Global force and moment in rectangular tanks through a modal method for wave sloshing

Abstract

Basing on a modal description of the sloshing phenomenon, formulas for the global force and moment acting on two-dimensional rectangular tanks are proposed. These are extensively validated through comparison with experimental data for roll motions at different angles of excitement. Moreover, to extend the applicability of the modal method to the most violent breaking cases, a diffusive variant of the scheme is proposed. This relies on the use of a proper diffusive term in the continuity equation and allows for the overcoming of some numerical issues related to the sloshing dynamics in very shallow waters. Finally, a qualitative description of the interaction between diffusion, dispersion and nonlinearities has been proposed for the present modal scheme, along with a physical interpretation of the diffusive term.

Analytical solution of capsizing moments in ship chamber under pitching excitation

“…Details of the adopted series are summarized in Table 2. The series 1 and 2 are compared to the modal method with diffusion, 12 while the series 3 to 8 are adopted in comparison with the experimental results. 8…”

“…Table 3 shows the free surface elevation at different locations, which are calculated by the Housner theory and Antuono and Lugni 12 under series 1. It can be seen that the maximum value of η=0.027m at the tank walls (x=±0.47m) is consistent with η*=0.030m, while there are small differences at other locations.…”

“…The study conducted by Verhagen and Wijngaarden 8 applies the one-dimensional gas flow theory to the fluid oscillations, and calculates the shape of the hydraulic jump under sway and roll motions. The investigations conducted by Antuono 9–12 propose a modal description and derive formulas of the global force and moment for the most violent breaking cases, which are extensively validated through comparison with experimental data for roll motions. The theoretical method and experiment results are of great value to explore analytical solutions for the shallow water sloshing in the ship chamber.…”

“…Analytical solutions of the capsizing moments shall then be derived relying on the use of Euler equations and the method of separation of variables. Subsequently, the proposed model and analytical solutions are going to be extensively validated through comparisons with the modal theory of Antuono and Lugni 12 and the experimental results of Verhagen and Wijngaarden. 8 Finally, a qualitative description of the interaction between the forcing frequency, capsizing moments and fluid natural frequency will be focused on.…”

Pitch stability analysis of high-lift wire rope hoist vertical shiplift under shallow water sloshing–structure interaction

“…General linear 9–11 and nonlinear 12–16 sloshing in rectangular tanks have been thoroughly studied based on different theories during the past decades. But for the shallow water sloshing in the rectangular shiplift chamber, almost no nonlinear and no water resonance occurs even under earthquake conditions according to the running observation 17 and the “Safety and Reliability Assessment Report of the Three Gorges Water Conservancy Shiplift (Comprehensive Report)”.…”