Page 68 - Wind Energy Handbook

42 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 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 condi-
tions, 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 be dissipated
as heat. Nevertheless, we can begin an analysis of the aerodynamic behaviour of
wind turbines without any specific turbine design just by considering the energy
extraction process. The general device that carries out this task is called an actuator
disc (Figure 3.2).
Upstream of the disc the stream-tube has a cross-sectional area smaller than that
of the disc and an area larger than the disc downstream. The expansion of the
stream-tube is because the mass flow rate must be the same everywhere. The mass
of air which passes through a given cross section of the stream-tube in a unit length
of time is rAU, where r is the air density, A is the cross-sectional area and U is the