Evolutions of strain rate and dissipation rate of kinetic energy in turbulent premixed flames

The statistical behaviors of the evolutions of the components of the strain rate tensor and Favre-averaged dissipation rate of kinetic energy are analyzed using direct numerical simulations of statistically planar turbulent premixed flames propagating into forced unburned gas turbulence for different turbulence intensities spanning a range of different Karlovitz numbers. The pressure Hessian contribution and the combined molecular diffusion and dissipation terms are found to play dominant roles in the transport equations of diagonal strain rate components and the Favre-averaged dissipation rate of kinetic energy for flames with small Karlovitz numbers. By contrast, the leading order balance is maintained between the strain rate, vorticity, and molecular dissipation contributions for flames with large Karlovitz numbers, similar to non-reacting turbulent flows. The contributions of the terms arising from the correlation between pressure and density gradients and pressure Hessian in the strain rate and dissipation rate of kinetic energy transport equations weaken in comparison to the magnitude of the molecular dissipation contribution with an increase in Karlovitz number. These behaviors have been explained in terms of the alignments of vorticity, pressure gradient, and pressure Hessian eigenvectors with strain rate eigendirections. The magnitudes of the terms in the transport equation of the Favre-averaged dissipation rate of kinetic energy are also found to increase with increasing Karlovitz number, which is explained with the help of a detailed scaling analysis. This scaling analysis also explains the leading order contributions to the dissipation rate of kinetic energy for different combustion regimes.