Environmental Engineering Reference
In-Depth Information
Other models of turbulence spectra have been used for wind turbine design and
analysis, such as the Davenport spectra [1961; see Sundar and Sullivan 1981], the Dryden
spectra [see Holley et al. 1981], and the von Karman spectra [see Connell 1981]. The von
Karman spectra, which depend upon integral turbulence length scales, agree well with
atmospheric data in the high frequency range. They are, however, based on the assumption
that the turbulence is isotropic (equal in all directions), which is not realistic near the
ground. Moreover, turbulence length scales are difficult to estimate for general design
purposes, and the influence of atmospheric stability cannot be readily incorporated.
Therefore, Equation 8-16 and others which include effects of boundary layer stability are
recommended for representing atmospheric turbulence spectra.
Turbulence and Turbulence Intensity
Turbulence is not only a qualitative term for wind fluctuations, but it is also a funda-
mental, quantitative measure of the unsteadiness of the wind. Adapting Equation (8-3c) so
that it represents the components of turbulence in three directions, we have
s 0,a = RMS [ u a ( t ) - U a ]
(8-17)
where, as before, the subscript a refers to direction x, y, or z , with x parallel to the steady
wind. Hence, U x = U and U y = U z = 0. The value of the turbulence is a function of the
time period selected for averaging the wind speed to determine U.
Turbulence intensity (also known as relative turbulence intensity ) is defined as the ratio
of the turbulence to the steady wind speed. Turbulence intensity is typically measured when
characterizing the wind regime at a turbine site, using the same wind speed data recorded
for the purpose of calculating seasonal and annual average wind speeds. Normalizing the
turbulence by the steady wind speed tends to produce a characteristic range of intensities
for a given site, but these intensities are by no means constant. Turbulence intensity has
been found to vary with the same parameters as wind shear: surface roughness, wind
speed, elevation, atmospheric stability, and topographic features. Equations for predicting
turbulence intensity in the absence of measurements will be presented here, but only direct
measurements are recommended for the final stages of site selection and turbine design.
Predicting turbulence intensity generally begins with estimating the ratio of the vertical
component of turbulence to the friction velocity , s 0, z / U * [Barr et al. 1974 and Panofsky and
Dutton 1984]. For neutral atmospheric stability this ratio is approximately 1.3 [Frost 1980].
It has been observed that under neutral conditions s 0 ,z is dependent upon the steady wind
speed and the surface roughness length, z o . Experimental results indicate that vertical gusts
are primarily a function of small-scale roughness features, whereas lateral and longitudinal
gusts are influenced by large-scale surface features.
Because of the lack of mathematical models for the influence of terrain features and
atmospheric stability on s 0 ,x and s 0 ,y , it has been proposed that the ratios of these
components to the vertical turbulence be treated as functions of altitude only, according to
the following relationships for elevations less than 600 m [Frost et al. 1978]:
s 0, x /s 0, z = (0.177 + 0.00139 z ) - 0.4
(8-18a)
s 0, y /s 0, z = (0.583 + 0.00070 z ) - 0.8 ,
z < 600 m
(8-18b)
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