Aerogeradores

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 wouldnot have done it justice; recourse to text books would have been necessary anyway. Some direction on which aerodynamics topics are necessary 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, incompressible flow is required together with the concept of continuity. For Sections 3.4 and 3.10 an understandingof 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 isessential, 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 ofair 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 forall 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 accelerationsand

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AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

Figure 3.1 The Energy Extracting Stream-tube of a Wind Turbine

forces this would require. Pressure energy can be extracted in a step-like manner, however, and all wind turbines, whatever their design, operate in this way. The presence of the turbine causes the approaching air, upstream, gradually to slow down such that when the airarrives at the rotor disc its velocity is already lower than the free-stream wind speed. The stream-tube expands as a result of the slowing down and, because no work has yet been done on, or by, the air its static pressure rises to absorb the decrease in kinetic energy. As the air passes through the rotor disc, by design, there is a drop in static pressure such that, on leaving, the air is below theatmospheric pressure level. The air then proceeds downstream with reduced speed and static pressure – this region of the flow is called the wake. Eventually, far downstream, the static pressure in the wake must return to the atmospheric level for equilibrium to be achieved. The rise in static pressure is at the expense of the kinetic energy and so causes a further slowing down of the wind. Thus,between the far upstream and far wake conditions, no change in static pressure exists but there is a reduction in kinetic energy.

3.2 The Actuator Disc Concept
The mechanism described above accounts for the extraction of kinetic energy but in no way explains what happens to that energy; it may well be put to useful work but some may be spilled back into the wind as turbulence and eventually...