Wind turbine acoustics - Wind Power Generation and Wind Turbine Design - page 171

algebraic relationships are deduced to model both the emitted sound power level
and sound spectrum. There are a multitude of models in the literature for each
noise generation mechanism, in the followings the most widespread models
being presented.

6.2.1 Trailing edge noise
Grosvelds model (cited in [4]) is based on a frozen turbulent pattern convected
downstream over the trailing edge and predicts the A-weighted sound pressure
level as:

⎛

5

⎞

d Δ

S UD

L = 10 log n + K f ( ) + C

⎜ ⎟ (12)

pA 10 b

2

r

⎝ ⎠

The shape of the spectrum is given by

⎧

− 4

⎫

4 1.5

⎡ ⎤

⎛ St ' ⎞ ⎛ St ' ⎞

⎪ ⎪

⎢ ⎥

Kf ( ) = 10 log + 0.5

⎨ ⎬ ( 13)

⎜ ⎟ ⎜ ⎟

10

⎝ St ⎠ ⎝ St ⎠

⎢ ⎥

⎪ ⎪

max

⎣

max

⎦

⎩ ⎭

and the Strouhal numbers are defi ned as

f d

(14 )

St ' = , St = 0.1

max

U

The empirical constant is C = 5.44 dB and the directivity factor is determined as:

2

sin q / 2

2

D (, ) sin qy = y

(15 )

[ ]

2

(1 + M cos q ) 1 + ( M − M ) cos q

C

Thus the sound pressure level depends on the fi fth power of the velocity. Brooks
et al. [18] developed a more complex model to predict the trailing edge noise,
accounting for the length of the blade segment, angle of attack and separating the
contributions from the suction end pressure sides:

L /10 L /10 L /10

(16 )

L = 10 log (10

p, a

+ 10

p,s

+ 10

p,p

)

p 10

where the individual contributions have the form:

⎛ ⎞

⎛

*5

⎞

d MsD Δ t

i i

L = 10 log + K + C

⎜ ⎟ ⎜ ⎟ (17 )

p, i 10 i i

2

r St

⎝ ⎠ ⎝ ⎠ peak

s the chord length, D
the directivity function (given by a similar relationship to eqn (15)), K i are shape
functions for the spectra and C i empirical constants. The peak Strouhal numbers
St peak have also empirical values.

d i being the displacement thickness, M the Mach number, Δ