A new wall-damping function for large eddy simulation employing Kolmogorov velocity scale

A new wall-damping function, based on the Kolmogorov velocity scale, for large eddy simulation (LES) is proposed, which accounts for the near-wall effect. To calculate the Kolmogorov velocity scale, uε, the dissipation rate of turbulent energy, ε, is needed. In LES, however, the dissipation rate is generally not solved, unlike in the Reynolds averaged Navier–Stokes (RANS) simulations, e.g., k-ε models. Although, in some previous studies, the dissipation rate of the subgrid-scale (SGS) turbulent energy, εSGS, is used instead of ε in calculating the Kolmogorov velocity scale, the scale obtained using such a method overly depends on the grid resolution employed and is generally inappropriate. Accordingly, the wall-damping function using the incorrect velocity scale also depends on the grid resolution and gives an inadequate wall effect. This is because εSGS contains only the components in the scale smaller than the grid-filter width, which obviously varies with the grid resolution employed. In this study, to overcome this problem, we propose a method for estimating the Kolmogorov velocity scale with a technique of conversion in LES, and the estimated one is utilized in the wall-damping function. The revised wall-damping function for LES is tested in channel flows and a backward-facing step flow. The results show that it yields a proper near-wall effect in all test cases which cover a wide range of grid resolution and Reynolds numbers. It is also shown that all three kinds of SGS models incorporating the present wall-damping function provide good predictions, and it is effective both in one-equation and 0-equation SGS models. These results suggest that the use of the proposed wall-damping function is a refined and versatile near-wall treatment in LES with various kinds of SGS models.

Research highlights► A method for estimating the dissipation rate of turbulent energy in LES is proposed. ► As a result, a wall-damping function based on Kolmogorov scale is available in LES. ► The damping effect has little dependency on the grid resolution employed. ► This damping function is free from a wall-friction velocity, preventing inaccuracy. ► This wall-damping function can be incorporated into various kinds of SGS models.