Objectives Since the early 21st century, driven by the integration of ship engineering and fluid mechanics, the research and development of large container ships and special vessel types have become key drivers of global trade, energy transportation, and port dredging. With the intelligent upgrading of canal networks, ship navigation efficiency has significantly improved, while safety control requirements for navigation have increased, necessitating more refined studies of hydrodynamic characteristics. Therefore, the study of various hydrodynamic coefficients is crucial, as they are directly related to the maneuvering performance of ships. Current research methods primarily include theoretical calculations, empirical formulas, model tests, and numerical simulations, with model tests and numerical simulations being the two main approaches. Planar motion mechanism tests provide the core experimental data for studying the dynamic hydrodynamic characteristics of ships through six-degree-of-freedom motion simulations. Due to the high cost and lengthy duration of model experiments, numerical simulation technology has emerged as a cost-effective and efficient tool for hydrodynamic coefficient research, aided by turbulence model optimization and parallel computing techniques.

Methods The naoe-FOAM-SJTU solver, developed on the open source platform OpenFOAM, is capable of handling dynamic overlapping grids. This solver integrates a self-developed multi-body six-degree-of-freedom motion solver module, enabling full simulation of various working conditions in ship planar motion mechanism tests and facilitating comprehensive dynamic coupling analysis of fluid and moving body interactions. For grid processing, the Suggar++ overlapping grid interpolation program is employed to generate domain connectivity information, ensuring accurate data transmission and stable coupling of flow field data between overlapping grids. In this study, the dynamic overset grid method is used in conjunction with the unsteady RANS equation and SST k-ω turbulence model for numerical simulation. The SST k-ω model effectively combines the high accuracy of the k-ω model in the near-wall region with the robustness of the k-ε model in the far-field flow by solving the RANS equation in a closed form. The model significantly enhances the prediction accuracy of complex flows, especially separated flows, by introducing a mixing function and constraining the viscosity of turbulent vortices. Based on the above numerical methods, a systematic hydrodynamic numerical simulation and analysis of the swaying motion of the KVLCC1 ship model were carried out in both deep and shallow water environments, with varying water depth-to-draft ratios.

Results  The comparison with experimental results shows that the errors in sway force amplitude, yaw moment amplitude, and phase angle relative to the experimental values are mostly around 5%, verifying the feasibility of using the overlapping grid method to calculate ship hydrodynamic forces. This result further confirms that the selected calculation model accurately reflects the actual conditions and ensures the effectiveness and credibility of numerical simulations for engineering applications. In both deep and shallow waters, the hydrodynamic coefficients in shallow water are significantly greater than in deep water, which is closely related to the shallow water effect. This effect can lead to a deterioration in the ship's maneuverability in shallow water, particularly during large steering maneuvers, where maneuverability may be seriously impacted. Additionally, the amplitude of sway force and the amplitude of the yaw moment are found to be linearly related to the dimensionless quantity v' of sway velocity amplitude. The shallow water effect significantly increases the flow velocity on both sides of the hull and the bottom of the ship. In areas where the flow velocity gradient increases, the regions with faster flow velocity in deep water are mainly concentrated at the bow and stern, while in shallow water, these regions extend across the entire bottom of the ship. In deep water, the velocity distribution behind the stern is more stable compared to shallow water. Regarding the wake, under deep water conditions, the wake is relatively stable, fully developed, and exhibits a more regular shape than under shallow water conditions. In shallow water, the low-velocity and low-pressure areas in the wake are more pronounced than in deep water, caused by the insufficient development of the wake due to limited space in the z direction. Additionally, the forebody bilge vortex is less developed in shallow water due to the restricted vertical space.

Conclusions This research provides valuable insights for ship maneuverability analysis.