An Asymptotic Theory of Supersonic Turbulent Interactions in a Compression Corner

Abstract

In this paper we present a theoretical analysis of the interaction of an unseparated supersonic turbulent boundary layer with a shallow two-dimensional compression corner. In these flows the pressure rises in two stages: an abrupt, nearly discontinuous jump, followed by a more gradual rise to the inviscid wedge value far downstream. The downstream flow in the gradual part of the pressure rise is now fairly well understood. In 1969, Roshko and Thomke [1] and later Elfstrom [2] showed that this could be accurately predicted with a simple inviscid rotational flow model, provided that a suitable cut-off or slip velocity was applied to the initial velocity profile and adjusted to match the steep part of the pressure rise. Later, in 1984, Agrawal and Messiter [3] developed a rational asymptotic theory for this problem based on the limits of small wedge angle and large Reynolds number. Their approach is closely related to asymptotic theories previously developed for other turbulent interaction problems in Refs. [4–11]. Agrawal and Messiter [3] showed that their theory could predict the gradual part of the pressure rise without the need to introduce an empirical slip velocity. Unfortunately, their theory was singular at the corner and could not describe the flow in the steep part of the pressure rise. In the present paper we briefly describe a new asymptotic theory that applies to the near corner region covering the steep part of the pressure rise.