Journal of Applied Nonlinear Dynamics
ApproximateWeakly NonlinearModel of gas Dynamics EquationsWith Utilized Korobeinikov’s Chemical Reaction
Journal of Applied Nonlinear Dynamics 4(4) (2015) 425437  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 twodimensional detonation field on a surface of a twodimensional 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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