A mechanism of thrust enhancement on a heaving plate due to flexibility at moderately low Reynolds numbers

A numerical study is conducted to investigate the force mechanisms for a 3D heaving flexible plate from the perspective of a diagnostic force element analysis. The problem is relevant to a flapping fish-tail simplified as a flat plate with the leading edge held heaving in the space. The flow is assumed to be laminar with the Reynolds numbers fixed at Re=200 or 500, and the Strouhal number St ranging from 0.1 to 0.6, and the flexure amplitude of the plate a0 from 0.1 to 0.25 (dimensionless). As the finite plate is set into unsteady motion, complicated vortex patterns around the plate are generated. It is shown that heaving, whilst increasing thrust generation, also reduces the frictional drag, yet the flexibility promotes thrust generation at the expense of accruing more frictional drag. In the literature, the force (thrust) exerted on the tail-mimicking plate is largely credited to the vortices (vorticity) in the wake. However, this study performs a regional force analysis to show that the vorticity in the wake region supplies approximately 20-30% of the total thrust, especially in the cases of strong thrust generation. Comparable contributions come also from the regions direct above and below the heaving plate (mainly including the attached vortices) as well as from the two side regions (mainly including the tip vortices) next to the flexible plate. In addition, the potential motion associated with the unsteady flapping and the contribution from the surface vorticity are non-negligible constituent force components. The relative importance of the various force contributions was analyzed in detail, and the results may shed light on how a flapping tail generates propulsive efficiency above the critical Strouhal number St=0.2.