Effects of wall roughness on drag and lift forces of a particle at finite Reynolds number

In order to investigate drag and lift forces exerted on a spherical particle induced by a uniform shear flow bounded by rough wall, we have conducted numerical simulations at finite shear Reynolds number in the range of 2 ≤ Re ≤ 100. The gap between the particle and the rough bed (δ˜) is the second important parameter, which was also varied from the limiting case of particle sitting on the bed (δ˜=0) to the particle being more than one diameter away from the bed. A fully developed undisturbed ambient shear flow over a rough bed, made of hemispherical elements on a flat wall, was first obtained without the spherical particle, whose purpose is to serve as reference and provide the undisturbed flow. A spherical particle was then located near this rough bed and subjected to the ambient shear flow. Drag and lift forces exerted on the particle located over the rough bed were computed and compared with those for a particle similarly located over a smooth bed. The wall roughness in general increased the drag and lift coefficients over their smooth-wall values. But, at lower Reynolds numbers of Re ≤ 5, the lift coefficient was observed to decrease substantially as the particle location approached the wall (δ˜→0). When the particle is located away from the bed, the hydrodynamic forces over the rough bed are close to those over a smooth bed. In general, at moderate Reynolds numbers, we observe the drag and lift correlations developed by Zeng et al. (2009) for the smooth wall can be used for the rough wall as well, provided the particle Reynolds number and δ are appropriately defined.