Page 64 - Fluid Mechanics and Thermodynamics of Turbomachinery

Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency 45
Diffuser performance parameters

The diffusion process can be represented on a Mollier diagram, Figure 2.12b,
by the change of state from point 1 to point 2, and the corresponding changes in
pressure and velocity from p 1 and c 1 to p 2 and c 2 . The actual performance of a
diffuser can be expressed in several different ways:

(1) as the ratio of the actual enthalpy change to the isentropic enthalpy change;
(2) as the ratio of an actual pressure rise coefficient to an ideal pressure rise co-
efficient.
For steady and adiabatic flow in stationary passages, h 01 D h 02 , so that
1
2
h 2 h 1 D .c 2 c /. (2.44a)
2 1 2
For the equivalent reversible adiabatic process from state point 1 to state point 2s,
2
1
h 1 D .c 2 c /. (2.44b)
.h 2s 1 2s
2
A diffuser efficiency, D , also called the diffuser effectiveness, can be defined as
2
2
h 1 / D .c 2 c //.c 2 c /. (2.45a)
D D .h 2s h 1 //.h 2
1 2s 1 2
In a low speed flow or a flow in which the density can be considered nearly
constant,
p 1 //
h 2s h 1 D .p 2
so that the diffuser efficiency can be written
2
p 1 //f .c 2 c g. (2.45b)
D D 2.p 2
1 2
Equation (2.45a) can be expressed entirely in terms of pressure differences, by
writing
h 1 / h 1 /
h 2 h 2s D .h 2 .h 2s
2
1
D .c 2 c / .p 2 p 1 // D .p 01 p 02 // ,
2 1 2
then, with eqn. (2.45a),
h 1 / 1
.h 2s
D D D
.h 2s h 1 / .h 2s h 2 / 1 .h 2s h 2 //.h 2s h 1 /
1
D . .2.46/
1 C .p 01 p 02 //.p 2 p 1 /
Alternative expressions for diffuser performance
(1) A pressure rise coefficient C p can be defined:
p 1 //q 1 , (2.47a)
C p D .p 2
1
2
where q 1 D c .
2 1
For an incompressible flow through the diffuser the energy equation can be written
as
1 2
1 2
p 1 / C c D p 2 / C c C p 0 / , (2.48)
2 1 2 2