Theory of weakly nonlinear self sustained detonations

TL;DR

This paper develops a theoretical framework for weakly nonlinear self-sustained detonations using asymptotic analysis, simplifying complex equations to a manageable model that captures key dynamical behaviors in multiple dimensions.

Contribution

It introduces a novel reduced model derived from the reactive Navier-Stokes equations that accurately describes the dynamics of weakly nonlinear detonations.

Findings

Model captures steady-state structure and stability spectrum.

Reproduces bifurcation sequences and chaos in 1D detonations.

Describes cellular structures in multi-dimensional detonations.

Abstract

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations.