Tong W. Wind Power Generation and Wind Turbine Design

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Wind Turbine Acoustics 175

review of the computational methods for aeroacoustic predictions is given in

[ 27 ]. Direct solution of the acoustic ﬁ eld by solving the compressible Navier-

Stokes equations being computationally too expensive for practical applica-

tions, the most promising approaches for aeroacoustic computations are the

hybrid methods. The hybrid methods are based on the observation that for low

Mach numbers the amplitude of the acoustic ﬂ uctuations is several orders of

magnitude smaller than the hydrodynamic ﬂ uctuations. Based on this scale

separation the governing equations can be divided into a set of ﬂ ow equations

and a set of acoustic equations having sources determined by the ﬂ ow vari-

ables. Such hybrid approaches have several advantages as compared to direct

computations. First, the acoustic ﬁ eld can be computed on a larger domain

than the ﬂ ow ﬁ eld, ﬂ ow computations are needed only in regions where sig-

niﬁ cant noise is generated. Second, the solution methods for incompressible/

semi-compressible ﬂ ows are faster than for compressible ﬂ ows. Additional

gain in computational effort is due to the possibility of having larger mesh

spaces in the acoustic solver and the fact that for the acoustics commonly only

one equation has to be solved.

Lighthill's analogy (presented earlier in this section) was the ﬁ rst method to

separate the acoustics from the ﬂ ow computations. Recently, a more systematic

approach has been presented by Slimon et al. [ 28 ]. Their method is based on the

expansion about incompressible ﬂ ow. The compressible ﬂ ow variables are

expanded in a power series in e

= g M

246

0123

pp p p peee=+ + + +

( 32 )

246

0123

rr erer er=+ + + +

(33 )

246

0123ii i i i

uu u u ueee=+ + + +

(34 )

Figure 16: Comparison of two-dimensional NACA 0012 data to predictions for a =

7.8

at several Mach numbers (after [ 26 ]).

176 Wind Power Generation and Wind Turbine Design

246

0123

TT T T Teee=+ + + +

(35)

Substituting the decomposed variables in the compressible Navier-Stokes equa-

tions and grouping terms with the same order in e , equation sets with different

approximations are derived. The zeroth order approximations e

–2

describe the ther-

modynamic ﬁ eld, the ﬁ rst order approximations e

–0

the hydrodynamic ﬁ eld and the

second order approximations e

describe compressibility effects. The results of

this method can be written in the form of Lighthill’s acoustic analogy. For further

details the reader should consult [ 28 ].

Once the acoustic sources are determined, there are two main strategies for the

computation of the acoustic ﬁ eld: analytical computation of the sound pressure

level at the observer position or numerical computation of the noise propagation.

When the acoustic ﬁ eld is governed by a non-homogeneous wave equation having

elementary acoustic sources (monopoles, dipoles or quadrupoles) of the form:

1 '(,) '(,)

(,)()

pxt pxt

Qxt f

∂∂

−=

∂∂

∂





(36 )

and f is the surface over which the sources are distributed, using the free-space

Green's function d ( g )/4 p r , with g = t − t + r / c the solution can be written in an

integral form:

(,)( )()

4'(,) dd

Qy f g

pxt y

td d

∞

−∞ −∞

∫∫



(37 )

In eqn ( 37 )



is the observer position vector, y



the source position vector, r the

distance between the source and the observer and t is the source time. This equa-

tion can be integrated after variable transformations. Further details can be found

e.g. in [ 24 ] where the Ffowcs Williams − Hawkings equation is solved to determine

the noise generated by helicopter rotors. Recently, Filios et al. [ 29 ] combined a low

order panel method with prescribed wake-shape and the integration of the Ffowcs

Williams − Hawkings equations to predict the noise generated by the NREL wind

turbine. In their work only the monopole and dipole sources have been considered,

the noise generated by velocity ﬂ uctuations (quadrupoles) being neglected.

This previously described integral approach is based on the assumption that the

observer is far enough to consider the waves propagating from individual sources

spherical. Also, propagation effects (reﬂ ection, absorption, refraction) are neglected.

An alternative method is to solve numerically the CAA equation(s) on an acous-

tic grid (which does not need to be identical to the ﬂ ow grid). Although this

approach is computationally more expensive, it allows the consideration of propa-

gation effects and gives a more detailed three-dimensional picture of the radiated

acoustic ﬁ eld. Moroianu and Fuchs used Large Eddy Simulations to compute the ﬂ ow

ﬁ eld around a single wind turbine [ 30 ]. The acoustic sources provided by the LES

computations have been used in a separate acoustic solver to compute the corre-

sponding noise generated by the wind turbine. Figure 17 shows an instantaneous

snapshot of the radiated acoustic ﬁ eld and the sound pressure levels around the

Wind Turbine Acoustics 177

wind turbine. A similar approach has been used in [ 31 ] where the acoustic sources

have been imposed in two instances to model the noise emitted by two wind tur-

bines. The isocontours of the sound pressure level are shown in Fig. 18 . The ﬂ ow

computations in [ 30 , 31 ] are based on a ﬁ nite volume approach with unstructured

sliding grids leading to very large computational efforts. Szasz and Fuchs [ 32 ] used

a ﬂ ow solver based on the ﬁ nite difference approach with Cartesian structured grids

to compute the acoustic sources. The solid boundaries have been accounted for using

the immersed boundary method, the acoustic solver was the same as in [ 30 , 31 ]. This

approach to compute the ﬂ ow ﬁ eld turned out to be very efﬁ cient and it has been

recently developed further to compute the ﬂ ow around several wind turbines. In this

way the effect of the wind turbine wakes on the noise generation of downstream

wind turbine can be accounted for. Figure 19 shows the vortical structures around

four wind turbines visualized by the l

method.

6.4 Noise propagation models

As it was mentioned above, the solution of the compressible Navier-Stokes

equations includes both noise generation and propagation. For large problems,

Figure 17: Instantaneous snapshot of the acoustic pressure ﬂ uctuation ﬁ eld (top)

and the radiated sound pressure levels (bottom).

Figure 18: Sound pressure levels emitted by two wind turbines.

178 Wind Power Generation and Wind Turbine Design

however, this approach is computationally costly, leading to the development of

several noise propagation models during the years. A review of the noise propaga-

tion models are presented in [ 4 ].

6.4.1 Spherical spreading model

The simplest propagation model is to assume spherical spreading. This implies

that the sources are considered point sources and all the parameters enumerated

in Section 4.2 are neglected, except the distance to the observer. According to the

spherical propagation model the sound pressure level decreases with 6 dB for a

doubling of the source − observer distance.

6.4.2 VDI 2714

One of the most simple and widely used models is the VDI 2714 method, where the

sound pressure level at a receiver is given by the following empirical formula [ 4 ]:

p w dagvbs

L L DKLLLLLL= ++−−−−−−

(38 )

where D accounts for the source directivity, K is a correction for the reﬂ ec-

tion of sound due to the presence of vertical walls ( K = 0 dB for sound sources

located in the free ﬁ eld, K = 3 dB above the ground, and K = 6 dB or K = 9

dB when two or three perpendicular surfaces are present, respectively). L

= 10

log

(4 p r

) accounts for the inﬂ uence of the source − observer distance. The air

absorption effect is represented by L

= a r . The ground effects are modeled as

[4.8 (2 / )(17 (300 / ))]Lhr r=− +

where h

is the average of the source and

observer heights. The last three terms in eqn ( 38 ) account for the inﬂ uence of the

vegetation, buildings and screens, respectively.

Figure 19: Large-scale vortices around four wind turbines visualized by the l

method.

Wind Turbine Acoustics 179

6.4.3 Ray-tracing models

In order to account for complex landscapes and the meteorological effects, more

advanced methods were needed. The ray-tracing models describe the propagation of

the acoustic waves by the path along which the waves propagate (rays). For spherical

spreading (no solid objects, no temperature gradients and no wind) the rays will be

straight lines emerging from the source. When solid objects are present the rays will

be reﬂ ected, while the presence of wind or temperature gradients will curve the rays.

The DELTA model (cited in [ 4 ]) has two steps. First, a modiﬁ ed source height

is calculated based on the arrival angle of the ray, in this way accounting for ray

curvature (see Fig. 20 ):

coshhd q=+

′

(39)

The receiver height is not corrected, because it is much smaller than the source

height and the error which is introduced by neglecting the correction is minimal.

In the second step the noise propagation is computed as if no atmospheric effects

would be present.

Recently, Prospathopoulos and Voutsinas [ 33 ] used a more advanced ray-tracing

model to compute the sound propagation even from wind turbine parks. In their

model the noise source is assumed to be located at the rotor center. The propaga-

tion of the noise is computed in three steps:

ﬁ nding the eigenrays 1.

calculating the energy losses along the eigenrays 2.

reconstructing the sound pressure level by summing up the contribution of the 3.

eigenrays

When computing the energy losses, both the atmospheric and ground absorp-

tion, wave refraction and diffraction and atmospheric turbulence effects have been

taken into account. Good agreements have been obtained with experimental

measurements for several testcases.

Figure 20: Modiﬁ ed source height due to curved sound path (after [ 4 ]).

180 Wind Power Generation and Wind Turbine Design

7 Noise reduction strategies

In the previous sections it has been shown that there are a multitude of parameters

which inﬂ uence the generation and propagation of wind turbine noise. In the fol-

lowings a short list of noise reduction strategies is given:

• Blade − tower interaction . For downwind turbines, the rotor blades passing the

wake of the tower, the noise levels are signiﬁ cantly larger than for upwind tur-

bines (see e.g. [ 19 , 34 ]). For this reason, new wind turbines have upwind con-

ﬁ gurations, even if technically there are additional issues associated with them

(like the bending of the blades because of the wind load towards the tower and

not away like in the downwind case).

As it was shown in Section 6.2., the emitted sound power levels are propor-•

tional to the ﬁ fth power of the blade speed. Thus, an efﬁ cient way of reducing

the emitted noise levels is to decrease the angular speed of the rotor. This ap-

proach is currently employed, but it has the drawback, that it involves also

a reduction of the generated electric power, thus the efﬁ ciency of the wind

turbine decreases.

The experiments of Oerlemans • et al. [ 16 ] showed that blade surface smooth-

ness affects the emitted noise levels, clean blades emitting considerably less

noise than the rough ones.

The shape of the • blade cross section and the angle of attack is crucial on the

emitted sound pressure levels. Large angles of attack and thick airfoils lead to

separation and vortex shedding with increased noise levels. Marsden et al. [ 35 ]

reported an 89% noise reduction from an airfoil by optimizing its cross section

to eliminate the low-frequency vortex-shedding.

• Trailing edge shape . Blake (cited in [ 4 ]) observed that an airfoil with ﬂ at pres-

sure side and beveled suction side produces the least noise. Serrations on the

trailing edge have also the potential to reduce the emitted noise levels by break-

ing up the large-scale structures and reducing by this the low-frequency oscil-

lations. Nevertheless further research is needed to ﬁ nd optimal conﬁ gurations,

since discrepancies are observed between the theoretically predicted and

measured values [ 4 ].

• Trailing edge material. As it was discussed in Section 6.2, trailing edge noise is

mainly attributed to the ampliﬁ cation of the turbulent vortex caused pressure

ﬂ uctuations by the presence of the airfoil surface. By using porous or ﬂ exible

materials there is a potential to reduce these reﬂ ections and by this also the

emitted noise levels (see e.g. Hayden, cited in [ 4 ]).

Several experimental measurements have been carried out to evaluate the •

inﬂ uence of blade tip shape on the emitted noise levels but no proﬁ les could

be found which consistently reduced the noise levels for each measurement

condition.

• Masking . Bolin [ 13 ] has shown that masking the wind turbine noise by adding

‘positive’ noise from natural sources (trees, waves) can be an efﬁ cient way for

the increase of the acceptance of wind turbines, especially in quiet areas, where

Wind Turbine Acoustics 181

even low sound pressure levels (below the admissible limits) can be experienced

as annoying. Björkman [ 34 ] carried out longtime measurements at several wind

turbine sites in southern Sweden. At the site located next to Lund low correla-

tion was observed by the wind speed and the registered noise levels which were

explained by the fact that the wind turbine noise was masked by other noise

sources.

8 Future perspective

Recently, van den Berg [ 15 ] showed that even if the noise limitation standards

were taken into account already in the design phase, the inhabitants living in the

surrounding of a new wind park were still annoyed by the emitted noise levels.

The two main reasons for the annoyance were found to be the inaccurate predic-

tion of the equivalent noise levels and the impulsive character of the sound. Thus

there is a need for improved models. First, there is need of improving the Category

III models to achieve detailed knowledge about the generated sound ﬁ eld already

in the design phase. The inﬂ uence of atmospheric stability and turbulence level,

landscape shape, type of vegetation or the presence of sea waves have to be evalu-

ated. Also, the impacts of the interaction of wind turbine wakes in wind turbine

farms are not well understood. Another important issue related to wind turbines

operating in cold areas is the ice accretion on the wind turbine blades. Since the

deposition of the ice affects the blade cross section it affects also the character of

the emitted noise. Thus acoustic measurements might be used to detect ice deposi-

tion. Recently, Fuchs and Szasz used a coupled Lagrangian − Eulerian approach to

model ice accretion [ 36 ]. From a legislative point of view there is a need for more

accurate and ﬂ exible, but at the same time not too complicated models. Such mod-

els will lead to noise regulations which will increase the power production of the

wind turbines without impairing the well-being of the nearby residents.

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