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Journal of Applied Nonlinear Dynamics 4(4) (2015) 425--437 | DOI:10.5890/JAND.2015.11.008

Ranis N. Ibragimov$^{1}$; Sayavur Bakhtiyarov$^{2}$

$^{1}$ GE Global Research, 1 Research Circle, Niskayuna, NY 12309, USA

$^{2}$ Department of Mechanical Engineering, New Mexico Tech, Socorro, NM 87801, USA

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Abstract

The main purpose is to develop an analytic approach for investigating the wave front propagation on a surface of a cylinder that can be used a descriptor of a detonation engine. The analysis is based on a weakly nonlinear approximated gas dynamic equations with incorporated approximation of the Korobeinkov’s chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. We found that the wave fronts can be expressed analytically in explicit form for special classes of flow (e.g. isentropic gas flow). In more general cases, the dynamics of wave fronts can still be determined explicitly provided that the wave front is known at initial time and the exact solution, or its approximation is known a priori, e.g. from experimental or numerical analysis.

Acknowledgments

The author is grateful to Narendra Joshi from GE Corporate for productive discussions on the topic.

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