Environmental Engineering Reference
In-Depth Information
11.1.2 Displacement Height
One reason the wind shear can vary with height is that the wind flow is displaced
above the ground by vegetation, such as a dense, closed-canopy forest. The effective
ground level where the wind speed profile reaches zero is then some distance, known
as the displacement height , above the actual ground level. The displacement height
depends on the height and density of the surrounding vegetation and on the distance
of the vegetation from the base of the tower. As a rule of thumb, for dense vegetation
close to the tower, it is 0.6-0.9 times the vegetation height (1). The shear exponent
calculated with respect to the displacement height d is as follows:
log v 2 /
v 1
log
(
h 2 /
h 1 )
α ( d )
h 1
] = α ( g )
h 2 =
(11.3)
h 1
h 2
log[
(
h 2
d
)/(
h 1
d
)
log[
(
h 2
d
)/(
h 1
d
)
]
The superscripts (d) and (g) denote the shear exponent referenced to the displacement
height and ground, respectively. Since the fraction on the right is always less than
1, the shear exponent with respect to the displacement height is always less than the
shear exponent with respect to the ground.
Now let us suppose that the exponent relative to the displacement height remains
constant with height (this is equivalent to saying that the displacement effect is respon-
sible for all the change in shear with height). Then, the shear with respect to ground
between the top anemometer height and the hub height is given by
log[
(
h h
d
)/(
h 2
d
)
]
log
(
h 2 /
h 1 )
α ( g )
h 2 h h = α ( g )
(11.4)
h 1 h 2
log
(
h h /
h 2 )
log[
(
h 2
d
)/(
h 1
d
)
]
This equation is valid only for heights greater than the displacement height. The
adjusted exponent is always smaller than the observed exponent relative to ground; in
other words, the displacement effect causes the shear exponent relative to ground to
decrease with height.
As an illustration, suppose the wind shear exponent measured between 40 m ( h 1 )
and 60 m ( h 2 ) is 0.35 and the tower is surrounded by dense, leaf-covered trees that
are 15 m tall on average. The analyst estimates a displacement height ( d ) of roughly
two-thirds the tree height, or 10 m. The projected shear exponent from 60 m to the
hub height ( h h )of80mis
log
(
70
/
50
)
log
(
60
/
40
)
0
.
35
×
) ×
=
0
.
325
log
(
80
/
60
log
(
50
/
30
)
representing a 7% decrease over the observed exponent. Figure 11-1 shows the change
in apparent shear relative to the ground for various combinations of observed shear
exponent and displacement height for tower heights of 40 and 60 m and a hub height
of 80 m.
A directionally weighted displacement height can be calculated if sufficient infor-
mation is available; site photos can be helpful in this regard. The displacement height
Search WWH ::




Custom Search