Page 168 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Compressors and Fans 149
2
Writing the stage load factor as D C p T 0 /U , then the stage stagnation
temperature rise is,
2 2 °
T 0 D U /C p D 0.3 ð 275 /1005 D 22.5 C.
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),

.
1// p
T 0II NT 0 p 0II
D 1 C D ,
T 0I T 0I p 0I
where N is the required number of stages. Thus
" #
.
1// p
T 01 p 0II 293 1/3.11
N D 1 D [5 1] D 8.86.
T 0 p 0I 22.5
A suitable number of stages is therefore 9.
The overall efficiency is found from eqn. (2.36).
" # " #
.
1//
.
1// p
p 0II p 0II
tt D 1 1
p 0I p 0I
D [5 1/3.5 1]/[5 1/3.11 1] D 86.3%.

Estimation of compressor stage efficiency
h 01 / can be found from
In eqn. (5.9) the amount of the actual stage work .h 03
the velocity diagram. The losses in total pressure may be estimated from cascade
data. This data is incomplete however, as it only takes account of the blade profile
loss. Howell (1945) has subdivided the total losses into three categories as shown
in Figure 3.11.

(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

C D D C Dp C C Da C C Ds
D C Dp C 0.02 s/H C 0.018C 2 .5.28/
L
using the empirical values given in Chapter 3.
Although the subject matter of this chapter is primarily concerned with two-
dimensional flows, there is an interesting three-dimensional aspect which cannot
be ignored. In multistage axial compressors the annulus wall boundary layers