A PrioriDirect Numerical Simulation Modelling of the Curvature Term of the Flame Surface Density Transport Equation for Nonunity Lewis Number Flames in the Context of Large Eddy Simulations

Abstract

A Direct Numerical Simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with Lewis numbers Le ranging from 0.34 to 1.2 has been used to analyse the statistical behaviours of the curvature term of the generalised Flame surface Density (FSD) transport equation, in the context of the Large Eddy Simulation (LES). Lewis number is shown to have significant influences on the statistical behaviours of the resolved and sub-grid parts of the FSD curvature term. It has been found that the existing models for the sub-grid curvature term C sg do not capture the qualitative behaviour of this term extracted from the DNS database for flames with Le << 1. The existing models of C sg only predict negative values, whereas the sub-grid curvature term is shown to assume positive values within the flame brush for the Le = 0.34 and 0.6 flames. Here the sub-grid curvature terms arising from combined reaction and normal diffusion and tangential diffusion components of displacement speed are individually modelled, and the new model of the sub-grid curvature term has been found to capture C sg extracted from DNS data satisfactorily for all the different Lewis number flames considered here for a wide range of filter widths.