Page 133 - Fluid Mechanics and Thermodynamics of Turbomachinery

114 Fluid Mechanics, Thermodynamics of Turbomachinery

FIG. 4.14. Total-to-static efficiency of a 50% reaction axial flow turbine stage (adapted
from Horlock 1966).

Calculations of turbine stage performance have been made by Horlock (1966)
both for the reversible and irreversible cases with R D 0 and 50%. Figure 4.14
shows the effect of blade losses, determined with Soderberg’s correlation, on the
total-to-static efficiency of the turbine stage for the constant reaction of 50%. It
is evident that exit losses become increasingly dominant as the flow coefficient is
increased.

Stresses in turbine rotor blades

Although this chapter is primarily concerned with the fluid mechanics and ther-
modynamics of turbines, some consideration of stresses in rotor blades is needed
as these can place restrictions on the allowable blade height and annulus flow area,
particularly in high temperature, high stress situations. Only a very brief outline
is attempted here of a very large subject which is treated at much greater length
by Horlock (1966), in texts dealing with the mechanics of solids, e.g. Den Hartog
(1952), Timoshenko (1957), and in specialised discourses, e.g. Japiske (1986) and
Smith (1986). The stresses in turbine blades arise from centrifugal loads, from
gas bending loads and from vibrational effects caused by non-constant gas loads.
Although the centrifugal stress produces the biggest contribution to the total stress,
the vibrational stress is very significant and thought to be responsible for fairly
common vibratory fatigue failures (Smith 1986). The direct and simple approach
to blade vibration is to “tune” the blades so that resonance does not occur in the