Page 241 - Fluid Mechanics and Thermodynamics of Turbomachinery

222 Fluid Mechanics, Thermodynamics of Turbomachinery
16

12 b 2 ¢ 0
Pressure ratio, p 03 /p 01 8 15° 30° 45°
=

4

0.8 1.2 1.6 2.0
Blade Mach number, M u
FIG. 7.13. Variation of pressure ratio vs blade Mach number of a centrifugal compressor
for selected back sweep angles (
D 1.4, c D 0.8, D 0.9, 2 D 0.375).

sweep of the vanes at a given blade speed causes a loss in pressure ratio. In order to
maintain a given pressure ratio it would be necessary to increase the design speed
which, it has been noted already, increases the blade stresses.
With high blade tip speeds the absolute flow leaving the impeller may have a
Mach number well in excess of unity. As this Mach number can be related to the
Mach number at entry to the diffuser vanes, it is of some advantage to be able to
calculate the former.
Assuming a perfect gas the Mach number at impeller exit M 2 can be written as

2
c 2 2 c 2 2 T 01 T 2 c T 01
2
2
M D D Ð Ð D , (7.25)
2 2 2 2
a a a
2 T 01 T 2 2 01 T 2
2
since a 2 D
RT 01 and a D
RT 2 .
01 2
Referring to the outlet velocity triangle, Figure (7.7)
0
2
2
2
2
c D c C c 2 D c C . c / ,
2 r2 2 r2 2
where
0
c 0 2 D U 2 c r2 tan ˇ ,
2
2
c 2 2 2 0 2
D C .1 2 tan ˇ / . .7.26/
2
2
U 2
From eqn. (7.2), assuming that rothalpy remains essentially constant,