Theory of weakly nonlinear self-sustained detonations

Handle URI:
http://hdl.handle.net/10754/622344
Title:
Theory of weakly nonlinear self-sustained detonations
Authors:
Faria, Luiz ( 0000-0001-8159-4442 ) ; Kasimov, Aslan R.; Rosales, Rodolfo R.
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.
KAUST Department:
Applied Mathematics and Computational Science Program
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.
Publisher:
Cambridge University Press (CUP)
Journal:
Journal of Fluid Mechanics
Issue Date:
3-Nov-2015
DOI:
10.1017/jfm.2015.577
Type:
Article
ISSN:
0022-1120; 1469-7645
Sponsors:
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.
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program

Full metadata record

DC FieldValue Language
dc.contributor.authorFaria, Luizen
dc.contributor.authorKasimov, Aslan R.en
dc.contributor.authorRosales, Rodolfo R.en
dc.date.accessioned2017-01-02T09:08:27Z-
dc.date.available2017-01-02T09:08:27Z-
dc.date.issued2015-11-03en
dc.identifier.citationFaria 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.en
dc.identifier.issn0022-1120en
dc.identifier.issn1469-7645en
dc.identifier.doi10.1017/jfm.2015.577en
dc.identifier.urihttp://hdl.handle.net/10754/622344-
dc.description.abstractWe 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.en
dc.description.sponsorshipL.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.en
dc.publisherCambridge University Press (CUP)en
dc.subjectchaosen
dc.subjectdetonation wavesen
dc.subjectnonlinear instabilityen
dc.titleTheory of weakly nonlinear self-sustained detonationsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.identifier.journalJournal of Fluid Mechanicsen
dc.contributor.institutionDepartment of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, United Statesen
kaust.authorFaria, Luizen
kaust.authorKasimov, Aslan R.en
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