Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

150 Fluid Mechanics, Thermodynamics of Turbomachinery
Stage loss relationships and efficiency
From eqns. (5.1) and (5.3) the actual work performed by the rotor on unit mass of
fluid is DW = h03 - h 01. The reversible or minimum work required to attain the same
final stagnation pressure as the real process is
using the approximation that Dh = TDs.
The temperature rise in a compressor stage is only a small fraction of the absolute
temperature level and therefore, to a close approximation.
(5.4)
Again, because of the small stage temperature rise, the density change is also small and
it is reasonable to assume incompressibility for the fluid. This approximation is applied
only to the stage and a mean stage density is implied; across a multistage compressor
an appreciable density change can be expected.
The enthalpy losses in eqn. (5.4) can be expressed as stagnation pressure losses as
follows. As h02 = h 03 then,
since p0 - p = 1 – 2 rc 2 for an incompressible fluid.
Along the isentrope 2 - 3s in Figure 5.3, Tds = 0 = dh - (1/r)/dp, and so,
Thus, subtracting eqn. (5.6) from eqn. (5.5),
Similarly, for the rotor,
The total-to-total stage efficiency is,
It is to be observed that eqn. (5.9) also has direct application to pumps and fans.
(5.5)
(5.6)
(5.7)
(5.8)
(5.9)