Finite Element Analysis of Sloshing in Axi-Symmetric Vessels

Abstract

The present paper investigates externally-induced sloshing in axi-symmetric liquid containers, with emphasis on industrial spherical containers, using an efficient numerical formulation, based on modal analysis. Assuming ideal and irrotational flow, small-amplitude free-surface elevation, and considering appropriate trigonometric functions for the sloshing potential, a two-dimensional eigenvalue problem is obtained for zero external excitation, which is solved through a variational (Garlerkin) formulation that uses triangular finite elements. Subsequently, based on an appropriate decomposition of the container-fluid motion, and considering the eigenmodes of the corresponding eigenvalue problem, an efficient methodology is proposed for externally-induced sloshing, through the calculation of the corresponding sloshing (or convective) masses. Numerical results are obtained for sloshing frequencies and masses in spherical vessels and a conical vessel with a semi-vertex angle of 45 degrees. It is shown that, in most of the cases, consideration of only the first sloshing mass is adequate to represent the dynamic behaviour of the liquid container quite accurately and could be used for design purposes. The numerical results are in very good comparison with other analytical or numerical solutions, and available experimental data.