The current work focusses on investigating previously formulated subfilter mixing models for scalar variance and dissipation prediction in large eddy simulation (LES) of turbulent reacting flows. Three different models based on the local equilibrium assumption (Pierce, C. D., & Moin, P. Physics of Fluids (10), 3041, 1998), the second-moment transport equation (STE), and the variance transport equation (VTE) (Kaul, C. M. et al. Proceedings of the Combustion Institute (34), 1289-1297, 2013) are assessed. The emphasis of the investigation is placed on the effects of the discretization errors on the prediction of sub-filter variance and scalar dissipation rates.
Estimation of subfilter quantities is a crucial procedure for LES. Among other subfilter quantities, the subfilter variance of the mixture fraction is particularly important for LES of non-premixed combustion because of the role it plays in the prediction of mixing of the fuel and co-flow at the molecular level. Previous works have assumed an equilibrium between the production and dissipation of the variance at these subfilter scales, and models based on this assumption have been developed with dynamic estimation of a model constant. Recent works have focused on eliminating this assumption of local equilibrium of production and dissipation of variance. Two of these approaches were studied and implemented for a non-premixed flame and their results are compared. In the first approach, the subfilter variance was calculated by solving the transport equation for the second moment of the mixture fraction (STE). The second approach solved the transport equation for the subfilter scalar variance itself (VTE). Both models incorporate the same modeled quantity for the scalar dissipation rate. It is seen from the results that the STE approach substantially overpredicts the subfilter variance. This discrepancy is attributed to the error generated due to the discrete version of the product rule for differentiation that is used when deriving the equation for the subfilter variance from the second and first moment transport equation for the mixture fraction. This error acts as an artificial source term and results in the overprediction of the subfilter variance in the STE approach. The contribution of this artificial source term is found to be much larger than that of the actual production term. Due to this susceptible nature of the STE approach to numerical errors, it is suggested to calculate the subfilter variance by solving a transport equation for it, i.e., the VTE approach. A dynamic approach for the model coefficient of the subfilter scalar dissipation in the VTE approach is also implemented. This model is used to simulate the Sandia Flame D with a 1-D Conditional Moment Closure (CMC) combustion model. The results show satisfactory agreement with experimental data.