Modelling of the tangential strain rate term of the Flame Surface Density transport equation in the context of Reynolds Averaged Navier–Stokes simulation

Abstract

The modelling of the tangential strain rate term in the Flame Surface Density (FSD) transport equation in the context of Reynolds Averaged Navier–Stokes (RANS) simulations of turbulent premixed combustion has been addressed by a priori analysis of a Direct Numerical Simulation (DNS) database of statistically planar freely propagating flames with wide variations of Damköhler number Da, heat release parameter τ and global Lewis number Le. It has been found that the dilatation rate contribution to the FSD transport strengthens with increasing value of τ and decreasing value of Le. The behaviour of the normal strain rate term shows significant differences in response to Da and Le. It has been found that the normal strain rate contribution to the FSD transport remains a sink term for the flames with high and small values of Da and Le, respectively, where the effects of strain rate induced by heat release achem overcome the effects of turbulent straining aturb. By contrast, the effects of aturb overcomes the effects of achem for low Da flames with Le⩾1, which leads to a positive value of the normal strain rate term towards the unburned gas side, but this term becomes negative towards the burned gas side due to strong achem overcoming aturb in the regions of intense heat release. The strengthening of the dilatation rate and achem at small and large values of Le and Da, respectively, is explicitly taken into account to propose new models for the strain rate contributions to the FSD transport. The new model is shown to satisfactorily capture the effects of Damköhler number Da, heat release parameter τ, and global Lewis number Le, on the tangential strain rate term of the FSD transport equation for all the cases considered in this study.