Environmental Engineering Reference
In-Depth Information
Yaw of HAWT Rotors
All HAWTs operate for some fraction of the time with their rotor axis misaligned with
the wind azimuth. It is common for a rotor to encounter yaw angles of 30 deg for periods as
long as several minutes. Active-yaw-controlled rotors typically respond to a time-averaged
wind direction with averaging times of several minutes. Some free-yaw rotors which have
been designed to operate with the rotor downwind of the tower have been observed with the
rotor operating upwind of the tower for extended periods. Many HAWTs operate continu-
ously with a small yaw error. Others have experienced high rates of yaw rotation which have
caused fatigue failures induced by gyroscopic loadings.
Historically, yaw-related problems have been one of the leading causes of turbine down-
time in California wind power stations. These problems are of two types: loss of
yaw stabil-
ity
, and excessive
yaw-induced loads
. Yaw stability is particularly important for free-yaw
HAWTs which rely on aerodynamic forces to achieve proper orientation with respect to
the wind. The wind turbines of the 1930s used a tail vane in order to obtain yaw stability.
However, a modern free-yaw HAWT, with its rotor downwind of the tower, obtains its yaw
stability from the aerodynamic forces on the rotor.
The presence of a yaw error causes changes in the aerodynamic forces normal to and tangen-
tial to the airfoils as the blades rotate. In a rigid-hub wind turbine, both the normal and tangential
forces can contribute to a moment about the yaw axis. In a HAWT with a teetered rotor, the
tangential forces are dominant in producing this yaw moment. A yaw moment arises from blade-
to-blade differences in aerodynamic loading. Thus, when making analytical estimates of the yaw
moment, greater accuracy is required than in the determination of rotor thrust or rotor torque,
because the aerodynamicist must now evaluate small differences between large numbers.
Aerodynamic Analysis of a Yawed Rotor
The aerodynamic behavior of a yawed wind turbine has been examined by Glauert
[1935a], Miller [1979], de Vries [1985], Hansen [1992], and Croton
et al.
[1999]. Addition-
ally, a review article by Hansen and Butterfield [1993] contains a discussion of yaw aero-
dynamics. Aerodynamic analysis of the power extracted from the wind stream by a yawed
rotor is complicated by the fact that the wake is skewed, so that wake cross-sections are
elliptical rather than round. This modifies the induced velocity at the rotor. Large cyclic
changes also occur in blade angles-of-attack because of yaw error, and this has been shown
to cause dynamic stall [Hansen 1992]. Yaw moments are particularly sensitive to dynamic
stall because of the asymmetry produced by stall hysteresis. As noted by Ribner [1948], most
of the yaw force is generated at the inboard stations of the rotor, near the hub. Additionally,
tower shadow, and wind shear (both vertical and horizontal) are known to contribute to the
differential blade loading that causes yaw misalignment.
Glauert's contribution to the aerodynamic analysis of a yawed rotor is expressed as a
modification of the momentum equation, Equation (5-9), as follows:
dT
= 2
a
r
U U dA
(5-43)
(
U
cosDY -
a U
)
2
+
U
2
sin
2
DY
U
=
where
U
¢ = component of the free-stream wind speed shown in Figure (5-19) (m/s)
Yaw Error and Power Output
It has been observed that even relatively small yaw errors (± 10 deg or less) can reduce
the power output of a HAWT significantly. Anderson
et al
. [1982] measured the power
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