Analysing combustion waves in a model with chain branching

Authors

  • Harvinder Singh Sidhu
  • V. V. Gubernov
  • Geoffry N. Mercer

DOI:

https://doi.org/10.21914/anziamj.v49i0.310

Abstract

We analyse the travelling wave solutions in an adiabatic model with two-step chain branching reaction mechanism. We show that the behaviour of the combustion waves are similar to the case of the corresponding nonadiabatic one-step reaction, namely there is residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. We also analyse how the speed of the travelling wave solutions and the residual amount of fuel left behind the fuel change, as control parameters are varied. References
  • 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
  • G. Joulin, A. Linan, G. S. S. Ludford, N. Peters and C. Schmidt-Laine, Flames with chain-branching/chain-breaking kinetics, SIAM J. Appl. Math., 45, 1985, 420--434.
  • A. Linan, A theoretical analysis of premixed flame propagation with an isothermal chain-branching reaction Insituto Nacional de Technica Aerospacial ``Esteban Terradas'' (Madrid), USAFOSR Contract No. E00AR68-0031, Technical Report No. 1, 1971.
  • A. Makino, Fundamental aspects of the heterogeneous flame in the self propagating hightemperature synthesis (SHS) process, Prog. Energy Combust. Sci., 27, 2001, 1--74.
  • A. G. Merzhanov and E. N. Rumanov, Physics of reaction waves, Rev. Mod. Phys., 71, 1999, 1173--1211. doi:10.1103/RevModPhys.71.1173
  • H. Pitsch, and M. Bollig, 1994, FlameMaster, A Computer Code for Homogeneous and One-Dimensional Laminar Flame Calculations, RWTHAachen, Institut fur Technische Mechanik, 1994.
  • A. L Sanchez, G. Balakrishnan, A. Linan and F. A. Williams, Relationships between bifurcation and numerical analyses for ignition of hydrogen-air diffusion flames, Combust. Flame, 105, 1996, 569--590.
  • A. L. Sanchez, A. Lepinette, M. Bolling, A. Linan, and B. Lazaro, 2000, The reduced kinetic description of lean premixed combustion, Combust. Flame, 123, 2000, 436--464.
  • K. Seshadri, N. Peters and F. A. Williams, 1994, Asymptotic analyses of stoichiometric and lean hydrogen-air flames, Combust. Flame, 96, 1994, 407--427.
  • P. L. Simon, S. Kallidasis and S. K.Scott, Inhibition of flame propagation by an endothermic reaction, IMA J. Appl. Math., 68, 2003, 537--562. doi:10.1093/imamat/68.5.537
  • J. K. Bechtold and C. K. Law, The structure of premixed methane-air flames with large activation energy, Combust. Flame, 97, 1994, 317--338. doi:10.1016/0010-2180(94)90024-8
  • J. Warnatz, U. Maas and R. W. Dibble, Combustion: physical and chemical fundamentals, modelling and simulation, experiments, pollutant formation, Springer, Berlin, 1996.
  • 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
  • C. K. Westbrook and F. Dryer, Simplified reaction mechanisms for the oxidation of Hydrocarbon Fuels in Flames, Combust. Sci. Tech., 27, 1981, 31--43.
  • Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich and G. M Makhviladze, The mathematical theory of combustion and explosions Consultants Bureau, New York, 1985.
  • J. W. Dold, R. O. Weber, R. W. Thatcher and A. A. Shah, Flame Ball With Thermally Sensitive Intermediate Kinetics Combust., Combust. Theory Mod., 7, 2003, 175--203.
  • 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.
  • V. V. Gubernov, G. N. Mercer, H. S. Sidhu and R. O. Weber, Evans function stability of combustion waves. SIAM J. Appl. Math., 63, 2003, 1259--1275. doi:10.1137/S0036139901400240

Published

2007-10-15

Issue

Section

Proceedings Engineering Mathematics and Applications Conference