Transonic shear flow in a three-dimensional channel

Abstract

Inviscid transonic shear flow in a rectangular channel is considered; opposite walls are parallel except in the region of interest, where one pair of opposing walls form a nozzle-like constriction. The flow exhibits the essential features found in an axial-flow rotor of zero stagger angle, where the relative velocity is transonic, the constricted passage being similar to the channel formed between two adjacent blades. Analytical solutions, valid to second order, are presented for the case where the ratio of the order of the change in velocity caused by the variation in flow area to the order of the change in velocity across the channel due to the shear is unity. The case where this ratio is small compared with one is discussed, as is the problem formulation for a flow with a shock wave in the passage