Hydrodynamic benefits of frequency-modulated bursting of a self-propelled flexible plate

The penalty immersed-boundary method was utilized to investigate the hydrodynamics of frequency-modulated bursting in a three-dimensional self-propelled flexible plate. In the vertical direction, the frequency-modulated bursting was imposed at the leading edge of the plate, while the plate was free to move in the horizontal direction to realize the self-propelled plate. Two kinds of frequency-modulated bursting were chosen: a hawk-like bursting and a lark-like bursting. For comparison, simulations for a sinusoidal bursting were also performed. The energy transformation between the elastic energy and the x-direction kinetic energy was examined and the phase difference between the leading edge and the trailing edge were analyzed to explore the hydrodynamic benefits of the frequency-modulated bursting. The presence of two local peaks during stroke reversal substantially improved the cruising speed. The high acceleration during the fast upstroke led to an increase of the elastic energy. The cruising speed increased when the accumulated elastic energy was transferred to the x-direction kinetic energy. Vortical structures were checked to investigate the interactions between the plate and surrounding fluid. The role of bending rigidity of the plate for the frequency-modulated bursting was also examined. The average cruising speed of the plate with the lark-like bursting was 66.9% larger than that of the plate with the sinusoidal bursting.