Van der Waals shock polars with multiple or supersonic critical points

TL;DR

This paper demonstrates that the van der Waals equation of state allows for shock polars with multiple and supersonic critical points, revealing complex shock reflection phenomena not present in ideal gases.

Contribution

It shows that van der Waals eos can produce shock polars with multiple and supersonic critical points, expanding understanding of shock reflection behavior.

Findings

Van der Waals eos permits shock polars with supersonic critical points.

Multiple critical points can lead to four or more reflected shocks.

At least two reflected shocks are weak-type, with deflection angle increasing with shock strength.

Abstract

It is shown that the $\gamma$-van der Waals equation of state (eos) permits shock polars with supersonic critical points, corresponding to critical or strong-type shock reflections that are supersonic, which is not possible for ideal gas. It is also shown that general van der Waals eos permit polars with multiple critical points, corresponding to four or more reflected shocks for same deflection angle. Of these reflected shocks at least two are weak-type, i.e.\ deflection angle increasing with increasing shock strength, so that standard literature has no criteria to select one of the two. Both phenomena can be found with Hugoniot curves entirely in the region of convex and thermodynamically stable eos, avoiding the coexistence region and satisfying various shock stability criteria.