Mathematics, Vol. 13, Pages 2419: Analysis of the Limiting Values of Thermodynamic Parameters for Jouguet Detonation

Mathematics doi: 10.3390/math13152419

Authors:
Andriy A. Avramenko
Igor V. Shevchuk
Margarita M. Kovetskaya
Yulia Y. Kovetska
Dmytro V. Anastasiev

An analytical study of the interaction of an ideal gas flow with a detonation wave was performed with account for the activation energy of chemical processes. Based on the modified Rankine-Hugoniot conditions, the effect of heat release on the limiting characteristics of detonation was analyzed. A dependence of the limiting value of the exponent Arrhenius number on the Mach number before the shock wave has been obtained. As the Mach number increases, the limiting value of the Arrhenius number decreases. An equation has been derived for determining the limiting value of the compression ratio in the shock wave. The effect of heat release intensity on the limiting compression ratio in a shock wave was elucidated. Also studied were effects of the Mach number and the Arrhenius number on the limiting compression ratio in a detonation wave. A condition for determining the critical value of the Arrhenius number necessary for the onset of detonation was obtained. Effects of the Mach number and the exponent of the Arrhenius number ArE on the critical value of the amplitude Arrhenius number ArА were discussed. The symmetry analysis of the gas flow parameters when passing through a detonation wave was performed.

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