Direct Numerical Simulations of high Karlovitz number premixed flames for the analysis and modeling of the displacement speed.

Abstract

An a priori model for premixed turbulent flame combustion in the thin reaction zone (TRZ) regime is presented. This a priori model is deduced from the analysis of data from a series of direct numerical simulations (DNS) of stoichiometric (ϕ=1.0) premixed turbulent iso-octane flames, with Karlovitz number ranging from 2.9 to 46.2. For each case two flames are considered: one with unity Lewis numbers to isolate the effect of turbulence on the flame, and one with non-unity Lewis numbers to study the influence of differential diffusion. First the reaction zone is shown to remain thin for each flame, leading to focus this study on a specific iso-surface in the reaction zone and how it is affected by turbulence. Second, the displacement speed Sd on this iso-surface shows a differentiate dependency on tangential strain rate and curvature. This dependency is modeled through an expression of Sd formally similar to the ones used in laminar flame theories, but using two effective turbulent Markstein lengths in place of the laminar ones. These lengths are shown to depend on the Lewis number and to decrease when the Karlovitz number increases, in agreement with previous studies showing a reduction of the effective Lewis number with the Karlovitz. From these DNS, an extension of the coherent flame model (CFM) to the TRZ regime is proposed, using a fine-grained flame surface density (FSD) located in the reaction zone. Models for the displacement speed, the tangential strain rate, and the stretch due to curvature are proposed. The a priori evaluation of these closures shows a significant improvement compared to the flamelet formulations.