The Effect of Sub-Grid Modeling on Large-Eddy Simulations of a Compressible Mixing Layer

Large-eddy simulations (LES) of a compressible mixing layer at high Reynolds number (Reθ = 220,000) were carried out to study the effect of various sub-grid modeling approaches. All terms of the Reynolds stress transport equation (RSTE) were computed and used to estimate the amount numerical dissipation present in the solution. It was demonstrated that the numerical dissipation replaces any unresolved turbulent dissipation, acting as a sub-grid model and validating the implicit LES approach. Explicit sub-grid models, Smagorinsky and dynamic Smagorinsky, are compared to the implicit approach. Results show that the amount of numerical dissipation varied inversely with the dissipation from the sub-grid models and the total dissipation from both sources remained the same. A study varying the coefficient in the Smagorinsky model was undertaken to find an optimal value where all the turbulent dissipation is produced by the sub-grid model and the effect of the numerical dissipation on the RSTE is minimized. This optimal value was much higher than those normally used. The dynamic Smagorinsky model, where the coefficient is computed within the model, yielded results similar to the standard Smagorinsky model with a coefficient 4 times smaller than the optimal value. Using an explicit sub-grid model reduces the number and increases the size of the turbulent eddies present in the solution as compared to implicit LES. A grid resolution study showed that explicit sub-grid modeling yielded better grid convergence than the implicit simulations. Grids containing at least 41 points across the mixing layer thickness were required to reduce the errors in the peak Reynolds stresses to below 10 percent. Spectra of turbulent kinetic energy indicate that the sub-grid modeled cases show the turbulent dissipation beginning at lower-frequencies, reducing the extent of the inertial subrange. Simulations were also performed at lower Reynolds numbers (Reθ = 22,000, 2,200 and 220). The flow was found to be largely Reynolds number independent until the simulation Reynolds number fell below the mixing transition Reynolds number at Reθ = 220. At this point the flow characteristics changed dramatically.