Environmental Engineering Reference
In-Depth Information
Since Equation 16.9 has no analytical solution, it is solved numerically using a
finite differencing technique, a standard CFD method.
Deep-Array Wake Models.
In the past several years, researchers have become
aware that the current generation of wake models may underestimate wake losses in
large wind projects with multiple rows of wind turbines. The crux of the problem
appears to be that the leading wake models, including the Park, modified Park, and
EV models, ignore two-way interactions between the atmosphere and the turbines (6).
Each turbine extracts energy from the wind passing through its rotor plane, creating
a zone of reduced speed extending some distance downstream. Upstream and outside
this zone of influence, it is assumed the ambient wind is unaffected.
Both theory and experiment suggest that for large arrays of wind turbines, this
assumption does not hold. The presence of numerous large wind turbines in a limited
area can alter the wind profile in the planetary boundary layer (PBL), both within and
around the array, thereby reducing the amount of energy available to the turbines for
power production. Experimental data supporting this hypothesis comes mainly from
offshore wind projects, where the contrast between the drag induced by the turbines
and the relatively low roughness of the ocean surface makes the so-called deep-array
effect especially pronounced. Onshore, the effect is attenuated, but theory suggests it
may nonetheless be significant in large projects.
It has become clear that new models are required that can simulate deep-array
wake effects with reasonably good accuracy. Predicting the overall impact of a large
wind turbine array is a complex problem involving dynamic interactions between the
turbines and various properties of the atmosphere, including vertical and horizontal
gradients of temperature, pressure, and speed, as well as turbulence. This problem can
be solved completely only through sophisticated numerical modeling requiring very
fast computers. However, it may be hoped that simplified approaches will work well
enough for wind projects likely to be developed in the next several years.
The most widely implemented deep-array wake model is based on a theory
advanced by Sten Frandsen (7), in which an infinite array of wind turbines is
represented as a region of uniform high surface roughness. The roughness imposes
drag on the atmosphere, causing a downstream change in the structure of the PBL
and, in particular, a reduction in the free-stream wind speed at the turbine hub height.
According to this theory, the wind farm equivalent roughness
z
00
is given by
⎛
⎝
−
⎞
⎠
κ
c
t
+
κ/
z
00
=
h
h
exp
(16.13)
z
0
)
2
ln
(
h
h
/
In this equation,
h
h
is the hub height,
is the von Karman constant (about 0.4),
z
0
is
the background roughness between turbines, and
c
t
is the distributed thrust coefficient,
defined as
κ
π
8
s
d
s
c
c
t
=
C
t
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