A filtered-laminar-flame PDF sub-grid scale closure for LES of premixed turbulent flames. Part I: Formalism and application to a bluff-body burner with differential diffusion

A sub-grid scale closure for Large Eddy Simulation (LES) of turbulent combustion based on physical-space filtering of laminar flames is discussed. Applied to an unstructured grid, the combustion LES filter size is not fixed in this novel approach devoted to LES with refined meshes, but calibrated depending on the local level of unresolved scalar fluctuations. The context is premixed or stratified flames, the derived model relies on four balance equations for mixture fraction and its variance, and a progress variable and its variance. The proposed formalism is based on a presumed probability density function (PDF) derived from the filtered flames. Closures for the terms of the equations that are unresolved over LES grids are achieved through the PDF. The method uses flamelet tabulated detailed chemistry and is first applied to the simulation of laminar flames (1D and 2D) over various grids for validation, before simulating a turbulent burner studied experimentally by Sweeney et al. (2012). Since this burner also features differential diffusion effects, the numerical model is modified to account for accumulation of carbon in the recirculation zone behind the bluff-body. A differential diffusion number based on the gradient of residence times is proposed, in an attempt to globally quantify differential diffusion effects in burners.