A-priori Direct Numerical Simulation assessment of models for generalized sub-grid scale turbulent kinetic energy in turbulent premixed flames

The fidelity of Large Eddy Simulation (LES) in the context of turbulent premixed combustion modelling depends on the complex coupling between turbulence and chemical reactions occurring at the unresolved scale. Although LES of combustion systems is becoming increasingly popular, the closures for sub-grid scale (SGS) stresses have mostly been derived assuming constant density flows. Similar to the unclosed scalar flux, the behaviour of the SGS stresses depends on the balance between heat release and turbulence, and it has been shown recently that counter-gradient transport (CGT) can occur for the stress tensor when the isotropic part of the stress tensor is not properly accounted for. This leads to a negative correlation between the predictions obtained from an eddy viscosity type model and the stresses obtained from Direct Numerical Simulation (DNS). In the present work the modelling of the isotropic part of the stress tensor, closely related to the generalised sub-grid scale kinetic energy, is considered in detail. To this end the interplay between SGS dilatation effects and unresolved velocity fluctuations is analysed using a-priori DNS analysis of turbulent, statistically planar flames with different values of global Lewis number and heat release parameter. Well-known models for generalised sub-grid scale kinetic energy have been assessed in the context of turbulent premixed combustion and detailed physical explanations for their behaviour have been provided. Further, the effects of SGS dilatation rate on the anisotropy of the SGS stresses have been highlighted using a variant of the Lumley triangle.