Flame structure from a kinetic model for chemical reactions

Marzia Bisi; Maria Groppi; Giampiero Spiga

doi:10.3934/krm.2010.3.17

Article Contents

2010, Volume 3, Issue 1: 17-34. Doi: 10.3934/krm.2010.3.17

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Flame structure from a kinetic model for chemical reactions

1.
Dipartimento di Matematica, Università di Parma, Viale G.P. Usberti 53/A, I-43100 Parma
2.
Dipartimento di Matematica, Università di Parma, V.le G.P. Usberti 53/A, 43100 Parma
3.
Dipartimento di Matematica, Universitá di Parma, V.le G.P. Usberti 53/A, 43100 Parma

Received: August 31, 2009

Revised: October 31, 2009

Published: February 2010

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Abstract

Steady one-dimensional flame structure is investigated in a binary mixture made up by two components of the same chemical species undergoing binary irreversible exothermic reactive encounters. A kinetic model at the Boltzmann level, accounting for chemical transitions as well as for mechanical collisions, is proposed and its main features are analyzed. In the case of slow chemical reactions and collision dominated regime, the model is the starting point for a consistent derivation, via suitable asymptotic expansion of Chapman-Enskog type, of reactive Navier-Stokes equations at the fluid-dynamic scale. The resulting set of ordinary differential equations is investigated in the frame of the qualitative theory of dynamical systems, and numerical results are presented and briefly commented on for illustrative purposes.

Keywords:

Kinetic theory; Irreversible chemical reactions; Deflagration waves.

Mathematics Subject Classification: 82C40, 80A25, 76V05.

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