Vorticity Modeling of Blade Wakes behind Isolated Annular Blade-Rows: Induced Disturbances in Swirling Flows

Abstract

A general analysis is proposed for studying the fluid-mechanical behavior of blade wakes from an annular blade-row in highly swirling flow. The coupling between the centrifugal force and the vorticity, which is inherent to highly swirling flows, can significantly modify the wake behavior from that in a two-dimensional situation. In steady flow, theoretical considerations show that a blade wake consists primarily of two distinct types of vorticity: (1) trailing vorticity shed from the blade due to a spanwise variation in blade circulation; and (2) vorticity associated with defects in stagnation pressure (or rotary stagnation in relative coordinate system). Three types of disturbances can be identified in the resulting three-dimensional disturbance field: (1) the exponentially decaying type (potential, irrotational), (2) the purely convected type (rotational), and (3) the nonconvected type (both rotational and irrotational parts). Type (3) arises because of the interaction of centrifugal and Coriolis forces with (1) and (2). It is found that near the blade row the nonconvected disturbances grow linearly in magnitude with the axial distance. However, although those nonconvected disturbances associated with the trailing vorticity (also called Beltrami vorticity) persist for moderate distances downstream, they eventually decay inversely with the axial distance, irrespective of the types of swirl distribution. In contrast, those parts of nonconvected disturbances which are induced by the vorticity caused by (rotary) stagnation pressure defects persist indefinitely downstream for any type of swirl other than free-vortex. In the limit of free-vortex swirl, all disturbances decay at least inversely with the axial distance downstream.