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Tr. Mat. Inst. Steklova, 2013, Volume 281, Pages 55–67 (Mi tm3465)  

This article is cited in 1 scientific paper (total in 2 paper)

Stability of a flame front in a divergent flow

A. G. Kulikovskiia, N. T. Pashchenkob

a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
b Research Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We study the evolution of perturbations on the surface of a stationary plane flame front in a divergent flow of a combustible mixture incident on a plane wall perpendicular to the flow. The flow and its perturbations are assumed to be two-dimensional; i.e., the velocity has two Cartesian components. It is also assumed that the front velocity relative to the gas is small; therefore, the fluid can be considered incompressible on both sides of the front; in addition, it is assumed that in the presence of perturbations the front velocity relative to the gas ahead of it is a linear function of the front curvature. It is shown that due to the dependence (in the unperturbed flow) of the tangential component of the gas velocity on the combustion front on the coordinate along the front, the amplitude of the flame front perturbation does not increase infinitely with time, but the initial growth of perturbations stops and then begins to decline. We evaluate the coefficient of the maximum growth of perturbations, which may be large, depending on the problem parameters. It is taken into account that the characteristic spatial scale of the initial perturbations may be much greater than the wavelengths of the most rapidly growing perturbations, whose length is comparable with the flame front thickness. The maximum growth of perturbations is estimated as a function of the characteristic spatial scale of the initial perturbations.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00034
Ministry of Education and Science of the Russian Federation NSh-1303.2012.1
This work was supported by the Russian Foundation for Basic Research (project no. 11-01-00034) and by a grant of the President of the Russian Federation (project no. NSh-1303.2012.1).


DOI: https://doi.org/10.1134/S0371968513020064

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 281, 49–61

Bibliographic databases:

Document Type: Article
UDC: 535.5
Received in September 2012

Citation: A. G. Kulikovskii, N. T. Pashchenko, “Stability of a flame front in a divergent flow”, Modern problems of mechanics, Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 281, MAIK Nauka/Interperiodica, Moscow, 2013, 55–67; Proc. Steklov Inst. Math., 281 (2013), 49–61

Citation in format AMSBIB
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\by A.~G.~Kulikovskii, N.~T.~Pashchenko
\paper Stability of a~flame front in a~divergent flow
\inbook Modern problems of mechanics
\bookinfo Collected papers. Dedicated to Academician Andrei Gennad'evich Kulikovskii on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2013
\vol 281
\pages 55--67
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3465}
\crossref{https://doi.org/10.1134/S0371968513020064}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1727280}
\elib{http://elibrary.ru/item.asp?id=20193379}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 281
\pages 49--61
\crossref{https://doi.org/10.1134/S0081543813040068}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000322390600006}


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    This publication is cited in the following articles:
    1. A. T. Il'ichev, V. V. Kozlov, D. V. Trechshev, A. P. Chugainova, “Andrei Gennad'evich Kulikovskii (on his 80th birthday)”, Russian Math. Surveys, 68:6 (2013), 1145–1155  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. G. Kulikovskii, “Evolution of perturbations on a steady weakly inhomogeneous background. complex Hamiltonian equations”, Pmm-J. Appl. Math. Mech., 81:1 (2017), 1–10  crossref  mathscinet  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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