Page 246 - Fluid Mechanics and Thermodynamics of Turbomachinery

Centrifugal Pumps, Fans and Compressors 227
Although the absolute Mach number at the impeller tip can be obtained almost
directly from eqn. (7.28) it may be instructive to find it from
c 2 c 2
M 2 D D
a 2 .
RT 2 / 1/2
2
2
where c 2 D .c C c / 1/2
2 r2
c r2 DPm/. 2 2 r t b 2 / D 2/.2 ð 2 ð 0.288 ð 0.011/ D 50.3 m/s
c 2 D s U 2 D 400 m/s.
p
2
2
Therefore c 2 D .400 C 50.3 / D 402.5 m/s.
Since h 02 D h 01 C W
h 2 D h 01 C W 1 2
c .
2 2
4
c //C p D 295 C .18.1
Therefore T 2 D T 01 C .W 1 2 8.1/10 /1005
2 2
D 394.5K.
Hence,
402.5
M 2 D p D 1.01.
.402 ð 394.5/

The diffuser system
Centrifugal compressors and pumps are, in general, fitted with either a vaneless
or a vaned diffuser to transform the kinetic energy at impeller outlet into static
pressure.

Vaneless diffusers
The simplest concept of diffusion in a radial flow machine is one where the swirl
velocity is reduced by an increase in radius (conservation of angular momentum) and
the radial velocity component is controlled by the radial flow area. From continuity,
since Pm D Ac r D 2 rb c r , where b is the width of passage, then
r 2 b 2 2 c r2
c r D . (7.30)
rb
Assuming the flow is frictionless in the diffuser, the angular momentum is constant
and c D c 2 r 2 /r. Now the tangential velocity component c is usually very much
larger than the radial velocity component c r ; therefore, the ratio of inlet to outlet
diffuser velocities c 2 /c 3 is approximately r 3 /r 2 . Clearly, to obtain useful reduc-
tions in velocity, vaneless diffusers must be large. This may not be a disadvantage
in industrial applications where weight and size may be of secondary importance
compared with the cost of a vaned diffuser. A factor in favour of vaneless diffusers
is the wide operating range obtainable, vaned diffusers being more sensitive to flow
variation because of incidence effects.
For a parallel-walled radial diffuser in incompressible flow, the continuity of mass
flow equation requires that rc r is constant. Assuming that rc remains constant, then