The water exit problem, which is ubiquitous in ocean engineering, is a significant research topics in the interaction between navigators and water. The study of the water exit problem can help to improve the structural design of marine ships and underwater weapons, allowing for better strength and movement status. However, the water exit problem involves complex processes such as three-phase gas–liquid–solid coupling, cavitation, water separation, liquid surface deformation, and fragmentation, making it challenging to study. Following work carried out by many researchers on this issue, we summarize recent developments from three aspects: theoretical research, numerical simulation, and experimental results. In theoretical research, the improved von Karman model and linearized water exit model are introduced. Several classical experimental devices, data acquisition means, and cavitation approaches are introduced in the context of experimental development. Three numerical simulation methods, namely, the BEM (Boundary Element Method), VOF (Volume of Fluid), and FVM (Finite Volume Method) with LES (Large Eddy Simulation) are presented, and the respective limitations and shortcomings of these three aspects are analyzed. Finally, an outlook on future research improvements and developments of the water exit problem is provided.

This work studies the water-exit problems of slender cylinders under various conditions through experimental investigation. An experimental platform was equipped with high-speed photography. A total of 13 experimental cases with varying head shapes (conical, spherical, and truncated cone designs), length-to-diameter ratios (5:1–7:1), ejection velocities (7.24–17.93 m/s), and elastic moduli (227.36–279.14 MPa) were conducted to capture water-exit characteristics. The investigation identified ejection velocity as the predominant parameter governing cavity morphology and stability, with higher velocities correlating to increased cavity dimensions and reduced drag coefficients by 54%. Conical head shape resulted in superior drag reduction characteristics, forming a typical cigar-shaped cavity with clear and regular boundaries. Additionally, an increased length-to-diameter ratio substantially improved drag reduction performance by 33%. Material elastic moduli proved crucial for water-exit stability, as cylinders with lower moduli experienced severe bending deformation and even trajectory changes, while higher moduli cylinders maintained their form with minimal deformation. This study illuminates the physical mechanisms of slender body water-exit under multi-factor coupling conditions, providing experimental evidence and theoretical guidance for cross-media vehicle design and underwater equipment optimization.

In this paper, we present a parameter-free particle relaxation technique to improve the accuracy and stability of smoothed particle hydrodynamics (SPH). Instead of imposing a background pressure, particles are regularized following the criteria of 0th-order consistency, i.e., the gradient of a constant to be zero. Specifically, the modifications of particles' position are solved by a gradient decent method according to the error between zero value and the gradient of a constant. This modification decreases the integration error and leads a more uniform particles distribution. A set of challenging benchmarks including lid-driven cavity flow, Taylor-Green vortex, FSI (fluid-solid interaction) problem, 2D (two-dimensional) dam-break case, and water exit of a cylinder are investigated to validate the effectiveness of the present technique for addressing the well-known tensile instability and particle clumping problems. Finally, the study of 3D (three-dimensional) dam-break against an obstacle demonstrates the stability and versatility of the present method.

The water exit problem, which is ubiquitous in ocean engineering, is one of the significant research topics in the interaction between navigators and water. The study of the water exit problem can help to improve the structure design for marine ships and underwater weapons for better strength and movement status. However, the water exit problem involves complex processes such as gas-liquid-solid three-phase coupling, cavitation, water separation, liquid surface deformation and fragmentation, making it challenging to study. According to the works carried out by many researchers towards this issue, we summarize the recent developments from three aspects, i.e. theoretical research, numerical simulation and experimental results. In theoretical research, the improved von Kaman model and linearized water exit model are introduced. Several classical experimental devices, data acquisition means and cavitation are introduced in experimental development. Three methods, namely, BEM(boundary element method), FVM(finite volume method) and LES(large eddy simulation) are concluded for numerical simulation. The limitations and shortcomings of these three aspects are then analyzed. Finally, an outlook on the future research improvements and developments of the water exit problem is provided.

This work investigates the water exit problems of slender cylinders under various con-ditions by experiment. The experimental platform is designed with a high-speed pho-tography. 13 experimental cases with varying head shapes, length-to-diameter ratios, ejection velocities, and elastic moduli was conducted to capture water-exit character-istics. The investigation identified ejection velocity as the predominant parameter governing cavity morphology and stability, with higher velocities correlating to in-creased cavity dimensions and reduced drag coefficients. Conical head shape resulted in superior drag reduction characteristics, forming a typical cigar-shaped cavity with clear and regular boundaries. Additionally, an increased length-to-diameter ratio sub-stantially improved drag reduction performance. Material elastic moduli proved cru-cial for water-exit stability, as cylinders with lower moduli experienced severe bending deformation and even trajectory changes, while higher moduli cylinders maintained their form with minimal deformation. This study illuminates the physical mechanisms of slender body water-exit under multi-factor coupling conditions, providing experi-mental evidence and theoretical guidance for cross-media vehicle design and under-water equipment optimization.