Page 267 - Fluid Mechanics and Thermodynamics of Turbomachinery

248 Fluid Mechanics, Thermodynamics of Turbomachinery
Practical values of N for well-designed nozzle rows in normal operation are usually
in the range 0.90 6 N 6 0.97.
(ii) Rotor loss coefficients

At either the design condition (Figure 8.4), or at the off-design condition dealt
with later (Figure 8.5), the rotor passage friction losses can be expressed in terms
of the following coefficients.
The enthalpy loss coefficient is,

2
1
R D .h 3 h 3s //. w /. (8.20)
3
2
The velocity coefficient is,
(8.21)
R D w 3 /w 3s
which is related to R by
1
R D 1 (8.22)
2
R
The normal range of for well-designed rotors is approximately, 0.70 6 R 6 0.85.

Optimum efficiency considerations

According to Abidat et al. (1992) the understanding of incidence effects on the
rotors of radial and mixed flow turbines is very limited. Normally, IFR turbines are
made with radial vanes in order to reduce bending stresses. In most flow analyses
that have been published of the IFR turbine, including all earlier editions of this text,
it was assumed that the average relative flow at entry to the rotor was radial, i.e. the
incidence of the relative flow approaching the radial vanes was zero. The following
discussion of the flow model will show that this is an over-simplification and the flow
angle for optimum efficiency is significantly different from zero incidence. Rohlik
(1975) had asserted that “there is some incidence angle that provides optimum flow
conditions at the rotor-blade leading edge. This angle has a value sometimes as high
as 40 ° with a radial blade.”
The flow approaching the rotor is assumed to be in the radial plane with a velocity
c 2 and flow angle ˛ 2 determined by the geometry of the nozzles or volute. Once the
fluid enters the rotor the process of work extraction proceeds rapidly with reduction
in the magnitude of the tangential velocity component and blade speed as the flow
radius decreases. Corresponding to these velocity changes there is a high blade
loading and an accompanying large pressure gradient across the passage from the
pressure side to the suction side (Figure 8.5a).
With the rotor rotating at angular velocity  and the entering flow assumed to
be irrotational, a counter-rotating vortex (or relative eddy) is created in the relative
flow, whose magnitude is , which conserves the irrotational state. The effect
is virtually the same as that described earlier for the flow leaving the impeller of
a centrifugal compressor, but in reverse (see Chapter 7 under the heading “Slip
factor”). As a result of combining the incoming irrotational flow with the relative