Page 310 - Wind Energy Handbook

284 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES

180
160
Out-of-plane
140

120
(kNm) 100

80
60
40 In-plane

20
0

-20
0 60 120 180 240 300 360
Rotor azimuth angle (degrees)
Figure 5.33 Blade Root Bending Moment in Steady Wind

The out-of-plane moment is always positive, the mean value being dominated by
the aerodynamic thrust on the blade. There is a systematic variation with azimuth
resulting from the wind shear, giving a lower load at 1808 azimuth (bottom dead
centre) than at 08. A sharp dip at 1808 is also visible, and this is the effect of the
tower shadow (the reduction in wind speed in the vicinity of the tower). The blade
out-of-plane vibrational dynamics contribute a significant higher-frequency varia-
tion.
In turbulent wind, the loads take on a much more random appearance, as shown
in Figure 5.34. The out-of-plane load in particular is varying with wind speed and,
as this is a pitch-controlled machine, with pitch angle. The in-plane load is more
regular, as it is always dominated by the reversing gravity load.
Spectral analysis provides a useful means of understanding these variations.
Figure 5.35 shows auto-spectra of the blade root out-of-plane bending moment and
the hub thrust force. The out-of-plane bending moment is dominated by peaks at all
multiples of the rotational frequency of 0.8 Hz. These are caused mainly by the
rotational sampling of turbulence by the blade as it sweeps around, repeatedly
passing through turbulent eddies. Wind shear and tower shadow also contribute to
these peaks. A small peak due to the first out-of-plane mode of vibration at about
3.7 Hz is just visible. There is also a significant effect of the first tower fore–aft
mode of vibration at about 0.4 Hz.
This tower effect is also visible in the spectrum of the hub thrust force. However,
this force is the sum of the shear forces at the roots of the three blades. These forces
are 1208 out of phase with each other, with the result that the peak at the rotational
frequency (1P) is eliminated, as are the peaks at multiples of this frequency such as