Page 130 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Turbines: Two-dimensional Theory 111
a 2
b 3

c 2
b 2 w
3
c 3
w 2
U
FIG. 4.12. Velocity diagram for turbine stage with axial exit flow.

2.0

= DW/U 2 e =140° 120° 100° 80°

R
Stage loading coefficient, y 1.0 0.92 0.90 0.875 0.85 0.80 0.75 0.70 60° 40°

20°

0
0.2 0.4 0.6 0.8 1.0
Flow coefficient, f = c /U
x
FIG. 4.13. Total-to-total efficiency contours for a stage with axial flow at exit.

Specifying , , the unknown values of the loss coefficients, R and N , can be
derived using Soderberg’s correlation, eqn. (4.12), in which

1
1
1
ε N D ˛ 2 D tan . / / and ε R D ˇ 2 C ˇ 3 D tan .1/ / C tan [. 1// ].
From the above expressions the performance chart, Figure 4.13, has been derived.
An additional limitation is imposed on the performance chart because of the reac-
tion which must remain greater than or, in the limit, equal to zero. From eqn. (4.22a),

R D .tan ˇ 3 tan ˇ 2 / D 1 .
2 2

Thus at the limit, R D 0, the stage loading coefficient, D 2.