Page 243 - Fluid Mechanics and Thermodynamics of Turbomachinery

224 Fluid Mechanics, Thermodynamics of Turbomachinery

b 2 = 0
¢
15°
1.2
30°

M 2 45°

0.8

0.4
0.8 1.2 1.6 2.0
Blade Mach number, M u
FIG. 7.14. Variation of impeller exit Mach number vs blade Mach number of a centrifugal
compressor for selected back sweep angles (
D 1.4, D 0.9, 2 D 0.375).

and possible stall and flow instability. Several researchers (e.g. Rodgers and Sapiro
1972) have shown that the optimum flow angle is in the range 60 ° <˛ 2 < 70 ° .
Backswept vanes give a reduction of the impeller discharge Mach number, M 2 ,at
any given tip speed. A designer making the change from radial vanes to back swept
vanes will incur a reduction in the design pressure ratio if the vane tip speed remains
the same. To recover the original pressure ratio the designer is forced to increase the
blade tip speed which increases the discharge Mach number. Fortunately, it turns
out that this increase in M 2 is rather less than the reduction obtained by the use of
backsweep.
Illustrative Exercise. Consider a centrifugal compressor design which assumes
0
the previous design data (Figures 7.13 and 7.14), together with ˇ D 0 ° and a blade
2
speed such that M u D 1.6. From Figure 7.13 the pressure ratio at this point is 6.9
and, from Figure 7.14, the value of M 2 D 1.27. Choosing an impeller with a back
0
sweep angle, ˇ D 30 ° , the pressure ratio is 5.0 from Figure 7.13 at the same value
2
of M u . So, to restore the original pressure ratio of 6.9 the blade Mach number must
be increased to M u D 1.8. At this new condition a value of M 2 D 1.125 is obtained
from Figure 7.14, a significant reduction from the original value.