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followed by a blade section of an imaginary HAWT rotor. The wind speed at each anemom-
eter is continuously recorded. Samples from each record are then taken sequentially from
consecutive anemometers around the circle, with the sampling interval time determined by
the rotational speed and the number of anemometers. Interpolations are made between con-
secutive samples in order to synthesize a continuous record which represents the wind speeds
that a blade section would experience in the rotating frame of reference.
VPA measurements have shown that the time-varying wind speed acting at a section of a
rotating wind turbine blade is
harmonic
in nature, with frequencies equal to multiples of the
rotor speed. These wind speed harmonics can produce a
forced harmonic response
(cyclic
motions at the harmonic frequencies) in the lapwise direction (
i.e.
out of the plane of revolu-
tion), thereby increasing blade fatigue stresses.
Model of R-S Turbulence for Predicting Blade Fatigue Loads
Equations have been developed with which to estimate the sizes of the wind harmonic
speeds as input into HAWT structural-dynamics computer codes [Spera 1995]. These equa-
tions are based on R-S turbulence test data and veriied against loads measured on the 2.5
MW Mod-2 HAWT [Boeing 1982]. Additional information on turbulence deined in a rota-
tional frame of reference is given in Chapter 8.
Rotationally-Sampled Turbulence Data
The R-S turbulence data used in this model were measured by researchers from Battel-
le's Paciic Northwest Laboratory (PNL) using a VPA located near Clayton, New Mexico
(Connell and George 1983a and 1983b, and George and Connell 1984). The dimensions of
this array were a center elevation
H
C
= 30.5 m and a sampling radius
R
C
= 19.0 m, and the
rotational frequency was 0.667 Hz.
Power spectral densities
(PSDs) of 8.5-min segments
of the synthesized wind speed were created using a Fast Fourier Transform (FFT) technique.
Integration of a PSD over a selected frequency band then gave the
variance
of wind speeds
within this band. R-S turbulence in the frequency band is the square-root of this variance.
Dividing the turbulence by the steady wind speed at the center of the VPA (Anemometer 1 in
Fig. 2-24) then gives the R-S turbulence intensity for the selected frequency band.
Table 2-8 presents typical data reported by PNL researchers for one data segment. A
total of 17 data segments form the basis of the following R-S turbulence model. Of these,
10 were for atmospheric stability conditions ranging from neutral to unstable, while 7 were
for stable conditions. Stable atmospheres typically result in larger vertical gradients in wind
speed and smaller mixing between winds at different elevations. For a discussion of the
inluence of atmospheric stability on wind shear, see Chapter 8 [Frost and Aspliden]. Only
the longitudinal component of turbulence was measured during these VPA tests. Therefore,
lateral and vertical turbulence components are not included explicitly in the R-S turbulence
model presented here.
Dependence on Wind Shear
The turbulence intensities for each harmonic frequency of the 17 data segments like that
in Table 2-7 were examined to determine their dependence, if any, on the vertical wind shear
across the VPA. It was found that
-
Only the irst harmonic turbulence intensity varies signiicantly with normal-
ized wind shear (wind shear per unit of wind speed at hub elevation), and its
variation is linear.
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