Objectives Since the beginning of the 21st century, driven by the integration of ship engineering and fluid mechanics technology, the research and development of large container ships and special ship types has become a key carrier to support global trade, energy transportation and port dredging. With the intelligent upgrading of the canal network, the ship 's navigation efficiency has been significantly improved while its navigation safety control has put forward higher requirements for the refined study of hydrodynamic characteristics. Therefore, the study of various hydrodynamic coefficients is particularly important, which is related to the advantages and disadvantages of ship maneuvering performance. The current research methods mainly include theoretical calculation, empirical formula, model test and numerical simulation. Model test and numerical simulation are two main research methods. The planar motion mechanism test provides the core experimental data for the study of dynamic hydrodynamic characteristics of ships through six-degree-of-freedom motion simulation. In view of the high cost and long period limitation of model experiments, numerical simulation technology has become an economical and efficient means of hydrodynamic coefficient research through turbulence model optimization and parallel computing.

Methods The naoe-FOAM-SJTU solver developed based on the open source platform OpenFOAM has the ability to handle dynamic overlapping grids. The solver integrates a self-developed multi-body six-degree-of-freedom motion solver module, which can be used to completely simulate various working conditions in the ship planar motion mechanism test and realize the full dynamic coupling analysis of fluid and moving body. In terms of grid processing, the Suggar++ overlapping grid interpolation program is used to generate Domain Connectivity Information, which ensures the accurate transmission and stable coupling of flow field data between overlapping grids. In this study, the dynamic overset grid method is used, combined 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 and the robustness of the k-ε model in the far-field flow by solving the RANS equation in a closed form. The model significantly improves 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, we carried out a systematic hydrodynamic numerical simulation and analysis of the swaying motion of the KVLCC1 ship model in deep water and shallow water environment with different water depth draft ratios.

Results The comparison with the experimental results shows that the errors of sway force amplitude, yaw moment amplitude and phase angle with the experimental values are mostly about 5 %, which verifies the feasibility of using the overlapping grid method to calculate the ship hydrodynamic force. This result further verifies that the selected calculation model can accurately reflect the actual situation and ensure the effectiveness and credibility of numerical simulation in engineering applications. In the deep and shallow waters, the hydrodynamic coefficient in shallow water is significantly greater than that in deep water, which is closely related to the shallow water effect, which will lead to the deterioration of the maneuverability of the ship in shallow water. Especially in the large steering, the maneuverability of the ship may be seriously affected, and the amplitude of the sway force and the amplitude of the yaw moment are linearly related to the dimensionless quantity v' of the sway velocity amplitude. The shallow water effect can significantly increase the flow velocity on both sides of the hull and the bottom of the ship. For the area where the flow velocity gradient increases, the area with faster flow velocity in deep water is mainly concentrated in the bow and stern position, and the shallow water is distributed throughout the bottom of the ship. In the deep water environment, the velocity distribution of the section behind the stern is more stable than that in the shallow water. As far as the wake behind the ship is concerned, the wake is relatively stable and fully developed under deep water conditions, and the shape is more regular than that under shallow water conditions. In the shallow water condition, the low velocity and low pressure area in the wake is more than that in the deep water condition, which is caused by the insufficient development of the wake due to the limited space in the z direction. The forebody bilge vortex also has insufficient development due to the limited vertical space under shallow water conditions.

Conclusions The research can provide reference for ship maneuverability analysis.