Subfilter scalar variance modeling for large eddy simulation
Accurate models for the mixing of fuel and oxidizer at small, unresolved flow length scales are critical to the predictive skill of large eddy simulation (LES) of turbulent combustion. Subfilter scalar variance and subfilter scalar dissipation rate are important parameters in combustion modeling approaches based on a conserved scalar, but are prone to numerical and modeling errors due to the nature of practical LES computations. This work examines the errors incurred in these models using a novel method that couples LES scalar modeling with direct numerical simulation (DNS) of homogeneous isotropic turbulence and offers modeling and numerical techniques to address these errors. In the coupled DNS-LES method, DNS velocity fields are evolved simultaneously with LES scalar fields. The filtered DNS velocities are supplied to the LES scalar equations, instead of solving the LES momentum equations. This removes the effect of errors in the filtered scalar evolution from the scalar modeling analysis. Results obtained using the coupled DNS-LES approach, which permits detailed study of physics-related and numerical errors in scalar modeling, show that widely used algebraic dynamic models for subfilter scalar variance lack accuracy due to faulty equilibrium modeling assumptions and sensitivity to numerical error. Transport equation models for variance show superior performance, provided that the scalar dissipation rate model coefficient is set appropriately. For this purpose, a new dynamic approach for nonequilibrium modeling of subfilter scalar dissipation rate is developed and validated through a priori tests in an inhomogeneous jet flow and using the coupled DNS-LES method for assessment of numerical error effects. Explicit filtering is assessed as means to control numerical error in LES scalar modeling and the scalar equations are reformulated to account for the explicit filtering technique. Numerical convergence of the mean subfilter scalar variance prediction with increasing grid resolution is demonstrated.