Hydrodynamics of a three-dimensional self-propelled flexible plate.

A three-dimensional self-propelled flexible plate in a quiescent flow was simulated using the immersed boundary method. The clamped leading edge of the flexible plate was forced into a vertical oscillation, while free to move horizontally. To reveal the hydrodynamics of the plate, the averaged cruising speed ($\bar{U}_{C})$, the input power ($\bar{P})$, and the swimming efficiency ($\eta )$ were analyzed as a function of the bending rigidity ($\gamma )$ and the flapping frequency ($f)$. The velocity field around the plate and the exerted force on the plate were demonstrated to find out the dynamic interaction between the plate and the surrounding fluid. The kinematics of the plate, the maximum angle of attack ($\phi _{max})$, and the mean effective length ($\bar{L}_{eff})$ were examined accounting for the hydrodynamics of the self-propelled flexible plate. The vortical structures around the plate were visualized, and the influence of the tip vortex on the swimming efficiency was explored qualitatively and quantitatively.