Steady-state liquid sloshing in a rectangular tank with a slat-type screen in the middle: Quasilinear modal analysis and experiments

Two-dimensional resonant liquid sloshing in a rectangular tank equipped with a central slat-type screen is studied theoretically and experimentally with focus on nonsmall solidity ratios of the screen (0.5≲Sn≲0.95), nonlarge number of slots (N≲50), and steady-state conditions. The tank is horizontally and harmonically excited with frequencies in a range covering the two lowest primary-excited natural sloshing resonance frequencies in the corresponding clean tank. The liquid depth is finite. Theoretical analysis is based on the multimodal method with linear free-surface conditions and a quadratic pressure drop condition at the screen expressing an “integral” effect of the screen-induced cross-flow separation (or jet flow). New experimental data on the maximum wave elevations at the wall are compared with the theoretical predictions. Very good agreement is shown for the smallest forcing amplitudes (the forcing amplitude-to-tank width ratio is ≈0.001). Increasing the nondimensional forcing amplitude to ≈0.01 leads to discrepancies due to secondary resonance causing the energy context from the two primary-excited antisymmetric modes to other, first of all, symmetric modes. A further increase of the nondimensional forcing amplitude to 0.03 leads to more complex secondary resonance effects. Specific surface wave phenomena, e.g., wave breaking, are experimentally observed and documented by photographs and videos.