Environmental Engineering Reference
In-Depth Information
The exponent a is not a constant, but varies with the roughness of the terrain, tempera-
ture gradients in the atmosphere over the site, and steady wind speed [Justus and Mikhail
1976, Spera and Richards 1979]. Equations (2-3) and (2-4) can be combined to give
¥
U
R
(
z
/
z
R
)
3
a
f
W
(
z
R
)
dU
ò
e
W
= 0.5r
(2-5)
0
Placing the wind shear exponent a inside the integration permits it to vary with wind
speed
U
. The Weibull model for
f
W
at the reference elevation
z
r
is as follows:
f
W
= (8, 760 /
C
R
)
k
R
(
U
/
C
R
)
k
R
-1
exp - (
U
/
C
R
)
k
R
(2-6)
where
C
R
= empirical Weibull
scale factor
for winds at the reference elevation (m/s)
k
R
= empirical Weibull
shape factor
for winds at the reference elevation
exp [ ] = exponential function of [ ]
The
annual average wind speed
at a selected elevation can be expressed in terms of the
Weibull factors as
U
A
(
z
) =
C
(
z
)G[1+
k
(
z
)] » (0.90 ± 0.01)
C
(
z
)
(2-7)
where
U
A
(
z
) = annual average wind speed at elevation
z
(m/s)
C
(
z
),
k
(
z
) = Weibull scale (m/s) and shape factors at elevation
z
, respectively
G [ ]
= gamma function of [ ]
DOE/NASA Reference Design Site and Reference Wind Regime
The characteristics of a
reference design site
were speciied for the U. S. Federal Wind
Energy Program (described in Chapter 3, Part A) in the 1970's in order to provide a uniform
basis for research and development projects. This design site was one with level terrain and
an annual average wind speed of 14 mph (6.24 m/s) at a reference elevation of 30 ft (9.1
m), and a wind shear exponent of 1/7. Early wind resource studies indicated that this site
description was representative of large areas in the U. S. and around the world suitable for
installation of wind turbines. In the early 1980's, during the development of megawatt-scale
HAWTs for the U. S. Department of Energy, NASA engineers further deined the frequency
distribution and vertical proile of a
reference wind regime
in the following terms:
z
R
= 10.0
m
a
R
= 0.351 - 0.192 log(
U
R
)
C
R
= 7.17
m
/
s
k
R
= 2.29
r
R
= 1.225
kg
/
m
2
(2-8)
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