Performance of Flamelet Models with Epsilon Tracking for Diffusion Flame Simulations

TL;DR

This paper introduces an epsilon-based flamelet model for diffusion flames that improves physical consistency by better coupling subgrid and resolved-scale quantities in RANS simulations.

Contribution

The work proposes a new compressible flamelet formulation using epsilon as the tracking variable, addressing limitations of the conventional FPV model.

Findings

The epsilon-based model restores physical consistency in heat release predictions.

It effectively couples subgrid flamelet behavior with resolved-scale strain rates.

The model enables more accurate simulation of turbulent diffusion flames.

Abstract

This work examines the physical consistency of the conventional Flamelet Progress Variable (FPV) model for diffusion flame simulations and and introduces a new compressible flamelet formulation that employs the turbulent kinetic energy dissipation rate, $\epsilon$, as the tracking variable. Two-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations are conducted for a reacting, transonic, turbulent mixing layer to assess the coupling between resolved-scale and subgrid flamelet quantities, with emphasis on the role of strain rate. The FPV model is found to decouple resolved-scale and subgrid strain rates, leading to the preferential selection of equilibrium flamelet solutions in regions of high strain and resulting in nonphysical predictions of heat release and species composition. The proposed $\epsilon$-based formulation restores physical consistency by relating the subgrid flamelet strain rate to $\epsilon$, allowing the flamelet to respond to the local resolved-scale strain field. The inclusion of resolved-scale species transport enables advective and diffusive redistribution of products across locally quenched regions. The results indicate that $\epsilon$ offers a physically consistent tracking variable that connects the sub-grid flamelet model to resolved-scale RANS computations.