Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

154 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 5.5. Simplified off-design performance of a compressor stage (adapted from
Horlock 1958).
The values of yd and fd chosen for a particular stage design determines the value of t.
Thus t is fixed without regard to the degree of reaction and, therefore, the variation of
stage loading at off-design conditions is not dependent on the choice of design reaction.
However, from eqn. (5.13) it is apparent that, except for the case of 50% reaction
when a1 = b2, the reaction does change away from the design point. For design reactions
exceeding 50% (b 2 > a1), the reaction decreases towards 50% as f decreases;
conversely, for design reactions less than 50% the reaction approaches 50% with diminishing
flow coefficient.
If t is eliminated between eqns. (5.20a) and (5.20b) the following expression results,
(5.21)
This equation shows that, for a given design stage loading yd, the fractional change
in stage loading corresponding to a fractional change in flow coefficient is always
the same, independent of the stage reaction. In Figure 5.6 it is seen that heavily loaded
stages (yd Æ 1) are the most flexible producing little variation of y with change of
f. Lightly loaded stages (yd Æ 0) produce large changes in y with changing f.
Data from cascade tests show that yd is limited to the range 0.3 to 0.4 for the most efficient
operation and so substantial variations of y can be expected away from the design
point.
In order to calculate the pressure rise at off-design conditions the variation of stage
efficiency with flow coefficient is required. For an ideal stage (no losses) the pressure
rise in incompressible flow is given by
(5.22)