Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

It is reasonable to take the stage efficiency as equal to the polytropic efficiency since
the stage temperature rise of an axial compressor is small. Denoting compressor inlet
and outlet conditions by subscripts I and II respectively then, from eqn. (2.33),
where N is the required number of stages. Thus
A suitable number of stages is therefore 9.
The overall efficiency is found from eqn. (2.36).
Estimation of compressor stage efficiency
Axial-flow Compressors and Fans 157
In eqn. (5.9) the amount of the actual stage work (h03 - h01) can be found from the
velocity diagram. The losses in total pressure may be estimated from cascade data.
These data are incomplete however, as it takes account of only the blade profile loss.
Howell (1945) has subdivided the total losses into three categories as shown in Figure
3.13.
(i) Profile losses on the blade surfaces.
(ii) Skin friction losses on the annulus walls.
(iii) “Secondary” losses by which he meant all losses not included in (i) and (ii) above.
In performance estimates of axial compressor and fan stages the overall drag coefficient
for the blades of each row is obtained from
(5.28)
using the empirical values given in Chapter 3.
Although the subject matter of this chapter is primarily concerned with twodimensional
flows, there is an interesting three-dimensional aspect which cannot be
ignored. In multistage axial compressors the annulus wall boundary layers rapidly
thicken through the first few stages and the axial velocity profile becomes increasingly
peaked. This effect is illustrated in Figure 5.7, from the experimental results of Howell
(1945), which shows axial velocity traverses through a four-stage compressor. Over the
central region of the blade, the axial velocity is higher than the mean value based on
the through-flow. The mean blade section (and most of the span) will, therefore, do less
work than is estimated from the velocity triangles based on the mean axial velocity. In