Blade Element Calculations - Small Wind Turbines: Analysis, Design, and Application - page 94

Fig. 5.12 Visualization of
the tip vortex of a two-blade
10 m diameter wind turbine
in the NASA Ames 80 by
120 ft wind tunnel. Photo
from Dr Scott Schreck,
NREL
above 0.50 is a reasonable target with the current design methodology. This
suggestion is reinforced by the study by Selig and Coverstone-Carroll [ 9 ]; they
used ''genetic algorithms'' to search for optimal blade designs using aerofoil
sections including those considered in this chapter and in Chap. 3 . They obtained a
maximum C P of 0.53. ''Evolutionary'' optimisation for multi-dimensional blade
design is the subject of Chap. 7 .
In addition to a high C P , it is important to have as broad a range of k as possible
over which performance is close to the optimal. The need for this was noted for
constant speed turbines in the discussion of Figs. 1.5 and 1.6 . It is also true for
variable speed turbines, even though the reasons are less obvious. A narrow or
''peaky'' performance curve would require a very accurate control system to adjust
the blade speed to maintain the optimum k as the wind speed varies. This task is
made more difficult because the wind speed is not usually monitored on small
turbines, whereas nearly all large machines have an anemometer mounted on the
nacelle. Furthermore, some wind speed and direction changes occur too rapidly for
a turbine to follow without suffering huge dynamic loads, so that even variable
speed turbines of necessity operate at varying k.
There are a number of ways in which blade performance can be related to the
Betz-Joukowsky limit. The first is just to compare the actual C P to the Betz-
Joukowsky value of 16/27 and attempt some sort of trial-and-error searching. Here
the comparison is taken further by the apparently circuitous route of investigating
the structure of the wake behind the blades in terms of its vortex structure that was
introduced in Chap. 3 . By Kelvin's theorem for the conservation of circulation in
an otherwise inviscid fluid, the simplest possible consequence of the generation of
bound vorticity by the blades is that vorticity of strength C must be shed into the
wake at the blade tips, much as the bound vorticity of an aircraft's wing feeds the
wing tip vortices that are often visualized in contrails. In contrast, blade tip vor-
tices are helical, as demonstrated by the beautiful flow visualization of Fig. 5.12 .
In the far-wake—well downstream of the blades—R ? , the wake and vortex radius,
and p ? , the pitch, which measures the distance between successive turns of the