Multiplicity of detonation regimes in systems with a multi-peaked thermicity

TL;DR

This paper explores multiple detonation regimes in systems with multi-peaked thermicity, revealing complex steady states, embedded shocks, and the stability of various solutions through analysis and simulations.

Contribution

It introduces a detailed analysis of multiple quasi-steady detonation states with multi-peaked thermicity, highlighting the stability and singularity behavior of these regimes.

Findings

Multiple steady states with different velocities exist.

Embedded shocks link weak and strong solutions behind sonic points.

Shocks are quasi-stable and influence detonation dynamics.

Abstract

The study investigates detonations with multiple quasi-steady velocities that have been observed in the past in systems with multi-peaked thermicity, using Fickett's detonation analogue. A steady state analysis of the travelling wave predicts multiple states, however, all but the one with the highest velocity develop a singularity after the sonic point. Simulations show singularities are associated with a shock wave which overtakes all sonic points, establishing a detonation travelling at the highest of the predicted velocities. Under a certain parameter range, the steady-state detonation can have multiple sonic points and solutions. Embedded shocks can exist behind sonic points, where they link the weak and strong solutions. Sonic points whose characteristics do not diverge are found to be unstable, and to be the source of the embedded shocks. Numerical simulations show that these shocks are only quasi-stable. This is believed to be due in part to a feature of the model which permits shocks anywhere behind a sonic point.