Asymptotic Solutions for Supersonic Rotational Flow around a Convex Corner Using a New Coordinate System

摘要

A coordinate system consisting of the left-running characteristics (alpha = constant) and the streamlines (psi = constant) is used. The governing equations are derived in terms of alpha and psi for a two-dimensional, steady, supersonic, rotational, inviscid flow of a perfect gas. The equations are applied to the problem of an initially parallel, supersonic, rotational flow which expands around a convex corner. The velocity of the incoming flow at the wall is considered to be either supersonic or sonic. For each case, solutions uniformly valid in the region near the leading characteristic and in the region near the corner are found for the Mach angle and flow-deflection angle in terms of their values on the leading characteristic and at the corner. In the second case, a transonic similarity solution is found and composite solutions are constructed for each region. Comparisons are made with existing exact numerical results. (Author)