Natural sloshing frequencies and modes in a rectangular tank with a slat-type screen

Being installed in tanks, screens play the role of slosh-suppressing devices which may strongly change resonant sloshing frequencies and yield an extra nonlinear damping due to cross-flow resulting in either flow separation or jet flow. Employing the linear sloshing theory and domain decomposition method, we construct an accurate analytical approximation of the natural sloshing modes in a rectangular tank with a slat-type screen at the tank middle. Two-dimensional irrotational flow of an ideal incompressible liquid is assumed. Because the considered flow model does not account for flow separation and jet flow at the screen, the velocity field is locally singular at the sharp edges. The constructed solution captures this singularity. Analyzing this solution establishes a complex dependence of the natural sloshing frequencies on the solidity ratio, the number of submerged screen gaps, the liquid depth, and the position of perforated openings relative to the mean free surface. Results are compared with experimental data. Natural surface wave profiles are discussed in the context of a jump of the velocity potential at the screen and the local inflow component to the screen.