Strain-Rate-Consistent $\varepsilon$-Based Non-Premixed Flamelet Model

This numerical study examines a strain-rate inconsistency in the conventional flamelet/progress-variable (FPV) formulation for non-premixed combustion and proposes an alternative coupling based on the turbulence kinetic energy dissipation rate, $\varepsilon$.

Two-dimensional Reynolds-averaged Navier-Stokes (RANS) simulations of a transonic accelerating reacting mixing layer are performed using one-step kinetics, a conventional FPV model, and the proposed $\varepsilon$-$Z$ flamelet model.

The analysis focuses on the relation between the RANS-computed mean strain-rate field and the local strain rate imposed on the flamelet through the coupling between the flow computation and the flamelet library.

In the FPV formulation, the flamelet state is selected through a transported progress variable, whose evolution is governed by advection, diffusion, and chemical production rather than by the local strain-rate environment.

The present results show that this can lead to preferential sampling of near-equilibrium flamelet states in high-strain regions, thereby weakening the intended connection between the computed flow field and the strain-rate-controlled flamelet response.

In the $\varepsilon$-$Z$ formulation, $\varepsilon$ is used to infer the imposed flamelet strain rate, $S^*$, so that the local flamelet state is directly constrained by the modeled turbulence field and the pressure-dependent flammability limit.

Selected species are transported explicitly, allowing products to persist through locally quenched regions, while a reactant-availability scaling limits tabulated source terms when the transported composition departs from the flamelet manifold.