Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

Power coefficient, C P
0.6
0.4
0.2
0
1
6 8
10
J = 12
4
2 3 4
Number of blades, Z
Wind Turbines 355
FIG. 10.16. Effect of tip–speed ratio and number of blades on power coefficient
assuming zero drag.
performance (axial force and power) has been calculated for CL = 0.6, 0.8 and 1.0 (with
l = 1.0) for a range of J values. Figure 10.17 shows the variation of the axial force coefficient
CX plotted against J for the three values of C L and Figure 10.18 the corresponding
values of the power coefficient CP plotted against J. A point of particular interest
is that at which CX is replotted as CX/(JCL) all three sets of results collapse onto one
straight line, as shown in Figure 10.19. The main interest in the axial force would be
its effect on the bearings and on the supporting structure of the turbine rotor. A detailed
discussion of the effects of both steady and unsteady loads acting on the rotor blades
and supporting structure of HAWTs is given by Garrad (1990).
N.B. The range of the above calculated results is effectively limited by the nonconvergence
of the value of the axial flow induction factor a at, or near, the blade tip
at high values of J. The largeness of the blade loading coefficient, l = ZlCL/(8pr), is
wholly responsible for this non-convergence of a. In practical terms, l can be reduced
by decreasing CL or by reducing l (or by a combination of these). Also, use of the tip
correction factor in calculations will extend the range of J for which convergence of a
can be obtained. The effect of any of these measures will be to reduce the amount of
power developed. However, in the examples throughout this chapter, in order to make
valid comparisons of performance the values of lift coefficients and chord are fixed. It
is of interest to note that the curves of the power coefficient C P all rise to about the
same value, approximately 0.48, where the cut-off due to non-convergence occurs.