Sloshing Effects under Longitudinal Excitation in Horizontal Elliptical Cylindrical Containers with Complex Baffles

Abstract

Assuming that an ideal liquid has irrotational, incompressible, and inviscid flows, a mathematical model is presented to efficiently and simply study liquid sloshing problems under longitudinal excitation in horizontal cylindrical containers with complex baffles. A semianalytical scaled boundary finite-element method (SBFEM) is combined with the zoning technique to solve the liquid sloshing problem. This method can significantly increase the efficiency and accuracy of the calculation using few nodes. Using scaled boundary coordinates with both radial and circumferential directions, the analytical solution in the radial direction can be obtained through approximation in the circumferential direction via a discretization technique similar to that used in the FEM. Thus, the entire calculation domain can be analyzed based on the problem boundary. Continued-fraction expansion is applied to build the eigenvalue problem, and the interior eigenvectors are solved by using asymptotic expansion in detail. Based on the previously mentioned decomposition and eigenvalue problem, the corresponding sloshing mass and motion equations are proposed by an efficient methodology. The simplicity and efficiency of SBFEM applied to sloshing problems with different baffles are obtained through numerical examples. This paper investigates the effects of the arrangement and length of different baffles and liquid fill levels on the sloshing frequencies, modes, and response. The conclusions illustrate that SBFEM can easily and semianalytically achieve good results for complex sloshing problems with singularity and complex geometry by placing the scaling centers at the tip of the baffles with very few degrees of freedom.