Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

158 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 5.7. Axial velocity profiles in a compressor (Howell 1945). (Courtesy of the
Institution of Mechanical Engineers.)
theory it would be expected that the tip and root sections would provide a compensatory
effect because of the low axial velocity in these regions. Due to stalling of these
sections (and tip leakage) no such work increase actually occurs, and the net result is
that the work done by the whole blade is below the design figure. Howell (1945) suggested
that the stagnation enthalpy rise across a stage could be expressed as
(5.29)
where l is a work done factor. For multistage compressors Howell recommended for
l a mean value of 0.86. Using a similar argument for axial turbines, the increase in
axial velocity at the pitch-line gives an increase in the amount of work done, which is
then roughly cancelled out by the loss in work done at the blade ends. Thus, for turbines,
no work done factor is required as a correction in performance calculations.
Other workers have suggested that l should be high at entry (0.96) where the annulus
wall boundary layers are thin, reducing progressively in the later stages of the compressor
(0.85). Howell & Bonham (1950) have given mean work done factors for compressors
with varying numbers of stages, as in Figure 5.8. For a four-stage compressor
the value of l would be 0.9 which would be applied to all four stages.
Smith (1970) commented upon the rather pronounced deterioration of compressor
performance implied by the example given in Figure 5.7 and suggested that things are
not so bad as suggested. As an example of modern practice he gave the axial velocity
distributions through a 12-stage axial compressor, Figure 5.9(a). This does illustrate
that rapid changes in velocity distribution still occur in the first few stages, but that the
profile settles down to a fairly constant shape thereafter. This phenomenon has been
referred to as ultimate steady flow.
Horlock (2000) used the term repeating stage that is “a stage deeply embedded in
the compressor where axial equilibrium state is reached,” which seems a more precise
description of the effect than the term ultimate steady flow.