Performance of Flamelet Models with Epsilon Tracking for Diffusion Flame Simulations

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.