%0 Journal Article
%T Modelling of the Curvature Term of the Flame Surface Density Transport Equation for Large Eddy Simulations
%A Mohit Katragadda
%A Nilanjan Chakraborty
%J Journal of Combustion
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/915482
%X A simplified chemistry based three-dimensional Direct Numerical Simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of turbulent Reynolds number has been used for the a priori modelling of the curvature term of the generalised Flame Surface Density (FSD) transport equation in the context of Large Eddy Simulation (LES). The curvature term has been split into the contributions arising due to the reaction and normal diffusion components of displacement speed and the term originating from the tangential diffusion component of displacement speed. Subsequently, these contributions of the curvature term have been split into the resolved and subgrid contributions. New models have been proposed for the subgrid curvature terms arising from the combined reaction and normal diffusion components and the tangential diffusion component of displacement speed. The performances of the new model and the existing models for the subgrid curvature term have been compared with the corresponding quantity extracted from the explicitly filtered DNS data. The new model for the subgrid curvature term is shown to perform satisfactorily in all cases considered in the current study, accounting for wide variations in LES filter size. 1. Introduction Flame Surface Density (FSD) based reaction rate closure is one of the popular methods of turbulent premixed combustion modelling in the context of Reynolds Averaged Navier Stokes (RANSs) simulations [1, 2]. The FSD based modelling has recently been extended to Large Eddy Simulations (LESs) [3¨C12]. The generalised FSD is defined as [3¨C10] where is the reaction progress variable and the overbar indicates a LES filtering operation. The transport equation of is given by [1, 4¨C7, 9, 11]: where is the th component of flame normal vector and is the displacement speed, and are the surface-weighted and Favre filtered values of a general quantity . The final term on the right hand side of (1) originates due to flame curvature and thus this term (i.e., ) is referred to as the curvature term [4¨C7, 9, 11]. It is evident from (1) that the curvature dependence of plays a key role in the statistical behaviours of£¿£¿ and this was confirmed in previous a priori Direct Numerical Simulation (DNS) based analyses [9, 11]. It was previously demonstrated [9, 11] that the existing models for the subgrid curvature term often do not capture its correct qualitative and quantitative behaviours, particularly in the Thin Reaction Zones (TRZ) regime flames. Moreover, the model parameters for the
%U http://www.hindawi.com/journals/jc/2012/915482/