Environmental Engineering Reference
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to 0.075. Lower values produce longer-lived wakes such as might be seen offshore.
Higher values produce wakes that decay faster.
Eddy Viscosity (EV) Model.
The EV model was developed in the late 1980s
around the same time as the Park model (5). Unlike Park, which adopts a purely
empirical approach, the EV model is a kind of CFD model that solves the following
simplified form of the Navier-Stokes equations:
U
δ
U
δ
V
δ
U
δ
r
=
r
δ (
r
δ
U
/δ
r
)
x
+
(16.9)
δ
r
The equation is in cylindrical coordinates:
r
is the radius from the center line of the
rotor and
x
is the distance downstream.
U
is the speed in the downwind direction,
and
V
is the radial speed. The parameter
is the eddy viscosity, which represents the
friction exerted by adjacent turbulent eddies.
The initial wake-induced wind speed deficit is assumed to be a Gaussian (bell-
shaped) curve, which starts 2 rotor diameters downstream of the turbine. At the center,
the speed deficit (again, as a fraction of the free-stream speed) is
ε
I
0
1000
δ
v
c
=
C
t
−
0
.
05
−
[16
C
t
−
0
.
5]
(16.10)
I
0
is the ambient turbulence intensity. The shape of the deficit curve is given by the
Gaussian equation,
r
2
w
2
v
c
e
−
δ
v
(
r
)
=
δ
(16.11)
where the effective wake width
w
is defined by
C
t
w
=
R
(16.12)
8
δ
v
c
(
1
−
0
.
5
δ
v
c
)
R
is the rotor radius.
Once initialized, the wake propagates downstream, expanding and dissipating as
the air within it mixes with the surrounding free-stream air. The rate of mixing is
determined by the eddy viscosity, which is a function of the ambient turbulence—the
greater the turbulence, the greater the rate of mixing and the faster the wake
deficit decays. Thus, the EV model contains no empirical wake decay constant:
the decay rate is determined by the model equations, and the only inputs, aside
from the characteristics of
the turbine, are the ambient speed and turbulence
intensity.
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