Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

198 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 6.12. Variation in axial velocity with axial distance from the actuator disc.
At the disc, x = 0, eqn. (6.43) reduces to eqn. (6.41). It is of particular interest to note,
in Figures 6.9 and 6.10, how closely isolated actuator disc theory compares with experimentally
derived results.
Blade row interaction effects
The spacing between consecutive blade rows in axial turbomachines is usually sufficiently
small for mutual flow interactions to occur between the rows. This interference
may be calculated by an extension of the results obtained from isolated actuator
disc theory. As an illustration, the simplest case of two actuator discs situated a distance
d apart from one another is considered. The extension to the case of a large
number of discs is given in Hawthorne and Horlock (1962).
Consider each disc in turn as though it were in isolation. Referring to Figure 6.13,
disc A, located at x = 0, changes the far upstream velocity cx•1 to cx•2 far downstream.
Let us suppose for simplicity that the effect of disc B, located at x = d, exactly cancels
the effect of disc A (i.e. the velocity far upstream of disc B is cx•2 which changes to
cx•1 far downstream). Thus, for disc A in isolation,
where |x| denotes modulus of x and H = rt - r h.
For disc B in isolation,
(6.44)
(6.45)
(6.46)
(6.47)
Now the combined effect of the two discs is most easily obtained by extracting from
the above four equations the velocity perturbations appropriate to a given region and