Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

R
1 2 3 8
3
CP = P ( prR cx
)= ( -aaj
) ¢ j
2
1 2
J Ú 1 d
rh
This equation converts to optimum conditions by substituting eqn. (10.56) into it, i.e.
C
P
I/R
(a)
(b)
0.2
0.1
8 J 2
= ( -a)
( a-) j j
J Ú 1 4 1 d
2 jh (10.64)
where the limits of the integral are changed to jh and J =WR/cx1. Glauert (1935) derived
values for CP for the limit range j = 0 to J (from 0.5 to 10) by numerical integration
and the relative maximum power coefficient z. These values are shown in Table 10.10.
So, to obtain a large fraction of the possible power it is apparent that the tip–speed ratio
J should not be too low.
HAWT blade section criteria
0
0.25
0.5
r/R
0.75 1.0
Wind Turbines 361
FIG. 10.20. Examples of variation of chord length with radius. (a) Optimal variation of
chord length with radius, according to Glauert theory, for C L = 1.0; (b) A typical blade
planforn (used for the Micon 65/13 HAWT).
TABLE 10.10. Power coefficients at optimum conditions
J z CP J z CP
0.5 0.486 0.288 2.5 0.899 0.532
1.0 0.703 0.416 5.0 0.963 0.570
1.5 0.811 0.480 7.5 0.983 0.582
2.0 0.865 0.512 10.0 0.987 0.584
The essential requirements of turbine blades clearly relate to aerodynamic performance,
structural strength and stiffness, ease of manufacture and ease of maintenance
in that order. It was assumed, in the early days of turbine development, that blades with
high lift and low drag were the ideal choice with the result that standard aerofoils, e.g.
NACA 44XX, NACA 230XX, etc. (where the XX denotes thickness to chord ratio, as