Wind Turbine Noise Modeling Based on Amiet's Theory: Effects of Wind Shear and Atmospheric Turbulence

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Effects of Wind Shear and Atmospheric Turbulence

Yuan Tian, Benjamin Cotté

To cite this version:

Yuan Tian, Benjamin Cotté. Wind Turbine Noise Modeling Based on Amiet’s Theory: Effects of

Wind Shear and Atmospheric Turbulence. Acta Acustica united with Acustica, Hirzel Verlag, 2016,

102 (4), pp.626-639. �10.3813/AAA.918979�. �hal-01356102�

Wind Turbine Noise Modeling Based on Amiet’s

Theory: Effects of Wind Shear and Atmospheric

Turbulence

Y.Tian,B.Cotté

Institute of Me hani al S ien es and Industrial Appli ations (IMSIA), ENSTA ParisTe h, CNRS, CEA,EDF,UniversitéParis-Sa lay,828,bddesMaré haux, 91762Palaiseau edex,Fran e. benjamin. otteensta.fr

Summary

Broadband noise generated aerodynami ally is the dominant sour e for a modern wind turbine. Inthis paper, trailing edge noise and turbulent inow noiseare modeledusingAmiet's theoryto predi twindturbinenoisespe tra,dire tivityandamplitudemodulation.First,by omparingmodel predi tionswithwindtunnelexperimentsfromtheliterature,weshowthatawallpressurespe tral modelthatin ludestheee tofanadversepressuregradientisneededto orre tlypredi ttrailing edge noise spe tra. Then, we adaptthe model to rotating blades and ompare sound power level spe tra of trailing edge noise with eld measurements, assuming a onstant wind speed prole. A good agreement is found at frequen ies higher than approximately 1000Hz, but the levels are underestimatedatlowerfrequen ies.Finally,wea ountforwindshearandatmospheri turbulen e ee tsusing theMonin-Obukhovsimilaritytheory.Onthe onehand,weshowthatangle ofatta k variationsduetowind shear anprodu easigni ant hangeinthe wall pressure spe traof some bladese tions,espe iallyinstableatmospheri onditions,eventhoughthisee tisnot learlyseen onthetrailingedgenoisespe traatthere eiver.Ontheotherhand,turbulentinownoisedoesvary withatmospheri onditions,and ontributessigni antlytothenoiseradiatedbyawindturbineat lowfrequen ies.Whenbothme hanismsare onsidered,thepredi tedsoundpowerlevelspe traare ingoodagreementwithmeasurements.

PACSno.43.28.Ra,43.50.Nm

1. Introdu tion

Windturbinenoiseisoneofthemain on ernforthe a eptan e of wind farms by the neighborhood [1℄. Formodernmegawatt-sizedwind turbines, itis gen-erally admitted that broadband aerodynami noise is dominant, with three main noise sour es to on-sider [1, 2, 3℄: turbulent inow noise, trailing edge noise, and stall noise. Turbulent inow noise is due totheintera tionofatmospheri turbulen ewiththe bladeleadingedge; itslevel depends onthestrength of the turbulent u tuations. Trailing edge noise is aused by the s attering of the turbulent boundary layerat theblade trailingedge; it isthusreferredto as airfoil self-noise. When the blade angle of atta k (AoA)in reases,theboundarylayerbe omespartially separatedandeventually ompleteseparationorstall is a hieved. This is a very intense noise me hanism alledseparationor stallnoise.

Re eived0 0, a epted0 0.

A main feature of wind turbine noise is the am-plitude modulation (AM), aused by therotation of the blades, whi h is believed to be the most annoy-ing feature of this noise sour e [1℄. As explained in the proje t Wind Turbine Amplitude Modulation fundedbyRenewableUK[4,3,5℄,itis ommonto dis-tinguish betweennormalamplitudemodulation, also alledswish,andenhan edorotheramplitude modu-lation,also alledthump.NormalAM orrespondsto thesound levelvariationofafewde ibelsthat mod-ern wind turbines normally produ e, mostly noti e-able lose to the turbine in the rosswinddire tion. On theother hand,enhan edAMis observedin the far-eld (typi ally more than 600m), mostly in the downwind dire tion,and anrea h10dBormore.

In order to a urately predi t wind turbine noise, itisimportanttounderstandtheroleofatmospheri onditions.Windshearisoften itedasanimportant fa torexplainingsoundpressurelevelshigherthan ex-pe ted andenhan ed AM[6, 4℄.Under stable atmo-spheri onditions,typi allyat night,thewindspeed in reasefrom thebottom tothetopofthe rotor an

belarge,sotheAoA hangessigni antlyduringone blade rotation. Furthermore, wind speed is usually small lose to the ground when high wind shear is present,whi hmeansthattheba kgroundnoise,also alled wind noise orvegetation noise [7℄, is low and willnotmaske ientlywindturbine noise.Another important atmospheri parameter is the strength of turbulentvelo ityu tuations,whi hmostlyimpa ts turbulentinownoise.This strengthdependson the atmospheri onditions,andmayalsobestrongly en-han ed if a wind turbine is in the wake of another turbine[3,5℄.

Tobetterunderstandwindturbinenoiseandits as-so iated amplitudemodulation, it is thus important toproposeamodelthat takesinto a ountthemain noise me hanisms and the inuen e of atmospheri onditions.Threemaintypesofmodelshavebeen pro-posed intheliterature.First,asemi-empiri almodel hasbeenbuiltontheextensivemeasurementsof air-foil self-noise made by Brooks et al.[8℄. This model, sometimes alled BPM model, has been applied to windturbinenoisewithsomesu essbyZhuetal.[9℄ andOerlemans etal.[2 ℄.It ishoweverdi ultto as-sess the validity limits of su h a model, sin e it is basedonmeasurementsforaNACA0012airfoilthat isnotrepresentativeofthe airfoilsusedin wind tur-bineappli ations.

Se ond, models based on a ousti analogies have been proposed. There have been a few attempts to apply the frequen y-domain models proposed by Amiet for turbulent inow noise [10℄ and trailing edge noise [11℄ to wind turbines, e.g. in the study of Glegget al.[12℄. Also, Leeet al.[13℄ re ently pro-posed atrailingedgenoisemodel basedonthe time-domain solution of the Ffow s Williams-Hawkings equation[14℄. Although these models are promising, theyhavenotbeenthoroughlyvalidatedforwind tur-binenoiseappli ations.Inthe aseofAmiet's model for trailingedge noise,for example,one ofthe main di ultyis tohavea ess to wallpressurestatisti s, whosemodelingremainsonopenissue[15,16,17,18℄. Third,numeri altoolsofComputationalFluid Dy-nami saregettingmoreandmorepopularinthe on-textofwindturbinenoise.ReynoldsAveraged Navier-Stokes (RANS) simulations an be used to provide information on the turbulent boundary layer devel-opingoveranairfoil. An approa h onsistingin ou-pling a RANS ow solver to the TNO-Blake model to predi t the wall pressurespe trum hasbeen pro-posed byseveralresear hgroups[17,18℄,and isable to apture adverse pressure gradientand turbulen e anisotropyee ts.Hybridapproa hesforairfoilnoise predi tion based on Large Eddy Simulation (LES) havealsobeendeveloped.Forinstan e,Shenetal.[19℄ proposedaLES-basedapproa hthat onsistsin split-tingthe ompressibleowprobleminto avis ous in- ompressibleowpartandan invis ida ousti part.

This approa h has been applied to both symmetri andasymmetri airfoils[19,17℄.

Inthis paper,wepropose aphysi ally-basedwind turbinenoisepredi tionmodelbasedonAmiet's the-ory in order to obtaina urate predi tionsin an ef- ient way. Both turbulent inownoise and trailing edge noiseare onsidered,and predi tionresults are validated against measurements from the literature. In order to a ount for windshear and atmospheri turbulen e ee ts, we use the Monin-Obukhov simi-laritytheorythatpredi tswindspeedprolesand tur-bulen eparametersin theatmospheri surfa elayer. We fo us in this paper on wind turbine noise lose to the sour e (typi ally 100m away),and study dif-ferent phenomena su h as dire tivity and amplitude modulation. Thus, in the following,the term ampli-tudemodulation (AM)meansnormalAM.Although only near-eld results are presented here, our long-termgoalisto ouplethissour emodeltoa propaga-tionmodel in order topredi t wind turbine noiseat largedistan es(greaterthan1km),andthustobetter understandthepossible ausesofenhan edAM.

Thepaperis organizedasfollows.First,Se tion 2 presents Amiet's analyti al model for turbulent in-ow noise and trailing edge noise of a xed airfoil anditsvalidationagainstwindtunnelmeasurements. Then, in Se tion 3, we apply the trailingedge noise model to a full size wind turbine and ompare pre-di tionstoeldmeasurements onsideringa onstant windprole(nowind shear).Finally,theinuen e of windshearand atmospheri turbulen eonwind tur-bine noiseisstudiedin Se tion4.

2. Amiet'sanalyti al model for

turbu-lentinownoise and trailing edge noise

2.1. Turbulentinow noise 2.1.1. Originalmodelforaxedplate

An airfoil in aturbulentowexperien esa u tuat-ing liftloadingwhi h will resultin thegeneration of sound. Amiet derivedairfoil response fun tions that relatethewavenumberspe trumofthein oming tur-bulen e to the lift u tuations over the blade sur-fa e[10℄.Theseliftu tuations anbeseenasdipoles distributedalongtheairfoilsurfa ethate iently ra-diatenoisetothefar-eld.

Amiet's model is based on linearized thin-airfoil theory,and theairfoilis redu edto aatplate with zerothi knessandzero angleof atta k,with span

L

and hord

c

,asseenin Figure1.Theowisuniform with velo ity

U

, and a re eiveris pla ed in the far-eld at

(x

R

, y

R

, z

R

)

. The model is based on several assumptions:

1.the in oming turbulen e u tuation is onsidered tobesmall omparedtothemeanowvelo ity;

y

x

(x

R

,y

R

,z

R

)

z

U

L

c

Figure 1:S hemati s for Amiet's model applied to a xedatplate.

2.theintera tionbetweenthe airfoiland the turbu-lentowisinvis idsothattheproblemisredu ed tosolvinglinearized Eulerequations;

3.the turbulen e is frozen, so that turbulent gust properties are un hangedwhile it is onve ted by themean ow,and its velo ity u tuation is rep-resentedin termsof hordwiseandspanwisewave numbers,here

K

x

and

K

y

respe tively.

The problem an be des ribed by a linearized Helmholtzequationasso iatedwithproperboundary onditions[10,20℄, whi hform aS hwarzs hild prob-lem that anbe solvedanalyti ally.Forlargeaspe t ratio,thatis

L/c > 3

,thefar-eldpowerspe tral den-sity(PSD)ofa ousti pressure

S

pp

isgivenby[10,20℄:

S

pp

(x

R

, y

R

, z

R

, ω) =

 ρ

0

kc z

R

2S

2

0



2

πU

L

2

Φ

ww

 ω

U

,

ky

R

S

0

 







L

_{T I}



x

R

,

ω

U

,

ky

R

S

0









2

,

(1)

where

ω

is the angular frequen y,

k = ω/c

0

is the a ousti wavenumber,

ρ

0

is the airdensity,

c

0

is the speedofsound,

S

0

isamodieddistan ebetweenthe sour e and the observer, and

L

T I

is the turbulent inow noise transfer fun tion that onne ts the air-foil surfa epressureu tuation to thea ousti pres-sureatthefar-eldpoint.Wenegle tthese ond-order trailing-edge orre tioninthe al ulationofthe trans-ferfun tion,asgivenbyEq. (4)ofRef.[20℄,be ause it is small for the hords and frequen ies onsidered in this study. Thus

L

T I

is obtainedfrom Eq. (3) of Ref.[20℄.

Finally,

Φ

ww

is the two-dimensional energy spe -trum, modeled here by a von Kármán spe trum for homogeneousandisotropi turbulen e[10,20℄:

Φ

ww

(K

x

, K

y

) =

4

9π

σ

2

u

K

2

e

ˆ

K

2

x

+ ˆ

K

y

2

(1 + ˆ

K

2

x

+ ˆ

K

y

2

)

7/3

,

(2)

with

σ

u

the standarddeviation ofturbulentvelo ity u tuations,

K

e

= 1/L

outer

the wave number orre-sponding to the turbulen e outer s ale

L

outer

, and

ˆ

K = K/K

e

the normalized turbulent wave number.

L

outer

isrelatedtotheturbulen eintegrallengths ale

Λ

by

Λ = L

outer

/1.339

[10℄.

2.1.2. Airfoilthi kness orre tionforturbulent in-ownoise

Severalauthorsin ludingRogerandMoreau[20℄and Devenport et al.[21℄ have shown that turbulent in-ow noisestrongly depends on the airfoil thi kness. A thi kerairfoiltends toredu e theturbulentinow noise level. This ee t is not taken into a ount in Amiet's original model. We propose herean empiri- al orre tion based on the data shown in Figure 6 ofReferen e[20℄.Theredu tionlevel

SP L

R

in dBis al ulatedbylinearinterpolationbasedonthesedata:

SP L

R

(dB) =

9

50

(e/c)

(e/c)

ref

f

U

(Λ/c)

ref

(Λ/c)

,

(3)

where

e

is the airfoil maximum thi kness, and

Λ

is theturbulentintegrallengths ale.Thesubs ript

ref

stands for the values of referen e experimental data from aNACA0012airfoil, whi h are

(e/c)

ref

= 0.12

and

(Λ/c) ≈ 0.1

.

Note that

SP L

R

providesapurethi kness orre -tionbutdoesnot ontaintheee tof amberaswell as nose radius ( urvature). Another approa h that ould be onsidered in future studies would be to orre t the in ident turbulen e spe trum based on rapid distortion theory, as proposed by Roger and Moreau[20℄.

2.1.3. Modelvalidationagainstwindtunnel experi-ments

First, model predi tions are ompared to the mea-surementsofPatersonand Amiet[22℄in Figure2for a NACA 0012 of hord 23 m, with Ma h numbers between 0.12 and 0.50. The turbulen e intensity is 45%, and the longitudinal integral length s ale is

3.0

m. Theagreementbetweenmodel and measure-mentsisgreatlyimprovedwhenthethi kness orre -tion is in luded, whi h is expe ted sin e this set of data wasused to obtainEq. (3). Thethi kness or-re tion ishighest forhigh frequen iesand lowMa h numbers.

Se ond, themeasurementsof Devenport et al.[21℄ foraS831airfoilof hord91 mare onsidered.This airfoilwhosemaximumthi knessis

18%

ofthe hord is typi ally used in wind turbine appli ations. The Ma hnumberis0.08,theturbulen eintensity

3.9 %

, and the longitudinal integral length s ale

82

m. In Figure 3,model predi tionswith and without thi k-ness orre tionare omparedtothemeasurementsat anglesofatta kof

0

o

and

2

o

.Thethi kness orre tion slightlyimprovesthe agreementbetweenpredi tions and measurements, but isnot su ientto providea satisfyingagreementbelow200Hz. Thisdis repan y anbeattributed to AoA, urvature and amber ef-fe ts.AsnotedbyDevenportetal.[21℄,turbulent in-ownoiseisalmostindependentofAoAforsymmetri airfoilssu hasNACA0012, butis inuen edbythe airfoil geometry for theS831. This is learly seenin

100

200

500

1000

2000

5000

20

30

40

50

60

70

80

Frequency (Hz)

SPL (dB re. 20

µ

Pa)

M=0.12

M=0.18

M=0.27

M=0.36

M=0.50

Figure 2: Turbulent inow noise predi tions with (dashedlines)andwithout(solidlines)thi kness or-re tionfor aNACA 0012airfoil. Thesymbols orre-spondtothemeasurementsofRef.[22℄( oloronline).

10

2

10

3

50

55

60

65

70

75

80

Frequency (Hz)

SPL

1/3

(dB)

0

o

2

o

4

o

Figure 3: Turbulent inow noise predi tions with (bla k dashed lines) and without (bla k solid lines) thi kness orre tionforaS831airfoil.Theresultsare ompared to the measurements (bla ksymbols) and predi tions (gray lines) of Devenport et al.[21℄ for AoAof

0

o

,

2

o

and

4

o

.

the predi tions of Devenport et al.[21℄ for AoA be-tween

0

o

and

4

o

, reprodu ed in Figure 3.These pre-di tions are based on a panel method des ribed in Ref. [23℄ that exa tlya ountsfor theairfoil geome-try.Figure 3showsthat Devenportet al.predi tions orre tly apturethethi knessee t,andthatthe ef-fe t of AoA is signi ant, with a de rease of about 4dB between

0

o

and

4

o

. Even though Amiet's pre-di tionstend to overestimatethe noiselevels in this ase,one must keep in mind that theMa h number isverysmallintheDevenportetal.experiment,thus thedis repan yseeninFigure3 anbe onsideredas aworst ases enarioforwind turbineblades.

2.2. Trailingedgenoise

2.2.1. Originalmodelforaxedplate

Amiet's model originally proposed for turbulent in-ownoise anbeextendedto trailingedgenoise[11℄.

Assuminglargeaspe tratio,thePSDoftrailingedge noiseatfar-eld anbewrittenas[11,24℄:

S

pp

(x

R

, y

R

, z

R

, ω) =

 kcz

R

4πS

2

0



2

_L

2

Φ

pp

(ω)l

y



ω,

ky

R

S

0

 







L

_{T E}

 ω

U

,

ky

R

S

0









2

,

(4)

where

Φ

pp

is thewallpressureu tuationspe trum,

l

y

isthespanwise orrelationlength,estimatedbythe Cor os model, and

L

T E

is the transfer fun tion for trailing edge noise. Roger and Moreau [20℄ showed that the se ond-order leading-edge orre tion has a signi ant ontributioninthe al ulationofthe trans-ferfun tiononlyfor

kc < 1

.This onditionisnot en- ounteredforthe ongurationsstudiedhere,so

L

T E

is simplyobtainedfrom Eq. (11)of Ref. [20℄. As ex-plainedbyRogerandMoreau[20℄,thisexpression in- ludesthein identpressurejump orre tionproposed byAmiet[25℄.

2.2.2. Wallpressurespe tralmodels

InAmiet'strailingedgenoisemodel,oneofthemost important input parameters is the spe trum of wall pressureu tuations.An a urateestimation of this spe trum anbedoneexperimentally,ornumeri ally withdire tnumeri alsimulation(DNS)orlargeeddy simulation(LES),butitremainsverydi ultin pra -ti esoamodelmustbeusedinstead.Asa ompletion ofhismodel,Amietproposedanempiri alexpression basedonthes alingvariable

ω = ωδ

˜

∗

_/U

e

,with

δ

∗

the boundarylayerdispla ementthi knessand

U

e

the ex-ternalvelo ity.Morere ently,Goody[15℄proposedan improvedwall pressurespe trum model that onsid-ersReynoldsee t.However,alltheses alingmodels are basedonzeropressuregradient(ZPG) ow on-ditions, thatare onlysuitableforaatplateat zero in iden e.Forarealairfoil,anadversepressure gradi-ent(APG) owisusuallypresentonthesu tionside nearthetrailingedge.Rozenbergetal. [16℄proposed amodelthat takesintoa ounttheAPG ee t,and redu es to Goody's model for zeropressuregradient onditions.Theysuggestedthatnormalizedwall pres-surespe trum anbepresentedas:

Φ

pp

(ω)U

e

τ

2

max

δ

∗

=

[2.82∆

2

_(6.13∆

−0.75

_{+ F}

1

)

A

1

]

4.2

_∆

Π

+ 1 ˜

ω

2

[4.76˜

ω

0.75

_{+ F}

1

]

A

1

+ [8.8R

−0.57

T

ω]

˜

A

2

,

(5)

wherethemainparametersofthemodelare[16℄:

•

thewakestrengthparameter

Π = 0.8(β

c

+ 0.5)

3/4

,

•

the Clauser parameter

β

c

=

θ

τ

w

dp

dx

that ompares pressure for es on the boundary layerto the wall shearfor es,

•

the ratio of boundary layerthi kness to displa e-mentthi kness

∆ = δ/δ

∗

•

theratiooftheoutertoinnerboundarylayertime s ales

R

T

=

δ

U

e

ν

u

2

τ

,

with

θ

the momentum thi kness,

τ

w

the wall shear stress,

τ

max

themaximumshearstressalongthe nor-mal dire tion,and

dp

dx

thepressuregradient. Finally,

A

1

,

A

2

and

F

1

areempiri al oe ientsgivenby:

A

1

= 3.7 + 1.5β

c

,

(6)

A

2

= min(3, 19/pR

T

) + 7,

(7)

F

1

= 4.76

 1.4

∆



0.75

[0.375A

1

− 1].

(8)

Theseparameters anbe al ulatedusingCFDtools. Inthisstudy,XFOILversion6.96isusedtoobtain

U

e

,

δ

∗

,

θ

,theskinfri tion oe ient

C

f

andthepressure oe ient

C

p

atthetrailingedge.Theboundarylayer thi knessisobtainedusingthefollowingrelation[26℄:

δ = θ

∗



3.15 +

1.72

H

k

− 1



+ δ

∗

,

(9) where

H

k

= δ

∗

_/θ

∗

isthekinemati shapefa tor. We annotestimate

τ

max

dire tlyfromXFOIL,soweuse theapproximation

τ

max

≈ τ

w

=

1

2

ρU

2

_C

f

thatisvalid while the boundary layer remains atta hed. Finally, the pressure gradient is obtained from

C

p

between 99%and100%ofthe hord.

2.2.3. Modelvalidationagainstwindtunnel experi-ments

Tovalidate Amiet's model andevaluatetheee t of the adverse pressure gradient, results with Goody's model for ZPG and Rozenberg's model for APG are omparedto experimental datafromBrooksand Hodgson[27℄foraNACA0012airfoilandfrom Kam-ruzzamanetal.[17℄ foraNACA

64

3

-

418

airfoil.

We onsider rst the surfa e pressure measure-ment of Brooks and Hodgson for a sensor lo ated at 1.854 m from the trailing edge. The airfoil is a NACA 0012 of hord 61 m at zero in iden e, and theinowvelo ityis69.5m/s.Figure 4(a) ompares ZPG and APG wall pressure spe trawith the mea-sured spe trum. TheAPG model isseen to in rease thespe trallevelbelow 5kHzwhi h provides a bet-teragreement omparedtothemeasurements.In Fig-ure 4(b),sound pressurelevel (SPL) predi tionsare ompared to experimental values. Predi ted results are losertothemeasurementsusingtheAPGmodel. Kamruzzaman et al.[17℄ have performed surfa e pressuremeasurementsonanasymmetri NACA

64

3

-418

airfoil of hord 60 m onbothpressure and su -tionsides.Theinowvelo ityis62m/sandtheAoA is

0

o

. The boundary layerdispla ementthi kness

δ

∗

andmomentumthi kness

θ

∗

al ulatedbyXFOILare ompared to measuredvalues in TableI.Asso iated wall pressurespe traare plotted in Figure 5(a).On thesu tionside,thepredi tionsaremu h losertothe measurementsusingtheAPGmodel omparedtothe

δ

∗

(mm)

θ

∗

(mm) Experiment 6.76 2.99 XFOIL 5.97 3.07

Table I: Boundary layer parameters al ulated by XFOILandmeasuredbyKamruzzamanetal.[17℄on thesu tionsideatthetrailingedgeforanAoAof

0

o

.

ZPGmodel,althoughthelevelsarestilllowerthanthe measured ones. On the pressureside, only the ZPG model is used be ause pressure gradients are small. Figure 5(b) omparesthe SPL spe trum predi tions to the measurements. Using the APG model on the su tionsideandtheZPGmodelonthepressureside, abetteragreementis foundalthoughthepredi tions stillunderestimatethemeasuredvalues.

Asa on lusion,itis learthattheadversepressure gradient hasanimportant ee t on theSPL predi -tion,howeveritsmodelingisstillanopenissueinthe aeroa ousti s ommunity. Some re ent studies have shown that turbulen e anisotropyee ts need to be in ludedtoimprovethemodela ura y,usingfor in-stan etheTNO-Blakemodel[17,18℄.

3. Appli ationon a fullsize wind

tur-bine with onstant windproles

In this se tion, we onsider a onstant wind prole (nowindshear)andnoatmospheri turbulen e.Thus onlytrailingedgenoiseis onsideredintheSPL pre-di tions.

3.1. Modeladaption toa rotatingbladewith spanwise-varying ow onditions

Amiet's model was originally developed for a xed plate.A simplemethod to a ountfor the blade ro-tating motion onsists in approximating it by a se-riesoftranslationsfromdis reteangularpositions,as explainedby S hlinkerandAmiet [28℄.This approx-imationhasre entlybeenrevisited byBlandeauand Joseph [29℄ and by Sinayoko et al. [30℄ by ompari-sonwithanalyti almodelsthattreattherotation ef-fe tsexa tly.They on ludedthattheapproximation isvalidoverawiderangeoffrequen iesforwind tur-bineappli ations.UsingBlandeauandJoseph expres-sions[29℄,frequen ylimits anbeobtainedasa fun -tionofdistan efromanobservertothewindturbine aswellasReynoldsnumberen ounteredbyea hblade se tion.Thelowfrequen ylimitsareabout15Hzand 120Hzforanobserverlo atedrespe tively100mand 1000m away from the wind turbine. The upper fre-quen ylimitin reaseswithReynoldsnumber.Inour study,theaverageReynoldsnumberisaround

4×10

6

, whi hleadstoanupperfrequen ylimitfrom1kHzto 5kHzfromtheroottothetip.Sin emostofthewind turbine noise is produ ed by the outer part of the

10

3

10

4

70

75

80

85

90

Frequency (Hz)

Φ

pp

(dB re. 20

µ

Pa)

Experiment

APG model

Goody model

10

3

10

4

20

25

30

35

40

45

Frequency (Hz)

SPL (dB re. 20

µ

Pa)

Experiment

APG model

Goody model

(a) (b)

Figure4:(a)Wallpressurespe traand(b)far-eldSPLpredi tedbyAPGandZPGmodelsandmeasuredby BrooksandHodgson[27℄ foraNACA0012airfoil.

10

3

10

4

60

65

70

75

80

85

90

95

Frequency (Hz)

Φ

pp

(dB re. 20

µ

Pa)

Suction side

Pressure side

10

3

10

4

40

45

50

55

60

65

70

Frequency (Hz)

SPL

1/3

(dB re. 20

µ

Pa)

Measurement

APG model

ZPG model

(a) (b)

Figure 5: (a) Wall pressure spe tra on the su tion side (bla k lines) and on the pressure side (gray lines) measuredbyKamruzzamanet al.[17℄ (symbols)and predi tedby APG(solidlines)andZPGmodels(dashed lines)models.(b)Thirdo tavebandspe traoffar-eldSPLusingAPGorZPGmodelonthesu tionsideand ZPGmodelonthepressureside.

blade, as observed by Oerlemans et al. [31℄, results are al ulatedupto5kHzinthefollowing.

The Dopplerfa tor relates theobserver frequen y

ω

to the emission frequen y

ω

e

at the sour e [28, 30℄. As shown by S hlinker and Amiet [28℄ and Sinayoko et al. [30℄, the instantaneous PSD at the observer for an azimuthal blade position

γ

is

S

pp

(x

0

, ω, γ) = (ω

e

/ω)S

pp

′

(x, ω

e

, γ)

, where

x

0

and

x

orrespond respe tively to the observer oordi-nates in the hub and blade oordinate systems,and

S

′

pp

(x, ω

e

, γ)

isgivenbyEquation(4)(orEquation(1) whenturbulentinownoiseis onsidered)foraxed blade. They also derived an expression for the

az-imuthallyaveragedspe trum:

S

pp

(x

0

, ω) =

1

2π

Z

2π

0

ω

e

ω

S

pp

(x

0

, ω, γ)dγ

=

1

2π

Z

2π

0



ω

_e

ω



2

S

pp

′

(x, ω

e

, γ)dγ.

(10)

Anotherissuerelated toblade rotationisthat the owisnotuniformalongthespan,within oming ve-lo ity strongly in reasing from root to tip. To treat these spanwise-varying onditions, it is ommon to ut theblade intoshort segmentsorstripswhile as-suming the segments are independent, whi h means thesegmentspanmustbegreaterthan thespanwise turbulen e orrelationlength.Asaresult,theoverall noiseradiatedbythebladeisthelogarithmi sumof the ontributionsfromallbladesegments.

0

10

20

30

40

50 −2

0

2

−2

0

2

0

10

20

30

40

50 −2

0

2

−2

0

2

Figure6:Geometryofthe45m-blade utinto 8 seg-mentswithouttwist(left)andwith twist(right).All dimensionsarein meters.

Wind speedat Rotorspeed hubheight(m/s) (rpm)

ase1 6 13

ase2 8 14

Table II: Mean parametersfor thetwoexperimental test- asesfromReferen e[32℄.

3.2. Congurations

Thewind turbine under study is a2.3MW Siemens SWT 2.3-93 with atowerheight(ground to hub) of 80m,and three 45Bbladesoflength 45m that have ontrollablepit h angle.The hordlengthis3.5mat the root of the blade and 0.8m at the tip, and we assumealinearvariationin-betweenasshownin Fig-ure6.Thesedatainadditiontothesoundpowerlevel measurementsarefoundinReferen e[32℄forthetwo asessummarized inTableII.

ANACA63-415airfoilis hosenfortheblade pro-le, be ause it is a ommonly used airfoil in mod-ern wind turbines, and it is visually similar to B45 blades[33℄. To hoose thenumberofbladesegments, wede ideinthis studyto keepa onstantaspe t ra-tioof 3,sothatthelargeaspe tratioapproximation ofAmiet's modelis satised.Thisled usto utea h bladeinto8segments,asshowninFigure6.Thespan isalwayslargerthan0.5m,thelargestspanwise orre-lationlengtha ordingto Cor osmodel. Finally, the blade twist is hosen so that the AoA is

4

o

with a onstant wind prole for all segments, whi h is the anglewherethemaximumliftdragratioisfoundfor a Reynolds numberof

4 × 10

6

. A s hemati s of the twisted blade as it is modeled in the al ulationsis representedin Figure6.

3.3. Soundpower al ulationand omparison with measurements

Assumingfreeeld onditions,thesound powerlevel

SW L

is obtainedby

SW L = SP L + 10 log

10

(4πR

2

)

, with

R

the distan e from the rotorto the observer. TheSWL predi tions are ompared to the measure-mentsinFigures7and8forthetwo asesdes ribedin

10

2

10

3

50

55

60

65

70

75

80

85

90

Frequency (Hz)

SWL

1/3

(dBA)

Total prediction (APG)

Total prediction (ZPG)

Suction side (APG)

Suction side (ZPG)

Pressure side (ZPG)

Measurements

Figure 7:Third o taveband spe traof sound power levelfor ase1(

U = 6

m/s) onsideringAPGorZPG modelsoftrailingedgenoise.

10

2

10

3

55

60

65

70

75

80

85

90

95

Frequency (Hz)

SWL

1/3

(dBA)

Total prediction (APG)

Total prediction (ZPG)

Suction side (APG)

Suction side (ZPG)

Pressure side (ZPG)

Measurements

Figure 8:Third o taveband spe traof sound power levelfor ase2(

U = 8

m/s) onsideringAPGorZPG modelsoftrailingedgenoise.

TableII.Theobserverislo atedontheground

100

m downwind,and thespe traareazimuthally averaged asgivenbyEquation(10).UsingtheAPGmodel on the su tion side, the predi tions agree well at high frequen ies, above200Hzfor ase1 and 1000Hz for ase2.Forboth ases,trailingedgenoiseisdominated bythesu tionside ontribution atlowerfrequen ies, and by the pressure side ontribution at higher fre-quen ies. Using theZPG model onthe su tionside, thepredi tionsareupto10dBlower omparedtothe APGmodelpredi tions,andarelowerthan measure-mentsoverthewholefrequen yrange.Atlow frequen- ies,bothmodel predi tionsunderestimate the mea-surements, whi h anbe attributed to the fa t that other noise me hanisms dominate in this frequen y range,aswill beseenin Se tion4.4.

3.4. Dire tivityandamplitudemodulation Thehorizontaldire tivityofoverallSPLisplottedin Figure9(a)for ases1and2.Themaximumlevelsare

20

30

40

50

30

210

60

240

90

270

120

300

150

330

180

U=6m/s

_U=8m/s

0

2

4

6

8

10

30

210

60

240

90

270

120

300

150

330

180

U=6m/s

0

U=8m/s

(a) (b)

Figure9:Horizontaldire tivityof(a)overallSPLand(b)amplitudemodulationstrength,withthewind oming fromtheleft.

obtainedupwindanddownwind,whilethe minimum levelsarefound rosswind,whi hisinagreementwith typi aleldmeasurements losetoawindturbine[2℄. Thisshape anbeexplainedbythedire tivityof trail-ingedgenoise, omingfromtheassumptionofdipole distributionin Amiet's theory.Thisdire tivityis de-terminedbytheorientationoftheblade.

Amplitudemodulationis ausedbytherotationof theblades,andhasafrequen yof1/3theblade rotat-ingfrequen yfora3-bladedwindturbine.Subtra ting themeanSPLfromtheSPLatea hbladeazimuthal position

γ

,we an visualizeAMin Figure 10for ob-serversindownwindand rosswinddire tion.TheAM isalmostidenti alfor ases1and2.Thevariationsare smallinthedownwinddire tion,andmu hmore im-portantinthe rosswinddire tions.WedenetheAM strengthasthedieren ebetweenminimumand max-imumvaluesofSPLoverbladeazimuthalposition

γ

. TheAMstrengthisapproximately4dB(A) rosswind andlessthan0.3dB(A)downwind.Figure9(b)shows thedire tivityofAMstrengthfor ases1and2.Large valuesofAM strength, ofupto 10dB(A),arefound in thevi inityof the rosswinddire tions,where the minimum overall SPL values are found a ordingto Figure9(a).Thesepredi tionsareingoodqualitative agreement with eld measurements [2℄, and an be explainedbyrotationanddire tivityee ts.

4. Inuen eof atmospheri

turbu-len e and wind shear

4.1. Monin-Obukhovsimilaritytheory

Monin-ObukhovSimilarityTheory(MOST)is onsid-eredtostudytheinuen eofatmospheri turbulen e andwindshearonwindturbinenoise.Thistheory ap-plies to theatmospheri surfa elayer,where surfa e uxesare relatively onstant,andis validoveraat

0

100

200

300

−3

−2

−1

0

1

2

Blade position

γ

(°)

AM (dBA)

U=6m/s

U=8m/s

Figure 10: Amplitude modulation in downwind (dashed lines)and ross-wind(solid lines)dire tions for ases 1 and 2. The observer is 100m awayfrom thewind turbine,andAMisobtainedbysubtra ting fromthemeanSPLfromSPL(

γ

).

and homogeneousground[34,35, 36℄. The main pa-rametersofthemodelarethefri tionvelo ity

u

∗

and thesensibleheatux

H

,orequivalentlythe tempera-tures ale

T

∗

.Thestabilityoftheatmosphereisthen des ribedbytheObukhovlength

L

∗

givenby[34,36℄:

L

∗

= ¯

T u

2

∗

/(κgT

∗

) = −

ρ

0

C

p

¯

T u

3

∗

κgH

,

(11) with

T

¯

thepotential temperature,

κ = 0.41

thevon Kármán onstant,

g

thegravitya eleration,and

C

p

thespe i heatofdryair.Theatmosphereis unsta-ble when

L

∗

< 0

(

H > 0

) and stable when

L

∗

> 0

(

H < 0

).Whentheshearprodu tionofturbulen eis mu hlargerthanthebuoyantprodu tion,the atmo-sphereis alledneutraland

1/L

∗

≈ 0

(

H ≈ 0

).

The mean velo ity prole as a fun tion of height

z

anthen beobtainedusingsimilarityrelations[37, 34℄:

U (z) =

u

∗

κ



ln

 z

z

0



− ψ

u



,

(12)

Case1:

U (80

m

) = 6

m/s

H

(W/m

2

)

u

∗

(m/s)

L

∗

(m) -10 0.29 235 0 0.37 Inf 40 0.42 -168 Case2:

U (80

m

) = 8

m/s

H

(W/m

2

)

u

∗

(m/s)

L

∗

(m) -25 0.38 200 -10 0.46 905 0 0.49 Inf 40 0.53 -348 200 0.58 -92

Table III: MOST parameters used in the study for ases1and2.

where

z

0

isthesurfa eroughnesslengthandthe fun -tion

ψ

u

depends on the stability of the atmosphere. In neutral onditions,

ψ

u

= 0

and the lassi al log-arithmi prole is re overed. These velo ity proles are sometimes alled Businger-Dyerproles, and we usein this study aslightlymodiedversionof these proles detailed in Appendix A. Using MOST, it is also possible to predi t turbulen e parameters that vary with height to represent the inhomogeneity of the atmospheri boundary layers. The von Kármán spe trum of Equation (2) is used, but with height-dependent standard deviation of turbulent velo ity u tuations

σ

u

and integral length s ale

Λ

that are des ribedinAppendix A.

Sin e detailed parameters on erning the atmo-spheri onditions during the wind turbine noise measurements are not mentioned in Referen e [32℄, we hoose realisti parameters found in the liter-ature. The heat ux

H

typi ally varies over the range

−50

W/m

2

to 600W/m

2

during a diurnal y- le [34℄. Following Ostashev and Wilson [38℄, we se-le tavalueof200W/m

2

formostlysunny onditions, and 40W/m

2

for mostly loudy onditions.For sta-ble onditions,typi allyo urring atnight, valuesof

−10

W/m

2

and

−25

W/m

2

are hosen for

H

. Then wededu ethefri tionvelo ityfromEquation(12)so thatthemeanvelo ityathubheightis6m/sfor ase1 or8m/sfor ase2,using

z

0

= 0.1

m.Theresultsare summarizedinTableIII.Resultsfor

H = −25

W/m

2

and200W/m

2

arenotshownfor ase1be ausethey yield

|L

∗

| < 50

m,and it is generally admitted that MOST is only valid for

|z/L

∗

| < 1 − 2

[35℄. Let us note that for

H = 200

W/m

2

and

U (80

m

) = 8

m/s, the validity of MOST mightbe questionable for the highestpartoftherotor.

The dierent possible wind proles are plotted in Figure11for ase2.Thewindshearis learlystronger in stable onditions ompared to neutral or unsta-ble onditions.The windspeedin reasesfrom 6.2to 9.5m/sbetweenthebottomandtoppartsoftherotor for

H = −25

W/m

2

, while it remains lose to 8m/s

2

4

6

8

10

0

50

100

150

U(z) (m/s)

z (m)

H = 0 (neutral)

H = −10W/m

2

H = −25W/m

2

H = 40W/m

2

H = 200W/m

2

Figure 11: Mean wind proles

U (z)

for the atmo-spheri onditions des ribed in Table III for ase 2 (

U (80

m

) = 8

m/s).Theminimumandmaximum ro-torheightsareshownusingbla kdashedlines.

for unstable onditions. Similar results are obtained for ase 1 so they are not plotted here. The turbu-len e parameters

σ

u

and

Λ

are plotted for ase 2in Figure12.UsingexpressionsgivenbyCheinet[36℄,

σ

u

isindependentofheightinneutralandunstable on-ditions,whileitin reaseswithheightinstable ondi-tions.Theintegrallengths alealwaysin reaseswith height, but in a mu h qui ker way in stable atmo-spheres.Theturbulen elevelasso iatedwiththevon Kármánspe trumwillthusbea ombinationofthese twoee ts, asthis levelin reaseswith in reasing

σ

u

andde reaseswithin reasing

Λ

.

4.2. Ee tofwind shearon windturbine trailingedgenoise

The noise radiated by a wind turbine depends on windshear,mostlybe auseanin reaseinwindspeed auses an in rease of the AoA seen by a blade seg-ment. Asan example,the variationof AoAoverthe rotorplaneduetowindshearisplotted in Figure13 for ase2with

H = −25

W/m

2

.ThemaximumAoA variationoveronerotationisapproximately

±1.5

o

for the tip segment. As a result, the turbulent bound-ary layerparameters vary with blade azimuthal po-sition

γ

. Forinstan e, Figure 14 shows thevariation of the displa ementthi kness

δ

∗

s

on the su tion side forthedierentwindproles orrespondingto ase2. Theboundarylayerthi knessofthe tipsegment de- reases from

γ = 0

, where the blade is pointing up to

γ = 180

o

, where thebladeis pointingdown.This de reaseismostsigni antforthestableatmosphere with

H = −25

W/m

2

. These hanges in boundary layerparameters auseasigni ant hangeinthewall pressurespe traplotted inFigure15asafun tion of

γ

.Thespe tralpeakshiftstohigherfrequen ywhen the blade goes from top to down positions, orre-spondingtoade reaseofAoAfrom

5.2

o

to

2.5

o

.These spe tral variations due to wind shear are in good

0

0.5

1

1.5

0

50

100

150

σ

_u

(m/s)

z (m)

H = 0 (neutral)

H = −10W/m

2

H = −25W/m

2

H = 40W/m

2

H = 200W/m

2

0

100

200

300

400

500

0

50

100

150

Λ

(m/s)

z (m)

H = 0 (neutral)

H = −10W/m

2

H = −25W/m

2

H = 40W/m

2

H = 200W/m

2

(a) (b)

Figure 12: (a) Standard deviation of turbulent velo ity u tuations

σ

u

and (b) integral length s ale

Λ

for

U (80

m

) = 8

m/s.Theminimumandmaximumrotorheightsareshownusingbla kdashedlines.

Figure13:AoAvariationindegreesduetowindshear for

U (80

m

) = 8

m/sand

H = −25

W/m

2

.

agreement with surfa e pressure measurements per-formed in the framework of the DANAERO proje t forasimilarsize windturbine[5,Figure25℄.

Thissigni antee tofwindshearontheemission sideis mu h lesspronoun edon there eiverside, as anbe seenin the sound powerlevel spe traof Fig-ure 16 al ulated at a re eiver100m downwind.On thesu tionside, a

SW L

in reaseisobservedathigh frequen ies, of approximately 1dB(A) at 2kHz and 3dB(A) at 4kHz. However, this in rease is not ob-served on the pressure side, and sin e pressure side levels dominate above2kHz, the maximum in rease due to windshear is only 0.4dB(A)at 2kHzon the totaltrailingedgenoisespe trum.Thefa tthatlevel variationsdue to wind shear are lesspronoun ed on the re eiverside (Figure 16) ompared to the emis-sion side (Figure 15) may be explained by the fa t thatthe3bladesandallthebladesegmentsare on-sideredto al ulate theazimuthally-averagedspe tra ofFigure16,thusvariationsduetowindsheartendto beaveragedout.Wemustkeepinmindthatstronger

0

100

200

300

4

5

6

7

8

9

γ

(°)

δ

*

s

(mm)

H = 0 (neutral)

H = −10W/m

2

H = −25W/m

2

H = 40W/m

2

H = 200W/m

2

Figure 14: Variationof displa ementthi kness

δ

∗

s

on thesu tionsideasafun tionof bladeazimuthal po-sition

γ

forthetipsegmentandfor ase2.Thethi k dashedline orrespondstothereferen evaluewitha onstantwindof8m/s.

10

2

10

3

60

65

70

75

80

85

90

Frequency (Hz)

Φ

pp

(dB re. 20

µ

Pa)

No wind shear (AoA = 4°)

γ

= 0° (AoA = 5.2°)

γ

= 60° (AoA = 4.7°)

γ

= 120° (AoA = 3.3°)

γ

= 180° (AoA = 2.5°)

Figure 15: Wall pressure spe tra

Φ

pp

onthe su tion side for dierent blade azimuthal position

γ

for the tipsegment, onsidering ase2with

H = −25

W/m

2

10

2

10

3

60

65

70

75

80

85

Frequency (Hz)

SWL

1/3

(dBA)

No wind shear (suction side)

No wind shear (pressure side)

H = −25W/m

2

(suction side)

H = −25W/m

2

(pressure side)

Figure 16: Third o tave band spe trum of

SW L

for trailing edge noise on pressure and su tion side for ase2withnowindshearandwith

H = −25

W/m

2

.

windshearthanthosepredi tedbyMOSTusually ex-istinreality,be auseinpra ti etheterrainmightnot beatandhomogeneous(topographyee ts),and be- auseothersour esofinhomogeneitiessu has large-s aleturbulen eor wakesof otherturbines mightbe present[4,3,5℄.

4.3. Ee tofatmospheri turbulen e on wind turbineturbulentinownoise Amiet'smodelforturbulentinownoisedire tly de-pends on the turbulen e spe trum

Φ

ww

, as seen in Equation(1).ItismodeledusingavonKármán spe -trum with turbulen eparameters

σ

u

and

Λ

that de-pendonheightorequivalentlyonthebladeazimuthal position

γ

.Figure17showshowtheturbulen e spe -trumvarieswith

γ

forthetipsegmentat100Hz.The maximum spe tral levels are found for the unstable atmospherewith

H = 200

W/m

2

duringthewhole ro-tation,whi h anbeexplainedbytherelativelyhigh valueof

σ

u

andlowvalueoftheturbulentlengths ale

Λ

asso iatedwiththis ase(seeFigure12).Thesame trendsareobservedforotherfrequen ies.

Figure 18 shows the azimuthally-averaged

SW L

spe tra al ulatedat are eiver100m downwind as-so iatedwiththesameatmospheri onditions.Asit ouldbeforeseenfrom Figure 17,themaximum lev-elsareobtainedfor

H = 200

W/m

2

andtheminimum levelsfor

H = 0

and

H = 40

W/m

2

.The dieren es are signi ant  up to 2dB(A)  between the dif-ferent atmospheri onditions.Asalready mentioned previously for trailing edge noise, we must keep in mind that stronger turbulent variations than those predi ted by MOST may exist in reality, espe ially whenawindturbinehappenstobeinthewakeof an-otherturbine[3,5℄.To on ludethispart,letusnote that the leading edge thi kness orre tion presented inSe tion2.1.2hasanegligibleee tonthenal re-sults.Indeed,integrallengths ales

Λ

aremu hlarger than the blade hord

c

, thus

Λ/c

in Equation 3 is

0

50

100

150

200

250

300

350

−56

−54

−52

−50

−48

−46

γ

(°)

Φ

ww

(

γ

) (dB)

H = 0

H = −10W/m

2

H = −25W/m

2

H = 40W/m

2

H = 200W/m

2

Figure17:Variationsofturbulen espe trum

Φ

ww

as a fun tion of blade azimuthal position

γ

for the tip segment at 100Hz and for the various atmospheri onditions orrespondingto ase2.

10

2

10

3

75

80

85

90

Frequency (Hz)

SWL

1/3

(dBA)

H = 0

H = −10W/m

2

H = −25W/m

2

H = 40W/m

2

H = 200W/m

2

Figure 18: Third o taveband spe trum of

SW L

for turbulentinownoiseandforthevariousatmospheri onditions orrespondingto ase2.

largeand

SP L

R

issmall,withamaximumredu tion of0.3dBobtainedfortheroot segment.

4.4. Combinedee tsofwindshearand at-mospheri turbulen e

4.4.1. Soundpowerlevelpredi tions

The total

SW L

spe train ludingboth trailingedge noiseandturbulentinownoiseare omparedto mea-surementsof Referen e[32℄ in Figures 19and 20 for ases1and2.We onsiderhereaneutralatmosphere (

H = 0

),whi h meanstheturbulentinownoise lev-els are relatively low a ording to Figure 18. It ap-pearsthat turbulentinownoiseis dominant at low frequen ies, upto 300to 500Hz, while trailing edge noise is dominant at higher frequen ies. The agree-ment between predi tions and measurements is now quitesatisfa toryalongthewholefrequen yband.For ase1,predi tionsslightlyoverestimatethe measure-mentsatlowfrequen y,whi hmightindi atethatthe

10

2

10

3

60

65

70

75

80

85

90

Frequency (Hz)

SWL

1/3

(dBA)

Total prediction

Trailing edge noise

Turbulent inflow noise

Measurements

Figure 19: Third o tave band spe trum of

SW L

for trailing edge noise and turbulent inow noise for ase1and

H = 0

(neutralatmosphere).

10

2

10

3

65

70

75

80

85

90

95

Frequency (Hz)

SWL

1/3

(dBA)

Total prediction

Trailing edge noise

Turbulent inflow noise

Measurements

Figure 20: Third o tave band spe trum of

SW L

for trailing edge noise and turbulent inow noise for ase2and

H = 0

(neutralatmosphere).

turbulent inow noise needs some improvements at thesefrequen iesand/orthattheatmospheri turbu-len e parameters are not well modeled. For ase 2, theexperimental spe tralpeakaround 400Hzis not apturedbythemodel,whi hmaybedueto the ab-sen eofothernoisesour esinthepredi tionssu has separation/stallnoise.

4.4.2. Dire tivityandamplitudemodulation

Thehorizontaldire tivitiesofoverallSPLandofAM strength are plotted in Figure 21 for a neutral at-mosphere(

H = 0

).Resultsaregivenfortrailingedge noiseonly,turbulentinownoiseonlyandforthetotal noise.Itappearsthat themaximaofoverallSPLfor the3 urvesarefoundupwindanddownwind,andthe minimaarefound rosswind(

90

o

_{± 2}

o

and

270

o

_{± 2}

o

). Asalreadyseenin Se tion3,theAMstrengthisless than 1dB in the upwind and downwind dire tions, andis maximum lose to the rosswinddire tion,at slightly dierentdire tions for thethree urves.The

Trailing edge

Leading edge

Figure 22: Normalized dire tivity of trailing edge noiseand turbulentinownoisefor thetip segment. Dashedlines:

f = 500

Hz;solidlines:

f = 4000

Hz.

AMstrengthrea hesamaximumof10dBalittle up-windfortrailingedgenoise,of9dBalittledownwind for turbulent inow noise, and of only 4dB exa tly rosswindforthetotalnoise.

To explain these dieren es, let us look rst at the dire tivity of one blade segment in the oordi-nate system of the blade, as shown in Figure 22. Amiet's model predi ts that trailing edge noise ra-diation ismaximumtowardsthe leadingedge of the blade,whileturbulentinownoiseradiationis maxi-mum towards the trailing edge. The normalized di-re tivity are frequen y-dependent, with more lobes appearingwithin reasingfrequen y.This dire tivity pattern,aswellasthetwistingoftheblade s hemat-i allyrepresentedinFigure6,doexplainthat the di-re tionswheretheminima arefoundareslightly dif-ferentforthetwonoiseme hanisms.

To better understand the dire tivity of AM strength, it is also useful to look at the variation of

SP L

asa fun tion of blade azimuthal position

γ

shownin Figure 23for dire tions

270

o

and

278

o

. At

270

o

, exa tly rosswind,trailingedge noise and tur-bulent inow noisevariationsare in phase and their levels are omparable, whi h explains that the total noisefollowsthesametrendwithsimilarAMforthe three urves. At

278

o

, slightly downwind, the situ-ationis quitedierentwithbothme hanismshaving outofphasevariationsandturbulentinownoise lev-elsbeing loseto theirminimumvalues.As aresult, the totalnoisemostlyfollowsthetrailingedge noise variationsanditsAMstrengthisonly3dB(A),mu h smaller than the 9dB(A) obtained for turbulent in-ownoise.

5. Con lusionand future work

Inthispaper,Amiet's analyti almodel forturbulent inownoiseandtrailingedgenoiseisappliedfor om-putewindturbinenoise.First,wevalidatedthemodel

30

40

50

30

210

60

240

90

270

120

300

150

330

180

0

Total

Trailing

edge noise

Turbulent

inflow noise

2

4

6

8

10

30

210

60

240

90

270

120

300

150

330

180

0

(a) (b)

Figure 21: Dire tivity of (a) overall SPL and (b) amplitude modulation strength 100m away from the wind turbinefor ase2and

H = 0

(neutralatmosphere).

0

100

200

300

25

30

35

SPL(

γ

) (dBA)

τ

= 270°

Total

Trailing edge noise

Turbulent inflow noise

0

100

200

300

30

35

40

Blade position

γ

(°)

SPL(

γ

) (dBA)

τ

= 278°

Figure 23: Amplitude modulation for trailing edge noise,turbulentinownoiseand fortheoverallnoise atanhorizontalangleof

270

o

(top)andof

278

o

(bot-tom) with respe t to the wind dire tion, for ase 2 and

H = 0

.

predi tions by omparison with wind tunnel exper-iments from the literature. We showed that trailing edge noise predi tions are improved when the ee t of an adverse pressure gradientis in luded. Wealso foundthat anempiri althi kness orre tion for tur-bulentinownoisemaybe onsideredto a ountfor theredu tionofnoiseleveldue toairfoilthi kness.

Then, the model is adapted to rotating blades to predi t wind turbine noise in the simple ase where the wind speed is onstant with height and

turbu-lent inow noise is negle ted. Model predi tions are ompared to results from the literature for a 93 m-diameter2.3MWwindturbine.Thesoundpowerlevel predi tionsareingoodagreementwithmeasurements athighfrequen ieswhentheAPGmodelisused,but underestimate them at low frequen ies. The predi -tionsofdire tivityandamplitudemodulationarealso inagreementwithresultsfromtheliterature losetoa windturbine,withmaximumSPLandminimumAM strengthdownwindandupwind,whileminimumSPL and maximum AM strength are found in rosswind dire tions.

In the last part, we took into a ount windshear andturbulen eee tsusingtheMonin-Obukhov sim-ilaritytheorythatisvalidin theatmospheri surfa e layeroveratand homogeneousground. Ontheone hand, we showed that wind shear auses variations ofangleofatta kthatarelargestinstable onditions (typi allyatnight).Althoughtheangleofatta k vari-ationsduetowindshearprodu easigni ant hange in thewallpressurespe traat someblade segments, the in reasein thetrailingedge noisespe traat the re eiveris almostnegligible.Ontheotherhand, tur-bulent inow noisedoesvarysigni antlydepending on atmospheri onditions. When both me hanisms are onsidered,SWLspe traareinmu hbetter agree-mentwithmeasurements,withturbulentinownoise dominating at low frequen y(below 400Hz approxi-mately).Dire tivitiesofoverallSPLandAMare sim-ilarforbothme hanismsandforthetotalnoise,with an AM strength that rea hes at most 4dB(A) for thetotalnoise, omparedtoupto 10dB(A)forea h me hanism onsideredindividually.

Several perspe tives an be mentioned as a on-tinuationof thepresentwork.On thesour e side, it would be importantto model separation/stallnoise, that o urs when the AoArea hes largevalues. Re- entstudieshaveshownthat thisnoiseme hanismis

agood andidate forexplainingtheenhan ed ampli-tude modulation observed in the eld [4℄. Also, the ee ts of stronger wind shear and largerturbulen e u tuations ouldbestudied,whi hwouldrequireto onsider eld measurementsortheoreti altoolsthat are more advan ed than MOST. Finally, to be able topredi tthenoiseper eived by potentialneighbors at large distan es from a wind turbine, we envisage to ouplethepresentsour emodelto apropagation model that takes into a ount atmospheri u tua-tionssu hastheParaboli Equationmodel[39℄.

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ampli-tudemodulation of wind turbine noise. In: Wind TurbineAmplitudeModulation:Resear htoImprove Understanding as to its Cause and Ee t. Renew-ableUK,2013.

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Zhu,M.Hansen,F.Bertagnolio,H.Madsen: Valida-tionsand improvementsofairfoiltrailingedgenoise predi tionmodels usingdetailedexperimentaldata. WindEnergy15(2012)4561.

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fromrealairfoilsinturbulen e.JournalofSoundand Vibration329(2010)34703483.

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tran-soni andlowreynoldsnumberairfoils.AIAAJournal 25(1987)21682179.

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A. Expressions for the velo ity

pro-les and atmospheri turbulen e

parameters

A.1. Velo ityproles

Themeanvelo ityprole

U (z)

giveninEquation(12) involvesafun tion

ψ

u

that depends onthe stability oftheatmosphere.Foranunstableatmosphere(

L

∗

<

0

)[37,34℄:

ψ

u

= 2 ln

 1 + x

2



+ ln

 1 + x

2

2



− 2 arctan x +

π

2

,

(13) with

x = (1 − 16z/L

∗

)

1/4

. For a stable atmosphere (

L

∗

> 0

)[37,34℄:

ψ

w

=

(

−5z/L

∗

for

z/L

∗

≤ 0.5,

−7 ln (z/L

∗

) −

_z/L

4.25

∗

+

0.5

(z/L

∗

)

2

− 0.852

elsewhere

.

A.2. Atmospheri turbulen eparameters Wedetailinthisse tiontheexpressionsforthe height-dependent standard deviation of turbulent velo ity u tuations

σ

u

and integral length s ale

Λ

appear-ing in thevon Kármán spe trum. Cheinet [36℄ gives thefollowingempiri alrelationshipsforthe varian e

σ

2

u

:

σ

u

2

=















u

2

∗

h

α

1

+

_|L

1

∗

|

(α

2

z

i

+ α

3

z)

i

2/3

if

L

∗

< 0,

u

2

∗



1.73 + 3.3



z

L

∗



0.5



2

if

L

∗

> 0,

with

z

i

themixed layerheight(set to1000m),

α

1

=

5.2

,

α

2

= 0.52

, and

α

3

= 0

in the surfa e layer

(

z ≤ 0.1z

i

). Bothexpressions yield

σ

2

u

= 3.0u

2

∗

when

L

∗

→ ∞

(neutral onditions).

The integral length s ale

Λ = L

outer

/1.339

, with

L

outer

theouters aleinthevonKármánmodelgiven by[36℄:

L

outer

=



1.91

σ

2

u

C

2

u



3/2

.

(14)

C

2

u

isthestru tureparameterofmomentum u tua-tionsparametrizedasfollows:

C

u

2

=

u

2

∗

z

2/3

f

u

 z

L

∗



,

(15) where

f

u

(ξ) =







3.9



_1−7ξ

1−ξ

− ξ



2/3

for

ξ ≤ 0,

3.9 (1 + 5ξ)

2/3

for

ξ > 0,

with

ξ = z/L

∗

.Both expressionsyield

L

outer

= 1.8 z

forpurelyshear-driventurbulen e,i.e.for

ξ = 0

(neu-tral onditions).