WIND ENERGY SYSTEMS - Cd3wd

Chapter 4—Wind Turbine Power 4–9
r m ω m to the wind speed u. Thistip speed ratio is defined as
λ = r mω m
(10)
u
where r m is the maximum radius of the rotating turbine in m, ω m is the mechanical angular
velocity of the turbine in rad/s, and u is the undisturbed wind speed in m/s.
The angular velocity ω m is determined from the rotational speed n (r/min) by the equation
ω m = 2πn
60
rad/s (11)
The variation of C p with λ for the Sandia 17-m Darrieus[10] is shown in Fig. 9. This
particular machine will be used for illustration purposes in this chapter. All horizontal axis
propeller turbines and other Darrieus machines will have generally similar curves. This curve
is for a machine similar to the one shown in Fig. 1.5 with the difference being that each blade
has two struts extending from the blade to the center of the vertical shaft. Performance is
somewhat better without the aerodynamic losses introduced by the struts, but this will not
affect our discussion. This particular machine has a rotor diameter of 16.7 m, a rotor height
of 17 m, and a rotor swept area of 187 m 2 .
Figure 9: Coefficient of performance C p versus tip-speed ratio λ for Sandia 17-m Darrieus
turbine. Two blades; 42 r/min.
The size of this machine was chosen on the basis of available aluminum forming equipment
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001