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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Nonlinear Evolution and Persistence of Cellular Patterns in Self-Sustained Two-Dimensional Detonations

Journal of Vibration Testing and System Dynamics 6(4) (2022) 387--411 | DOI:10.5890/JVTSD.2022.12.004

S. Roy Choudhury$^1$, Hardeo M. Chin$^2$, Sheikh Salauddin$^3$, Kareem A. Ahmed$^3$

$^1$ Department of Mathematical Sciences, University of Central Florida, Orlando, FL 32816

$^2$ Physics Division, Lawrence Livermore National Laboratory, Livermore, CA, 94550

$^3$ Department of Mechanical and Aerospace Engineering, Propulsion and Energy Research Laboratory, University of Central Florida, Orlando, FL 32816

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Abstract

A nonlinear theory for the development and persistence of cellular two-dimensional patterns behind the shock front in self-sustained detonations is developed. A recent, significantly simplified and carefully-validated, detonation model is used as the basis for the analysis.In the spirit of earlier investigations of a variety of hydrodynamic and hydromagnetic instabilities, crossed-field microwave sources, tokamak edge plasmas, and other areas, our first approach here replaces the actual numerically computed equilibrium profiles by box-shaped ones having a jump discontinuity. The results for both the shapes and dimensions of the persistent two-dimensional cells picked out by our nonlinear analysis agree well with those in earlier simulations for the same sets of parameters. Our theory goes further, allowing predictions of non-trivial regions in the multiparameter space where persistent two-dimensional cells are possible. The only significant discrepancy from numerical results is in the wavelength of the cellular patterns along the reaction channel.Approximations of actual equilibrium profiles by step discontinuities, as done here, are most accurate for long-wavelength regimes where the waves essentially do not register the actual spatial profiles. Future work towards remedying the above discrepancy will be based on generalized normal forms in the spirit of what is usually referred to as 'collective coordinate' analysis, involving coefficients which are integrals over the spatially inhomogeneous equilibrium profiles.

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