MODELLING THE BEHAVIOUR OF HOMOGENEOUS EXPLOSION IN A CLOSED VESSEL WITH THREE-STEP REACTION MODEL
Abstract
This study presents numerical simulations of a spatially homogeneous explosion in a closed vessel having thermal and chain-branching reaction models. The simulations are performed using three-step models of chemical kinetics. A fourth-order Runge-Kutta method was used to carry out the simulations. The result of the study revealed that when values of crossover temperature, , is sufficiently less than unity, the homogeneous explosion is described by the purely three-step chain-branching reaction model. While for greater than unity, the homogeneous explosion exhibits a considerable thermal explosion structure. This indicates that the crossover temperature influence the nature of explosion and hence determines the exothermicity of the reaction (thermal explosion) or its chain character (branched-chain explosion). For more exploration, there may be need to extend to an asymptotic method. For further study, it was suggested that higher values of activation energy and the crossover temperature may be investigated.
References
Birkan, M. A. and Kassoy, D. R. (1986) the unified theory for chain branching thermal explosions with dissociation-recombination and confinement effects. Combustion Science and Technology. Gordon and Breach, Great Britain. 44, pp.223-256.
Blythe, P. A., Kapila, A. K. and Short, M. (2006) Homogeneous ignition for a three-step chain-branching reaction model. Kluwer Academic Publishers, Netherlands. 7(34).
Bonilla, L. L., Sanchez, A. L. and Carretero M. (2000). The description of homogeneous branched-chain explosions with slow radical recombination by self-adjusting time scales. Journal of Applied Mathematics. SIAM. 61(2), PP.528-550
Dold, J. W. and Kapila, A. K. (1991) Comparison between Shock initiations of Detonation Using Thermally-Sensitive and Chain-Branching Chemical Models. Combustion and Flame. Elsevier Science publishing Co., Inc. 85, pp.185-194
Espenson, J. H. (1995) Chemical kinetics and reaction mechanisms. McGraw-Hill, Inc. Singapore. Second Edition.
Gray B. F. and Yang C. H. (1965). On the unification of the thermal and chain theories of explosion limits. The Journal of Physical Chemistry, 69(8), pp. 2747-2750
Hwang, S. M., Ryu S. O., DeWitt K. J. and Rabinowitz M. J. (2005) High temperature rate coefficient measurements H + O2 chain-branching and chain-termination reaction. Chemical Physics Letters. Elsevier United State, 408 pp. 107-111
Kapila, A. K. (1978) Homogeneous branched-chain explosion: Initiation to completion. Journal of Engineering Mathematics. Alphen aan den Rijn, Netherlands. 12(3), pp.221-235.
Liang, Z. and Bauwens, L. (2005) Detonation structure with pressure-dependent chain-branching kinetics. Proceedings of the Combustion Institute. Elsevier United State. 30, pp.1879-1887
Louise and Spilsbury, R. (2007) CHEMICAL REACTIONS-Building blocks of matter. Heinemann Library, Great Britain.
Ng, H. D. and Lee, J. H. S. (2003) Direct initiation of detonation with a multi-step reaction scheme. Journal of Fluid Mechanics. 476(3), pp.179-211.
Pilling, M. J. and Seakins, P. W. (1995) Reaction kinetics. Oxford University Press, New York, United States.
Sharpe, G. J. and Maflahi, N. (2006) Homogeneous explosion and shock initiation for a three-step chain-branching reaction model. Journal of fluid mechanics. Cambridge University Press,566, pp. 163-194
Sharpe, G. J. and Short, M. (2004) Shock-induced ignition of thermally sensitive explosives. IMA Journal of Applied Mathematics, 69, pp.493-520
Short, M. and Dold, J. W. (1996) Linear Stability of a Detonation Wave with a Model Three-Step Chain-Branching Reaction. Mathematical Computer Modelling. 24(8), pp.155-123
Short, M. and Quirk, J. J. (1997) On the non-linear stability and detonability limit of a detonation wave for a model three-step chain branching reaction. Journal of Fluid Mechanics. 339(2), pp.89-119
Turner, P. R. (1994) Numerical analysis. Macmillan Press Ltd, Houndmills, Malaysia.
Copyright (c) 2023 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
