Skipping performance and hydrodynamic mechanisms of a hydrofoil-shaped vehicle with different bottom configurations

Near-water-surface skipping vehicles use repeated water-surface impacts and rebounds to maintain high-speed motion near the free surface. Successful rebound with a stable water-exit attitude after each water contact is therefore essential for continued skipping. Among the factors governing this process, the bottom configuration plays a critical role in determining the hydrodynamic loads and pitching response. Therefore, this study investigates the skipping performance and hydrodynamic mechanisms of a hydrofoil-shaped vehicle with different bottom configurations. A high-fidelity numerical framework combining the finite volume method, volume-of-fluid model, improved delayed detached eddy simulation, overset mesh technology, adaptive mesh refinement, and a six-degree-of-freedom dynamic fluid-body interaction solver is established. The numerical method is validated through skipping experiments, showing good agreement in free-surface evolution and attitude response, with additional validation provided by the pitching-moment comparison. A flat-bottom model and three NACA-airfoil-based models are compared under different water-entry inclination angles. Under the investigated initial kinematic and dynamic conditions, only the NACA 2412 model achieves successful skipping in all investigated cases. Its downward-convex bottom reduces the local water-entry angle and impact velocity, thereby weakening the initial slamming load and pitch-down moment. More importantly, it promotes faster wetted-region development and earlier forward migration of the pressure center, thereby generating a sustained pitch-up restoring moment that suppresses the accumulated pitch-down motion. During water exit, the pressure center moves backward and produces a pitch-down restoring moment that limits excessive pitch-up rotation. These alternating restoring moments enable the NACA 2412 model to recover a stable water-exit attitude and achieve successful skipping. By contrast, the flat-bottom, NACA 4412, and NACA 6412 models fail to provide sufficient cumulative pitch-up restoring effects to reverse the previously accumulated pitch-down motion. These results indicate that successful skipping depends not only on reducing the initial impact load, but also on regulating the temporal evolution of wetted-region development, pressure-center migration, and hydrodynamic restoring moments.