Study of the Instability and Dynamics of Detonation Waves using Fickett's Analogue to the Reactive Euler Equations

Abstract

The instability behaviour of detonation waves are studied using Fickett's model with a 2-step reaction model with separately controlled induction and reaction zones. This model acts as a simplified toy-model to the reactive Euler equations allowing for more clarity of the detonation phenomenon. We numerically simulate a 1D self-supported detonation and investigate the pulsating instability behaviour. We are able to clarify the governing mechanism behind the pulsations through a characteristic analysis describing the coupling that takes place between the amplification of the compressions waves and the alteration to the induction timing. We examine the acceleration phase of the pulsations and determine an analytical solution to describe the strength of the amplification. Fickett's model is as well shown to reproduce the same period doubling bifurcation with increasing sensitivity of the induction rate, and route to chaos as seen in the full reactive Euler equations.