Page 147 - Wind Energy Handbook

THE AERODYNAMICS OF A WIND TURBINE IN STEADY YAW 121

velocity is much greater than the normal velocity but it is the latter which most
influences the variation in angle of attack at the important, outboard sections of the
blades, shown in Figure 3.66.
At the inboard sections of the blades it is the variation in tangential velocity
which mostly influences the angle of attack variation and this is largely as a result
of the changing geometry with azimuth angle rather than the effect of induced
velocity.

3.10.10 Blade forces for a rotor in steady yaw

Once the flow induction factors have been determined blade forces can then be
calculated. Although the flow expansion velocity is excluded from the determina-
tion of the flow induction factors, on the grounds that the consequent blade forces
do not cause any change in the momentum of the flow because flow expansion is
not present in the developed wake, it must be included when the blade forces are
calculated. The flow expansion velocity should be dependent on an overall average
value of the axial flow induction factor but it is more convenient to use the annular
average value as determined by Equations (3.137) and (3.138).
The flow angle and the angle of attack need to be determined anew at each blade
element position ì and at each blade azimuth position Ł because the flow expansion
velocity must now be included, so Equation (3.131) is used in its unmodified form.
Drag must also be included in the determination of forces even if it was not in the
calculation of the induced velocities.
The blade force per unit span normal to the plane of rotation is
d 1 2
F x ¼ rW cC x (3:140)
dr 2
which will vary with the azimuth position of the blade. The total force normal to
the rotor plane can be obtained by integrating Equation (3.138) along the blade
length for each of the blades, taking account of their azimuthal separation, and
summing the results. The total normal force will also vary with rotor azimuth.
Similarly, the tangential blade force per unit span is

20
15
α
10
ψ
5 180 270
90
0
0
0.2
0.4
r/R 0.6 0.8
1
Figure 3.66 Angle of Attack Variation at 308 of Yaw