Numerical Study Of Ship-to-ship Hydrodynamic Interaction In Restricted Waters Based On High-order Panel Method

Ship-to-ship hydrodynamic interaction has close relation with ships' navigation safety,and is one of the most important research issues of ship's maneuverability and safety in restricted waters.With the rapid development of shipping industry,the intensity of ship navigation is increasing continuously.Meanwhile,the development of ships towards large-scale and rapidness leads to more frequent occurrence of ship-to-ship hydrodynamic interaction phenomenon.The increasing intensity of ship navigation and the development of ships towards large-scale have made the relative distance between two ships smaller,while the high speed of ships made the relative speed between ships larger.Because the construction speed of ports and waterways cannot keep up with the pace of development of ships,the existing ports and waterways have become narrower and shallower relatively,and the bank effect and the shallow water effect have become two important factors that cannot be ignored with respect to ship's navigation safety.Therefore,the study on the hydrodynamic interaction between ships sailing in restricted waters becomes more important.This dissertation aims to develop a three-dimensional potential theory program by using a high-order panel method based on NURBS,and apply it to predict the ship-to-ship hydrodynamic interaction between two ships travelling along parallel course in restricted waters.For this purpose,the following aspects of research work are mainly carried out in this dissertation: developing a three-dimensional high-order panel method based on NURBS and the corresponding computer program;applying the developed computer program to study numerically the ship-to-ship hydrodynamic interaction in shallow water with constant water depth,the ship-to-ship hydrodynamic interaction in narrow and shallow canal with constant water depth,and the ship-to-ship hydrodynamic interaction in shallow water with irregular seabed.In the high-order panel method based on NURBS,the hull geometry is represented by the third-order NURBS,while the distributed source is described by the third-order B-spline.The boundary integral equation is discretized with respect to the NURBS panels on the hull surfaces and satisfied at the corresponding collocation points,i.e.,the vertices of the panels.Under the assumption of low travelling speed,the effect of free surface elevation is neglected and the undisturbed free surface is treated as a rigid wall.After the velocity potential is determined,the unsteady Bernoulli equation is used to calculate the dynamic pressure distribution on the hull surface at each instant,and the hydrodynamic interaction forces and moment of surge force,lateral force and yaw moment are obtained by integrating the dynamic pressure along the wetted surfaces of the hull.The problem of ship-to-ship hydrodynamic interaction is solved in time-domain.During the whole process of ship-to-ship hydrodynamic interaction from the starting to the ending moments,the time-stepping method is used to update the positions of each ship and the velocity potential of the source distribution at each instant.For the ship-to-ship hydrodynamic interaction in shallow water with constant water depth,the undisturbed free surface and the flat seabed are treated as two mirror faces,and the infinite image method is used to deal with the effects of free surface and finite water depth.Taking the Wigley hulls,elliptic cylinders and tankers as study objects,three typical cases of ship-to-ship hydrodynamic interaction,i.e.,a moving ship passing by a moored ship,two ships meeting and a moving ship overtaking another moving ship,are investigated respectively.Firstly,detailed convergence study with respect to the panel size,time step and the truncated terms of the infinite image Green function is undertaken.On this basis,validation of the present numerical method is conducted: The validation for the Wigley ships is achieved by comparing the present numerical results with the calculation results by using the slender-body theory or RANS-based CFD method,while the validation for the elliptic cylinders and tankers is achieved by comparing the present numerical results with the corresponding experimental data.On the basis of validation,influencing factors,such as the lateral distance between ships,the ratio of water depth to draught and ship's speed,are investigated by a series of calculation and comparison,and the influence tendency of these factors on the ship-to-ship hydrodynamic interaction are obtained.For the ship-to-ship hydrodynamic interaction in narrow and shallow canal with constant water depth,both vertical bank and sloping bank are considered and the bank effect is taken into account by distributing singularity sources on the bank.Two Wigley ships are taken as study objects,and three typical cases of ship-to-ship hydrodynamic interaction mentioned above are investigated.Influencing factors,such as the lateral distance between ship and bank,the sloping angle of bank,the ratio of water depth to draught and ship's speed,are investigated by a series of calculation and comparison,and the influence tendency of these factors on the ship-to-ship hydrodynamic interaction are obtained.For the ship-to-ship hydrodynamic interaction in shallow water with irregular seabed,since the infinite image method is not valid,the boundary condition on the seabed is satisfied by distributing source on the seabed.This treatment is applicable to arbitrary irregular seabed.Firstly,the case of ships meeting in shallow water with constant water depth is considered for validation.The numerical results of infinite image method are compared with those by distributing source on the seabed to validate the method of distributing source on the seabed.On this basis,the numerical method is extended to deal with inclined seabed,stepped seabed and wavy seabed.The ship-to-ship hydrodynamic interaction is investigated,and the comparisons of the numerical results demonstrate the influence tendency of different seabeds on the ship-to-ship hydrodynamic interaction.The NURBS-based high-order panel method developed in this dissertation can reasonably predict the ship-to-ship hydrodynamic interaction in restricted waters.The outcome of this study has a certain guiding significance for ship safely maneuvering and control in restrict waters.The developed computer program can provide an effective platform for further study on more complicated cases of ship-to-ship hydrodynamic interaction problem.