Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency 53
where c2 — is the mean square of the velocity in the cross-section and Q = AU, i.e.
From eqn. (2.56) the change in static pressure is found as
(2.57)
(2.58)
From eqn. (2.51), with eqns. (2.47a) and (2.47b), the diffuser efficiency (or diffuser
effectiveness) can now be written:
Substituting eqn. (2.58) into the above expression,
where v is the total pressure loss coefficient for the whole diffuser, i.e.
(2.59)
(2.60)
Equation (2.59) is particularly useful as it enables the separate effects due the changes
in the velocity profile and total pressure losses on the diffuser effectiveness to be found.
The first term in the equation gives the reduction in hD caused by insufficient flow diffusion.
The second term gives the reduction in hD produced by viscous effects and represents
inefficient flow diffusion. An assessment of the relative proportion of these
effects on the effectiveness requires the accurate measurement of both the inlet and exit
velocity profiles as well as the static pressure rise. Such complete data is seldom derived
by experiments. However, Sovran and Klomp (1967) made the observation that there
is a widely held belief that fluid mechanical losses are the primary cause of poor performance
in diffusers. One of the important conclusions they drew from their work was
that the thickening of the inlet boundary layer is primarily responsible for the reduction
in hD. Thus, insufficient flow diffusion rather than inefficient flow diffusion is often
the cause of poor performance.
Some of the most comprehensive tests made of diffuser performance were those of
Stevens and Williams (1980) who included traverses of the flow at inlet and at exit as
well as careful measurements of the static pressure increase and total pressure loss in
low speed tests on annular diffusers. In the following worked example, to illustrate the
preceding theoretical analysis, data from this source has been used.
EXAMPLE 2.5. An annular diffuser with an area ratio, AR = 2.0 is tested at low speed
and the results obtained give the following data: