Abstract
Shallow-water sloshing motions in a three-dimensional rectangular tank are investigated. The Boussinesq-type equations in terms of velocity potential and the finite-difference scheme are applied for the solutions of numerical model. Through linking the rate of decay of the wave amplitudes to the energy dissipation due to the friction at the tank walls, a linear damping term is proposed and added into the free surface boundary condition. Taking the tank under excited frequencies near the lowest natural frequency, the maximum transient wave amplitudes and steady-state wave amplitudes of sloshing motions at the tank wall are presented and verified by the experimental results given in the literature. The characteristics of sloshing motions in tank under different coupled excitations are studied. The results indicate that coupled surge-sway excitations lead to the weaker nonlinear sloshing motions in tank than the single degree of freedom excitations. The intersection of sloshing wave crest lines finally tend to the diagonal line of the tank under the coupled surge-sway excitations with different amplitudes. And the irregular free surface oscillations appear at the corners of the tank excited by the coupled surge-sway-roll-pitch-yaw harmonic motions.
Highlights
The phenomenon of liquid sloshing draws a great deal of attention from many researchers in the field of fluid dynamics
A nonlinear, dispersion and dissipation model was developed in Lepelletier and Raichlen [12] to describe the shallow-water sloshing in two-dimensional rectangular tank
The three-dimensional shallow-water sloshing motions were studied based on the Boussinesq-type equations
Summary
The phenomenon of liquid sloshing draws a great deal of attention from many researchers in the field of fluid dynamics. A time-independent Finite Difference Method (FDM) was used to simulate the liquid sloshing in a three-dimensional tank under coupled motions in Wu and Chen [2, 3] and Wu et al [4]. A nonlinear, dispersion and dissipation model was developed in Lepelletier and Raichlen [12] to describe the shallow-water sloshing in two-dimensional rectangular tank. The maximum transient and steady-state wave amplitudes were compared between numerical and experimental results when the excited frequencies near the lowest resonant frequency. The Boussinesq-type depth-averaged equations were used in Antuono et al [15] for the two-dimensional shallow-water sloshing in the rectangular tank. The Boussinesq-type equations in terms of velocity potential was used in Su and Liu [17] for simulating two-dimensional shallow-water sloshing. The aforementioned studies about the shallow-water sloshing mostly focused on the two-dimensional wave motions near the lowest resonant frequency. The numerical results may help to understand the complicated three-dimensional shallow-water sloshing motions
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