A Simple And Efficient Method For The Coupled Motions Of Multiple Bodies In Waves

The analysis of hydrodynamic problems is an important subject of ship security and design. The hydrodynamics of a single structure in waves, such as a ship or a production platform, are usually calculated by the three-dimensional source-sink distribution method. But difficulties in actual computations may arise for calculations of the interaction of multiple bodies, since a lot of source panels are needed for this kind of numerical calculations, especially for a high wave frequency case. The computation work increases with the increase of size and number of structures. So for multiple-bodies case, a simple and efficient method is called for. The method proposed by Lean et al is a possible choice for such a purpose. This method approximates a ship cross section by a rectangle with the same area of the original ship section, and divides the flow field into inner domain below the ship bottom and the outer domain beside ship hull. The inner-domain velocity potential is given by a simple analytic solution, and the outer-domain velocity potential, given by a source-sink distribution along the contour of ship water area, is expanded over water depth as a Fourier series. The two velocity potentials are matched at the interface of two domains by matching condition. This method only solves the slender ship due to approximate a ship cross section.The present study extends Lean’s method to approximate a ship cross section and longitudinal section by a rectangle with the same area of the original ship section. So the flow fields under the ship can be considerd in cross direction and longitudinal direction. The method solves not only the slender ship but also the fat ship. Based on the method mentioned above, the paper provide the method for calculating the second order wave force of the ship. At the same time, the problem for piers is treated as the case with the gap between ship bottom and seabed being zero. The above simple method can yield a simple and efficient calculation method for the coupling of multiple ships and piers in waves. The paper has done the following jobs by using the method:(1) The paper calculates the case of many ships against vertical quay(a long rectangle pier adopted in calculation), analyses the interaction of the case of one ship and pier, the case of two ships and pier and the case of three ships and pier, and presents the ship responses. As the quay is made up of multiple piers, the paper calculates the interaction between the ship and quay; (2) The method has been used in the case of many ships in the harbor. The paper gives distribution characters of waves in the harbor including the presence of the ship in the harbor and nothing in the harbor, and calculates the wave forces and ship responses;(3) Frequency domain results using the method are applied in the model of time domain, so that the motion equations are founded in the time domain. In the same time, the dynamic analysis of the tank mooring system is conducted using the mathematical models to evaluate the force and response of the tank in a random sea sate. The results include the mooring line forces, the first order wave forces, the second order wave forces and the motions of the tank.