Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

U 2/c o
0.8
0.7
0.6
88
Radial Flow Gas Turbines 267
0.5
0.1 0.2 0.3 0.4 0.6 0.8 1.0
that peak efficiency values are obtained with velocity ratios close to 0.7 and with values
of exit flow coefficient between 0.2 and 0.3.
Rohlik (1968) suggested that the ratio of mean rotor exit radius to rotor inlet radius,
r3av/r2, should not exceed 0.7 to avoid excessive curvature of the shroud. Also, the exit
hub to shroud radius ratio, r3h/r 3s, should not be less than 0.4 because of the likelihood
of flow blockage caused by closely spaced vanes. Based upon the metal thickness alone
it is easily shown that
where t3h is the vane thickness at the hub. It is also necessary to allow more than
this thickness because of the boundary layers on each vane. Some of the rather
limited test data available on the design of the rotor exit comes from Rodgers and Geiser
(1987) and concerns the effect of rotor radius ratio and blade solidity on turbine efficiency
(see Figure 8.9). It is the relative efficiency variation, h/hopt, that is depicted as
a function of the rotor inlet radius–exit root mean square radius ratio, r2/r3rms, for various
values of a blade solidity parameter, ZL/D2 (where L is the length of the blade along
the mean meridion). This radius ratio is related to the rotor exit hub to shroud ratio, ,
by
From Figure 8.9, for r2/r3rms, a value between 1.6 and 1.8 appears to be the
optimum.
Rohlik (1968) suggested that the ratio of the relative velocity at the mean exit
radius to the inlet relative velocity, w 3av/w2, should be sufficiently high to assure a low
total pressure loss. He gave w3av/w 2 a value of 2.0. The relative velocity at the shroud
tip will be greater than that at the mean radius depending upon the radius ratio at rotor
exit.
86
c m3 /U 2
84
82 80
h ts = 78
FIG. 8.8. Correlation of attainable efficiency levels of IFR turbines against velocity
ratios (adapted from Rodgers and Geiser 1987).