Leray-alpha Regularization of the Smagorinsky-Closed Filtered Equations for Turbulent Jets at High Reynolds Numbers

Abstract: The article reports on blending of the Leray-alpha regularization with the conventional Smagorinsky subgrid-scale closure as an option for large-eddy-simulation of turbulent flows at very high Reynolds number on coarse meshes. The model has been tested in the self-similar far-field region of a jet at a range of Reynolds numbers spanning over two decades (4x10(3), 4x10(4) and 4x10(5)) on two very coarse meshes of 2x10(5) and 3x10(4) mesh cells. The results are compared with the well-resolved DNS for Re-D = 4 x 10(3) on 15 million cells and experimental data for higher Re numbers. While the pure Leray-alpha can fail badly at high Re numbers on very coarse meshes, a blending of the two strategies by adding a small amount of extra-dissipation performs well even at a huge jet Reynolds number of Re-D = 4 x 10(5) on a very coarse mesh (2x10(5) cells), despite the ratio of the typical mesh spacing to the Kolmogorov length exceeding 300. It is found that the main prerequisite for successful LES, both for the classic Smagorinsky and the blended Leray-alpha/Smagorinsky model, is to resolve the shear-length L-s = root epsilon/delta(3) (where is the shear-rate modulus), defined by the constraint Delta/L-s <1, where Delta is the typical mesh-cell size. For the mixed Leray-alpha/Smagorinsky model the regularization parameter should also be related to the shear-length rather than the local mesh size or Reynolds number, for which we propose a guide criterion alpha = 0.15 divided by 0.3 L-s .