Analytical modeling of liquid sloshing in a two-dimensional rectangular tank with a slat screen

Abstract

Potential-flow theory is employed with linear free-surface conditions, multimodal method, and a screenaveraged pressure-drop condition to derive an analytical modal model describing the two-dimensional resonant liquid motions in a rectangular tank with a vertical slat-type screen in the tank middle. The tank is horizontally excited in a frequency range covering the two lowest natural sloshing frequencies. The model consists of a system of linear ordinary differential [modal] equations responsible for liquid sloshing in compartments, as well as a nonlinear ordinary differential equation describing the liquid flow between the compartments. New experimental model tests on steady-state wave elevations near the tank wall are reported for the solidity ratios 0.328 ≤ Sn ≤ 0.963 where Sn is the ratio between the solid area and the full area of the screen. The experiments generally support the applicability of the model. The discrepancy can be explained by the free-surface nonlinearity. The screen acts as a damping mechanism for low and intermediate solidity ratios, but it causes an increase in the lowest resonant sloshing frequency at higher solidity ratios as if the screen had been replaced by an unperforated wall.

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

“…6 and 7. Additional examples of using this condition for liquid sloshing dynamics and external surface wave problems can be found in the papers by Molin 8 and Faltinsen et al 9 When Sn→ 1, the screen becomes a rigid wall. The modal solution employing the natural sloshing modes of the corresponding clean tank used in the aforementioned TLD analysis is then not more applicable.…”

“…The idea was to consider the modal solutions in the two screen-separated compartments and, thereafter, match these solutions at the screen by using continuity of the mean flux velocity and the averaged pressure drop condition which should play the role of transmission boundary conditions. An extension of this approach was done by Faltinsen et al 9 Realizing this idea showed success in describing ͑i͒ the resonance response amplitude for close to 1 ‫ء‬ ͑the first natural frequency for the corresponding clean tank͒, and ͑ii͒ the general qualitative fact of disappearance of the resonance peaks at 1 ‫ء‬ and 3 ‫ء‬ and appearance of the resonance peak at 2 ‫ء‬ ͑which is the lowest natural sloshing frequency for the compartments͒ as Sn→ 1. Due to quadratic nature of the pressure drop condition, the results on the resonance peaks depend on the forcing amplitude.…”

“…Furthermore, working on Ref. 9, we found out that this approach is not precise in identification of the resonance peak positions as the forcing amplitude becomes smaller and Sn tends to 1. Even though the experimental forcing amplitude was sufficiently small ͑the forcing amplitude-to-tank width is about 0.001͒, this theoretical approach gave wrong resonance peak position in a frequency range about 3 ‫ء‬ .…”

An analysis of screen arrangements for a tuned liquid damper

“…They conclude that a linear model is sufficient for preliminary TLD design. A similar theoretical basis has been used by Tait (2008) and Faltinsen et al (2011a) in their related investigations.…”

Sloshing-induced slamming in screen-equipped rectangular tanks in shallow-water conditions

“…7 To account for the exponential decay in the cross-flow velocity at the screen, a modified analytical modal model (QL1) based on QL0 was constructed using a multimodal method 7 for any solidity ratio. 13 Faltinsen and Timokha 14 analytically solved the natural sloshing frequencies and modes in a rectangular tank with slat-screens in the middle of the tank. They showed the dependence of these results on the solidity ratio and local properties of the screen, such as the number, position, and height of the slats near the still-water level (SWL).…”