Page 100 - Fluid Mechanics and Thermodynamics of Turbomachinery

Two-dimensional Cascades 81
0.6

0.5 h = 0.8
0.85
C pi 0.4 0.9 0.9

0.85
0.3 0.8
0.2
0 1.0 2.0 3.0
s/
FIG. 3.23. Efficiency correlation (adapted from McKenzie 1988).

Solution. From eqn. (3.6) the vector mean flow angle is found,
1
tan ˛ m D .tan ˛ 1 C tan ˛ 2 / D 1.2830.
2
From eqn. (3.42) we get the stagger angle,
0.213 D 1.0700.
tan D tan ˛ m
0
0
Thus, ˛ m D 52.066 and D 46.937 .
From eqn. (3.43), assuming that AVR D 1.0, we find
2
cos ˛ 1
Cp i D 1 D 0.4573.
cos ˛ 2
Using the optimum efficiency correlation, eqn. (3.44),
s/l D 9 ð .0.567 0.4573/,
∴ s/l D 0.9872.

To determine the blade camber we combine
0
υ D ˛ 2 ˛ D ˛ 2 /2
2
with eqn. (3.41), to get
˛ 2 C 1.1.s/l/ 1/3 46.937 44 C 1.1 ð 0.9957
D D
0.5 0.31.s/l/ 1/3 0.5 0.31 ð 0.9957
0
∴ D 21.08 .
According to McKenzie the correlation gives, for high stagger designs, peak effi-
ciency conditions well removed from stall and is in good agreement with earlier fan
blade design methods.

Turbine cascade correlation (Ainley)

Ainley and Mathieson (1951) published a method of estimating the performance
of an axial flow turbine and the method has been widely used ever since. In essence