechanism couldaffectthecurrentdatasetanditwillbescrutinizedinfuture campaigns.

Broadband noise is then inspected. Analytical trailing edge noisepredictionsbasedonthe correctedSchlinker& Amiet’s em-piricalwallpressuremodelareinfairly goodagreementwiththe PowerFLOWpredictionoverthewholeoperationalrange,withthe

exception of the hover case, for which the PowerFLOW

simula-tionseemstobeslightlyover-tripped.Globally,PowerFLOWresults areinfairagreementwiththemeasurementsoverthe entire fre-quency range,although the contamination dueto electricmotor noiseinvalidatethe currentdataset intherange1 to 6 kHz.For thecase J

=

0

.

6,themeasuredspectraexhibitaclearhumpinthe frequency range 4 to 20 kHz, and thisis due to the occurrence ofa laminar separationbubble. Thismechanism isabsent in the current tripped/turbulent high-fidelity simulation, as well in the analyticaltrailing-edgenoiseformulation.

Inorder to better illustrate theeffect ofblade tripping in re-lation with the occurrence of a laminar bubble at high advance

ratio, the noise spectra at microphone #7 for cases J

=

0 and

J

=

0

.

6 are compared againin Fig. 22, where the tripped blade

measurements are now included. In hover condition, untripped

andtrippedmeasurementsexhibitasimilarhigh-frequencytrend. Conversely,at J

=

0

.

6,thehigh-frequencyhumpdisappearsforthe trippedcase,thusresultinginadifferenceofmorethan10 dB

be-tweenuntripped andtrippedblademeasurements. Theuntripped

measurements are in very good agreement with the low-fidelity

prediction.

Finally,byrearranging thefourdatasets ina differentwayin Fig. 23, the spectral trends can be better highlighted and con-clusionsabout the experimental challenges andthe capability to predictlow-Reynoldsnumberpropellernoiseusinghigh- and low-fidelitymethodscanbeeasilydrawn.

Fig. 13. Noisepowerspectraldensity atadvanceratiosfrom 0 (top)to0.6 (bottom)atmicrophone#1 (left),and #7 (right).Comparisonbetweenmeasurementsand semi-analyticalbroadbandresultsbasedondifferentwallpressuremodels.

Fig. 15. Effect of trip location on noise spectra at microphone #7; J=0.24 (left), J=0.6 (right) and trip location (bottom).

Fig. 16. Iso-surfaces ofλ2at J=0.4 on the blade suction (left) and pressure side (right).

Fig. 17. Time-average velocity magnitude for: J=0 (left), J= .4 (middle) and J=0.8 (right).

Fig. 19. Thrust coefficient.

Fig. 20. Torque coefficient. 8. Noisesourcevisualization

As an illustration ofsome automatic post-processing capabili-tiesofthe3DSeVTOLaeroacousticworkflow,thebroadbandnoise sourcesareinvestigatedusingtwocomplementaryapproaches.The firstone,availableinOpty

∂

B-PFNOISESCAN,consistsinattributing to every surfelofthebladeandateverytimestep,thenoise contri-bution per unit of surface emitted towards a given microphone. The resulting unsteady surface field is Fourier transformed and then visualizedindifferentintegrationbandsasSPL/m2.The sec-ond approach, based on sequentialusage ofOpty

∂

B-FWHFREQ and

Opty

∂

B-BF,consistsinperformingabeam-forminganalysisforone bladeonlyintherotatingreferencesystem.Noisesourcemaps cu-mulatedoverthesamefrequencyrangesforthetwoanalysesare compared,providingsomeinterestingphysicalinsight.

Fig.24showsthenoisesourcemapsforthebladesuctionside forthreefrequencyranges,coveringtheBPFharmoniccountrange of3–10, 10–30and30–100. Thecolourmapsrangevalues corre-spond tothe unitsof dB/m2 _{forthe time-domainFW-H sources,}

and to noise power levels referred to the maximum value in a

band forthe beam-forming maps.Thesehave beencomputedby

usingan array ofmicrophones facingthe bladesuction side,but, duetotheintrinsicpropertiesofawavefield,alsosourceslocated onthebladepressuresidearedetected bythesourcelocalization algorithm.Indeed,sincethemicrophoneusedfortheFW-H time-domain source projection is located on the pressure side of the propeller (at 5D from the propeller hub and 45◦ from the pro-peller plane on the groundside), more consistent beam-forming

mapsare the onescomputedusingan array ofmicrophones

fac-ing the blade pressure side,which are shown inFig. 25.A cross checking of the two figures is therefore needed. For the sake of

completeness, it should be mentioned that the microphone

con-sidered for the FW-H calculation is the first one of the circular array used inRef. [46], which isat thesame directivity angleas thefirst microphoneofthe lineararrayofFig.5,butslightly far-therfromthepropeller.Noiselevelscanbereportedtothecurrent arraybyadding2 dB.

Inthe firstfrequency range,onlyfew sources are detected by thebeam-formingonthesuctionside,whereasthetripself-noise isdetected by thebeam-forming onthe pressure side. This con-firms a general observation in airfoil aeroacoustics, according to which the noise radiated towards one side of the airfoilcan be moresignificantlyinfluencedbyeventshappeningontheopposite side. Itis interesting to observe that one ofthe two sources de-tectedforthehover caseby thesuction-side beam-forming array islocatedinproximityoftheleadingedgeanditshouldberelated topressurefluctuationsinducedonthepressuresideoftheblade byaweakBVIphenomenonoccurringinhoverconditions,inline withpreviousobservations[1].

Inthe second frequencyrange the trailing-edge is more

rele-vant.The suction-side beam-forming mapsreveal the dominance

oftrailing-edgecontributionintheformadistributeduncorrelated sources alongthe edge,with relativelyhigher noisepower levels aroundaradial stationofabout75% forall valuesoftheadvance ratio.Asalreadypointedout,thebeam-formingarrayonthe pres-suresideisabletodetectthetripselfnoise.

Finally,inthethirdfrequencyrange,trailing-edgenoiseiswell evident in the suction-side beam-forming maps, with relatively highernoisepowerlevelsaroundaradialstationofabout85% for allvaluesoftheadvanceratio.

It isworth concludingthissection withan observation about oneofthe intrinsicchallengesofaeroacoustics. Thesurface noise

contributions computed using the time-domain FW-H approach

representthe effective noise contribution to a given microphone location, with the only caveat of a non-synchronous cumulation duetoDoppler effects(the signalreception timeis notthesame for all surface elements at a given source time due to Doppler effects). However, the SPL contour levels are not able to high-lighta specificcontributionofthetrailing-edge,asbeam-forming does. This is because trailing-edge noise is substantially a wave scatteringphenomenonandtheroleofthesignalphaseinthe con-structionoftheradiatedfieldisoffundamentalimportance. There-fore, sources could be visualized only by looking at the Fourier real/imaginarypartsinnarrowbandsofthesamequantityusedto computeSPLmaps,orthroughband-passfilteringofthetransient field. Conversely, the beam-forming resolves the source interfer-enceinastatisticalsense, by meansofthe cross-spectral matrix, andtherefore it is able to deliver an equivalent source distribu-tion.

9. Conclusions

A preliminary step towards the definition of a benchmark

problemforsmall UAVpropeller aeroacoustics was accomplished

through comparisons between measurements and

low-/high-fidelitypredictions.LBM/VLESsimulationswereperformedby trig-geringtheboundary layertransitionon thesuction side,without anexactknowledgeoftherealflowregimeintheuntripped phys-icaltests.However, thefavourableagreementsbetweenmeasured andpredicted broadband noise levels supported the presence of atransitional flow regime, atleastintheouter part oftheblade suction side. Thiswas also confirmedby analytical computations

based on a BEMT model which predicted a transition on the

suction side, mostly triggered by a laminar separation bubble. The BEMT-predicted transition line on the suction side was

lo-cated downstream the prescribed quarter-chord location in the

LBM/VLES simulations. Additional PowerFLOW simulations with

tripfollowingthespanwisetransitionlinepredictedbytheBEMT revealedthatthetriplocationdoesnotaffectthetonalnoise con-tent, whereas it affects the high-frequency broadband noise by

about 1 dB in hover condition, and up to 10 dB close to

Fig. 21. Noisepowerspectraldensityatadvanceratiosfrom0 (top)to0.6 (bottom)atmicrophone#1 (left),and#7 (right).Comparisonbetweenmeasurements,BEMTtonal results,semi-analyticalbroadbandresultsbasedoncorrectedSchlinker&Amiet’swallpressuremodelandPowerFLOW/PowerACOUSTICSresults.

Fig. 23. Noise power spectral density at microphone #7 for all values of the advance ratio.

Fig. 24. FW-Hintegralcontribution45◦fromtherotorplaneandbeam-formingnoisemapsonthebladesuctionsidealternatelyshownforcasesfrom J=0 (top)to J=0.8 (bottom).

Fig. 25. FW-Hintegralcontribution45◦ fromtherotorplaneandbeam-formingnoisemapsonthebladepressuresidealternatelyshownforcasesfrom J=0 (top)to J=0.8 (bottom).

ofthechordalongthewholespan.Thepresenceofalaminar sep-arationbubbleforthehighervaluesoftheadvancedratiocausing

a high-frequency humpin the noise spectrum was confirmedby

comparingmeasurements carriedoutwithoutandwithtransition striponthesuctionside.

An additional outcome of the present study is the accurate forces andtonal noise predictioncarried out usinga low-fidelity simulationchainthatcanbeexecutedinfewminutesformany op-eratingconditions.Thisprocesscoexistswiththehigh-fidelity pro-cessandcanbe reliablyusedforflight missionandnoise assess-ments.Acaveatstillexistsabouttherobustnessofsemi-analytical broadbandtrailing-edgenoisemodels,duetothesensitivityofthe WPSmodeltotheboundarylayerproperties.Thesimplestmethod bySchlinker&Amietseemstobethemostrobustoneandcanbe easilytunedtoaclassofrotorproblems.

New experimental campaigns will be conductedin the future withthegoaloffixingsomeoftheremainingissuesobserved

dur-ing the last campaign, and shed more light on a new research

question generated bythe presentstudy:theexistence ofan

ad-ditional noise generation mechanism due to the presence of a

laminarseparationbubbleandpossibletonalnoisefeedback mech-anisms.

Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting finan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto influencetheworkreportedinthispaper.

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