Effect of microscale protrusions on local fluid flow and mass transport in the presence of forced convection

Three-dimensional creeping flow around single, axisymmetric protrusions is studied numerically using the boundary-integral technique. Emphasis is placed upon cylindrical protrusions on plane walls for various height-to-radius (h-to-a) aspect ratios, but cones and sections of spheres protruding from plane walls are also briefly examined. The presented items include shear-stress distributions, shear-stress contours, extents of the fluid-flow disturbance, total forces and torques on the cylinders, streamlines, and skin-friction lines. Also included is a discussion of flow topology around axisymmetric geometries. No flow reversal is observed for cylindrical protrusions with aspect ratios greater than 2.4 to 2.6. At higher aspect ratios, the fluid tends to be swept around cylindrical protrusions with little vertical motion. At lower aspect ratios, the strength of the recirculation increases, and the recirculation region becomes wider in the transverse direction and narrower in the flow direction. Also, the recirculation pattern begins to resemble the closed streamline patterns in two-dimensional flow over square ridges. However, unlike two-dimensional flow, closed streamline patterns are not observed. For arbitrary axisymmetric geometries, the extent of the fluid-flow disturbance can be estimated with the total force that is exerted on the protrusion. When the same force is exerted on protrusions with different aspect ratios, the protrusion with the higher aspect ratio tends to have a greater disturbance in the flow direction and a smaller disturbance in the transverse direction. The total force exerted on cylindrical protrusions with rounded corners is only slightly lower than the total force exerted on cylindrical protrusions with sharp corners