LES and DNS of symmetrically roughened turbulent channel flows

A fully developed turbulent channel flow with symmetrically roughened walls is investigated, where the channel walls are roughened with square ribs, elongated along the span of the channel and are spaced uniformly in the streamwise direction at a constant pitch. The effects of Reynolds number variation on the statistical quantities, the near-wall dynamical structures and on the anisotropic nature of turbulence are studied at two Reynolds numbers Reτ= 180 and 400, where Reτ is based on the channel half-height h and the wall friction velocity uτ. Near-wall resolving large eddy simulations (LES) with different grid resolutions are carried out and validated with in-house direct numerical simulation (DNS) data. Turbulence anisotropy at both small and large scales of motion is investigated using anisotropic invariant maps. A variation in the anisotropic behavior of the flow in the near-wall region is noticed, where the flow is found to be more anisotropic at Reτ=180 than at Reτ=400. Also, the anisotropic behavior of the small-scale motions varies from the large-scale motions at Reτ=400. Two-point correlation and phase analysis using Hilbert transform reveals that the flow within the cavity is independent of the flow outside the cavity. The relatedness of the ‘worm-like’ vortical structures with the positive enstrophy production rate (ωiSijωj> 0) is investigated. The regions of positive enstrophy production rate are observed to be topologically ‘sheet-like’ predominantly at a height just above the rib. The regions of negative enstrophy production rate (ωiSijωj< 0) are less dominant, with a topology combination of weakly ‘sheet-forming’ and ‘tube-forming’. The statistical features could be captured by LES with a grid consisting of only one-fifth of the total number of grid points as that in the DNS mesh.