Thermal explosion in a hot gas mixture with organic gel fuel droplets |
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Authors: | Igor Goldfarb Vladimir Gol’dshtein J Barry Greenberg Ann Zinoviev |
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Affiliation: | (1) Department of Mathematics and Computer Sciences, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva, 84105, Israel;(2) Faculty of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa, 32000, Israel;(3) Department of Mathematics, Sami Shamoon College of Engineering, P.O. Box 45, Beer-Sheva, 84100, Israel |
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Abstract: | Recent experimental evidence has uncovered the peculiar behavior of certain gel droplets which, under appropriate ambient
thermal conditions, evaporate and burn in an oscillatory fashion. In this work a preliminary foray is made into the theoretical
analysis of the nature of the evolution of a hot gas mixture containing organic gel fuel droplets with oscillatory evaporation
within the context of thermal-explosion theory. The problem is modeled as a system of highly nonlinear singularly perturbed
ordinary differential equations. Non-dimensionalization of the equations enables identification of the parameters that play
a major role in determining the dynamical regimes of the system of equations. The method of integral manifolds is exploited
for the analysis and it is found, that for certain parametric regions, the system exhibits new dynamical behavior that is
quite different from that found for conventional liquid droplets. |
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Keywords: | Gel fuel droplets Singularly perturbed system of equations Theory of integral manifolds Thermal explosion |
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