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arXiv · 1407.8466

Theory of weakly nonlinear self sustained detonations

Luiz M. Faria·Aslan R. Kasimov·Rodolfo R. Rosales
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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.

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Luiz M. Faria, Aslan R. Kasimov, Rodolfo R. Rosales. 2014-07-31. Theory of weakly nonlinear self sustained detonations. https://doi.org/10.1017/jfm.2015.577

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