Design of Wind Turbines - Wind Energy: Renewable Energy and the Environment - page 105

FIGURE 6.5 The rotor imparts a rotation to the wake.

6.5.2 R OTATION
Angular momentum is

L r p (6.22)

Angular momentum, like momentum, is always conserved.
From conservation of angular momentum, since the disk is rotating, there will be a rotation imparted
to the wake in the opposite direction of the disk (Figure 6.5). From the conservation of energy,

KE up energy extracted (by rotor) KE wake KE (rotation of wake)

The torque acting on the rotor makes it rotate and power can be extracted. In order to obtain maxi-
mum power, a high angular velocity, Ω, and a low torque, T , are desirable because a large torque will
result in a large wake rotational energy (angular velocity of the wake W).

Power (rotor) T Ω

A similar analysis, as previously described, is used to obtain the power extracted where conser-
vation of angular momentum is included. An annular ring is considered, and an angular (tangential)
induction factor, ]' , is used. The main difference is that the rotor velocity is a function of the radius,
so the values have to be calculated for the annular ring.

6.6 AERODYNAMIC PERFORMANCE PREDICTION
The ratio of lift to drag for airfoils is around 100, so the two forces, which act at the quarter chord
of the airfoil, are represented by a force that makes the blade rotate, tangential force, and a force
trying to push the rotor over, perpendicular force. So if these lift and drag forces are calculated for a
blade, then the tangential and perpendicular forces are calculated and the performance of the rotor
can be predicted. If the angle between the blade path and the wind at the blade is & (see Figure 5.9 ),
then the tangential and perpendicular forces are

F (tan) L sin & − D cos &

(6.23)

F (per) L cos & D sin &

Notice that the perpendicular force will be larger than the tangential force, and at 90° there is only drag.