Page 254 - Wind Energy Handbook

228 DESIGN LOADS FOR HORIZONTAL-AXIS WIND TURBINES

expression for the resonant bending moment variation along the blade is given in
Section A5.8 of the Appendix, and it is plotted out for the example above in Figure
5.4, with the quasistatic bending moment variation alongside for comparison. It is
seen that the resonant bending moment diagram is closer to linear than the
quasistatic one, which approximates to a parabola.
A consequence of the much slower decay of the resonant bending moment out
towards the tip is an increase in the ratio of the resonant bending moment standard
deviation to the local steady moment with radius. This results in an increase in the
dynamic magnification factor, Q D , from 1.145 at the root to 1.69 at the tip for the
example above (see Figure 5.5).

5.7 Blade Loads During Operation

5.7.1 Deterministic and stochastic load components

It is normal to separate out the loads due to the steady wind on the rotating blade
from those due to wind speed fluctuations and analyse them in different ways. The
periodic loading on the blade due to the steady spatial variation of wind speed over
the rotor swept area is termed the deterministic load component, because it is
uniquely determined by a limited number of parameters – i.e., the hub-height wind
speed, the rotational speed, the wind shear, etc. On the other hand, the random
loading on the blade due to wind speed fluctuations (i.e., turbulence) has to be
described probabilistically, and is therefore termed the stochastic load component.
In addition to wind loading, the rotating blade is also acted on by gravity and
inertial loadings. The gravity loading depends simply on blade azimuth and mass
distribution, and is thus deterministic, but the inertial loadings may be affected by
turbulence – as, for example, in the case of a teetering rotor – and so will sometimes
contain stochastic as well as deterministic components.

5.7.2 Deterministic Aerodynamic Loads

Steady, uniform flow perpendicular to plane of rotor

The application of momentum theory to a blade element, which is described in
Section 3.5.3, enables the aerodynamic forces on the blade to be calculated at
different radii. Equations (3.51) or (3.51a) and (3.52) are solved iteratively for the
flow induction factors, a and a9, at each radius, enabling the flow angle, ö, the angle
of attack, Æ, and hence the lift and drag coefficients to be determined. The solution
2
of the equations is normally simplified by omitting the C term in Equation (3.51) –
y
2
an approximation which is justifed, because ó r C =C x is negligibly small away from
y
the root area.
For loadings on the outboard portion of the blade, allowance for tip loss must be
made, so Equations (3.51) and (3.52) are replaced by Equations (3.51b) and (3.52a) in
2
Section 3.8.5, (with the omission of the C term in Equation (3.51b) again being
y