Performance of Flamelet Models with Epsilon Tracking for Diffusion Flame Simulations

TL;DR

The paper addresses the mismatch between resolved-turbulence strain and subgrid flamelet state in FPV models for diffusion flames. It introduces an $\epsilon$-based flamelet framework where the flamelet inflow strain rate $S^*$ is inferred from the resolution-scale dissipation rate $\epsilon$, yielding a physically coherent coupling between subgrid chemistry and the resolved flow. Compared to One-Step Kinetics (OSK) and FPV, the $\epsilon$-based approach produces realistic flame standoff and quenching behavior, with explicit resolved-scale species transport enabling redistribution of products across locally quenched regions. The results demonstrate that $\epsilon$ can serve as a robust tracking variable for subgrid flamelet dynamics, improving extinction/ignition accuracy while remaining computationally efficient relative to full detailed-chemistry simulations, and point to future extensions to 3D LES and experimental validation.

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, $ε$, 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 $ε$-based formulation restores physical consistency by relating the subgrid flamelet strain rate to $ε$, 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 $ε$ offers a physically consistent tracking variable that connects the sub-grid flamelet model to resolved-scale RANS computations.

Figures (10)

• Figure 1: Flow configuration and computational grid.
• Figure 2: Left: Solutions to the flamelet equations presented as S-shaped curves for various background pressures. Right: $\mathbf{\widetilde{C}_{\mathrm{tab}}(\boldsymbol{\lambda})=\widetilde{C}(\boldsymbol{\lambda};\widetilde{Z},\widetilde{Z"^2},\bar{p})}$ relations for different combinations of $\mathbf{\widetilde{Z}}$ and $\mathbf{\widetilde{Z"^2}}$ at a pressure of 30 bar.
• Figure 3: Solutions to the flamelet equations parametrized by $\mathbf{S^*}$.
• Figure 4: Profiles of temperature and velocity at three different streamwise locations.
• Figure 5: Temperature contours for OSK (top), FPV (center) end $\boldsymbol{\epsilon}$-based (bottom) combustion models.