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Theory of weakly nonlinear self-sustained detonations

Published online by Cambridge University Press:  03 November 2015

Luiz M. Faria ,
Aslan R. Kasimov  and
Rodolfo R. Rosales
Luiz M. Faria
Affiliation:
Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Room 4-2226, 4700 KAUST, Thuwal 23955-6900, Saudi Arabia Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Aslan R. Kasimov*
Affiliation:
Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Room 4-2226, 4700 KAUST, Thuwal 23955-6900, Saudi Arabia
Rodolfo R. Rosales
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Nonlinear Dynamical Systems: Chaos Compressible Flows: Detonation waves Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 784 , 10 December 2015 , pp. 163 - 198
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Copyright
© 2015 Cambridge University Press 

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