Page 163 - Fluid Mechanics and Thermodynamics of Turbomachinery

144 Fluid Mechanics, Thermodynamics of Turbomachinery

FIG. 5.4. Asymmetry of velocity diagrams for reactions greater or less than 50%.

If R> 0.5 then ˇ 2 >˛ 1 and the velocity diagram is skewed to the right as shown
in Figure 5.4a. The static enthalpy rise in the rotor exceeds that in the stator (this
is also true for the static pressure rise).
If R< 0.5 then ˇ 2 <˛ 1 and the velocity diagram is skewed to the left as indi-
cated in Figure 5.4b. Clearly, the stator enthalpy (and pressure) rise exceeds that in
the rotor.
In axial turbines the limitation on stage work output is imposed by rotor blade
stresses but, in axial compressors, stage performance is limited by Mach number
considerations. If Mach number effects could be ignored, the permissible tempera-
ture rise, based on incompressible flow cascasde limits, increases with the amount of
reaction. With a limit of 0.7 on the allowable Mach number, the temperature rise and
efficiency are at a maximum with a reaction of 50%, according to Horlock (1958).

Stage loading

The stage loading factor is another important design parameter of a compressor
stage and is one which strongly affects the off-design performance characteristics.
It is defined by

h 03 h 01 c y2 c y1
D D . (5.14a)
U 2 U
With c y2 D U w y2 this becomes,

D 1 .tan ˛ 1 C tan ˇ 2 /, (5.14b)

where D c x /U is called the flow coefficient.