Equivalent analytical model for liquid sloshing in a 2-D rectangular container with multiple vertical baffles by subdomain partition approach

Abstract

An equivalent analytical model of sloshing in a two-dimensional (2-D) rigid rectangular container equipped with multiple vertical baffles is presented. Firstly, according to the subdomain partition approach, the total liquid domain is partitioned into subdomains with the pure interface and boundary conditions. The separation of variables is utilized to achieve the velocity potential for subdomains. Then, sloshing characteristics are solved according to continuity and free surface conditions. According to the mode orthogonality of sloshing, the governing motion equation for sloshing under horizontal excitation is given by introducing generalized time coordinates. Besides, by producing the same hydrodynamic shear and overturning moment as those from the original container-liquid-baffle system, a mass-spring analytical model of the continuous liquid sloshing is established. The equivalent masses and corresponding locations are presented in the model. The feasibility of the present approach is verified by conducting comparative investigations. Finally, by utilizing normalized equivalent model parameters, the sloshing behaviors of the baffled container are investigated regarding baffle positions and heights as well as the liquid height, respectively.