Environmental Engineering Reference
In-Depth Information
time-averaged
loadings; and those associated with the gustiness or turbulence of the wind,
which are predominantly
dynamic
in character. Thus, for the horizontal component of the
free-stream wind velocity we obtain
u
(
t
) =
U
+
g
(
t
)
(8-3a)
D
t
ò
g
(
t
)
dt
= 0
(8-3b)
0
D
t
1
D
t
ò
g
2
(
t
)
dt
= s
0
RMS
[
u
(
t
) -
U
] =
(8-3c)
0
where
u
(
t
) = instantaneous horizontal free-stream wind velocity (m/s)
U
= steady horizontal free-stream wind velocity (m/s)
g
(
t
)
=
fluctuating wind velocity; instantaneous deviation from
U
(m/s)
D
t =
averaging time interval (h)
RMS
[
] = root-mean-square average of [ ]
s
0
=
ambient
or
natural
turbulence (m/s)
The characteristics of both the steady wind and the fluctuating wind depend strongly
on the principal scale of interest. On the climatic or
macro-meteorological
scale, changes
in wind speed will be referred to as fluctuations in the steady wind, and
g
is neglected. In
the large-scale regime,
U
represents the field that appears when weather observations are
plotted and smoothed and is approximately equivalent to a one-hour average. In this regime
g
includes all microscale motions. Small-scale or
micro-meteorological
fluctuations, such
as those appearing in the anemometer record, will be referred to as
gusts
or
turbulence.
Figure 8-4 is a
wind energy spectrum
developed by Van Der Hoven [1957] which
shows that the majority of the fluctuating energy is contained at the macro- and micro-
meteorological scales, and that a region of low energy exists between them. The spectral
gap for periods between 0.1 and 5 hours defines a convenient range of averaging periods,
D
t
,
to which a steady wind speed can be referenced [Davenport 1967]. The period chosen
should be long enough to minimize
non-stationarities
,
and short enough to reflect short-
term storm activity. Periods from 10 minutes to one hour have been found to be suitable for
defining the steady wind speed, giving it only a weak dependence on the averaging period.
Panofsky and Dutton [1984] provide a clear discussion of different averaging techniques.
Steady wind speeds required for wind resource assessments may vary throughout each
day and from day to day, but they are still essentially constant relative to the dynamic
response frequencies of typical wind turbines. Much of the wind data used in assessment
methodologies, however, is derived from one-minute averages centered on the hour and
sampled once an hour or once every three hours (
one-hour
and
three-hour readings
,
respectively). Figure 8-4 clearly shows that a one-minute average wind (
i.e.
,
D
t
» 0.02 h)
contains a high level of fluctuation energy to which a wind turbine might be sensitive.
However, since the most extensive sources of wind data provide information in this for-
mat, one-minute averages are commonly used to formulate statistical data on the
frequency
distribution
(cumulative duration within a given wind speed range per year) and the
persis-
tence
(duration within a wind speed range per occurrence) of steady winds.
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