Nonlinear dynamics of self-sustained supersonic reaction waves: Fickett's detonation analogue

TL;DR

This paper explores the complex behavior of self-sustained supersonic reaction waves using an extended Fickett's model, revealing transitions from steady to chaotic waves and clarifying the origins of detonation instability.

Contribution

It introduces a modified Fickett's detonation model with a state-dependent energy term, predicting stable, pulsating, and chaotic wave behaviors, and explains the physical mechanisms behind wave instability.

Findings

Stable and pulsating waves are predicted.

Wave transitions follow Feigenbaum's route to chaos.

Clarifies physical origin of detonation instability.

Abstract

The present study investigates the spatio-temporal variability in the dynamics of self-sustained supersonic reaction waves propagating through an excitable medium. The model is an extension of Fickett's detonation model with a state dependent energy addition term. Stable and pulsating supersonic waves are predicted. With increasing sensitivity of the reaction rate, the reaction wave transits from steady propagation to stable limit cycles and eventually to chaos through the classical Feigenbaum route. The physical pulsation mechanism is explained by the coherence between internal wave motion and energy release. The results obtained clarify the physical origin of detonation wave instability in chemical detonations previously observed experimentally.