Transonic, Laminar High Reynolds Number Flow in Slender Channels

Abstract

The study deals with transonic laminar interacting boundary layers in channels which are so slender that the flow inside the inviscid core region can be treated as quasi-one-dimensional. The resulting interaction equations are found to admit eigensolutions, i.e. solutions for completely flat channel walls, which describe the transition from a supersonic to a subsonic state and can be interpreted as pseudo-shocks. A nozzle type geometry of the channel walls is, however, necessary to achieve a transition from subsonic to supersonic speeds. The interaction equations can then be used to design the nozzle shape such that it generates a desired pressure distribution.