Unsteady Disturbances in Swirling Turbomachinery Flows

Abstract

The propagation of small disturbances in an annular duct with a mean swirling flow is analyzed. It is shown that because of the centrifugal and Coriolis forces created by the mean swirl, the upstream disturbances can no longer be decomposed into distinct potential, rotational and entropic modes. A normal mode analysis shows that, for a rotational mean swirl, there are two distinct sets of discrete acoustic-vorticity eigenmodes. A pressure-dominated set whose eigenmodes propagate at near sonic speed and carry only small amount of vorticity, and a vorticity-dominated set of modes with only a small pressure associated with them and which accumulates with increasing density at the edges of a critical layer. The normal modes do not form a complete set and must be complemented with initial-value type solutions. A generalized definition for incident rotational waves (gusts) is proposed which accounts for both the eigenmodes and the initial-value solutions.