On the non-equilibrium models for subfilter scalar variance in large eddy simulation of turbulent mixing and combustion

Abstract

This paper presents an analysis of the discretization errors in the non-equilibrium models for the subfilter variance of the mixture fraction, a key quantity to model in large eddy simulation (LES) of turbulent mixing and combustion. Two discretely distinct formulations of the non-equilibrium models that solve the transport equations to obtain the subfilter variance, i.e., the second moment transport equation (STE) and the variance transport equation (VTE), are analyzed. By deriving discrete equations for the evolution of subfilter variance by the two formulations, it is seen that the difference originates primarily from the product rule of differentiation applied to the scalar convection term, which does not hold discretely. LES of scalar mixing in a planar jet is performed to illustrate the outcome of the analysis. Results show that the discrete product rule error is significant and of the same order as the production and dissipation terms on average. A priori analysis using direct numerical simulation (DNS) data for scalar mixing in homogeneous isotropic turbulence is also performed. From the analysis, it is seen that the VTE model under-predicts the subfilter variance, whereas the STE model over-predicts it substantially with sharp oscillations.