Unsteady swirling flows in annular cascades, Part 1: Evolution of incidentdisturbances

A theory is developed for the interaction of an unsteady incident disturban ce with an annular cascade in a mean swirling flow. IL is shown that the ce ntrifugal and Coriolis forces caused by the mean swirl couple the acoustic and vortical disturbance modes and can lead to the formation of a critical layer. A normal mode analysis shows that, for moderate subsonic Mach number s, the eigenmodes, which may not form a complete set, are segregated into p ressure-dominated and vorticity-dominated modes. A complete description of incident disturbances is proposed in terms of the pressure-dominated eigenm odes and a spatially developing initial-value solution. For the special cas e of a potential mean swirl, the vortical modes are uncoupled from the acou stic modes, and their vorticity grows linearly as they propagate downstream . For a general vortical mean swirl the vorticity-dominated spatially devel oping disturbances may oscillate or amplify (decay) depending on the radial distribution of the mean swirl. The analysis clearly indicates a significa nt effect of the mean-How swirl on the evolution of the incident disturbanc es and therefore on the blade upwash.