RESEARCH ON THE SWIMMING CHARACTERISTICS OF STINGRAYS BASED ON THE MPF PROPULSION MODE OF MODIFIED WAVE EQUATION

The median and/or paired fin propulsion (MPF) mode has attracted increasing attention from bionics researchers due to the efficient and stable swimming ability of rays. In this study, a ray species with triangle-like pectoral fins was selected for bionic modeling. Focusing on its swimming posture and propulsion mode, a dual-fin symmetric motion model was established by improving the wave equation. The computational fluid dynamics (CFD) method combined with dynamic mesh technology was employed to conduct numerical simulations, exploring the propulsion mechanism and swimming characteristics. Based on these findings, the effects of different parameters, including pectoral fin wave frequency, wave amplitude, and body wave wavelength, on the swimming ability of MPF-mode rays were investigated by varying these biological characteristics. The results revealed that distinct low-pressure centers emerged at the tips of the pectoral fins during both the upward and downward flapping phases, with the majority of propulsion force generated by the vorticity difference at the fin tips. During the upward and downward flapping of both fins, the fish body generated periodic lift, and the peak lift coefficient increased with higher flapping frequency and amplitude. Under the same initial velocity and fish body motion state, the vertical displacements of the fish body reached 2.32 m and 1.81 m, respectively, at 3 Hz andA= 0.125L, achieving the maximum vertical lift increase. The body wave wavelength determined the primary position of pectoral fin fluctuation. Whenλ= 0.6L, indicating a primary oscillation point closer to the neutral longitudinal plane, the mean propulsion force coefficient averages at a mere 0.02. Conversely, whenλ= 1.05L, positioning the primary oscillation near the pectoral fin tips, the fish exhibits a significantly higher mean propulsion force coefficient of 0.14.The findings of this study can serve as a foundation for the design and fabrication of bionic underwater robotic fish based on the MPF propulsion mode.