Hydrodynamics of Butterfly-Mode Flapping Propulsion of Dolphin Pectoral Fins with Elliptical Trajectories

Abstract

This article aims to numerically study the hydrodynamic performance of the bionic dolphin equipped with a pair of rigid pectoral fins. We use dynamic-grid technology and user-defined functions to simulate a novel butterfly-mode flapping propulsion of the fins. This pattern of propulsion is composed of three angular degrees of freedom including the pitch angle ϕp, the azimuth angle ϕa and the roll angle ϕr, which can be divided into four stages for analysis within a single cycle. The stroke of one single pectoral fin can be approximated as an ellipse trajectory, where the amplitudes of ϕa and ϕp, respectively, determine the major and minor axes of the ellipse. The fluid dynamics involved in the specific butterfly pattern is mathematically formulated, and numerical simulation is conducted to investigate the propulsion quantitatively. The results show that the dolphin with a higher water striking frequency f can acquire higher propulsion speed and efficiency. Furthermore, the shape of the ellipse trajectory under different conditions could also have different propulsion effects. The periodic generation and disappearance of vortex structures in the butterfly flapping mode show the evolution process of fluid flow around a pair of pectoral fins, which reveals the influence of motion parameters on fluid dynamics under different working conditions.

Three-Dimensional Numerical Study of Hydrodynamic Interactions between Pectoral Fins and the Body of Aquatic Organisms

“…Webb et al [ 9 ] reported that the pectoral fin generates a cutting force for postural control and discussed its role in improving postural stability. In addition, while many pectoral fin studies have focused on rays [ 10 , 11 ], recent years have shown the effects of pectoral fins in a wide variety of aquatic organisms, including dolphins and turtles [ 12 , 13 ]. The pectoral fins play an auxiliary role in propulsion by flexion of the body to achieve maneuverability such as a change of direction and postural stability, but they also serve as an organ that further enhances the propulsive performance of aquatic organisms.…”