Excess Streamwise Vorticity and Its Role in Secondary Flow

Abstract

The purpose of this paper is, firstly, to show how the concept of excess secondary vorticity arises naturally from attempts to recover three-dimensional flow details lost in passage-averaging the equations governing the flow through gas turbines. An equation for the growth of excess streamwise vorticity is then derived. This equation, which allows for streamwise entropy gradients through a prescribed loss term, could be integrated numerically through a blade-row to provide the excess vorticity at the exit to a blade-row. The second part of the paper concentrates on the approximate methods of Smith (1) and Came and Marsh (2) for estimating this quantity and demonstrates their relationship to each other and to the concept of excess streamwise vorticity. Finally the relevance of the results to the design of blading for gas turbines, from the point of view of secondary flow, is discussed.