Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

260 Fluid Mechanics, Thermodynamics of Turbomachinery
impeller of a radially bladed centrifugal compressor with the same number of vanes as
the turbine rotor. Following Whitfield and Baines (1990), an incidence factor, l, is
defined, analogous to the slip factor used in centrifugal compressors:
The slip factor most often used in determining the flow angle at rotor inlet is that devised
by Stanitz (1952) for radial vaned impellers, so for the incidence factor
l= 1- 063 . p Z ª 1-2 Z
Thus, from the geometry of Figure 8.5b, we obtain
(7.18a)
(8.23)
In order to determine the relative flow angle, b 2, we need to know, at least, the values
of the flow coefficient, f2 = c m2/U 2 and the vane number Z. A simple method of determining
the minimum number of vanes needed in the rotor, due to Jamieson (1955), is
given later in this chapter. However, in the next section an optimum efficiency design
method devised by Whitfield (1990) provides an alternative way for deriving b 2.
Design for optimum efficiency
Whitfield (1990) presented a general one-dimensional design procedure for the IFR
turbine in which, initially, only the required power output is specified. The specific
power output is given:
and, from this a non-dimensional power ratio, S, is defined:
(8.24)
(8.25)
The power ratio is related to the overall pressure ratio through the total-to-static
efficiency:
(8.26)
If the power output, mass flow rate and inlet stagnation temperature are specified, then
S can be directly calculated but, if only the output power is known, then an iterative
procedure must be followed.
Whitfield (1990) chose to develop his procedure in terms of the power ratio S and
evolved a new non-dimensional design method. At a later stage of the design when the
rate of mass flow and inlet stagnation temperature can be quantified, then the actual
gas velocities and turbine size can be determined. Only the first part of Whitfield’s
method dealing with the rotor design is considered in this chapter.
Solution of Whitfield’s design problem
At the design point it is usually assumed that the fluid discharges from the rotor in
the axial direction so that with cq3 = 0, the specific work is