Environmental Engineering Reference
In-Depth Information
Noise from Vortex Shedding at the Trailing Edge
Another broadband noise source is associated with vortex shedding caused by the
bluntness of the trailing edge. This phenomenon is analogous to the shedding noise from
wings with blunt trailing edges, as well as from flat plates, and struts [Schlinker and Amiet
1981; Brooks and Hodgson 1980]. The expression derived in Grosveld [1985] for the noise
from the blunt trailing edge of one blade is
R
SPL
1/3
(
f
) = 10 log
10
ò
F
c
dr
+
K
c
(7-6a)
0
B V
5.
r
t
sin
2
(q/2) sin
2
y
(1 +
M
cos q)
3
[1 + (
M
-
M
c
) cos q]
2
d
2
(7-6b)
F
c
=
f
peak
=
0.1
V
r
t
(7-7)
where
t
= trailing edge thickness (m)
y = angle between the segment-to-receiver line and its horizontal projection
in the rotor plane (rad)
K
c
=
frequency-dependent scaling factor (dB; Figure 7-15)
The corresponding
K
c
has its maximum value when
f
reaches
f
peak
(Figure 7-15). Once
again, sound pressure levels for the rotor are obtained by integrating the contributions of
all acoustic sources over the length of each blade and adding the results.
Example Calculations and Measurements of HAWT Broadband Noise
Figure 7-16 illustrates the relative contributions of the broadband noise components
calculated by using Equations (7-3) to (7-7) for a large-scale HAWT with an upwind rotor.
The calculations are in the form of one-third-octave band spectra for each of the broadband
components identified. Also included is the summation of the components. As shown in
Figure 7-16, inflow turbulence contributes noise over the whole frequency range and
dominates the spectrum at frequencies below about 500 Hz. Effects of boundary-layer
interaction also contribute noise over a wide frequency range but are most significant at
higher frequencies. On the other hand, the noise spectrum of the trailing edge wake is
sharply peaked; the maximum for the example turbine is near 1,250 Hz.
Figure 7-17 presents sound pressure levels calculated by using the methods of Grosveld
and compares them with acoustic far-field measurements for a large, upwind-rotor HAWT
and two different downwind-rotor HAWTs. Good agreement is shown in all cases. Note
that the validation of Equations (7-3) to (7-7) has been limited to acoustic radiation in the
upwind and downwind directions only.
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