Spectral kinetic energy transfer by advective processes in turbulent premixed reacting flows is examined using data from a direct numerical simulation of a statistically planar turbulent premixed flame. Two-dimensional turbulence kinetic-energy spectra conditioned on the planar-averaged reactant mass fraction are computed through the flame brush and variations in the spectra are connected to terms in the spectral kinetic energy transport equation. Conditional kinetic energy spectra show that turbulent small-scale motions are suppressed in the burnt combustion products, while the energy content of the mean flow increases. An analysis of spectral kinetic energy transfer further indicates that, contrary to the net down-scale transfer of energy found in the unburnt reactants, advective processes transfer energy from small to large scales in the flame brush close to the products. Triadic interactions calculated through the flame brush show that this net up-scale transfer of energy occurs primarily at spatial scales near the laminar flame thermal width. The present results thus indicate that advective processes in premixed reacting flows contribute to energy backscatter near the scale of the flame.

A Lagrangian analysis approach is used to examine the effects of heat release on the dynamics of the enstrophy during highly turbulent premixed combustion. The analysis is performed using data from a direct numerical simulation of a statistically planar premixed methane–air flame at a Karlovitz number of 100. Through cumulative, conditional, and correlation analyses, we show, consistent with prior studies, that vortex stretching and baroclinic torque both increase enstrophy at these highly turbulent conditions, while viscous transport and dilatation both lead to enstrophy destruction. However, although vortex stretching and viscous transport are individually an order of magnitude greater than all other terms in the enstrophy budget, the cumulative and combined effect of these two terms along Lagrangian trajectories is roughly only twice as large as the combined cumulative effect of dilatation and baroclinic torque. Moreover, trajectories that exhibit an increase in enstrophy through the flame are found to frequently have cumulative contributions from budget terms outside a single standard deviation of the mean contribution, indicating that enstrophy production at such highly turbulent conditions is associated with relatively infrequent but large values of dynamical terms. Lagged correlations further reveal a small but measurable contribution of baroclinic torque in enstrophy production, but these increases are overwhelmed, on average, by concurrent decreases in enstrophy due to viscous transport and dilatation. Taken together, these results provide further understanding of enstrophy dynamics in highly turbulent premixed flames.

Hybrid turbulence models that can accurately reproduce unsteady three-dimensional flow physics across the entire range of grid scales and turbulence dynamics from Reynolds-averaged Navier–Stokes (RANS), through large-eddy simulation (LES), down to direct numerical simulations (DNS) are of increasing interest to the turbulence modeling community. However, despite decades of research and development, the basic tasks of eliminating poor-performing hybrid RANS-LES models and accelerating adoption of superior models through well-designed validation and verification have yet to occur. As a step in this direction, in this work we evaluate thirteen different hybrid RANS-LES models via systematic grid refinement of decaying homogeneous isotropic turbulence. We further derive a novel mathematical framework for assessing the energy partitioning dynamics of each Hybrid RANS-LES model, wherein model-to-model variations in energy partitioning can be interpreted as different feedback mechanisms operating on a low-dimensional nonlinear dynamical system. We found that model forms similar to the flow simulation methodology—also often termed very-large eddy simulation—are dynamically inconsistent with DNS at all resolutions. Additionally, we found a strong dynamical similarity in the feedback mechanisms of all models related to detached eddy simulation and partially averaged Navier–Stokes that is inherent to their general model forms.