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Through high-fidelity numerical simulation, the simple shear flow overregularly arranged micro pillars has been investigated. The essential issues tobe addressed include the characteristics of a simple shear flow overquadrilateral array of micro pillars, the effect of fluid inertia on the basicflow pattern, and the decomposition of the complex surface friction. Theresults show that the flow is characterized by a series of microscalerecirculating eddies in the gaps between the streamwise neighboring pillars.The recirculation of the micro eddies and the oscillation of the overhead flowclimbing over the pillar tips create a local flow advection. At smallerReynolds number, the fluid inertia is weak and the flow patterns aresymmetrical about the pillar center. When the Reynolds number is sufficientlylarge, the fluid inertia takes effect and breaks the symmetrical patterns. Theoverhead flow tilts downward, forming a spiral long-range advection between thefluid flow above pillar array and the flow in the spaces among micro pillars.The local advection and long-range advection constitute the transport mechanismin wall-normal direction. On micro-structured walls, the total frictionincludes the reaction forces of micro pillars due to flow shear and flowpressure at pillar surfaces and the reaction force of bottom plane due to flowshear on bottom surface. For larger Reynolds numbers, fluid inertia preventsthe fluid from flowing along the curved surface of micro pillars and reducesthe equivalent shear stress of the pillar reaction force due to flow shear. Atthe same time, the fluid inertia makes the overhead flow impact the windwardside of micro pillars more strongly and therefore increases the equivalentshear stress of the pillar reaction force due to flow pressure.

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