Finite Element Analysis of Externally-Induced Sloshing in Horizontal-Cylindrical and Axisymmetric Liquid Vessels

Motivated by the earthquake response of industrial pressure vessels, the present paper investigates externally-induced sloshing in horizontal-cylindrical and axisymmetric liquid containers. 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 (Galerkin) 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 horizontal circular cylindrical, spherical, and conical vessels. It is shown that, in those cases, consideration of only the first sloshing mass is adequate to represent the dynamic behavior of the liquid container quite accurately. For the case of a horizontal cylinder subjected to longitudinal external excitation, its equivalence with an appropriate rectangular container is demonstrated. The numerical results are in very good comparison with available semi-analytical or numerical solutions and available experimental data.