Environmental Engineering Reference
In-Depth Information
Turbulence
Referring once again to the energy spectrum of the wind shown in Figure 8-4, all of
the time variations in wind speed and direction with periods less than about 1/10 hour are
generally considered to be turbulence. These turbulent fluctuations in the micro-
meteorological range create unsteady, non-uniform aerodynamic forces on the wind turbine
that must be taken into account in the design of its structure and controls. By way of
introduction to the subject of turbulence, let us review the concept introduced earlier, that
wind loads on the turbine can be classified into two groups: those associated with the
steady wind speed, which are described as quasi-static or time-averaged ; and those
associated with the gustiness or turbulence of the wind, which are predominantly dynamic.
Expanding Equations (8-3) to represent a wind field instead of a streamtube, we have
(8-13a)
u ( y , z , t ) = U ( y , z ) + g ( y , z , t )
D t
g ( y , z , t ) dt dA = 0
(8-13b)
A r
0
D t
1
A r D t
RMS [ u ( y , z , t ) - U ( y , z )] =
g 2 ( y , z , t ) dt dA = s 0
(8-13c)
0
A r
where
y, z = lateral and vertical coordinates, respectively (m)
u ( y,z,t ) = instantaneous horizontal free-stream wind velocity field (m/s)
U ( y,z ) = steady horizontal free-stream wind velocity field (m/s)
g ( y,z,t ) = fluctuating wind velocity field; instantaneous deviation from U ( y,z ) (m/s)
A r = swept area of the rotor (m 2 )
D t = averaging time interval (h)
RMS [ ] = root-mean-square average of [ ]
s 0
= ambient or natural turbulence (m/s)
Equation (8-13c) states the common assumption that the turbulence is homogeneous ( i.e. ,
has the same structure over the swept area of the rotor). Wind models which describe
various fluctuating velocity field functions g ( y,z,t ) that create dynamic wind forces are
discussed in this section. The structural response to these dynamic forces is treated in
Chapters 10, 11, and 12.
Types of Turbulence Models
Mathematical models of the fluctuating or turbulent wind field at the rotor of a wind
turbine can be grouped into four categories of increasing complexity and realism [Stoddard
and Potter 1986], as follows:
1.
Non-uniform in space, steady in time ...... g = g(y,z,0)
2.
Uniform in space, unsteady in time ........ g = g(0,0,t)
3.
Non-uniform in space, unsteady in time .... g = g(y,z,t)
4.
Stochastic .............................. g = g(power spectrum vs.
discrete gust parameters)
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