The Unsteady Aerodynamics of Turbine Yaw and Over-Speed Protection - Small Wind Turbines: Analysis, Design, and Application - page 145

Chapter 8
The Unsteady Aerodynamics of Turbine
Yaw and Over-Speed Protection

8.1 Introduction

The analyses of power extraction and starting in the last six chapters assumed
effectively steady flow whereas all turbines operate in unsteady flow for most of
the time. The effects on turbine operation are significant and complex. They
include ''dynamic inflow'', the general name for the unsteady behaviour of the
axial and rotational induction factors, which in turn are influenced by the vortex
structure of the time-varying wake, as well as the unsteady lift and drag on the
blades, e.g. Leishman [ 1 , 2 ]. While important, these aspects are not critical for an
introductory treatment, if for no other reason than that a determination of the
turbine power curve will usually reproduce the design steady performance curve if
the turbine is well built and the testing is done to the appropriate IEC standard.
Unsteadiness, however, is unavoidable in examining yaw behaviour, the tur-
bine's motion about the vertical ''yaw'' or tower axis, in response to changes in wind
direction. This behaviour is important because a yaw ''error'', h, between the turbine
axis and the wind direction, reduces turbine power by the ratio cos 2 h to a first
approximation, see Sect. 1.2 . Thus a 20 yaw error reduces the power by a signif-
icant 12%. In addition, one of the IEC SLM Load Cases studied in the next chapter is
associated with yaw error. Most small wind turbines have a tail fin, as can be seen in
Figs. 1.2 and 6.1 . Their yaw response depends on tail fin area, moment of inertia,
and distance from the yaw axis. The shape of the tail fin is not usually critical.
Yaw behaviour is also connected with a number of important safety issues. For
example, and somewhat surprisingly at first sight, yawing can lead to significant
cyclic (and hence unsteady) gyroscopic loads. It is shown in Chap. 9 that these
loads are often the largest loads on the blade roots and rotor shaft of a small
turbine. To a first approximation, they are of the form

ð 8 : 1 Þ

M ¼ k N JXx

where M is the load (moment), k N is a numerical factor depending on the number of
blades, J is the moment of inertia of the blade (see Chap. 6 ), and x is the yaw rate.