Direct Numerical Simulation analysis of the Flame Surface Density transport equation in the context of Large Eddy Simulation

Abstract

Turbulent reaction rate closure modelling using the concept of Flame Surface Density (FSD) is now well-established in the context of Reynolds Averaged Navier Stokes (RANS) simulations. In the present study, three-dimensional DNS data is explicitly filtered in order to evaluate different terms of the FSD transport equation in the context of Large Eddy Simulation (LES). Existing sub-models for these unclosed terms are assessed with respect to the filtered DNS data, resulting in a recommended modelled form for each term. Previously assessed modelling of the propagation and curvature terms is combined with new model formulations for the turbulent transport and strain rate terms to produce a complete modelled FSD transport equation for use in LES. Displacement speed is shown to play a pivotal role in the modelling of several terms and its curvature dependence is explicitly accounted for in order to ensure that the FSD model will be valid in both the corrugated flamelets and the thin reaction zones regimes.