Evaluating the Cross-Scale Turbulent Kinetic Energy Flux in a Bluff Body Stabilized Premixed Flame

We study high-Karlovitz bluff body stabilized premixed methane-air flames in confined channel configurations with varying background pressure gradients to assess the mean directionality of the turbulent kinetic energy flux. The analysis is based on three-dimensional simulations using PeleLMeX, a low-Mach reacting flow code with adaptive mesh refinement and multi-step finite rate chemistry. We analyze the simulation data using spatial filtering at multiple length scales to directly compute the energy flux between filtered and sub-filter scales, allowing us to study the impact of coupled turbulence and pressure gradient interactions on the local turbulent energy backscatter. We find that mean kinetic energy backscatter is strong and spatially localized at all filter scales, and is associated with intermediate flame progress variables within the shear layer. We observe net backscatter downstream of the bluff body recirculation zone where mean pressure gradients are stronger due to the channel geometry and where there are strong density and velocity gradients due to combustion and flow acceleration, respectively. This suggests that subfilter-scale models should depend on local pressure gradients in large-eddy simulations of reacting flows. We also find that the coupling between the velocity and density gradients driven by the geometry and the flame can lead to significant backscatter that is not sufficiently captured by all methods of assessing the backscatter.