A proper velocity scale for modeling subgrid-scale eddy viscosities in large eddy simulation

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Abstract
The limitations of the commonly used Smagorinsky subgrid‐scale (SGS) eddy viscosity model in large eddy simulation (LES) of turbulent flows are that the model’s eddy viscosity constant must be optimized in different flows, and also that a damping function must be used to account for near‐wall effects. A new SGS model which mitigates these drawbacks is proposed, i.e., a more proper eddy viscosity velocity scale was determined by utilizing the third‐order terms in an anisotropic representation model of the Reynolds stresses [K. Horiuti, Phys. Fluids A 2, 1708 (1990)]. This method utilizes the direct numerical simulation (DNS) database for fully developed turbulent channel flow to show these drawbacks to be inherent in the use of an improper velocity scale, i.e., the total SGS energy component adopted in the Smagorinsky model. As a result, the SGS normal shear stress was alternatively employed as the velocity scale, thereby significantly improving the correlation with DNS data. Methods to correlate the SGS normal shear stress to the grid scale quantities are proposed and compared, and the resultant high accuracy of the scale‐similarity model to represent the SGS turbulence fluctuations is shown. The proposed SGS model was also tested in actual LES computations of turbulent channel flow, where it was found that the SGS eddy viscosity in the near‐wall region similarly acted as the conventionally used Van Driest damping function. This result is consistent with previous reports which assert that in the Reynolds averaged models, the rapid reduction of the Reynolds shear stress as the wall is approached is due to the preferential damping of the normal shear stress. It is shown that three eddy viscosity parameters contained in the proposed SGS model can be practically reduced to a single parameter, which is subsequently shown to be more universal and independent of the flow field than the Smagorinsky model constant. A qualitative interpretation for the variance of the Smagorinsky model constant in different flows is also provided via a correlation with the anisotropy of SGS turbulence intensities.