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In-Depth Information
D
W
ð
x
Þ/
s
1
=
3
ð
6
:
4
Þ
This spreading of the wake with distance downstream of the turbine leads
unavoidably to complex wake-wake interactions in larger wind parks. The for-
mulation for multiple wakes in WAsP is a quadratic superposition of the single
wakes (bottom-up approach, Barthelmie and Jensen
2010
)
2
2
¼
X
n
1
u
h
u
h0
1
u
hn
u
h0
ð
6
:
5
Þ
with n = 1,… N the contributions from N single wakes. Jensen (
1983
) derived for
an infinite number of turbines in a row the following asymptotic expression:
2
f
1
f
u
h
u
h0
a
1
a
D
D
þ
ks
¼
1
;
f
¼ð
1
a
Þ
ð
6
:
6
Þ
with the induction factor a = 1 - u
h
/u
h0
and the mean turbine distance s. Such
approaches decisively depend on the geometry of the wind parks and the wind
direction relative to the orientation of the turbine rows. We do not want here to
deal with the complications for special arrangements of turbines in a wind park,
but we want to analyse the overall efficiency of very large wind parks. Therefore,
we present an analytical top-down approach in
Sect. 6.2
to derive the mean fea-
tures dominating the efficiency of large wind parks.
Elliot and Barnard (
1990
), e.g., collected wind data at nine meteorological
towers at the Goodnoe Hills MOD-2 wind turbine site to characterize the wind
flow over the site both in the absence and presence of wind turbine wakes. The
wind turbine wake characteristics analyzed included the average velocity deficits,
wake turbulence, wake width, wake trajectory, vertical profile of the wake, and the
stratification of wake properties as a function of the ambient wind speed and
turbulence intensity. The wind turbine rotor disk at that site spanned a height of
15-107 m. The nine towers' data permitted a detailed analysis of the wake
behaviour at a height of 32 m at various downwind distances from 2 to 10 rotor
diameters (D). The relationship between velocity deficit and downwind distance
was surprisingly linear [i.e. n = 1in(
6.1
)], with average maximum deficits
ranging from 34 % at 2 D to 7 % at 10 D. Largest deficits were at low wind speeds
and low turbulence intensities. Average wake widths were 2.8 D at a downwind
distance of 10 D. Implications for turbine spacing are that, for a wind park with
a10-D row separation, park efficiency losses would be significantly greater for a
2-D than a 3-D spacing because of incremental effects caused by overlapping
wakes. Other interesting wake properties observed were the wake turbulence
(which was greatest along the flanks of the wake). The vertical variation of deficits
(which were greater below hub height than above), and the trajectory of the wake
(which was essentially straight).
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