Handbook of Turbomachinery Second Edition Revised - Ventech!

design fault in the radial-inflow turbine stator is too high a value of solidity,
resulting in excessive frictional losses. Based on turbine designs presented by
Rodgers [27] and the turbine used by Kofskey and Nusbaum [25], stator
vane radius ratios range from 1.2 to 1.3. For preliminary sizing exercises, a
value of about 1.25 may be taken as typical. The radius to the centerline of
the scroll inlet of the turbine from Kofskey and Nusbaum [25] is twice the
radius at stator inlet. Cross-section radius at scroll inlet is approximately
two thirds the stator inlet radius, so the maximum package radius is roughly
2.67 times the stator inlet radius. This represents a fairly large scroll,
commensurate with the high efficiency levels obtained during testing. For a
reduction in efficiency, the scroll size can be reduced.
An Example of Radial-Inflow Turbine Sizing
To demonstrate the concepts and guidelines described in this and preceding
sections, we will size a radial-inflow turbine for the same application as the
axial-flow turbine example presented earlier. The design requirements for
that turbine were:
1. Generates 100 hp at design point.
2. Operates at an overall pressure ratio of 3:1 in air.
3. Inlet pressure is 44.1 psia, and inlet temperature is 300 8F.
A procedure similar to that used in the axial-flow turbine sizing example will
be used here with a few modifications:
1. Determine available energy (isentropic enthalpy drop).
2. Guesstimate overall efficiency to calculate flow rate.
3. Calculate vector diagram based on optimum parameters.
4. Select specific speed based on Fig. 17.
5. Determine overall geometry.
6. Determine overall efficiency when equipped with a diffuser.
The process is iterative, since the efficiency determined in step 6 is used to
improve the efficiency guess made in step 2. The process is repeated until the
efficiencies from steps 2 and 6 agree. Perfect gas behavior is assumed, with
cp ¼ 0:24 Btu=lbm, g ¼ 1:4, and Rgas ¼ 53:34 ft-lbf=lbm- sec.
The isentropic overall enthalpy drop across the turbine is the same as
in the axial-flow turbine example:
Dhisentropic ¼ 0:24 Btu
lbm R
ð760 RÞ 1
" #
1
3
0:4=1:4
¼ 49:14 Btu
lbm
Note that more digits are carried through the calculations than indicated, so
Copyright © 2003 Marcel Dekker, Inc.