Modélisation asymptotique pour la simulation aux grandes échelles de la combustion turbulente prémélangée

We develop and evaluate a rigorous strategy of modeling and numerical simulation in turbulent premixed combustion. We are interested in the approach known by the name large eddy simulations (LES) where only the large scales are resolved while the effect of the unresolved scales (known as sub-grid scales) is modeled.

In the introductory chapter, we review the subject of turbulent premixed combustion and give some practical examples for motivation.

In chapter 2, we use the rigorous approach to propose a parameterization model for the turbulent speed enhancement of a premixed flame subject to a time-dependent shear flow. We show the existence of two limiting regimes according to which a turbulent premixed flame propagates: a slow regime where the speed enhancement due to turbulence is significant and a fast regime with very little speed enhancement.

The implementation of abstract theory of Majda-Souganidis requires the development of new numerical tools for partial differential equations of Hamilton-Jacobi type. In the homogenized equations, the effect of the small scales is represented by a nonlinear eigenvalue problem known as cell-problem whose numerical resolution is challenging. In chapter 3, we develop a new approach to solve this cell-problem. We transform this Hamilton-Jacobi equation into a system of conservation laws for the eigenfunction gradient. The solution of this non-linear problem is obtained by an iterative process of marching to steady state in the pseudo-time.

In chapter 4, we qualitatively analyze the dynamics of a premixed flame front subject to a two-dimensional flow of Childress-Soward type (combination of shears and eddies). In particular we generalize in a qualitative fashion the results of chapter 2.

Finally in chapter 5, through a specific setup, we demonstrate the utility of the rigorous asymptotic approach to evaluate the basis of the large eddy simulations strategy based on the flamelet sub-grid model. (Abstract shortened by UMI.)