Properties of reaction fronts in a non-adiabatic two stage exothermic-endothermic competitive reaction scheme

Abstract

We numerically derive the properties of reaction fronts arising in a pre-mixed one dimensional two staged non-adiabatic competitive exothermic-endothermic reaction scheme where both reaction pathways compete for the same fuel. We utilise FlexPDE and the method of lines to obtain numerical solutions for properties such as the front speed and stability over a range of parameter values such as the Lewis number and the ratios of enthalpies and activation energies. Steady and pulsating speeds are demonstrated for specific regions of the parameter space. We also show that in some circumstances there exists a chaotic regime of combustion wave propagation. References

• M. J. Antal and G. Varhegyi, Cellulose Pyrolysis Kinetics - The Current State of Knowledge, Industrial and Engineering Chemistry Research, 34(3):703–717, 1995 doi:10.1021/ie00042a001
• R. Ball, A. C. McIntosh and J. Brindley, Thermokinetic Models for Simultaneous Reactions: a Comparative Study, Combustion Theory and Modelling, 3(3):447–468, 1999. doi:10.1088/1364-7830/3/3/302
• S. K. Chan and R. Turcotte, Onset Temperatures in Hot Wire Ignition of AN-Based Emulsions, Propellants Explosives Pyrotechnics, 34(1):41–49, 2009. doi:10.1002/prep.200700288
• FlexPDE\(^{TM}\), PDE Solutions Inc, http://www.pdesolutions.com.
• V. V. Gubernov, A. Kobolov, A. Polezhaev and H. Sidhu, Period Doubling and Chaotic Transient in a Model of Chain-Branching Combustion Wave Propagation, Proceedings of the Royal Society A, 2011. doi:10.1098/rspa.2009.0668
• V. V. Gubernov, J. J. Sharples, H. S. Sidhu, A. C. McIntosh and J. Brindley, Properties of Combustion Waves in the Model with Competitive Exo- and Endothermic Reactions, Journal of Mathematical Chemistry, 50(8):2130–2140, 2012. doi:10.1007/s10910-012-0021-y
• V. V. Gubernov, H. S. Sidhu, G. N. Mercer, The Effect of Ambient Temperature on the Propagation of Nonadiabatic Combustion Waves, Journal of Mathematical of Mathematical Chemistry, 37(2):149–162, 2005. doi:10.1007/s10910-004-1447-7
• A. Hmaidi, A. C. McIntosh and J. Brindley, A Mathematical Model of Hotspot Condensed Phase Ignition in the Presence of a Competitive Endothermic Reaction, Combustion Theory and Modelling, 14(6):893–920, 2010. doi:10.1080/13647830.2010.519050
• D. A. Kessler, V. N. Gamezo and E. S. Oran, Simulations of Flame Acceleration and Deflagration-to-Detonation Transitions in Methane-Air Systems, Combustion and Flame, 157(11):2063–2077, 2010. doi:10.1016/j.combustflame.2010.04.011
• F. Liu, D. L. S. McElwain and C. P. Please, Simulation of Combustion Waves for Two-Stage Reactions, Proceedings of the 8th Biennial Computational Techniques and Applications Conference (CTAC97), pages 385–392, 1998.
• A. Makino, Fundamental Aspects of the Heterogeneous Flame in the Self-Propagating High-Temperature Synthesis (SHS) Process, Progress in Energy and Combustion Sciences, 27(1):1–74, 2001. doi:10.1016/S0360-1285(00)00004-6
• A. G. Merzhanov and E. N. Rumanov, Physics of Reaction Waves, Reviews of Modern Physics, 71(4):1173–1211, 1999. doi:10.1103/RevModPhys.71.1173
• C. P. Please, F. Liu and D. L. S. McElwain, Condensed Phase Combustion Travelling Waves with Sequential Exothermic or Endothermic Reactions, Combustion Theory and Modelling, 7(1):129–143, 2003. doi:10.1088/1364-7830/7/1/307
• W. E. Schiesser, The numerical method of lines: Integration of Partial Differential Equations, Academic Press, Inc, 1991.
• J. J. Sharples, H. S. Sidhu, A. C. Mcintosh, J. Brindley and V. V. Gubernov, Analysis of Combustion Waves Arising in the Presence of a Competitive Endothermic Reaction, IMA Journal of Applied Mathematics, 77(1):18–31, 2012. doi:10.1093/imamat/hxr072
• V. P. Sinditskii, V. Y. Egorshev, A. I. Levshenkov and V. V. Serushkin, Ammonium nitrate: Combustion Mechanism and the Role of Additives, Propellants Explosives Pyrotechnics, 30(4):269–280, 2005. doi:10.1002/prep.200500017
• J. Subrahmanyam and M. Vijayakumar, Self-Propagating High-Temperature Synthesis, Journal of Materials Science, 27(23):6249–6273, 1992. doi:10.1007/BF00576271
• R. Turcotte, S. Goldthorp, C. M. Badeen and S. K. Chan, Hot-Wire Ignition of AN-Based Emulsions, Propellants Explosives Pyrotechnics, 33(6):472–481, 2008. doi:10.1002/prep.200700276
• S. Walia, R. O. Weber, K. Latham, P. Petersen, J. T. Abrahamson, M. S. Strano, and K. Kalantar-zadeh, Oscillatory Thermopower Waves Based on Bi\(_2\)Te\(_3\) Films, Advanced Functional Materials, 21(11):2072–2079, 2011. doi:10.1002/adfm.201001979
• R. O. Weber, G. N. Mercer, H. S. Sidhu and B. F. Gray, Combustion Waves for Gases (\(Le=1\)) and Solids (\(Le\rightarrow \infty \)), Proceedings of the Royal Society of London A, 453(1960):1105–1118, 1997. doi:10.1098/rspa.1997.0062
• W. Y. S. Wee, J. J. Sharples, H. S. Sidhu and V. V. Gubernov, Analysis of a Two-Stage Competitive Endothermic-Exothermic Reaction Scheme, Proceedings of the 40th Australian Chemical Engineering Conference (CHEMECA 2012), submitted June 2012.