Environmental Engineering Reference
In-Depth Information
Annual Wind Energy Input
Consider a horizontal streamtube of wind, which is air lowing in an imaginary pipe with
all particles passing a given cross-section at the same speed. The wind power density at a
point in this streamtube is the luid-dynamic power per unit of cross-sectional area, given by
the following equation:
p W = 0.5r U 3
(2-2)
where
r = air density = 1.2250 kg/m 3 at sea-level standard (SLS) conditions
U = horizontal component of the steady free-stream wind speed (m/s)
Thus, wind power density is directly proportional to the cube of the wind speed, and this
fact is fundamental to both wind turbine design and site selection.
For purposes of calculating wind power density, wind speeds are usually averaged for
about 0.1 hour to obtain the steady wind speed . This averaging process eliminates higher-
frequency turbulence (instantaneous deviations from the average wind speed and direction)
whose effects would be too rapid or too local to inluence long-term energy conversion. The
term “steady” is a relative one and relates only to a selected averaging period and elevation.
The steady wind itself will vary over longer periods of time and with changes in elevation,
even at a speciic geographic location. Because of these variations, a meaningful measure of
the wind as a power source is the annual wind energy density , or
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U 3 f W ( z ) dU
(2-3)
e W ( z ) =
p W ( z ) dt = 0.5r
year
0
where
e W = annual wind energy density at elevation z (Wh/m 2 /y)
z = elevation above ground level, AGL (m)
f W
= frequency distribution function of U at elevation z [(h/y)/(m/s)]
Models of the Steady Wind
Two simple models are commonly used together to calculate the frequency distribution
function f W in terms of both wind speed and elevation. These are a Weibull model for the
frequency distribution function of wind speed at a speciied reference elevation , and a power-
law model for the variation of wind speed with elevation. The power-law equation for the
vertical proile of the steady wind speed or wind shear proile is
U ( z ) = U R ( z / z R ) a
(2-4)
where
U R = steady wind speed at the reference elevation, at the same time as U (m/s)
z R = reference elevation (m)
a = empirical wind shear exponent
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