Page 67 - Wind Energy Handbook

3

Aerodynamics of Horizontal-Axis

Wind Turbines

To study the aerodynamics of wind turbines some knowledge of fluid dynamics in
general is necessary and, in particular, aircraft aerodynamics. Excellent text books
on aerodynamics are readily available, a bibliography is given at the end of this
chapter, and any abbreviated account of the subject that could have been included
in these pages would not have done it justice; recourse to text books would have
been necessary anyway. Some direction on which aerodynamics topics are neces-
sary for the study of wind turbines would, however, be useful to the reader.
For Sections 3.2 and 3.3 a knowledge of Bernoulli’s theorem for steady, incom-
pressible flow is required together with the concept of continuity. For Sections 3.4
and 3.10 an understanding of vortices is desirable and the flow field induced by
vortices. The Biot–Savart law, which will be familiar to those with a knowledge of
electric and magnetic fields, is used to determine velocities induced by vortices. The
Kutta–Joukowski theorem for determining the force on a bound vortex should also
be studied. For Sections 3.5, 3.6 and 3.7 to 3.10 a knowledge of the lift and drag of
aerofoils is essential, including the stalled flow and so a brief introduction has been
included in the Appendix at the end of this chapter.

3.1 Introduction

A wind turbine is a device for extracting kinetic energy from the wind. By removing
some of its kinetic energy the wind must slow down but only that mass of air which
passes through the rotor disc is affected. Assuming that the affected mass of air
remains separate from the air which does not pass through the rotor disc and does
not slow down a boundary surface can be drawn containing the affected air mass
and this boundary can be extended upstream as well as downstream forming a long
stream-tube of circular cross section. No air flows across the boundary and so the
mass flow rate of the air flowing along the stream-tube will be the same for all
stream-wise positions along the stream-tube. Because the air within the stream-tube
slows down, but does not become compressed, the cross-sectional area of the
stream-tube must expand to accommodate the slower moving air (Figure 3.1).
Although kinetic energy is extracted from the airflow, a sudden step change in
velocity is neither possible nor desirable because of the enormous accelerations and