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Modélisation mathématique et numérique de la combustion de brouillards de gouttes polydispersés

Abstract : A Eulerian multi-fluid model is introduced in order to describe the evolution of polydispersed spray flames. It is rigorously derived from a kinetic level of description and has the capability to take into account droplets interactions, such as coalescence, an uncommon feature of Eulerian models. It is validated, in the case of diluted spray, by comparison with experimental measurements on laminar spray diffusion flames. It is also compared numerically with Lagrangian methods, in dense or diluted sprays cases. Moreover, its numerical analysis is conducted, in a case where the vaporization process is isolated. This analysis leads to the introduction of higher order methods, for the size space discretization. It also allows us to consider the propagation of planar polydispersed spray flames. This configuration is described by a reaction-diffusion system for a thermo-diffusive model of the gas, coupled with the kinetic model of the spray. The flame propagation is described by traveling waves for the whole system. To study the existence, we use topological degree methods for elliptic operators in unbounded domains. However, the kinetic model introduce an hyperbolic PDE. The results of the numerical analysis allows us to consider a discretization of the size space phase and yields to a finite dimensional dynamical system.We then add a diffusion coefficient in order to obtain an elliptic system and apply topological degree methods. Passing to the limit on the diffusion coefficient and then on the discretization step allows us to prove the existence of a planar propagating polydispersed spray flame.
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https://tel.archives-ouvertes.fr/tel-00185806
Contributor : Frédérique Laurent <>
Submitted on : Wednesday, November 7, 2007 - 11:08:54 AM
Last modification on : Wednesday, July 8, 2020 - 12:42:06 PM
Long-term archiving on: : Monday, April 12, 2010 - 1:34:52 AM

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  • HAL Id : tel-00185806, version 1

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Frédérique Laurent. Modélisation mathématique et numérique de la combustion de brouillards de gouttes polydispersés. Mathématiques [math]. Université Claude Bernard - Lyon I, 2002. Français. ⟨tel-00185806⟩

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