9 Hydraulic Turbines
334
This expression demonstrates that the ratio b 1 1
/ d and the degree of reaction must
increase in order to increase specific speed. As demonstrated in the previous section, the diameter ratio increases with increasing degree of reaction. These influences explain the meridional shapes shown in Fig. 9.12. Just as with pumps with doubly
curved blades, blade shapes may be designed by means of streamtubes, drawn in a
meridional section. The exact blade shape is not discussed any further here. Blade
design requires a study of the equilibrium of the various streamtubes and the flow
turning in each streamtube. The study results in the chord, the inlet angle and the
outlet angle of the blade segment in each streamtube. On the base thereof the blade
may be drawn (with the so-called Kaplan method).
In order to give an idea of the efficiency variation with s
W , Table 9.3 lists some
characteristic data based on the books of Vivier [3] and Dietzel [1]. The values
Table 9.3 Degree of reaction and outlet kinetic energy with Francis and Kaplan turbines
Francis
s
W
0.3
0.6
0.9
1.2
1.5
1.8
2.1
R
0.53
0.56
0.59
0.64
0.68
0.72
0.75
v
gH
2
2 2
/
0.025
0.035
0.050
0.075
0.090
0.100
0.105
Kaplan
s
W
2
3
4
5
R
0.80
0.85
0.88
0.90
v
gH
2
2 2
/
0.16
0.25
0.34
0.43
Fig. 9.12 Meridional section
shape depending on specific
speed with Francis turbines.
(Adapted from Vivier [3])