Theory of weakly nonlinear self-sustained detonations

Embargo End Date
2016-05-03

Type
Article

Authors
Faria, Luiz
Kasimov, Aslan R.
Rosales, Rodolfo R.

KAUST Department
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2015-11-03

Print Publication Date
2015-12

Date
2015-11-03

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.

Citation
Faria LM, Kasimov AR, Rosales RR (2015) Theory of weakly nonlinear self-sustained detonations. Journal of Fluid Mechanics 784: 163–198. Available: http://dx.doi.org/10.1017/jfm.2015.577.

Acknowledgements
L.M.F. and A.R.K. gratefully acknowledge research support by King Abdullah University of Science and Technology (KAUST). The research by R.R.R. was partially supported by NSF grants DMS-1007967, DMS-1115278, DMS-1318942, and by KAUST during his research visit to KAUST in November 2013. L.M.F. would like to thank S. Korneev and D. Ketcheson for their help with numerical computations.

Publisher
Cambridge University Press (CUP)

Journal
Journal of Fluid Mechanics

DOI
10.1017/jfm.2015.577

arXiv
1407.8466

Additional Links
https://dspace.mit.edu/bitstream/1721.1/116003/1/1407.8466.pdf

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