Theory of weakly nonlinear self-sustained detonations

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Journal of Fluid Mechanics, ISSN: 0022-1120, Vol: 784, Issue: 20, Page: 163-198

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Luiz M. Faria; Aslan R. Kasimov; Rodolfo R. Rosales
Cambridge University Press (CUP)
Physics and Astronomy; Engineering; chaos; detonation waves; nonlinear instability
article description
We propose a theory of weakly nonlinear multidimensional 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 multidimensional detonations.