Optimised mixing and flow resistance during shear flow over a rib roughened boundary

A series of numerical investigations has been performed to study the effect of lower boundary roughness on turbulent flow in a two-dimensional channel. The roughness spacing to height ratio, w/k, has been investigated over the range 0.12 to 402 by varying the horizontal rib spacing. The square roughness elements each have a cross-sectional area of (0.05 H)2, where H is the full channel height. The Reynolds number, Reτ is fixed based on the value of the imposed pressure gradient, dp/dx, and is in the range 6.3 × 103 − 4.5 × 104. A Reynolds Averaged Navier–Stokes (RANS) based turbulence modelling approach is adopted using a commercial CFD code, ANSYS-CFX 14.0. Measurements of eddy viscosity and friction factor have been made over this range to establish the optimum spacings to produce maximum turbulence enhancement, mixing and resistance to flow. These occur when w/k is approximately 7. It is found that this value is only weakly dependent on Reynolds number, and the decay rate of turbulence enhancement as a function of w/k ratio beyond this optimum spacing is slow. The implications for heat transfer design optimisation and particle transport are considered.