Environmental Engineering Reference
In-Depth Information
Wind shear power-law exponent:
a = a
0
1 - 0.55 log(
U
0
)
1 -
(12-6a)
0.55
a
0
log(
H
/10)
Surface roughness exponent:
a
0
= (
z
0
/10 )
0.2
(12-6b)
where
d
3
=
inclination of teeter axis from a normal to the blade axis (deg)
c
t
=
blade chord at tip (m)
D
=
rotor diameter (m)
Z
= site altitude above sea level (m)
H =
elevation of rotor hub above ground level (m)
N =
rotor speed (rpm)
w
c
=
blade first chordwise natural frequency (cpm)
z
0
=
surface roughness length (m) (See Table 8-3)
U
0
=
50th percentile (median) free-stream wind speed at hub elevation (m/s)
The hub-rigidity factor,
a
, varies from zero for a “pure” teetered hub to 1.0 for a rigid
hub and is a measure of the hub's out-of-plane resistance to once-per-revolution or
1P
loads.
(Modeling a rigid hub with a d
3
angle of 90 deg is done for mathematical convenience only;
there is no teeter shaft in this configuration.) The tower-blockage factor,
b
, defines the sever-
ity of tower wake effects on blade air loads. The tip-chord factor,
c
, is a measure of outboard
blade solidity (
i.e.,
ratio of blade
planform
area to swept area). The air-density factor,
d
, ap-
proximates the air density ratios in the U.S. Standard Atmosphere and altitude effects on the
dynamic pressure of the wind.
The chordwise dynamic-amplification factor,
e
, is the theoretical undamped amplifica-
tion of 1
P
cyclic forcing by gravity in the plane of rotation. The comparable amplification
factor for flatwise gravity loading of a coned rotor had no observable effect on the correla-
tion of calculated and measured cyclic loads. The apparent reason is the high aerodynamic
damping of the first flatwise bending mode. Finally, the wind-variability factor,
g
, is the
ratio of the total wind shear across the rotor disk to the mean wind speed at hub elevation.
Fatigue loading has been found to be very sensitive to this factor, because it is a measure of
the
wind speed variance
from both large-scale and small-scale turbulence. For wind power
station applications, this factor would be increased to account for generated turbulence from
other turbines.
Empirical Equations
In a large data base of this type, specific data points are selected to which the empirical
equations are fitted to obtain zero mean deviations and minimum standard deviations. In this
case the selected points are the 50th and 98th percentile loads (
i.e.,
50 percent and 2 percent
probabilities of exceedance) for each of the 13 cases. One reason for selecting these two
percentiles is that little fatigue damage occurs under loads smaller than the 50th percentile
load, so it is only necessary to define the lines in Figures 12-11 for ordinates larger than unity.
A second reason is that the 98th percentile load is near the upper limit of accuracy in most
probability distributions of test data. Very long run times with large numbers of data points
are needed to accurately define percentile levels at the logical next-higher choice, the 99.9th
percentile or “+ 3
σ
” level.
When the factors in Equations (12-5) are combined with the rotor diameter,
D
, and the
wind speed,
U
, and coefficients and exponents are adjusted for minimum overall deviations
(both mean and standard) between calculated and measured cyclic loads at the 50th and 98th
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