Theory of weakly nonlinear self sustained 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.
Cite
@article{arxiv.1407.8466,
title = {Theory of weakly nonlinear self sustained detonations},
author = {Luiz M. Faria and Aslan R. Kasimov and Rodolfo R. Rosales},
journal= {arXiv preprint arXiv:1407.8466},
year = {2023}
}