Abstract : To reduce fuel consumption and pollutant emissions, burner designers are more and more using lean premixed combustion. Nevertheless, this regime suffers from thermo-acoustic instabilities sometimes leading to severe damages. Large Eddy Simulation (LES) is a promising tool to better understand and control those phenomena, as shown through previous researches. In the majority of industrial applications, fuel is injected as a liquid phase, which has to be taken into account in numerical simulations. This thesis describes a strategy based on Euler-Euler formalism to simulate two-phase turbulent reactive flows in complex geometries. Discretisation of convective terms is a key issue to ensure the quality of a LES. A fine description of different convection numerical schemes (cell-vertex finite volume method, Taylor-Galerkin schemes) is first given. Then theoretical and practical error analyses are supplied and some possible improvements are proposed. Special attention is paid for the discretizations and boundary conditions at the computational domain borders. ONERA experimental burner is used to validate and evaluate the numerical methods aforementionned.
Eventually, three methodologies to determine section varying ducts acoustic impedances are presented and analysed. They provide inlet and outlet boundary conditions for industrial burners, especially for acoustic eigenmodes calculations.