Fonctions de transfert de flamme et énergies des pertubations dans les écoulements réactifs

The general objective of this thesis is to extend the understanding of combustion instabilities by testing models, physical concepts and numerical procedures, and by providing new numerical post-processing tools to do so. Flame Transfert Function (FTF) : four methods for the determination of Flame Transfer Functions (FTFs) in LES have been tested. A new method based on the forcing of the flame by a filtered white noise is used to obtain the FTF at all frequencies with only one unsteady LES. Disturbance Energies and Stability Criteria in reacting Flows : two stability criteria in reacting flows are derived. The first one extends the Rayleigh criterion by taking into account the influence of the heat flux fluctuation. The second criterion is nonlinear and is based on the analysis of the budjet of a newly derived nonlinear disturbance energy during a controled thermo-acoustic instability.