Abstract
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.
Highlights
Turbulent premixed combustion has practical applications in automotive engines and industrial gas turbines, and, several analyses focused on its physical understanding and a detailed review of the current state of the art can be obtained from the monograph by Peters[1] or the review papers by Veynante and Vervisch.[2]
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
It has been found that the pressure Hessian contribution and the combined molecular diffusion and dissipation terms remain the dominant contributors and the magnitudes of their mean values remain greater than the strain rate and vorticity contributions in the transport equations of the diagonal strain rate components and Favreaveraged dissipation rate of kinetic energy for flames with small turbulence intensities characterized by Da > 1 and Ka < 1
Summary
Turbulent premixed combustion has practical applications in automotive (e.g., spark ignition) engines and industrial gas turbines (e.g., lean premixed prevaporized gas turbine combustors), and, several analyses focused on its physical understanding and a detailed review of the current state of the art can be obtained from the monograph by Peters[1] or the review papers by Veynante and Vervisch.[2]. The present authors[27] analyzed the statistical behaviors of the different terms of principal strain rate transport equations for different turbulence intensities and Karlovitz numbers based on direct numerical simulations (DNS) of statistically planar turbulent premixed flames subjected to forced unburned gas turbulence This analysis[27] suggested that the terms arising from pressure gradient and pressure Hessian play important roles in the evolution of principal strain rates for small values of the Karlovitz number, and the contributions of these terms diminish with the increasing Karlovitz numbers. The main objectives of the current analysis are (a) to demonstrate the statistical behaviors of the different terms of the transport equation of the individual components of the strain rate tensor Sij, (b) to demonstrate the effects of turbulence intensity and Karlovitz number on the statistical behaviors of the different terms of the transport equations of strain rate and the Favre-averaged dissipation rate of kinetic energy, and (c) to provide physical explanations for the observed behaviors
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