Simulation of the early stage water flooding through an opening using boundary element method

When an underwater collision or explosion happens to a ship, the water will rush into the cabin through the broken opening. The water spike induced by hydrostatic pressure has the potential to destroy the facilities and structures inside the cabin, and the water flooding may threat the vitality of ship. Dynamic characteristics of this water spike during early flooding process is studied by a three-dimensional fast multipole boundary element method (FMBEM) based on the potential theory, in this article. The edge swap operation is elaborated and adopted, to eliminate the slender elements at the air-water interface, which helps us study the evolution of the inrush water and maintains the computational efficiency. The numerical model is validated by experimental data and the result from the finite volume method. The flooding process can be divided into the developing flow stage and the stable flow stage. The flow rate increases gradually during the former stage and reaches a constant value in the latter one. Through parametric study, we find that the water flooded through the opening earlier is subjected to the gravity for longer time and achieves larger velocity, which results in a slender water spike. When the opening gets deeper, the developing flow stage becomes shorter and the flow rate increases; whilst the increasing speed slows down with the growing depth. It is the area of the opening rather than the shape, that influences the flow rate and flooding velocity, and the maximum velocity in the horizontal direction appears at the transition time between the two stages. This study reveals that the water flooding spike has complex and non-linear dynamic behaviour, and helps lay the foundation of studying the interaction between high-speed water jet and the structures. It also shows that the FMBEM is suitable for dealing with the large scale moving boundary problems efficiently and accurately.