Numerical simulation of oscillating plates at the visco-inertial regime for bio-inspired pumping and mixing applications

Abstract

In this numerical study, flow driven by oscillating plates in a channel is investigated at the intermediate Reynolds regime by means of the arbitrary Lagrangian–Eulerian method. The effects of temporal asymmetry, Reynolds number, channel height, phase differences between adjacent plates, and orientation angle on pumping performance, which are unclear under temporally asymmetric linear plate kinematics, are studied. By examining efficiency measures, new insight is gained from energy, mixing, and combined flowrate/energy standpoints. Furthermore, the mixing performance of oscillating plates, which is to a large extent unknown at the visco-inertial regime, is scrutinized. By studying a finite number of plates, end effects that are not apparent in the more common studies on infinite plate/cilia arrays are accounted for. For a single plate, results show an almost threefold increase in the average flow rate between Reynolds numbers of 5 and 40 but a fall thereafter caused by the restriction of the flow by a region of circulation. The average flow rate and energy conversion efficiency increase by 20% when the orientation angle is increased from −4° to 12°, and a point of maximum flow generation is found at a plate length to channel height ratio of 0.7. For an array of five plates, a phase difference of 90° between adjacent plates (antiplectic metachronal wave) generates the largest flow, while a phase difference of 270° (symplectic metachronal wave) brings about the best mixing efficacy. This suggests that the optimal phase difference depends on the intended use of the device.