ROTATIONAL FLOW THROUGH CASCADES PART I. THE COMPONENTS OF VORTICITY

Abstract

The flow of a fluid with a non-uniform velocity passing through a cascade of turbine or compressor blades is examined theoretically to determine the nature of the components of vorticity in the direction of flow. Three such components are found, two lying in the stagnation streamline leaving the blade, and one distributed in the stream. The distributed secondary circulation is that due to the curving of the flow in a bend, or passage between the blades, as described by Squire and Winter. The trailing shed circulation is due to the change in circulation along the blade as found in the flow of a uniform fluid about a wing of finite span. The third components—the trailing filament circulation—is due to the stretching of the vortex filaments carried with the flow between the upper and lower stagnation streamlines in the wake of each blade. The application of these results to cascades and isolated serofoils is discussed briefly.