Page 224 - Fluid Mechanics and Thermodynamics of Turbomachinery

Centrifugal Pumps, Fans and Compressors 205
The conditions under which the rothalpy of a fluid is conserved in the flow through
impellers and rotors have been closely scrutinised by several researchers. Lyman
(1993) reviewed the equations and physics governing the constancy of rothalpy in
turbomachine fluid flows and found that an increase in rothalpy was possible for
steady, viscous flow without heat transfer or body forces. He proved mathematically
that the rothalpy increase was generated mainly by the fluid friction acting on the
stationary shroud of the compressor considered. From his analysis, and put in the
simplest terms, he deduced that:
.Uc / 1 C W f / Pm, (7.4)
h 02 h 01 D .Uc / 2
R
where W f DPm.I 2 I 1 / D n· ·W dA is the power loss due to fluid friction on the
stationary shroud, n is a unit normal vector, is a viscous stress tensor, W is the
relative velocity vector and dA is an element of the surface area. Lyman did not
give any numerical values in support of his analysis.
In the discussion of Lyman’s paper, Moore disclosed that earlier viscous flow
calculations of the flow in centrifugal flow compressors (see Moore et al. 1984)
of the power loss in a centrifugal compressor had shown a rothalpy production
amounting to 1.2 per cent of the total work input. This was due to the shear work
done at the impeller shroud and it was acknowledged to be of the same order
of magnitude as the work done overcoming disc friction on the back face of the
impeller. Often disc friction is ignored in preliminary design calculations.
A later, careful, order-of-magnitude investigation by Bosman and Jadayel (1996)
showed that the change in rothalpy through a centrifugal compressor impeller would
be negligible under typical operating conditions. They also believed that it was not
possible to accurately calculate the change in rothalpy because the effects due to
inexact turbulence modelling and truncation error in computation would far exceed
those due to non-conservation of rothalpy.

Diffuser
The fluid is decelerated adiabatically from velocity c 2 to a velocity c 3 , the static
pressure rising from p 2 to p 3 as shown in Figure 7.3. As the volute and outlet
diffuser involve some further deceleration it is convenient to group the whole
diffusion together as the change of state from point 2 to point 3. As the stagna-
tion enthalpy in steady adiabatic flow without shaft work is constant, h 02 D h 03 or
1 2
1 2
h 2 C c D h 3 C c . The process 2 to 3 in Figure 7.3 is drawn as irreversible, there
2 2 2 3
p 03 during the process.
being a loss in stagnation pressure p 02
Inlet velocity limitations

The inlet eye is an important critical region in centrifugal pumps and compressors
requiring careful consideration at the design stage. If the relative velocity of the inlet
flow is too large in pumps, cavitation may result with consequent blade erosion or
even reduced performance. In compressors large relative velocities can cause an
increase in the impeller total pressure losses. In high-speed centrifugal compressors
Mach number effects may become important with high relative velocities in the