Environmental Engineering Reference
In-Depth Information
Once the equivalent roughness is defined, the impact on the hub-height wind speed
deep within the array (i.e., where the PBL has reached equilibrium with the array
roughness) is estimated from meteorological theory under the assumption of a constant
geostrophic wind speed
G
and a neutral logarithmic profile throughout the PBL. The
result is approximated by the following equation.
0
.
07
ln
h
h
/
z
00
ln
h
h
/
z
00
z
0
v
h
v
h
=
z
0
(16.14)
Here,
v
h
and
v
h
are the hub-height speeds deep within the array and far upstream,
respectively. The results are plotted in Figure 16-8b.
An important issue with the Frandsen theory is that it does not address the wake
effects of individual turbines. Instead, it treats the array as an infinite sea of undif-
ferentiated surface drag. This means that the predicted wind resource at a particular
location does not depend on whether there are any turbines immediately upwind or
not, which is unrealistic. Furthermore, the roughness depends on the array density,
which implies that in practical application it would have to be recalculated every time
the layout is modified. Thus, to be useful for wind project design and optimization,
the Frandsen theory must either be modified or combined in some way with other
methods.
One solution that has been offered to this problem is to model turbines as discrete
roughness elements. Each turbine is surrounded by an area where the surface roughness
is increased. When the free-stream wind passes the front edge of this area, an IBL is
created which grows with distance downstream, and within which the wind shear
is increased. When the wind passes the rear edge of the rough area, another IBL is
created which grows at a different (generally slower) rate, and within which the shear
reverts to the normal, background value. The overall effect is to reduce the wind speed
at heights below the top of the first IBL.
The effect is illustrated in Figure 16-9, where the two IBLs cast by the first turbine
are shown. The top curve represents the IBL created by the high roughness of the
turbine, and the bottom curve represents the IBL created by the transition back to
the low ambient roughness between turbines. The two curves to the right show the
disturbed and free-stream wind speed profiles; the difference between them is the wind
speed deficit.
This general approach has been implemented in several programs including Wind-
Farmer and openWind. Published reports indicate that they are capable of matching
observed “deep-array” wake effects in offshore projects with reasonable accuracy.
Evidence from onshore projects is more in dispute (8, 9). Regardless, the amount of
data available to validate the models is exceedingly small, so it is safe to say that they
remain developmental, and it is unknown how well they will work at much larger
projects, either onshore or offshore. For the time being, caution argues for using one
of the available deep-array wake models in analyzing large projects with at least four
rows of turbines.
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