Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

152 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 5.4. Asymmetry of velocity diagrams for reactions greater or less than 50%.
If R < 0.5 then b 2 < a 1 and the velocity diagram is skewed to the left as indicated
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 temperature rise, based
on incompressible flow cascade 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 y is another important design parameter of a compressor
stage and is one which strongly affects the off-design performance characteristics. It is
defined by
With cy2 U - wy2 this becomes,
(5.14a)
(5.14b)
where f = cx/U is called the flow coefficient.
The stage loading factor may also be expressed in terms of the lift and drag coefficients
for the rotor. From Figure 3.5, replacing am with bm, the tangential blade force
on the moving blades per unit span is