Viscous solution of the triple shock reflection problem

TL;DR

This study numerically investigates how viscosity influences shock reflection mechanisms in triple-shock configurations, revealing that viscosity affects flow features but Kelvin-Helmholtz instabilities are unlikely to trigger rapid reactions in detonations.

Contribution

It provides new insights into the role of viscosity in shock reflection phenomena and the absence of Kelvin-Helmholtz instabilities in detonation-related shock interactions.

Findings

Viscosity influences shock reflection mechanisms.

A small wall jet and vortex formation depend on Reynolds number.

Kelvin-Helmholtz instabilities are absent at relevant Reynolds numbers.

Abstract

The reflection of a triple-shock configuration was studied numerically in two dimensions using the Navier-Stokes equations. The flow field was initialized using three shock theory, and the reflection of the triple point on a plane of symmetry was studied. The conditions simulated a stoichiometric methane-oxygen detonation cell at low pressure on time scales preceding ignition, when the gas was assumed to be inert. Viscosity was found to play an important role on some shock reflection mechanisms believed to accelerate reaction rates in detonations when time scales are small. A small wall jet was present in the double Mach reflection and increased in size with Reynolds number, eventually forming a small vortex. Kelvin-Helmholtz instabilities were absent and there was no Mach stem bifurcation at Reynolds numbers corresponding to when the Mach stem had travelled distances on the scale of the induction length. Kelvin-Helmholtz instabilities are found to not likely be a source of rapid reactions in detonations at time scales commensurate with the ignition delay behind the Mach stem.