Wind turbine acoustics - Wind Power Generation and Wind Turbine Design - page 168

Brooks et al. [18] measured the fl ow and the acoustic pressure around a set of
NACA 0012 airfoils with different chord lengths in an anechoic chamber. Eight
microphones have been used for the noise measurements. Based on the measure-
ment data, semi-empirical models have been developed to predict airfoil self-noise
(see Section 6.2).
In Europe there are two anechoic wind tunnels at the University of Oldenburg
and at the National Aerospace Laboratory (NRL) in the Netherlands [4]. These
facilities have been used also for the study of the airfoil self-noise, as well as for
the study of the noise due to turbulent infl ow.
The major drawback of wind-tunnel measurements is the self-noise of the wind
tunnel itself. The errors due to the background noise can be reduced for rotating
sources by using tracking methods. For stationary sources (e.g. airfoil cross sec-
tions) the error due to the background noise can be reduced by using multiple
microphones and cross-correlating the signals at different observer positions.
Fujii et al. [19] studied the noise generated by the interaction of the rotor blades
with the wakes of wind turbine towers. Towers with circular, elliptical and square
cross sections have been considered. Their measurements showed that the tower
with a slender elliptic cross section was the quietest, the loudest being the one with
the square cross section.

6 Noise prediction

The solution of the compressible Navier-Stokes equations includes inherently also
the generation and propagation of the acoustic pressure waves. This direct compu-
tational approach, however, involves several drawbacks, which make it applicable
only for relatively simple cases and to small Reynolds numbers [20 22]. One issue

is the small magnitude of the acoustic quantities (acoustic pressure and density
fl uctuations) as compared to the hydrodynamic quantities of the fl ow. The low-
amplitude acoustic fl uctuations require discretization schemes with high accu-
racy which are computationally demanding. Also, the timesteps are limited by the
sound speed and not the convection speed as it is the case of incompressible fl ow
simulations. As a result, there was a need to develop aeroacoustic models.
Lighthill [23] was the fi rst to derive a model for aerodynamically generated
sound. By rearranging the continuity and momentum equations he obtained the
following non-homogeneous wave equation for the acoustic density:

−

2

2 2

∂ ( r uu )

∂ r ' ∂ r ' ij

2
0

− c =

(10 )

2

∂ t ∂∂ xx ∂∂ xx

i i i j

where 0 is the acoustic density fl uctuation defi ned as the departure from

ambient conditions, and c 0 is the sound speed in the undisturbed ambient medium.
In the derivation of eqn (10) it was assumed that the ambient conditions are con-
stant and viscosity effects have been neglected. Equation (10) is called the Light-
hill analogy and describes the propagation (left-hand side, LHS) and generation
(right-hand side, RHS) of sound by the fl uid fl ow. The term on the RHS is the

r ′ = r − r