Circulation Distributions Caused by Secondary Flows

Abstract

In this paper the circulation distributions caused by secondary flows occurring in the cases of flows with nonuniform velocity profiles passing through an axial flow compressor or a turbine cascade, are treated theoretically. It is assumed that this nonuniformity is small and the threedimensional flow is divided into two parts, that is, the two-dimensional fundametal potential and the perturbation flow. Starting from the equation of motion, Smith's equation⁽³⁾ which relates the span-wise velocity with the circulation variation is derived. Secodary-flow vortices which are parallel to the main outlet-flow and cause span-wise velocity confined in the rectangular flow passage, are determined to satisfy Kutta's condition at the trailing edge, using the relationship between the span-wise velocity and the secondary circulation. The curves of coefficients which relate the circulation with a velocity profile, are calculated and the comparison with author's experiments is made with fairly good agreement.