Objectives The cross-medium "swarm" penetration of multiple vehicles has attracted significant attention from researchers worldwide. To investigate the mutual interference between two vehicles during high-speed water entry, a numerical simulation is performed to analyze the high-speed water entry process of two parallel cone-shaped vehicles with varying spacing.

Methods The present numerical model is based on Star CCM+. The turbulence calculations were performed using the Realizable k−ε turbulence model based on the Reynolds Averaged Navier-Stokes (RANS) approach. The volume of fluid (VOF) multiphase flow technique was employed to model the interaction of multiple fluids (air, water, and water vapor), capturing the motion of free surfaces within a single medium. The Schnerr-Sauer cavitation model was employed to calculate the vapor volume fraction, accounting for the phase change between water vapor and liquid. Additionally, the overset grid technology was applied to track the motion of the cylindrical projectile. The study explores the hydrodynamic characteristics, including the evolution of cavity shape, the pressure load on the head, and the motion trajectory of two parallel vehicles during water entry at different spacings d.

Results Upon contact with the surface, the vehicle's load and the impulsive pressure on the head increase dramatically, reaching their maximum values instantly for different spacings, and then they quickly decrease. At a spacing of d = 0.8D, the maximum impact load is more than 20% greater than that at d = 1.6D, and the corresponding maximum impact pressure on the head slightly increases, where D is the diameter of the vehicle. However, when d≥1.6D, the spacing has little effect on the maximum load and pressure on the vehicle. During the water entry process, the pressure distribution on the inner and outer sides of the heads of the dual-body vehicles becomes unbalanced. The smaller the spacing, the more significant this mutual influence, resulting in greater load differences between the two sides. The cavity shape develops freely on the outer side but is restricted on the inner side due to interference. Consequently, the vehicle's tail tilts inward, producing a tail slap phenomenon. However, as the spacing increases, the development and evolution of the internal cavities of the dual-body vehicles become more gradual.

Conclusions When the dual-body vehicle structure enters the water in parallel, the trend of cavity development becomes more pronounced. The degree of interference from adjacent projectiles is closely related to the distance between them. This numerical study provides engineering guidance for the load assessment of dual-body vehicles during high-speed vertical water entry.