Environmental Engineering Reference
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law model
(Eqns. (2-4) and (8-11), and Fig. 8-13) of the vertical gradient in the steady wind
speed. With this model the normalized wind shear can be calculated, as follows:
D
U
/
U
0
= [(
H
+
R
)/
z
R
]
a
- [(
H
-
R
)/
z
R
]
a
(2-29)
where
H =
hub elevation above ground level (m)
R =
tip radius of rotor (m)
z
R
= reference elevation above ground level
=
10 m
Scaling Clayton VPA Data to Other Radii and Elevations
To generalize Equations (2-28), we must now make additional assumptions about the
size effects of
R
and
H
on R-S turbulence intensity. First, the longer sampling paths and
sampling periods of larger rotors are assumed to result in larger wind speed variations around
the perimeter of the sampled circle. For simplicity, this relationship between increasing sam-
pling radius and increasing R-S turbulence intensity is assumed to be linear.
Second, the effects on R-S turbulence of center elevation,
H,
and surface roughness
length, z
0
,
are assumed to be approximately the same as these effects on longitudinal turbu-
lence measured at a ixed point. In accordance with Eqn. (8-19a) [Frost and Aspliden], the
following model is used:
s
0.52
ln(
H
/
z
0
)(0.177 + 0.00139
H
)
0.4
0,
x
U
0
(2-30)
=
where
s
0,
x
= longitudinal turbulence at a ixed point (m/s)
z
0
=
surface roughness length; see Table 8-3 (m)
Combining a linear effect of sampling radius with the effect of center elevation given in
Equation (2-30), we obtain the following equations for scaling the Clayton VPA data to a cir-
cular path of a different radius and hub elevation:
ln(
H
/
z
0
) (0.177 + 0.00139
H
)
0.4
n
/
U
0
(
n
/
U
0
)
C
s
R
R
C
C
(2-31)
=
s
ln(
H
/
z
0
)(0.177 + 0.00139
H
)
0.4
Substituting the Clayton VPA magnitudes of
R
and
H
into Equation (2-31), the scaling equa-
tions for the R-S turbulence intensities along the tip path of a general HAWT rotor are as
follows:
s
n
/
U
0
=
S
(s
n
/
U
0
)
C
(2-32a)
0.204
R
ln(
H
/
z
0
) (0.177 + 0.00138
H
)
0 .4
S
=
(2-32b)
where
S
= scaling factor at radius
R
relative to Clayton VPA harmonic amplitudes in
Equations (2-28)
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