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Pulsating instabilities in the Zeldovich–Liñán model

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Abstract

In this paper we numerically study the properties and stability of the travelling combustion waves in Zeldovich–Liñán model in the adiabatic limit in one spatial dimension. The structure and the properties of the combustion waves are found to depend on the recombination parameter, showing the relation between the characteristic times of the branching and recombination reactions. For small (large) values of this parameter the slow (fast) recombination regime of flame propagation is observed. The dependence of flame speed on the parameters of the model are studied in detail. It is found that the flame speed is unique, the combustion wave does not exhibit extinction as the activation energy is increased. The flame speed is a monotonically decreasing function of the activation energy. The results are compared to the prediction of the activation energy asymptotic analysis. It is found that the correspondence is good for the fast recombination regime and large activation energies. Stability of combustion waves is studied by using the Evans function method and direct integration of the governing partial differential equations. It is demonstrated that the combustion waves lose stability due to supercritical Hopf bifurcation. The neutral stability boundary is found in the space of parameters. The pulsating solutions emerging as a result of Hopf bifurcation are investigated. The amplitude of pulsations grow in a root type manner as the activation energy is increased beyond the neutral stability boundary.

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Authors and Affiliations

  1. I.E. Tamm Theory Department, P.N. Lebedev Physical Institute of Russian Academy of Sciences, 53, Leninskii prospect, Moscow, 119991, Russian Federation

    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

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

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Gubernov, V.V., Kolobov, A.V., Polezhaev, A.A. et al. Pulsating instabilities in the Zeldovich–Liñán model. J Math Chem 49, 1054–1070 (2011). https://doi.org/10.1007/s10910-010-9797-9

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  • DOI: https://doi.org/10.1007/s10910-010-9797-9

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