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Kinetic and Related Models (KRM)
 

Kinetic approach to deflagration processes in a recombination reaction

Pages: 259 - 276, Volume 4, Issue 1, March 2011      doi:10.3934/krm.2011.4.259

 
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Fiammetta Conforto - Dipartimento di Matematica, Università di Messina, Viale F. Stagno d'Alcontres 31 - 98166 Messina, Italy (email)
Maria Groppi - Dipartimento di Matematica, Università di Parma, V.le G.P. Usberti 53/A, 43100 Parma, Italy (email)
Roberto Monaco - Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24 - 10129 Torino, Italy (email)
Giampiero Spiga - Dipartimento di Matematica, Università di Parma, V.le G.P. Usberti 53/A, 43124 Parma, Italy (email)

Abstract: Steady one-dimensional flame structure is investigated in a binary gas mixture made up by diatomic molecules and atoms, which undergo an irreversible exothermic two--steps reaction, a recombination process followed by inelastic scattering (de-excitation). A kinetic model at the Boltzmann level, accounting for chemical encounters as well as for mechanical collisions, is proposed and its main features are analyzed. In the case of collision dominated regime with slow recombination and fast de-excitation, the model is the starting point for a consistent derivation, via suitable asymptotic expansion of Chapman-Enskog type, of reactive fluid-dynamic Navier-Stokes equations. The resulting set of ordinary differential equations for the smooth steady deflagration profile is investigated in the frame of the qualitative theory of dynamical systems, and numerical results for the flame eigenvalue and for the main macroscopic observables are presented and briefly commented on for illustrative purposes.

Keywords:  Kinetic theory; Irreversible chemical reactions; Deflagration waves.
Mathematics Subject Classification:  82C40, 80A25, 76V05.

Received: July 2010;      Revised: October 2010;      Available Online: January 2011.

 References