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Oscillatiory combustion waves in a chain branching model

ANZIAM Journal
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  • Chemistry


We consider an adiabatic model with a two step chain branching reaction mechanism, and use a numerical scheme to show that as the parameter characterizing the fuel properties is increased, the combustion waves begin to exhibit oscillatory behaviour. We show that this behaviour becomes more complex as the fuel parameter is further increased until extinction of the combustion reaction occurs. References A. Bayliss and B. J. Matkowsky, Two routes to chaos in condensed phase combustion, SIAM J. Appl. Math., 50, 1990, 437--459. J. W. Dold and R. O. Weber, Reactive-Diffusive stability of planar flames with modified Zeldovich-Linan kinetics. In: F.J. Higuera, J. Jime'nez and J.M. Vega (Eds), Simplicity, Rigor and Relevance in Fluid Mechanics: A volume in honor of Amable Linan, CIMNE (Barcelona), 2004. C. -G. Feng, Q. -X. Zeng, L. -Q. Wang and X. Fang, Study of the mechanism of oscillatory solid-phase combustion by a non-linear chemical kinetic model, J. Chem. Soc. Faraday Trans., 1996, 92, 2971--2975. doi:10.1039/FT9969202971 V. V. Gubernov, G. N. Mercer, H. S. Sidhu and R. O. Weber, Evans function stability of nonadiabatic combustion waves, Proc. R. Soc. Lond. A, 460, 2004, 2415--2435.doi:10.1098/rspa.2004.1285 V. V. Gubernov, H. S. Sidhu, and G. N. Mercer, Combustion waves in a model with chain branching reaction and their stability, Combust. Theory Mod., 12, 2008, 407--431. doi:10.1080/13647830701716948 V. V. Gubernov, H. S. Sidhu, and G. N. Mercer, Combustion waves in a model with chain branching reaction, J. Math. Chem., 39, 2006, 1--14. doi:10.1007/s10910-005-9000-x D. W. Mikolaitis, Adiabatic flame speeds and the {Z}eldovich-{L}inan model, Combust. Sci. and Tech., 49, 1986, 277--288.doi:10.1080/00102208608923918 A. G. Merzhanov and E. N. Rumanov, Physics of reaction waves, Rev. Mod. Phys., 71, 1999, 1173--1211. H. S. Sidhu, V. V Gubernov and G. N. Mercer, Analysing combustion waves in a model with chain branching, In Geoffry N. Mercer  and A. J. Roberts, editors, Proceedings of the 8th Biennial Engineering Mathematics and Applications Conference, EMAC-2007, vol 49 of ANZIAM J., October 2007, pages C100-C115, R. O. Weber, G. N. Mercer, H. S. Sidhu and B. F. Gray, Combustion waves for gases ($Le = 1$) and solids ($Le \rightarrow 1$), Proc. R. Soc. Lond. A, 453, 1997, 1105--1118. doi:10.1098/rspa.1997.0062

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