Page 210 - Fluid Mechanics and Thermodynamics of Turbomachinery

Three-dimensional Flows in Axial Turbomachines 191

FIG. 6.13. Interaction between two closely spaced actuator discs.

region and adding these to the related radial equilibrium velocity. For x 5 0, and to
c x11 the perturbation velocities from eqns. (6.44) and (6.46).

1 jxj jx υj
c x D c x11 .c x11 c x12 / exp exp . (6.48)
2 H H
For the region 0 5 x 5 υ,

1 jxj jx υj
c x D c x12 C .c x11 c x12 / exp C exp . (6.49)
2 H H
For the region x = υ,

1 jxj jx υj
c x D c x11 C .c x11 c x12 / exp exp . (6.50)
2 H H
Figure 6.13 indicates the variation of axial velocity when the two discs are
regarded as isolated and when they are combined. It can be seen from the above
equations that as the gap between these two discs is increased, so the perturba-
tions tend to vanish. Thus in turbomachines where υ/r, is fairly small (e.g. the front
stages of aircraft axial compressors or the rear stages of condensing steam turbines),
interference effects are strong and one can infer that the simpler radial equilibrium
analysis is then inadequate.

Computer-aided methods of solving the through-flow
problem

Although actuator disc theory has given a better understanding of the complicated
meridional (the radial-axial plane) through-flow problem in turbomachines of simple