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The effect of Lewis number variation on combustion waves in a model with chain-branching reaction

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Abstract

In this paper we investigate the linear stability and properties of the travelling premixed combustion waves in a model with two-step chain-branching reaction mechanism in the adiabatic limit in one spatial dimension. It is shown that the Lewis number for fuel has a significant effect on the properties and stability of premixed flames, whereas the Lewis number for the radicals has only quantitative (but not qualitative) effect on the combustion waves. We demonstrate that when the Lewis number for fuel is less than unity the flame speed is unique and is a monotonically decreasing function of the dimensionless activation energy. The combustion wave is stable and exhibits extinction for finite values of activation energy as the flame speed decreases to zero. For fuel Lewis number greater than unity the flame speed is a double-valued function. The slow solution branch is shown to be unstable whereas the fast solution branch is either stable or exhibits the onset of pulsating instabilities via the Hopf bifurcation. The evolution of these instabilities leads to flame extinction.

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References

  1. Y.B. Zeldovich, Teorii rasprostranenia plameni. Zh. Phys. Khim. 22, 27–49 (1948), English translation in NACA TM 1282 (1951)

    Google Scholar 

  2. A. Liñán, 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)

  3. Joulin G., Liñán A., Ludford G.S.S., Peters N.,Schmidt-Lainé C. (1985) Flames with chain-branching/chain-breaking kinetics. SIAM J. Appl. Math. 45:420–434

    Article  Google Scholar 

  4. Chao B.H., Law C.K. (1994) Laminar flame propagation with volumetric heat loss and chain branching-termination reactions. Int. J. Heat Mass Transfer 37:673–680

    Article  CAS  Google Scholar 

  5. Joulin G., Clavin P. (1979) Linear stability analysis of nonadiabatic flames: a thermal-diffusional model. Combust. Flame 1979:139–153

    Article  Google Scholar 

  6. Seshardi K., Peters N. (1983) The influence of stretch on a premixed flame with two-step kinetics. Combust. Sci. Technol. 33:35–63

    Article  Google Scholar 

  7. Mikolaitis D.W. (1986) Adiabatic flame speeds and the Zeldovich-Liñán model. Combust. Sci. Technol 49:277–288

    Article  CAS  Google Scholar 

  8. Tam R.Y. (1988) Stretch response and large heat release in the Zeldovich-Liñán model. Combust. Sci. Technol. 60:125–142

    Article  CAS  Google Scholar 

  9. Tam R.Y. (1988) Damköler-number ratio asymptotics of the Zeldovich-Liñán model. Combust. Sci. Technol. 62:297–309

    Article  CAS  Google Scholar 

  10. J.W. Dold, Premixed flames modelled with thermally sensitive intermediate branching kinetics. Combust. Theor. Model published online (2007)

  11. Gubernov V.V., Sidhu H.S., Mercer G.N. (2006) Combustion waves in a model with chain branching reaction. J. Math. Chem. 39:1–14

    Article  CAS  Google Scholar 

  12. Gubernov V.V., Mercer G.N., Sidhu H.S., Weber R.O. (2004) Evans function stability of nonadiabatic combustion waves. Proc. R. Soc. Lond. A 460:1259–1275

    Google Scholar 

  13. V.V. Gubernov, H.S. Sidhu, G.N. Mercer, Combustion waves in a model with chain branching reaction and their stability. Submitted to Combust. Theor. Model (2007)

  14. Evans J.W. (1972) Nerve axon equations: III stability of the nerve impulses. Indiana Univ. Math. J. 22:577–593

    Article  Google Scholar 

  15. Gubernov V.V., Mercer G.N., Sidhu H.S. (2006) Generalized compound matrix method. Appl. Math. Lett. 19:458–463

    Article  Google Scholar 

  16. Weber R.O., Mercer G.N., Sidhu H.S., Gray B.F. (1997) Combustion waves for gases (Le = 1) and solids (Le → ∞). Proc. R. Soc. Lond. A 453:1105–1118

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. P.N. Lebedev Physical Institute of Russian Academy of Sciences, 53, Leninskii Prospect, 119991, Moscow, Russia

    V. V. Gubernov, A. V. Kolobov & A. A. Polezhaev

  2. School of Physical, Environmental and Mathematical Sciences, University of New South Wales at the Australian Defence Force Academy, Canberra, ACT, 2600, Australia

    H. S. Sidhu & G. N. Mercer

Authors
  1. V. V. Gubernov
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  2. H. S. Sidhu
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  3. G. N. Mercer
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  4. A. V. Kolobov
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  5. A. A. Polezhaev
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Correspondence to H. S. Sidhu.

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Gubernov, V.V., Sidhu, H.S., Mercer, G.N. et al. The effect of Lewis number variation on combustion waves in a model with chain-branching reaction. J Math Chem 44, 816–830 (2008). https://doi.org/10.1007/s10910-008-9363-x

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  • DOI: https://doi.org/10.1007/s10910-008-9363-x

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