Page 259 - Wind Energy Handbook

BLADE LOADS DURING OPERATION 233

Wind shear

The increase of wind speed with height is known as wind shear. The theoretical
logarithmic profile, U(z) / ln(z=z 0 ), is usually approximated by the power law,
Æ
U(z) / (z=z ref ) for wind turbine design purposes. The appropriate value of the
exponent Æ increases with the surface roughness, z 0 , with a figure of 0.14 typically
quoted for level countryside, although the speed up of airflow close to the ground
over rounded hills usually results in a lower value at hill tops. As already noted,
IEC 61400-1 specifies a conservative value of 0.20.
In applying momentum theory to this case, the velocity component at right angles
Æ
to the plane of rotation is expressed as U 1 (1 þ r cos ł=z hub ) (1 a). The variation of
blade root bending moments with azimuth due to wind shear is illustrated in
Figure 5.11 for the example 40 m diameter stall-regulated machine, taking the
exponent as 0.20, the hub height as 40 m and considering hub-height wind speeds
of 10 m=s and 15 m=s. In the former case, the variation is nearly sinusoidal, but in
the latter case the root bending moments are effectively constant, as the blade is in
stall.

Tower shadow

Blocking of the air flow by the tower results in regions of reduced wind speed both
upwind and downwind of the tower. This reduction is more severe for tubular

350

Out-of-plane moment for U = 15 m/s
300
Aerodynamic root bending moment (kNm) 200 Rotational speed = 30 r.p.m. Out-of-plane moment for U = 10 m/s
250

150
Shear exponent = 0.2
Hub height = 40 m
100
In-plane moment for U = 15 m/s
50
In-plane moment for U = 10 m/s
0
0 30 60 90 120 150 180 210 240 270 300 330 360
Azimuth (degrees)
Figure 5.11 Variation of Blade Root Bending Moments with Azimuth due to Wind Shear,
for Typical 40 m Diameter Stall-regulated Machine Operating in Steady Hub-height Winds of
10 m=s and 15 m=s (shear exponent ¼ 0:2)