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Theory of weakly nonlinear self-sustained detonations

Author(s)
Faria, Luiz M.; Kasimov, Aslan R.; Rosales, Rodolfo
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Abstract
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.
Date issued
2015-11
URI
http://hdl.handle.net/1721.1/116003
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Journal of Fluid Mechanics
Publisher
Cambridge University Press (CUP)
Citation
Faria, Luiz M. et al. “Theory of Weakly Nonlinear Self-Sustained Detonations.” Journal of Fluid Mechanics 784 (November 2015): 163–198 © 2015 Cambridge University Press
Version: Author's final manuscript
ISSN
0022-1120
1469-7645

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