Handbook of Turbomachinery Second Edition Revised - Ventech!

f m ¼ 0:6; Db 1 ¼ 56:1 , which is acceptable from a manufacturing viewpoint.
Large negative inlet angles at the blade tip are to be avoided.
An Example of Turbine Sizing
In order to demonstrate the concepts described in this and preceding
sections, an example is presented of the sizing of a ‘‘typical’’ auxiliary
turbine for use in an aircraft application. The turbine is to be sized to meet
the following requirements:
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.
The object of this exercise is to determine the turbine size, flow rate,
and operating speed with a turbine design meeting the mechanical,
geometric, and manufacturing constraints outlined earlier. The following
procedure will be followed to perform this exercise:
1. Determine available energy (isentropic enthalpy drop).
2. Guesstimate overall efficiency to calculate flow rate.
3. Select the vector diagram parameters.
4. Calculate the vector diagram.
5. Determine the rotor overall geometry.
6. Calculate the overall efficiency based on Smith’s chart both with
and without a diffuser.
The process is iterative in that the efficiency determined in step 6 is then used
as the guess in step 2, with the process repeated until no change is found in
the predicted efficiency. We will also predict the turbine efficiency using
Soderberg’s correlation.
The first step is to calculate the energy available to the turbine using
Eq. (1). For air, typical values for the specific heat and the ratio of specific
heats are 0:24 Btu=ðlbm RÞ and 1.4, respectively. It is also necessary to
convert the inlet temperature to the absolute scale. We then have
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
exact agreement may not occur in all instances. The vector diagram is
calculated using the work actually done by the blade row; therefore, we need
to start with a guess to the overall efficiency of the turbine. A good starting
point is usually an overall efficiency of 0.8, including the effects of tip
Copyright © 2003 Marcel Dekker, Inc.