Development and analysis of vertical-axis wind turbines - Wind Power Generation and Wind Turbine Design - page 297

L

f

g Wr

a

W

D

U

q

b

Figure 16: Illustration of the kinematics of a variable pitch VAWT blade.

3.1.2 Variable pitch VAWTs
In the double-multiple-streamtube model described above the blade pitch is held
constant with respect to azimuth angle, b , i.e. the chord is perpendicular to the
radius arm of the rotor. However, it is a relatively simple matter to modify the
double-multiple-streamtube model to incorporate passive or active pitch control
[27, 29]. In addition, one can also model the effect that some investigators have
reported whereby an improvement in performance for fi xed pitch turbines can
be achieved if there is a slight toe out of the blades, as this reduces stall on the
upstream pass. However, the resolution of the lift and drag forces into the appro-
priate tangential and normal components can be algebraically tedious because of
the need to introduce new parameters for the blade pitch angle, g , and resultant

wind velocity angle, φ , as illustrated in Fig. 16.

3.1.3 Flow curvature and dynamic stall
The double-multiple-streamtube momentum model described above is a quasi-
steady-state model which relies on the lift and drag characteristics of the aerofoils
determined generally from steady-state wind tunnel tests or from inviscid or vis-
cous numerical simulations. It follows that this model does not inherently capture
a number of fl ow phenomena that occur in VAWTs in practice, for example, fl ow
curvature and dynamic stall.
The issue of “fl ow curvature” relates to the fact that the apparent air motion
relative to a blade of a VAWT has a curvature due to the rotation of the blade about
the rotor axis. This in effect changes the apparent angle of attack on the blade and
can be treated from a quasi-steady standpoint. The rate of pitching of the blade
relative to the undisturbed fl ow is equal to the rotational velocity of the rotor,
Ω

. Sharpe [23] proposes a correction to the normal force coeffi cient, d C n , based
on thin aerofoil theory to account for the pitching of the blade such that
d C n = (d C L /d R / W )/4. An indication of the magnitude of this effect is pro-

vided by Wilson [24] using previous work carried out at the Sandia National Labo-
ratories, which showed that fl ow curvature may result in an offset in the apparent

a )( c/R )( Ω