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**Flames as gasdynamic discontinuities.**
*(English)*
Zbl 0545.76133

In the present work we take flame structure into account and derive an equation for the propagation of the discontinuity surface for arbitrary flame shapes in general fluid flows. The structure of the flame is considered to consist of a boundary layer in which the chemical reactions occur, located inside another boundary layer in which transport processes dominate. We employ the method of matched asymptotic expansions to obtain an equation for the evolution of the shape and location of the flame front. Matching the boundary-layer solutions to the outer gasdynamic flow, we derive the appropriate jump conditions across the front. We also derive an equation for the vorticity produced in the flame, and briefly discuss the stability of a plane flame, obtaining corrections to the formula of L. D. Landau [On the theory of slow combustion, Acta Physicochimica URSS 19, 77 ff. (1944)] and G. Darrieus [Propagation d’un front de flamme, presented at Le congrès de mécanique appliquée (unpublished) (1945)].

### Keywords:

gasdynamic discontinuities; flame structure; propagation of the discontinuity surface; boundary layer in which the chemical reactions occur; boundary layer in which transport processes dominate; matched asymptotic expansions; shape and location of the flame front; jump conditions across the front
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\textit{M. Matalon} and \textit{B. J. Matkowsky}, J. Fluid Mech. 124, 239--259 (1982; Zbl 0545.76133)

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### References:

[2] | DOI: 10.1016/0094-5765(79)90031-6 |

[3] | Barenblatt, Prikl. Mekh. Tekh. Fiz. 2 pp 21– (1962) |

[4] | DOI: 10.1016/0094-5765(76)90001-1 |

[6] | DOI: 10.1137/0137051 · Zbl 0437.76065 |

[7] | Markstein, J. Aero. Sci. 18 pp 199– (1951) |

[8] | Landau, Acta Physicochimica URSS 19 pp 77– (1944) |

[9] | DOI: 10.1017/S0022112061000081 · Zbl 0098.41801 |

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