Environmental Engineering Reference
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in the outer half of the swept area and a coherence of zero in the inner half. In the inner half
of the swept area the higher harmonic amplitudes are assumed to be zero and have no affect
on fatigue loads. The radius separating the two half-areas is the mean radius,
R
m
, deined by
Equation (2-18a) as equal to 0.73
R
, where
R
is the tip radius.
Summary of Equations in the R-S Turbulence Model
r
R
S (
A
n
cos
n
y)
U
RS
=
U
0
+
(2-35a)
U
0
=
U
R
(
H
/
z
R
)
a
(2-35b)
D
U
=
U
R
[(
H
+
R
)/
z
R
]
a
- [
H
-
R
]/
z
R
]
a
(2-35c)
0.204 /
R
ln(
H
/
z
0
) (0.177 + 0.00138
H
)
0.4
S
=
(2-35d)
A
1
= -0.0440
S U
0
+ 0.4120 D
U
0
(2-35e)
If r ³ 0.73
R
:
A
2
= - 0.0496
S U
0
(2-35f)
A
3
= + 0.0366
S U
0
(2-35g)
A
4
= + 0.0295
S U
0
(2-35h)
A
5
= -0.0250
S U
0
(2-35i)
A
6
= -0.0218
S U
0
(2-35j)
If r < 0.73
R
:
A
n
= 0
n
= 2, 3, . . .
(2-35k)
where
U
RS
=
rotationally-sampled free-stream horizontal wind speed; quasi-static (m/s)
U
0
=
steady free-stream wind speed at hub elevation (m/s)
U
R
=
steady free-stream wind speed at reference elevation (m/s)
r =
radial distance from rotor axis (m)
R =
tip radius of rotor (m)
H =
elevation of hub above ground level (m)
S =
scale factor; referenced to Clayton VPA
z
0
=
surface roughness length (m)
z
R
=
reference elevation above ground level
=
10 m
n =
harmonic number
a
=
exponent in wind shear power law
y
=
azimuthal position in rotor swept area; 0 = down (deg)
A
n
=
amplitude of
n
th harmonic of wind speed distribution around circle of radius
R (m/s)
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