Environmental Engineering Reference
In-Depth Information
rotor is entirely engulfed by each gust, so only the longitudinal coordinate (
x
)
is required.
Note that the dimensional classification does not reflect the number of components of the
wind velocity vector that are included. Two- and three-dimensional (
i.e.
,
small-scale
turbulence
)
models define fluctuations in wind speed with length scales smaller than the
diameter of the rotor, and the lateral and/or vertical coordinates (
y, z
)
must be used.
Spectral Models of Continuous Turbulence
Structural fatigue life and the control of power output and HAWT rotor heading are
typically sensitive to
continuous turbulence
(
i.e.
,
wind fluctuations during routine
operations) which causes dynamic forces to act continuously on the rotor and its supporting
structure. Methods of analyzing continuous turbulence generally rely on
spectral models
or
deterministic gust models
,
combined with statistical exceedance values [Frandsen and
Christensen 1980, Raab 1980, Thresher
et al.
1981a, Sundar and Sullivan 1981, Thresher
et al.
1981b, Waldon and Hansen 1983].
Basic Equations
The basic relationships between the spectra of atmospheric turbulence and the spectra
of structural dynamic responses (such as motions, deformations, and loads) are contained
in the following general equation, which is written here for one component of the wind
velocity:
S
k
(
n
) = f
11
(
n
)
H
1
(
n
)
H
1
(
n
) + f
22
(
n
)
H
2
(
n
)
H
2
(
n
) +
¼
+
Re
[f
12
(
n
)
H
1
(
n
)
H
2
(
n
) + f
13
(
n
)
H
1
(
n
)
H
3
(
n
) +
¼
]
(8-14)
where
n
= circular frequency (rad/s)
S
k
= power spectrum of the dynamic response of the turbine parameter
k
which
has units of K (K
2
/rad/s)
f
ij
= two-point power spectrum of the wind velocity component
acting at points
i
and
j
(m
2
/s)
H
i
*
= complex conjugate of
H
i
(K/m/s)
H
i
= turbine parameter response transfer function (K/m/s)
Re
[ ] = real part of [ ]
This expression can be extended directly to two or three components of velocity and is
general within linear theory. It can be reduced to a simpler form depending on whether the
assumed turbulence is classified as one- or two-dimensional. If the turbulence can be
modeled as one-dimensional (i.e., large-scale turbulence relative to the rotor diameter)
Equation 8-14 can be simplified to the following form:
S
k
= f
x
(
n
)
H
x
(
n
)
H
x
(
n
) + f
y
(
n
)
H
y
(
n
)
H
y
(
n
) + f
z
(
n
)
H
z
(
n
)
H
z
(
n
)
(8-15)
The wind characteristics required to solve Equations (8-14) and (8-15) are contained
in the turbulence power spectra f
ij
(n)
,
and these will now be discussed. The primary focus
of this discussion is on spectra for wind over flat, homogeneous terrain, although a few
general comments will be made about spectra over complex terrain.
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