Trajectory behaviors and cavity evolution of the trans-media water-entry motion with pitch angular velocity of stone

Fluid–structure interaction (FSI) in stone-skipping motion represents a critical scientific challenge in aerospace engineering. While existing experimental and numerical studies on stone water-entry motion typically presume a fixed initial pitch angle, this investigation specifically examines the influence of initial pitch angular velocity on FSI behaviors. This study focuses on the influences of initial pitch angular velocity on FSI behaviors of the stone, and a comprehensive discussion of water-entry motion patterns based on numerical simulations is presented in this paper. Through comprehensive numerical simulations employing the smoothed particle hydrodynamics algorithm, we analyze stone position/attitude responses, cavity and splash evolution, and pressure fluctuations of the flow field. Our findings reveal several significant insights: (1) the water-entry motion of an inclined stone from air to water manifests in four distinct patterns; (2) initial impact angle and angular velocity are pivotal parameters governing post-impact dynamics; (3) stones with extremely large head-down angular velocity tend to overturn and submerge. And conversely, stones with substantial head-up angular velocity may initially skip before subsequent twice-water-entry; and (4) the maximum pressure in the flow field under different motion patterns shows different parameter sensitivity to initial impact angle. Our results advance understanding of FSI behaviors of the inclined water-entry problem, which could benefit trans-media vehicle design and reentry spacecraft analysis.