Environmental Engineering Reference
In-Depth Information
Table 1.3 Variation of z
0
and m with terrain from
Manwell et al. [
8
]
Type of terrain
z
0
(mm)
m
Calm open sea
0.2
0.104
Snow
3.0
0.100
Rough pasture
10.0
0.112
Crops
50.0
0.131
Scattered trees
100.0
0.160
Many trees
250.0
0.188
Forest
500.0
0.213
Suburbs
1500.0
0.257
City centres
3000.0
0.289
The values of m are from Eq.
1.16
should be by a factor of 0.738/1.225 = 0.602—a substantial 40%. The corre-
sponding change in the kinematic viscosity is by a factor of nearly 40%. This will
cause a similar decrease in the Reynolds numbers, which probably will not have a
large effect on optimal power but may influence starting performance.
1.6 The Variation in Wind Speed and Power
Output with Height
Example 1.3 showed the sometimes significant effect of the variation in density
with altitude and a similar variation will occur if the turbine experiences extremes
of temperature. The effects of tower (or nacelle) height, h, however, are more
closely associated with vertical variation in the wind speed. Typical values of h are
in the range 10-50 m, and are, therefore, small compared to the altitudes (say
5,000 m!) over which the air density and viscosity change significantly.
There are two main expressions used to describe the height dependence of the
mean wind speed, which will now be called U rather than U
0
as used previously.
The main reason to distinguish between U
0
and U is that U = U
0
only when the
height, z, is equal to h. The simplest expression for U(z) is the power law
m
U
ðÞ¼
Uh
ðÞ
z
h
r
ð
1
:
14
Þ
where h
r
denotes a ''reference height'' usually 10 m, and m is an exponent that
depends on the roughness of the surface. It is usually asserted that the logarithmic
''law''
U
ðÞ¼
Uh
ðÞ
ln z
=
z
ð Þ
ln h
r
=
z
0
ð
1
:
15
Þ
ð
Þ
is more accurate. z
0
is the ''roughness length''. Typical values of m and z
0
are
given in Table
1.3
. One possible relation between m and z
0
(in m) is given by
Eq. 2.3.28 of Manwell et al. [
8
]as
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