Environmental Engineering Reference
In-Depth Information
Wind Speed Models
Wind Shear Gradient
The vertical gradient in steady wind speed with elevation above and below the elevation
of the rotor axis is often modeled by a simple power law (see Chapters 2 and 8) as
U
(
z
) =
U
H
(
z
/
H
)
m
(11-7)
where
U
(
z
)
=
free-stream wind speed at elevation
z
(m/s)
U
H
= free-stream wind speed at hub elevation (m/s)
z
= elevation above ground level (m)
H
= elevation of the rotor hub (m)
m
= empirical wind shear exponent (same as a in Eqs. (2-4 and 8-11))
The wind speed gradient may be described in polar coordinates centered at the hub
elevation by a binomial series, as follows:
m
r
cos y +
H
H
U
(
z
) =
U
H
=
U
H
[1 +
W
S
(
r
,y)]
(11-8)
r
H
cos y +
m
(
m
- 1)
2
r
H
2
cos
2
y
W
S
(
r
, y)
m
(11-9)
where
r
= radial distance from the rotor axis (m)
W
s
= wind shear shape function
In this series expression, powers of
r/H
higher than 2 have been neglected.
Tower Shadow Deficit
The presence of the tower causes a deficit in the wind speed, with the downwind
reduction often referred to as
tower shadow
and the much-smaller upwind reduction as a
bow wave
effect. Here we shall refer to both as tower shadow. Neglecting any effects of
retardation by the rotor, we will assume that the deficit has a spatial distribution of the form
d
V
T
(
z
,y) = -
W
T
(y)
U
(
z
)
é
ê
ë
t
0
+
t
p
cos[
p
(y - p)]
f or
p- y
0
£ y£ p+ y
0
W
T
(y) =
(11-10)
0
elsewhere
p
=
k
p / y
0
(11-11)
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