The use of the finite element method in the simulation of liquid sloshing

A container partially filled with liquid and subjected to an external excitation will (depending on the degree of severity of the external forces) slosh in a characteristic manner. Two distinct approaches are attempted to model this phenomenon using the FEM. In the first approach adaptive meshing techniques are used whereas the second approach utilises a mechanical analogue. The adaptive meshing procedure employed is Arbitrary Lagrangian Eulerian (ALE) which combines features of the Lagrangian and Eulerian approaches. In the former material is confined within the deforming boundaries of the elements and in the latter the mesh is spatially fixed and material can flow through the elements. The procedure is implemented using an explicit Finite Element formulation and 2-D and 3-D solutions are presented. In the second approach, 2-D models are used to simulate sloshing by dividing the volume of the liquid in the enclosed container into two parts: 1) a volume of fluid which apparently remains stationary; 2) the remaining volume of fluid which participates in sloshing - its amplitude and frequency are governed by the external disturbances applied to the container. Even though the fluid lacks a shear retention capability there may exist an element of internal friction (due to viscosity effects and/or sliding against the container wall) such that, when the external source of excitation ceases, the motion exhibits a transitory decaying characteristic, with the fluid finally coming to rest. Therefore a successful model must include the effects of internal friction between the fluid and the container and the complex oscillatory motion of the sloshing fluid component. These are taken into account using mechanical analogues in an implicit Finite Element formulation of the problem. Details of the principles behind extending the method to a 3-D model are also presented. In both cases the computed results are compared with experimental data obtained from a tank subjected to a prescribed displacement.