Boundary element analysis of liquid sloshing in a three-dimensional liquid tank with porous structure

This paper investigates the liquid sloshing problem in three-dimensional tanks with a porous structure using the boundary element method (BEM). Based on linear potential flow theory and the Bernoulli equation, we present a discretization strategy along with a detailed derivation of the boundary element integral equation for the three-dimensional liquid sloshing problem. The problem can be transformed into a two-dimensional framework by employing boundary integral equations defined on the boundary as the governing equations. These equations are subsequently converted into algebraic equations through the interpolation of boundary elements, which significantly reduces the number of required nodes. The boundary conditions on both sides of the porous structure are established in accordance with Darcy's law and the Bernoulli equation. The study examines the sloshing behavior both in cubic, cylinder and annular cylinder liquid tanks, incorporating a porous baffle to mitigate the sloshing phenomenon. Numerical results demonstrate the accuracy and reliability of the proposed model, indicating that modifications to the length, width, shape, and other geometric dimensions of the porous baffle significantly influence the sloshing response of the liquid within the tank. Generally, a higher installation position of the transverse porous baffle within liquid tanks of varying shapes enhances the suppression of liquid sloshing, while the configuration of the vertical baffle is contingent upon the specific shape of the tank. Additionally, as the porous-effect parameter increases, the peak value of the responses initially decreases before subsequently increasing. In addition, the limitations of linear potential flow theory were analyzed, and future research directions were suggested.