Page 130 - Wind Energy Handbook

104 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

same basic theory as in Section 3.4 can be carried out for an actuator disc with a
wake skewed to the rotor axis by an angle ÷. There is an important proviso
however: it must be assumed that the bound circulation on the rotor disc is radially
and azimuthally uniform. As will be demonstrated the angle of attack of the blades
is changing cyclically and so it would be impossible for the uniform circulation
condition ever to be valid. What must be assumed is that the variation of circulation
around a mean value has but a small effect on the induced velocity and the wake is
therefore dominated by the vorticity shed from the blade tips by the mean value of
circulation.
The expansion of the wake again imposes a difficulty for analysis and so, as
before, it will be ignored (Figure 3.52).
The analysis of the yawed rotor was first carried out for purposes of under-
standing a helicopter rotor in forward flight by Coleman et al. (1945) but it can
readily be applied to a wind turbine rotor by reversing the signs of the circulation
and the induced velocities. An infinite number of blades is assumed as in the

z

∆Γ

y
χ
γ φ
∆Γ

Figure 3.52 A Yawed Rotor Wake without Wake Expansion

χ
aU tan ( )

2
U
γ

aU
g ψ
g ψ
γ
g ψ
g ψ

Figure 3.53 A Yawed Actuator Disc and the Skewed Vortex Cylinder Wake