Sloshing of liquid in partially liquid filled toroidal tank with various baffles under lateral excitation

A technique to study effect of various baffles on liquid oscillations in partially filled rigid toroidal tanks is first developed by extending the semi-analytical scaled boundary finite element method (SBFEM), which utilizes the advantages of both the boundary element (BEM) and finite element methods (FEM). As found in the BEM, only the boundary is discretized to reduce the space by one, and no fundamental solution is needed unlike the BEM. The calculated liquid domain is divided into several simple sub-domains so that the liquid velocity potential in each liquid sub-domain becomes the class C1 with continuity boundary conditions. Based on the linear potential theory and weighted residual method, the semi-analytical solutions of the liquid velocity potential corresponding to each sub-domain are obtained by means of SBFEM, where the geometry of each sub-domain is transformed into scaled boundary coordinates, including the radial and circumferential coordinates by using a scaling centre, and the finite-element approximation of the circumferential coordinate yields the analytical equation in the radial coordinate. By discretizing the flow boundaries, the integral equation governed on the boundary is formulated into a general matrix eigenvalue problem. Based on the eigenvalue problem and multimodal method, an efficient methodology is adopted to computer the sloshing masses and sloshing force. Accuracy, simple and fast numerical computations are observed by the convergence study, and excellent agreements have been achieved in the comparison of results obtained by the proposed approach with other methods. Meanwhile, several baffle configurations are considered including the horizontal bottom-mounted and surface-piercing ring baffles as well as their combination form, bottom-mounted and surface-piercing ring baffles as well as their combination, and free surface-touching baffles. The effects of baffled arrangement, the ratio b/a of elliptical cross section, liquid fill level, and baffles' length upon the sloshing frequencies, the associated sloshing mode shapes and sloshing forces are investigated in detail and some conclusions are outlined. The results show that the present method allows for the simulation of complex 3D sloshing phenomena using a relative small number of degrees of freedom while the mesh consists of two-dimensional elements only.