Analytic characterization of oblique shock waves in flows around wedges

TL;DR

This paper provides an analytical solution for the maximum wedge angle and shock angle in compressible flow around wedges, enhancing understanding of shock wave behavior and detachment conditions.

Contribution

It introduces a novel analytic characterization of maximum wedge angles and shock angles in flow around wedges, which was previously not explicitly known.

Findings

Analytic expression for maximum wedge angle

Analytic characterization of shock angle at sonic transition

Determination of shock detachment conditions

Abstract

We consider the compressible flow around triangular wedges in which oblique shock waves are formed. We report on the novel analytic solution regarding the evaluation of the maximum wedge angle beyond which the shock wave detaches from the wedge to promote the formation of a bow shock. In addition, the limit line at which the flow past the oblique shock becomes sonic is determined whereby an analytic characterization for the corresponding shock angle is presented.