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.

The statistical behaviour of turbulent kinetic energy transport in turbulent premixed flames is analysed using data from three-dimensional Direct Numerical Simulation (DNS) of freely propagating turbulent premixed flames under decaying turbulence. For flames within the corrugated flamelets regime, it is observed that turbulent kinetic energy is generated within the flame brush. By contrast, for flames within the thin reaction zones regime it has been found that the turbulent kinetic energy decays monotonically through the flame brush. Similar trends are observed also for the dissipation rate of turbulent kinetic energy. Within the corrugated flamelets regime, it is demonstrated that the effects of the mean pressure gradient and pressure dilatation within the flame are sufficient to overcome the effects of viscous dissipation and are responsible for the observed augmentation of turbulent kinetic energy in the flame brush. In the thin reaction zones regime, the effects of the mean pressure gradient and pressure dilatation terms are relatively much weaker than those of viscous dissipation, resulting in a monotonic decay of turbulent kinetic energy across the flame brush. 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 206 Flow Turbulence Combust (2011) 87:205-235 models are identified or new models are proposed where necessary. It is shown that the turbulent flux of turbulent kinetic energy exhibits counter-gradient (gradient) transport wherever the turbulent scalar flux is counter-gradient (gradient) in nature. A new model has been proposed for the turbulent flux of turbulent kinetic energy, and is found to capture the qualitative and quantitative behaviour obtained from DNS data for both the corrugated flamelets and thin reaction zones regimes without the need to adjust any of the model constants.

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The performance of algebraic flame surface density (FSD) models has been assessed for flames with nonunity Lewis number (Le) in the thin reaction zones regime, using a direct numerical simulation (DNS) database of freely propagating turbulent premixed flames with Le ranging from 0.34 to 1.2. The focus is on algebraic FSD models based on a power-law approach, and the effects of Lewis number on the fractal dimensionDand inner cut-off scaleηihave been studied in detail. It has been found thatDis strongly affected by Lewis number and increases significantly with decreasing Le. By contrast,ηiremains close to the laminar flame thermal thickness for all values of Le considered here. A parameterisation ofDis proposed such that the effects of Lewis number are explicitly accounted for. The new parameterisation is used to propose a new algebraic model for FSD. The performance of the new model is assessed with respect to results for the generalised FSD obtained from explicitly LES-filtered DNS data. It has been found that the performance of the most existing models deteriorates with decreasing Lewis number, while the newly proposed model is found to perform as well or better than the most existing algebraic models for FSD.