Environmental Engineering Reference
In-Depth Information
One of the most detailed sets of experimental data on gust shapes is that given by
Camp [1968]. These data suggest that a typical gust has an essentially exponential rise with
a long dwell and an exponential decay. This is a more severe gust than that given by
Equation (8-20) and may be preferred for predicting extreme wind loads. On the other
hand. Equation (8-20) may be preferable for fatigue load analysis. Other research indicates
that gust energy is the important parameter to preserve in any model used for dynamic
analysis.
Coherence Modeling of the Gust Environment
A model of the total gust environment experienced by a wind turbine includes the joint
probability distribution of magnitude and duration and frequency of occurrence. The
discrete gust environment of most interest here is that actually experienced by a wind
turbine. This environment is not identical to the typical time history of wind speed
measured by an anemometer, since the turbine responds to some spatially-averaged wind
field whose extent is considerably larger than that to which an anemometer responds, and
the turbine may be capable of changing pitch angle, teeter angle, and/or rotor speed to
“absorb” some parts of the gust environment. Therefore, selection of meaningful values
of gust magnitude and duration depends not only on statistical wind data from isolated
anemometers, but also on turbine size and dynamic response.
While discrete gust models are highly idealized representations of the actual wind, they
are quite useful for wind turbine analysis when the size of the gust is large enough to engulf
the entire rotor. For such cases, the wind speed may be assumed to be changing uniformly
across the rotor. Gust size is generally considered to be related to the gust duration, t.
The longer the duration, the larger the spatial dimensions of the gust. To estimate the
duration of a gust which will engulf a turbine rotor, it is convenient to use the so-called
coherence function [Frost et al. 1978].
Coherence is a dimensionless quantity between zero and unity that represents the degree
to which two events, separated in space, are alike in their time histories. If the two time
histories are identical their coherence is unity, and if they are completely unrelated their
coherence is zero. The coherence of two wind speeds measured at points separated in space
during a gust may be expressed empirically by the following equation:
coh a = exp (- d a D l a / U r t)
(8-21)
where
coh a = coherence between stations separated in the a direction
a = x (longitudinal), y (lateral), or z (vertical) direction
d a
= decay coefficient in the a direction
D l a
= distance between measurement stations separated in the a direction (m)
A physical explanation of Equation 8-21 is that for long durations or small separations the
coherence approaches unity, while for short durations or large separations there is no time
correlation between fluctuations “felt” at the two measurement stations.
Tentative values of the decay coefficients are d x = 4.5, and d y = d z = 7.5, based on
averages of coefficients reported in the literature [ e.g. , Davenport 1961, Ropelewski et al.
1973]. It is known that d is dependent on terrain roughness, atmospheric stability, and
spatial separation. Panofsky and Dutton [1984] discuss research which provides additional
insight on decay coefficients. Figure 8-21 shows the coherence model for lateral separation
compared with test data exhibiting typical scatter [Frost and Lin 1981].
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