SPH and ALE formulations for sloshing tank analysis

Design of fuel tanks requires the knowledge of hydrodynamic pressure distribution on the structure. These can be very useful for engineers and designers to define appropriate material properties and shell thickness of the structure to be resistant under sloshing or hydrodynamic loading. Data presented in current tank design codes as Eurocode, are based on simplified assumptions for the geometry and material tank properties. For complex material data and complex tank geometry, numerical simulations need to performed in order to reduce experimental tests that are costly and take longer time to setup. Different formulations have been used for sloshing tank analysis, including ALE (Arbitrary Lagrangian Eulerian) and SPH (Smooth Particle Hydrodynamic). The ALE formulation uses a moving mesh with a mesh velocity defined trough the structure motion. In this paper the mathematical and numerical implementation of the FEM and SPH formulations for sloshing problem are described. From different simulations, it has been observed that for the SPH method to provide similar results as ALE formulation, the SPH meshing, or SPH particle spacing needs to be finer than ALE mesh. To validate the statement, we perform a simulation of a sloshing analysis inside a partially filled tank. For this simple, the particle spacing of SPH method needs to be at least two times finer than ALE mesh. A contact algorithm is performed at the fluid structure interface and SPH particles. In the paper the efficiency and usefulness of two methods, often used in numerical simulations, are compared.