Page 92 - Wind Energy Handbook

66 AERODYNAMICS OF HORIZONTAL-AXIS WIND TURBINES

and by the time it reaches the edge viscosity has sapped much of the kinetic energy.
As the boundary layer flows around the disc edge it accelerates causing a large
drop in static pressure (Bernoulli). To flow around the disc edge would require very
high velocity and there is insufficient static pressure to provide the necessary
kinetic energy. The flow, therefore, separates from the disc and continues in the
general stream-wise direction. In the region directly behind the disc there is slow
moving, almost stagnant, air at the low static pressure of the flow separating at the
disc edge. At the front of the disc, at the very centre, the flow is brought to rest and
so there is a large increase in static pressure as the kinetic energy is converted to
pressure energy. Elsewhere on the front surface the flow moves radially with a
velocity, outside the boundary layer, which increases towards the disc edge. The
static pressure is generally higher on the front of the disc than on the rear and so
the disc experiences a pressure drag force.
A similar process happens with a spinning rotor at high tip speed ratios. The air
which does not pass through the rotor disc moves radially outwards and separates
at the disc edge causing a low static pressure to develop behind the disc; the drop
in static pressure caused by the separation increases as the tip speed ratio rises and
the axial flow factor increases. The air which does pass through the rotor emerges
into a low pressure region and is moving slowly. There is insufficient kinetic energy
to provide the rise in static pressure necessary to achieve the ambient atmospheric
pressure that must exist in the far wake. The air can only achieve atmospheric
pressure by gaining energy from the mixing process in the turbulent wake. The
shear layer in the flow between the free-stream air and the wake air is what
becomes of the boundary layer that develops on the front of the disc. The shear
layer is unstable and breaks up into the turbulence that causes the mixing and re-
energization of the wake air.

3.6.2 Modification of rotor thrust caused by flow separation

The low static pressure downstream of the rotor disc caused by the separation of
the free-stream flow at the edge of the disc and the high static pressure at the
stagnation point on the upstream side causes a large thrust on the disc, much larger
than that predicted by the momentum theory. Some experimental results reported
by Glauert (1926) for a whole rotor can be seen in Figure 3.16 where the simple
expression for the thrust force coefficient, as derived from the momentum theory
(C T ¼ 4a(1 a)), is given for comparison.
The thrust (or drag) coefficient for a simple, flat circular plate is given by Hoerner
(1965) as 1.17 but, as demonstrated in Figure 3.16, the thrust on the rotating disc is
higher. It might have been expected that when a ¼ 1 the rotor would have the same
thrust coefficient as the circular plate. The principal difference between the circular
plate and the rotor is that the latter is rotating and, as Hoerner also describes, this
causes energy to be dissipated in a thicker, rotating boundary layer on the upstream
surface of the rotor disc giving rise to an even lower pressure on the downstream
side.
It would follow from the above arguments that for high values of the axial
induction factor most of the pressure drop across the disc is not associated with