Wind Turbine Acoustics - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 423

Predicting Noise from a Single Wind Turbine

Extensive research studies have been conducted to predict noise from isolated airfoils,
propellers, helicopter rotors, and compressors. Many of those findings have helped identify
the significant noise sources of wind turbines and have helped develop methods for noise
prediction. This section summarizes the technology available for predicting the sound
pressure levels radiating from known sources of wind turbine noise, particularly from the
aerodynamic sources which are believed to be the most important.

Rotational Harmonics

Impulse noises like those shown in Figures 7-3 and 7-4 can be resolved into their
Fourier components (Figure 7-5), which are at the blade passage frequency and its inte-
ger multiples. Acoustic pulses arise from rapidly-changing aerodynamic loads on the blades
as they routinely encounter localized flow deficiencies which result in momentary
fluctuations in lift and drag. Airfoil lift and drag coefficients can be transformed into
thrust and torque coefficients, and these can be used to determine the unsteady blade loads
associated with periodic variations in the wind velocity. These variations may occur within
the tower wake, as indicated schematically in Figure 7-3, or within the swept area of the
rotor, through wind shear and small-scale turbulence.
Variations in blade loading can be represented by complex Fourier coefficients modified
by the Sears function to determine the effects of unsteady aerodynamics on the airfoil. The
Sears function represents aerodynamic loading on a rigid airfoil passing through a sinusoidal
gust [Sears 1941]. Following the model presented in Viterna [1981], a general expression
for the RMS sound pressure level of the nth harmonic can be derived in the following form:

Ö2 sin g

4p R e d M n m e i m (f - p/2) J x a m cos g - nB - m

a m

P n = (7-1a)

M n

M n = nB R e W
a 0

(7-1b)

where

P n = RMS sound pressure for the n th harmonic (N/m 2 )

n = sound pressure harmonic number ( n = 1, 2,...)

g, f = azimuth and altitude angles to the listener, respectively, referred to
the rotor thrust vector (rad)
R e = effective blade radius » 0.7 x tip radius, R (m)
d = distance from the rotor to the listener (m)
M n = Mach Number factor for the n th harmonic
m = blade loading harmonic index ( m = ..., -2, -1, 0, 1, 2,...)
J x = Bessel function of the first kind and of order x = nB - m
a m T , a m Q = complex Fourier coefficients for the thrust and torque forces acting at
R e , respectively (N)

B = number of blades

W = rotor speed (rad/s)

a 0 = speed of sound (m/s)