Large eddy simulation of a plane jet

Abstract

Large eddy simulations of spatially evolving planar jets have been performed using the standard Smagorinsky, the dynamic Smagorinsky, and the dynamic mixed models and model performance evaluated. Computations have been performed both at a low Reynolds number, Red=3000, in order to make comparisons with a previous DNS at the same Reynolds number, and at a higher value, Red=30 000, to compare with high Reynolds number experiments. Model predictions with respect to the evolution of jet half-width, centerline velocity decay, mean velocity profiles, and profiles of turbulence intensity are evaluated. Some key properties of the SGS models such as the eddy-viscosity constant and the subgrid dissipation are also compared. It is found that the standard Smagorsinsky model is much too dissipative and severely underpredicts the evolution of the jet half-width and centerline velocity decay. The dynamic versions of the Smagorinsky model and the mixed model allow for streamwise and transverse variation of the constant in the eddy-viscosity expression which results in much better performance and good agreement with experimental and DNS data. The mixed model has an additional scale-similarity part which, in a priori tests against filtered jet DNS data, is found to predict the subgrid shear stress profile. Although the subgrid shear stress obtained by the dynamic Smagorinsky model is substantially smaller than that obtained in the a priori tests using the jet DNS data, surprisingly, in the a posteriori computations, the dynamic Smagorinsky model performs as well as the dynamic mixed model. Analysis of the mean momentum equation gives the reason for such behavior: the resolved stress in computations with the dynamic Smagorinsky model is larger than it should be and compensates for the underprediction of the subgrid shear stress by the Smagorinsky model. The numerical discretization errors have been quantified. The error due to noncommutativity of spatial differentiation and physical space filtering on nonuniform grids is found to be small because of the relatively mild stretching used in the present LES. The modeling error is found to be generally smaller than the discretization error with the standard Smagorinsky model having the largest modeling error.