Page 51 - Wind Energy Handbook

TURBULENCE 25

L 1u ¼ 170:1m, or 5:67z for z , 30 m
(2:30)
L 1v ¼ 0:3333L 1u
L 1w ¼ 0:08148L 1u

or an isotropic von Karman model with
x L u ¼ 73:5m, or 2:45z for z , 30 m
(2:31)
x x x
L v ¼ L w ¼ 0:5 L u
Eurocode 1 (1997) specifies a longitudinal spectrum of Kaimal form with L 1u ¼
1:7L i , where

L i ¼ 300(z=300) å (2:32)

for z , 300 m, with å varying between 0.13 over open water to 0.46 in urban areas.
This standard is used for buildings, but not usually for wind turbines.
Figure 2.5 compares these various longitudinal turbulence spectra at 30 m height,
for a mean wind speed of 10 m/s. The surface roughness is 0.001 m, corresponding
to very flat land or rough sea, and the latitude is 508. There is reasonable agreement
between the various spectra in this situation, apart from the Eurocode spectrum
which is shifted to somewhat lower frequencies. Note the characteristic difference
between the Kaimal and von Karman spectra, the latter being rather more sharply
peaked. The improved von Karman spectrum (Equation 2.25) is intermediate in
shape.
30m height, 10m/s, z = 0.001m, 50 latitude
0
0.3

0.25 Eurocode

DS 472
0.2
Normalized spectrum 0.15 IEC 1400-1
Kaimal

IEC 1400-1
von Karman
0.1
Improved von
0.05 Karman

0
0.001 0.01 0.1 1

Frequency (Hz)
Figure 2.5 Comparison of Spectra over Smooth Terrain at 10 m/s