Modelling of sloshing for spherical tanks

The physics of liquid sloshing is not well understood. The impact event, the wave breaking and propagation are important for engineers. The sloshing phenomena is still an unsolved problem for scientists, when performed with scaled models, difficult to translate prototypes. It is critical to predict and to control sloshing in order to maintain safe operations in many engineering applications, such as in-ground storage and marine transport of liquid cargo. Modelling the dynamics of a spherical structure interacting with a fluid having a free surface is addressed in this study. In this Ph.D. thesis, numerical studies on three-dimensional sloshing have been performed. Contributions to the state of knowledge in predicting sloshing loads is the main objective of the proposed research. The subject of the present thesis is the development of a numerical solver to study the violent interaction of fluid with rigid structures. Among the many numerical models available, the Smoothed Particle Hydrodynamics (SPH) has been chosen as it proved appropriate in dealing with violent freesurface flows. Due to its Lagrangian and meshless character, it can naturally handle breaking waves and fragmentation that generally are not easily treated by standard methods. On the other hand, some consolidated features of meshbased methods, such as the solid boundary treatment, still remain unsolved issues in the SPH context. It has been used in a wide variety of astrophysical applications and hydro- dynamical problems. In coastal engineering, the problems are associated with propagating waves across the nearshore region, through the breaker line, and up the beach face. This area is difficult to model due to the moving boundary at the shoreline, wave breaking, and the variation in water depth from at least intermediate water depth to extremely shallow water. The SPH method is capable of dealing with problems with free surface, deformable boundary, moving interface, especially wave propagation and solid simulation. The SPH model, as one of the oldest Meshfree Particle Methods (MPM), is quickly approaching its mature stage. With the continuing improvements and modifications, the accuracy, stability and adaptivity of the model have reached an acceptable level for practical engineering applications. Few numerical methods can deal with the phenomena aforementioned, due to the high deformation of the free-surface and the numerous fragmentation of the liquid. When using finite element codes, a special treatment of the free-surface is need, as for instance the Level Set (LS) technique, or the Volume of Fluid (VOF) method, increasing the numerical cost of the code. To solve these problems, meshless methods based on a Lagrangian formulation can be more effective than the grid-based methods.