Page 94 - Wind Energy Handbook

68 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

considering the case of an airscrew in the windmill brake state where the angles of
attack are negative.
The flow field through the turbine under heavily loaded conditions cannot be
modelled easily and the results of this empirical analysis must be regarded as being
only approximate at best. They are, nevertheless, better than those predicted by the
momentum theory. For most practical designs the value of axial flow induction
factor rarely exceeds 0.6 and for a well-designed blade will be in the vicinity of 0.33
for much of its operational range.
For values of a greater than a T it is common to replace the momentum theory
thrust in Equation (3.16) with Equation (3.55), in which case Equation (3.51) is
replaced by

p ffiffiffiffiffiffiffiffi
(1 a) 2 ó r C x þ 4( C T1 1)(1 a) C T1 ¼ 0 (3:51a)
sin ö 2

in which the pressure drop caused by wake rotation in ignored as it is very small.
However, as the additional pressure drop is caused by edge flow separation then
this course of action is questionable and it may be more appropriate to retain
Equation (3.51).

3.7 Blade Geometry

3.7.1 Introduction

The purpose of most wind turbines is to extract as much energy from the wind as
possible and each component of the turbine has to be optimized for that goal.
Optimal blade design is influenced by the mode of operation of the turbine, that is,
fixed rotational speed or variable rotational speed and, ideally, the wind distribu-
tion at the intended site. In practice engineering compromises are made but it is still
necessary to know what would be the best design.
Optimizing a blade design means maximizing the power output and so a suitable
solution to blade element – momentum Equations (3.51) and (3.52) is necessary.

3.7.2 Optimal design for variable-speed operation

A turbine operating at variable speed can maintain the constant tip speed ratio
required for the maximum power coefficient to be developed regardless of wind
speed. To develop the maximum possible power coefficient requires a suitable
blade geometry the conditions for which will now be derived.
For a chosen tip speed ratio º the torque developed at each blade station is
maximized if

d 2
8ðºì a9(1 a) ¼ 0
da9