Thrust analysis of a heaving flexible plate by force element theory

In this study, we have conducted a numerical study of a uniform flow over a flexible plate in heaving motion. The flow is assumed to be laminar with the Reynolds numbers fixed at Re=500, and the Strouhal number St ranging from 0.1 to 0.6. The flow is complicated with three-dimensional vortices generated all around the finite body, in addition to the unsteady motion of the plate. In particular, we performed the force element analysis to examine the detailed force mechanisms of how individual flow components contribute to the thrust on the heaving plate. It is often considered in the literature that the flapping tail has thrust mainly produced by the wake behind the body (such as the theory of reverse Kármán vortex). However, the present analysis shows that the vorticity in the wake comprises around 30% of the total vorticity thrust, which in turn comprising about 22% of the total thrust. 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.