Shock Polar Analysis

Abstract

The simplest case in shock reflection is the reflection of a planar shock by a planar obstacle. In this case both the state ahead of the shock and the state behind the shock are assumed to be constant, so that algebraic computation based on the Rankine-Hugoniot conditions and the entropy condition are enough to determine the reflection. The Rankine-Hugoniot conditions imply that, when the flow parameters on one side of the shock are given, the flow parameters on the other side must locate on a special locus, called shock polar. In this chapter we will give a careful analysis on the properties of the shock polar, and solve some problems on planar shock reflection by applying these properties. Furthermore, the discussion based on the shock polar analysis can also be applied to the problems on reflection of non-planar shock. When people apply the theory of partial differential equations to treat more complicated problems in gas dynamics, the careful discussion on shock polar also offers some necessary preparations.