Abstract
A new criterion for thermal explosion in exothermically reacting systems for the case of arbitrary one-step conversions is proposed. The computation method is based on the analysis of the equation of maximum temperatures obtained for closed systems taking into account reactant consumption. The dependence of the maximum temperature on the Semenov and Todes parameters is bistable and the critical conditions are determined by the extremum conditions on the relevant parametric diagrams. The demarcation lines of ignition in the Todes criterion–Semenov criterion parametric plane are calculated for second-order exothermic reactions. Comparison of numerical and analytical calculations shows that they are in satisfactory agreement.
Similar content being viewed by others
References
D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics (Nauka, Moscow, 1987; Plenum, New York, 1969).
P. J. Coelho and N. Peters, “Numerical Simulation of a Mild Combustion Burner,” Combust. Flame 124 (3), 503–518 (2001).
M. A. Korchagin, V. Yu. Filimonov, E. V. Smirnov, and N. Z. Lyakhov, “Thermal Explosion of a Mechanically Activated 3Ni + Al Mixture,” Fiz. Goreniya Vzryva 46 (1), 48–53 (2010) [Combust., Expl., ShockWaves46 (1), 41–46 (2010)].
G. N. Gorelov and V. A. Sobolev, “Duck-Trajectories in a Thermal Explosion Problem,” Appl. Math. Lett. 5 (6), 3–6 (1992).
P. Gray and P. R. Lee, “Thermal Explosion and the Effect of Reactant Consumption on Critical Conditions,” Combust. Flame 9, 201–203 (1965).
D. R. Kassoy and A. Linan, “The Influence of Reactant Consumption on the Critical Conditions for Homogeneous Thermal Explosion,” Int. J. Mech. Appl. Math. 31 (1), 99–112 (1978).
B. F. Gray, “Critical Behaviour in Chemically Reacting Systems: An Exactly Soluble Model,” Combust. Flame 40, 37–45 (1973).
A. R. Shouman and S. A. El-Sayed, “Accounting for Reactant Consumption in the Thermal Explosion Problem. Part II: A Direct Solution with Application to the Frank-Kamenetskii Problem,” Combust. Flame 108 (1), 361–386 (1997).
A. R. Shouman and S. A. El-Sayed, “Accounting for Reactant Consumption in the Thermal Explosion Problem III. Criticality Conditions for the Arrhenius Problem,” Combust. Flame 113 (1), 212–223 (1998).
Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, Mathematical Theory of Combustion and Explosion (Nauka, Moscow, 1980; Plenum, New York, 1985).
F. G. Tricomi, Integral Equations (Interscience, New York, 1957).
A. G. Merzhanov, E. G. Zelikman, and V. G. Abramov, “Degenerate Modes of Thermal Explosion,” Dokl. Akad. Nauk SSSR 180 (1), 639–642 (1968).
A. N. Peregudov and V. T. Gontkovskaya, “Determination of the Boundaries of the Degeneracy Region of Thermal Explosion,” Dokl. Akad. Nauk 357 (4), 498–500 (1997).
J. E. Johnsson, P. Glarborg, and K. Dam-Johansen, “Kinetics of Homogeneous Nitrous Oxide Decomposition,” Combust. Flame 99, 212–223 (1994).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.Yu. Filimonov, K.B. Koshelev.
Published in Fizika Goreniya i Vzryva, Vol. 53, No. 5, pp. 53–63, September–October, 2017.
Rights and permissions
About this article
Cite this article
Filimonov, V.Y., Koshelev, K.B. Thermal explosion in closed systems: Criteria and critical conditions. Combust Explos Shock Waves 53, 538–547 (2017). https://doi.org/10.1134/S0010508217050069
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0010508217050069