Modelling of the Curvature Term of the Flame Surface Density Transport Equation for Large Eddy Simulations

Mohit Katragadda,Nilanjan Chakraborty

doi:10.1155/2012/915482

Abstract

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.

Highlights

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]
Models have been identified for individual components of the subgrid curvature term (i.e., Csg1 and Csg2) and the performances of these models have been compared to the corresponding quantities extracted from Direct Numerical Simulation (DNS) data
It has been found that the new models for Csg1 and Csg2 satisfactorily capture the statistical behaviours of the corresponding terms extracted from DNS data

Summary

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) [3,4,5,6,7,8,9,10,11,12]. The generalised FSD Σgen is defined as Σgen = |∇c| [3,4,5,6,7,8,9,10] where c is the reaction progress variable and the overbar indicates a LES filtering operation. The transport equation of Σgen is given by [1, 4,5,6,7, 9, 11]: ∂Σgen ∂t ∂ + u j Σgen ∂x j

Objectives

Results

Conclusion