Coordinated suction and blowing of a cylinder array for thrust generation

Abstract

Various systems of mechanical devices and natural organisms use the repeated expansion and contraction of deformable structures to draw in and blow out fluid. Instead of such deformable continuous structures, a system that consists of multiple discrete bodies can also generate a directional flow through the cooperative movement of the individual bodies. In this study, we numerically investigate the collective effects of a multi-body system composed of eight circular cylinders, each of which oscillates separately in the radial direction to generate thrust. The cylinder array performs cooperative motion regulated by three motion parameters: phase difference, oscillation amplitude and frequency at a low Reynolds number ( $Re = 10$ ). The phase difference between the cylinders is critical in determining the extent of the directional flow and the time-averaged thrust. The optimal phase difference that yields the maximum time-averaged thrust is consistent, regardless of the oscillation amplitude and frequency. However, the thrust generation performance becomes significantly weaker at a higher Reynolds number ( $Re = 100$ ). This highlights that the hydrodynamic blockage in gaps between cylinders, which is induced by strong viscous diffusion at the low Reynolds number, is essential for the cooperative force generation of multiple closely spaced bodies. A new dimensionless geometric parameter based on the motion of the array is proposed to characterize the degree of bias in the generated flow and it successfully predicts the trend in the time-averaged thrust at the low Reynolds number with strong hydrodynamic blockage.