Three-Dimensional Hydrodynamic Analysis of a Flexible Caudal Fin

Abstract

A 3D fluid–structure coupled simulation of a square flexible flapper, the basic model of a caudal fin, is performed to visualize the flow field around the caudal fin. A plate immersed in a water tank is driven to oscillate vertically by its leading edge. A quantitative analysis of the thrust generated by the plate, which is difficult to explore experimentally, is performed over a range of non-dimensional flapping frequencies 0.93 <f*< 1.47 to explore the mechanism of thrust generation in more detail. Comparisons are made between three different flapping frequencies around the structural resonance. Numerical results at different flapping frequencies provide a reasonable estimate of the trailing edge amplitude and phase lag of the motion of the plate’s leading and trailing edges. The pressure distribution and deformation of the plate are analyzed to estimate the time evolution of the maximum and minimum thrust generation during the flapping period. Variations in pressure distribution on the plate surface are mainly due to the displacement of the trailing edge relative to the leading edge. Thrust is mainly provided by the pressure difference at the trailing edge. The maximum thrust was found to correspond to the maximum relative deformation of the trailing edge. The optimum frequency f* = 1.2 corresponding to the maximum thrust generation does not coincide with the structural resonance frequency, but remains at a frequency slightly higher than the resonance. These results indicate that the relative deformation of the plate plays an important role in the estimation of the flow field and the associated thrust generation. The numerical results may provide new guidelines for the design of robotic underwater vehicles.