Drag measurements across patterned surfaces in a low Reynolds number Couette flow facility

Abstract

Understanding fluid dynamic drag, and its reduction, has always been a topic of primary concern. Direct drag measurements can be difficult to obtain with low viscosity fluids such as air or water. For this study a new low Reynolds number Couette facility was constructed to investigate surface drag. In this facility, mineral oil was used as the working fluid to increase the shear stress across the surface of the experimental models. A mounted conveyor creates a flow within a Plexiglas tank. The experimental model of a flat or patterned surface was suspended above the moving belt. The experimental plate was attached to linear bearings on a slide system that connects to a force gauge used to measure the drag. Within the gap between the model and moving belt a Couette flow with a linear velocity profile was created. Digital particle image velocimetry was used to confirm the velocity profile. A patterned surface, in this case consisting of 2-D cavities, was embedded into a large portion of a Plexiglas plate. First, the drag across a flat plate of the same size was measured and compared to theoretical values for laminar Couette flow. These results were found to be within 5% of predicted values following CD = 2/Re. The drag for a 2-D embedded square cavity model was then measured and compared to the flat plate results. A drag reduction of up to 20% was found for the lateral rib model at Re ~ 10 or less, with increasing drag reduction as the Re decreases. Lower drag reduction was found up to Re ~ 50, where the difference becomes negligible. Finally, the flow over the 2-D cavities was modeled with a partial slip at the bottom wall. Modeled average partial slip velocities were calculated from the drag measurements and reached values of 10-22% of the belt speed for Re < 10.