This study aims to systematically quantify the effects of fin-hull geometric configuration on the propulsion performance of bionic undulating-fin vehicles employing media and/or paired fin propulsion (MPF). It addresses the lack of a unified analysis of geometric parameters across different bionic underwater vehicles in existing research.

To this end, a universal parametric geometric model incorporating the hull and a pair of undulating fins was developed. The model innovatively introduces the ratio of fin width to hull width β as the core dimensionless geometric parameter. Based on this model, high-fidelity CFD numerical simulations were conducted to analyze the propulsion performance and flow field structure of the vehicle under different β values.

The results indicate that β has a nonlinear and significant influence on propulsion performance, and that an optimal range of β values exists for maximizing propulsion efficiency. Excessively small β values lead to insufficient thrust generation, whereas excessively large β values increase drag due to intensified fin-hull interactions that induce flow separation. Furthermore, β significantly modulates the magnitude of the pitching moment, imposing a critical constraint on the vehicle's attitude stability.

This study clarifies the design trade-off between efficiency and stability governed by the β parameter. The established parametric model and the identified underlying mechanisms provide a quantitative theoretical basis for the shape design of bionic underwater vehicles and lay a solid foundation for future research on multi-parameter coupling optimization and self-propulsion performance.

When the cavitation number drops to a certain critical value, the pressure at the leading edge of an underwater hydrofoil will decrease and cavitation will occur. In model test studies, it is difficult for a scale model hydrofoil to meet the Reynolds number of a real scale hydrofoil, so the critical cavitation number during cavitation initiation will be changed.

To this end, with reference to the NACA 0012 rudder used in the standard KCS ship with a speed of 24 knots, the hydrofoil cavitation characteristics are numerically simulated in the paper using the SST k-ω turbulence model and Schnerr-Sauer (S-S) cavitation model based on STAR-CCM+ software. According to different scale models, the surface flow field and cavitation distribution of the hydrofoil are calculated by changing the environmental pressure of the hydrofoil at different attack angles. In this way, the critical cavitation number corresponding to cavitation initiation is obtained, and the influence mechanism of the scale effect on the critical cavitation number is analyzed.

Through the analysis of the calculation results, it is concluded that with the decrease in scale, the size of the critical cavitation number at the corresponding attack angle of the hydrofoil will decrease, indicating that the scale effect caused by the difference in the Reynolds number is intensified.

Therefore, in model tests, in order to prevent the influence of the scale effect on the initial cavitation number, a hydrofoil of a smaller scale should not be selected.