The Unsteady Aerodynamics of Turbine Yaw and Over-Speed Protection - Small Wind Turbines: Analysis, Design, and Application - page 149

equations shown in Figs. 4.5 and 4.6 and implies that the pressure forces dominate
over viscous forces. Equation 8.2 appears to be accurate for delta, and other
shaped, wings for angles up to about 20-30. At small a, the lift is linear in a with
slope K p .
From the quasi-steady analysis of starting performance in Chap. 6 , it may be
thought that predicting tail fin yaw behaviour simply involves using the lift and
drag coefficients for a particular yaw angle to determine the normal force on the
tail fin at a given wind speed, and then calculating the product of this force and the
distance r in Fig. 8.3 to get the yaw moment acting on the turbine. However, this
approach ignores the location of the tail fin in the rotor wake, and the change in lift
and drag due to the changing wind direction and speed.
Consider first the wake in the vicinity of the tail fin. This is an topic of ongoing
research, and there is no consensus yet on what flow speed or direction to assume
when analysing tail fin aerodynamics. One assumption is that the tail fin is located
in the ''near wake'' region of the rotor wake, so that, U wake , the wind speed
experienced by the tail is

U wake ¼ U 0 1 a ð Þ ð 8 : 3 Þ

For optimum turbine operation, the axial induction factor, a = 0.33 and
U wake = 0.67U 0 , where U 0 is the undisturbed wind speed. It is not clear whether
the steady induction factor can always be used for unsteady flow.

8.3 Unsteady Aerodynamics of Tail Fins

There are at least two different ways to analyse the unsteady yaw dynamics of a
tail fin, both giving the same general result. For the present, the stabilising effects
of the blades are ignored. The first is to assume that static lift and drag are
applicable in unsteady conditions. The angle of attack on the tail fin is found by a
vector addition of the actual wind direction and the angular velocity of the tail fin
about the yaw axis as shown schematically in Fig. 8.4 . h is the angle between the
wind direction and the tail fin, U is the wind speed, and the subscript ''a'' refers to

Fig. 8.4 Schematic of tail fin
motion about the yaw axis

U a

.

θ

r

θ

U

θ a

F

r