Self-propelled flexible fin in the wake of a circular cylinder

The behavior of a self-propelled flexible fin behind a circular cylinder in a uniform flow was explored using the immersed boundary method. The transverse heaving motion of the leading edge of the fin was prescribed, whereas the lateral behavior was spontaneously determined by the hydrodynamic interactions between the fin and the fluid environment. Three different behaviors were observed: propulsion upstream, drift downstream, and holding stationary at an equilibrium position. In a uniform flow, the fin could not overcome the positive net drag, and it drifted downstream. By contrast, a fin in the wake of a cylinder was propelled toward the circular cylinder during the heaving motion. The trailing edge of the fin passively fluttered along the oncoming vortices, thereby propelling the fin upstream. During the upstream propulsion behavior, the fin was propelled through the vortex cores. The fin was observed to remain stationary at a heaving frequency equal to the vortex shedding frequency, and a slaloming behavior was observed between the oncoming vortical structures. The fin was not propelled toward the cylinder during the slaloming behavior; rather, it lingered at a certain streamwise distance from the cylinder. Several equilibrium positions were dynamically determined from the interaction between the fin and the vortical fluid environment. The equilibrium position depended on the initial longitudinal position and the phase of the fin heaving motion with respect to the phase of the vortex shedding. The power input required to drive the heaving motion was reduced during the slaloming behavior.