Roughness effects in laminar channel flow

The effects of roughness on the frictional drag and pressure drop in laminar channel flow are investigated numerically. The inflow is fully developed smooth wall flow, and square rib roughness, aligned normal to the bulk flow direction, is introduced as a step change. The roughness height and spacing are systematically varied, and the flow is examined as it develops over the rough wall and becomes fully developed. The length of the development region depends primarily on the roughness height, although the effects of spacing become more important as the height decreases. In the fully developed rough wall regime, the friction coefficients always increase with roughness when compared to the smooth wall case, but the increase depends crucially on the roughness height and to a lesser extent on the spacing. Using the constricted diameter in the definition of the friction factor collapses the data on the smooth wall value to within 10 % for all roughnesses studied here, with the remaining deviation increasing linearly with roughness spacing. The friction factors scale with the inverse of the Reynolds number, as seen elsewhere. The scaling of the development length and the friction coefficient can be explained by the relative contributions made by the pressure drop on each element and the skin friction acting over the surface area. These observations are examined in terms of the flow patterns in the vicinity of the roughness elements, which leads us to propose a definition for fully rough laminar flow.