Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

40 Fluid Mechanics, Thermodynamics of Turbomachinery
From eqn. (2.33), taking logs of both sides and re-arranging, we get,
Turbine polytropic efficiency
A similar analysis to the compression process can be applied to a perfect gas expanding
through an adiabatic turbine. For the turbine the appropriate expressions for an
expansion, from a state 1 to a state 2, are
(2.37)
(2.38)
The derivation of these expressions is left as an exercise for the student. “Overall”
isentropic efficiencies have been calculated for a range of pressure ratio and different
polytropic efficiencies and are shown in Figure 2.9. The most notable feature of these
results is that, in contrast with a compression process, for an expansion, isentropic efficiency
exceeds small stage efficiency.
Reheat factor
The foregoing relations obviously cannot be applied to steam turbines as vapours do
not in general obey the gas laws. It is customary in steam turbine practice to use a
FIG. 2.9. Turbine isentropic efficiency against pressure ratio for various polytropic
efficiencies (g = 1.4).