A-priori study of wall modeling in large eddy simulation

The velocity signal of a high quality wall-resolving large eddy simulation (WRLES) of fully-developed turbulent channel flow at Re_τ = 1000 is spatially averaged over cubic boxes of size corresponding to possible choices for grid-cell size in a wall-modeled (WM)LES of the same flow. Two box sizes are considered, as well as multiple wall-normal locations of the center of the box. After applying filtering in time, the generated velocity signals are used to study algebraic wall models with respect to their ability to accurately predict the wall shear stress, τ¯_w. In particular, models based on the Spalding and Reichardt laws are examined. The sensitivity of τ¯_w with respect to the wall-normal distance of the velocity sampling point, h, the wall model and its parameters, and also to the resolution of the WMLES grid is addressed. It is shown that by using wall models with the parameters calibrated to fit the WRLES mean velocity profiles, the mean of the wall shear stress can be accurately predicted, however, no improvement for the fluctuations of this quantity is achieved. To avoid dependence of the mean predicted τ¯_w on h, an integrated formulation of algebraic wall models is proposed and applied to Reichardt law, leading to improved results. Finally, an idea is described and examined to increase the correlation between the predicted τ¯_w and reference wall shear stress through dynamically adjusting the wall model parameters. To facilitate similar studies, the generated datasets for a-priori study of WMLES are made publicly available.