Page 125 - Fluid Mechanics and Thermodynamics of Turbomachinery

106 Fluid Mechanics, Thermodynamics of Turbomachinery
Correcting for aspect ratio with eqn. (4.13a),

N1 D 1.0694.0.993 C 0.021/5/ 1 D 0.0666.

For the rotor, tan ˇ 2 D .c y2 U//c x D .552 500//200 D 0.26,
∴ ˇ 2 D 14.55 deg.

Therefore,
tan ˇ 3 D U/c x D 2.5,

and ˇ 3 D 68.2 deg.
Therefore ε R D ˇ 2 C ˇ 3 D 82.75 deg,
Ł
2
D 0.04.1 C 1.5 ð 0.8275 / D 0.0812.
R
Correcting for aspect ratio with eqn. (4.13b)
R1 D 1.0812.0.975 C 0.075/5/ 1 D 0.0712.
The velocity ratios are:

2 2
w 3 c x
D 1 C D 1.16
U U
2
2 2
c 2 588 c x
D D 1.382; D 0.16
U 500 U
and the stage loading factor is,
W c y2 552
D D D 1.104
U 2 U 500
Therefore

1 0.0712 ð 1.16 C 0.0666 ð 1.382 C 0.16
D 1 C
ts 2 ð 1.104
D 1 C 0.1515

∴ ts D 0.869.
This result is very close to the value assumed in the first example.
It is not too difficult to include the temperature ratio T 3 /T 2 implicit in the more
exact eqn. (4.10) in order to see how little effect the correction will have. To calcu-
late T 3
1 2
W C c 276,000 C 20,000
2 3
T 3 D T 01 D 1123
C p 1148
D 865 K.
T 3 /T 2 D 865/973 D 0.89.