Effects of Lewis number on turbulent kinetic energy transport in premixed flames

Abstract

The effects of global Lewis number on the statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames are analysed using three-dimensional direct numerical simulation (DNS) data for freely propagating statistically planar flames with Lewis number ranging from 0.34 to 1.2. For flames with Lewis number significantly smaller than unity, it is observed that the turbulent kinetic energy is significantly augmented within the flame brush due to flame-generated turbulence. In these flames, it is demonstrated that effects of the mean pressure gradient and pressure dilatation are sufficient to overcome the effects of viscous dissipation. By contrast, for flames with Lewis number close to unity, it is found that the turbulent kinetic energy decays monotonically through the flame brush. In these flames, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation. The modelling of the various unclosed terms of the turbulent kinetic energy transport equation has been analysed in detail. The predictions of existing models are compared with corresponding quantities extracted from DNS data. Based on this a-priori DNS assessment, either appropriate models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient transport for the low Lewis number flames where the turbulent scalar flux is also counter-gradient in nature. However, for flames with Lewis number close to unity, the turbulent flux of turbulent kinetic energy exhibits predominantly gradient type transport. A new model has been proposed for the flux of turbulent kinetic energy in premixed flames and is found to capture the qualitative and quantitative behaviour obtained from DNS data for all the different Lewis numbers considered.