Page 137 - Wind Energy Handbook

THE AERODYNAMICS OF A WIND TURBINE IN STEADY YAW 111

1.5 1.5

Two blades Three blades
k = 0.01
Flow expansion function 1 k = 0.1 Flow expansion function 1 k = 0.1
k = 0.01

k = 0.2
0.5
0.5
k = 0.2
k = 0.3
k = 0.3
0 0
0 0.5 1 1.5 2 0 0.5 1 1.5 2
r/R r/R
Approximate
Exact
Figure 3.60 Approximate Flow Expansion Functions for Two- and Three-blade Rotors

And the tangential component is

÷ ÷
v0 ¼ aU 1 cos ł tan 1 þ F( ì)2 tan sin ł (3:119)
2 2

to which must be added the components of the wind velocity U 1
the normal component

U0 ¼ cos ª U 1 (3:120)
and the tangential component

(3:121)
V ¼ cos ł sin ª U 1
There is a radial (span-wise) velocity component but this will not influence the
angle of attack so can be ignored.
Clearly, from Equation (3.118), the Coleman theory determines the function K(÷),
see equation 3.108, as being
÷
K C (÷) ¼ 2 tan (3:122)
2

In addition there is the tangential velocity Ùr caused by blade rotation and also the
induced wake rotation but the latter will be ignored initially.
The velocities of Equations (3.118) to (3.121) will produce a lower angle of attack
when the azimuth angle ł is positive, see Figure 3.57, than when it is negative and
so the angle of attack will vary cyclically. When ł is positive the incident normal
velocity u} lies closer to the radial axis of the blade than when ł is negative. The