Aerodynamics of Horizontal-Axis Wind Turbines

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 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 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.

Figure 1 The Energy Extracting Stream-tube of a Wind Turbine

The presence of the turbine causes the approaching air, upstream, gradually to slow down such that when the air arrives 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 the atmospheric 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.