Modelling of the Curvature Term in the Flame Surface Density Transport Equation: A Direct Numerical Simulations Based Analysis

Abstract

A simple chemistry based three-dimensional Direct Numerical Simulations (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of Karlovitz number Ka, turbulent Reynolds number Re t, heat release parameter τ and global Lewis number Le has been used for the modelling of the curvature term of the generalised Flame Surface Density (FSD) transport equation in the context of Reynolds Averaged Navier Stokes (RANS) simulations. The curvature term has been split into the contributions arising due to the reaction and normal diffusion components of displacement speed (i.e. T1) and the term arising due to the tangential diffusion component of displacement speed (i.e. T2). Subsequently, the sub-terms (i.e. T1 and T2) of the curvature contribution to the FSD transport have been split into the closed (i.e. T1 r and T2 r) and unclosed (i.e. T1 ur and T2 ur) components. It has been found that T2 remains deterministically negative throughout the flame brush. However, the qualitative behaviour of T1 changes significantly depending upon the values of Ka, Re t and Le. Detailed physical explanations have been provided for the observed behaviours of the components of the curvature term. Moreover, it has been observed that the closed contributions of T1 and T2 (i.e. T1 r and T2 r) remains negligible in comparison to the unclosed contributions (i.e. T1 ur and T2 ur). Suitable model expressions have been identified for T1 ur and T2 ur in the context of RANS simulations, which are shown to perform satisfactorily in all cases considered in the current analysis, accounting for the variations in Ka, Re t, τ and Le.