Page 129 - Fluid Mechanics and Thermodynamics of Turbomachinery

110 Fluid Mechanics, Thermodynamics of Turbomachinery

3.0
h tt = 0.82 0.84 0.86
Stage loading coefficient, y = DW/U 2 2.0 e = 140° 120° 100° 0.92 0.90 0.86
0.88

R
80°
1.0
60°
0.82

0 40° 0.84
0.5 1.0 1.5
Flow coefficient, f = c /U
x
FIG. 4.11. Design point total-to-total efficiency and rotor flow deflection angle for a zero
reaction turbine stage.

The performance chart shown in Figure 4.11 has been derived using the above
expressions. This is similar in its general form to Figure 4.10 for 50 per cent reac-
tion, with the highest efficiencies being obtained at the lowest values of and ,
except that higher efficiencies are obtained at higher values of the stage loading but
at reduced values of the flow coefficient.

(3) Total-to-static efficiency of stage with axial velocity at exit
A single-stage axial turbine will have axial flow at exit and the most appropriate
efficiency is usually total-to-static. To calculate the performance, eqn. (4.10a) is
used:
2
2
2
1 . R w C N c C c /
3
1
2
D 1 C ,
ts 2W
2 2 2
D 1 C . R sec ˇ 3 C N sec ˛ 2 C 1/.
2
With axial flow at exit, c 1 D c 3 D c x , and from the velocity diagram, Figure 4.12,
tan ˇ 3 ,
tan ˇ 3 D U/c x , tan ˇ 2 D tan ˛ 2
2
2
2
sec ˇ 3 D 1 C tan ˇ 3 D 1 C 1/ ,
2 2 2
sec ˛ 2 D 1 C tan ˛ 2 D 1 C . / / ,
1 1
∴ D 1 C [ R .1 C / C N . C / C ].
2
2
2
2
ts 2