Page 116 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Turbines: Two-dimensional Theory 97
In initial calculations or, in cases where the static temperature drop through the
rotor is not large, the temperature ratio T 3 /T 2 is set equal to unity, resulting in the
more convenient approximations,

2 2 1
R w C N c 2
3
tt D 1 C , .4.9a/
2.h 1 h 3 /
2 2 2 1
R w C N c C c 1
3
2
ts D 1 C . .4.10a/
2.h 1 h 3 /
So that estimates can be made of the efficiency of a proposed turbine stage as part
of the preliminary design process, some means of determining the loss coefficients
is required. Several methods for doing this are available with varying degrees of
complexity. The blade row method proposed by Soderberg (1949) and reported
by Horlock (1966), although old, is still remarkably valid despite its simplicity.
Ainley and Mathieson (1952) correlated the profile loss coefficients for nozzle blades
(which give 100% expansion) and impulse blades (which give 0% expansion) against
flow deflection and pitch/chord ratio for stated values of Reynolds number and
Mach number. Details of their method are given in Chapter 3. For blading between
impulse and reaction the profile loss is derived from a combination of the impulse
and reaction profile losses (see eqn. (3.42)). Horlock (1966) has given a detailed
comparison between these two methods of loss prediction. A refinement of the
Ainley and Mathieson prediction method was later published by Dunham and Came
(1970).
Various other methods of predicting the efficiency of axial flow turbiness have
been devised such as those of Craig and Cox (1971), Kacker and Okapuu (1982)
and Wilson (1987). It was Wilson who, tellingly, remarked that despite the emer-
gence of “computer programs of great power and sophistication”, and “generally
incorporating computational fluid dynamics”, that these have not yet replaced the
preliminary design methods mentioned above. It is, clearly, essential for a design
to converge as closely as possible to an optimum configuration using preliminary
design methods before carrying out the final design refinements using computational
fluid dynamics.

Soderberg’s correlation

One method of obtaining design data on turbine blade losses is to assemble
information on the overall efficiencies of a wide variety of turbines, and from this
calculate the individual blade row losses. This system was developed by Soderberg
(1949) from a large number of tests performed on steam turbines and on cascades,
and extended to fit data obtained from small turbines with very low aspect ratio
blading (small height chord). Soderberg’s method was intended only for turbines
conforming to the standards of “good design”, as discussed below. The method was
used by Stenning (1953) to whom reference can be made.
A paper by Horlock (1960) has critically reviewed several different and widely
used methods of obtaining design data for turbines. His paper confirms the claim