In-depth characterization and analysis of simple shear flows over regularly arranged micro pillars, I. Effect of fluid inertia

Through high-fidelity numerical simulation, the simple shear flow over regularly arranged micro pillars has been investigated. The essential issues to be addressed include the characteristics of a simple shear flow over quadrilateral array of micro pillars, the effect of fluid inertia on the basic flow pattern, and the decomposition of the complex surface friction. The results show that the flow is characterized by a series of microscale recirculating eddies in the gaps between the streamwise neighboring pillars. The recirculation of the micro eddies and the oscillation of the overhead flow climbing over the pillar tips create a local flow advection. At smaller Reynolds number, the fluid inertia is weak and the flow patterns are symmetrical about the pillar center. When the Reynolds number is sufficiently large, the fluid inertia takes effect and breaks the symmetrical patterns. The overhead flow tilts downward, forming a spiral long-range advection between the fluid flow above pillar array and the flow in the spaces among micro pillars. The local advection and long-range advection constitute the transport mechanism in wall-normal direction. On micro-structured walls, the total friction includes the reaction forces of micro pillars due to flow shear and flow pressure at pillar surfaces and the reaction force of bottom plane due to flow shear on bottom surface. For larger Reynolds numbers, fluid inertia prevents the fluid from flowing along the curved surface of micro pillars and reduces the equivalent shear stress of the pillar reaction force due to flow shear. At the same time, the fluid inertia makes the overhead flow impact the windward side of micro pillars more strongly and therefore increases the equivalent shear stress of the pillar reaction force due to flow pressure.