Parametric study of sub-grid-scale flame--turbulence interactions in jet flames using a simplified kinetic model

Thermal expansion effects in turbulent premixed flames are known to invalidate gradient-diffusion assumptions of conventional eddy-viscosity-type turbulence models. The resulting counter-gradient transport can be accounted for in the Reynolds--Averaged Navier--Stokes (RANS) context by augmenting conventional dissipative models with thin-flame thermal-expansion source terms, but associated challenges in Large-Eddy Simulation (LES) are significant due to the dynamical nature of sub-grid-scale flame--turbulence interactions. Of particular concern is the active-cascade regime (moderate Karlovitz number; high Damk\"{o}hler number), in which large-scale shear production and small-scale thermal expansion compete to determine the local filter-scale energy dynamics. Using a single-step Arrhenius kinetic model, Reynolds- and Damk\"{o}hler-number-parameterized Direct Numerical Simulation (DNS) databases of turbulent premixed jet flames are obtained in the low- to moderate-Karlovitz-number regime. Competing effects of large- and small-scale production are analyzed using resolved and sub-grid-scale turbulence energy and scalar variance budgets, and modeling approaches are proposed.