Semi-analytical method for liquid sloshing in the rigid super-elliptical tank with the ring baffle

Tanks with super-elliptical cross-sections can improve space utilization. The effect of the submerged ring baffle on liquid sloshing in the tank is studied. The semi-analytical method is developed to solve the three-dimensional (3D) sloshing problem in the baffled non-axisymmetric tank, using linear potential theory by dividing the liquid domain into sub-domains. The formal solutions are obtained analytically for the 3D non-axisymmetric sub-domains with arbitrary cross-sections, allowing for the determination of natural frequencies and modes by substituting the formal solutions into the linearized free surface condition, the boundary conditions on the baffle and tank wall and the continuity conditions at the interfaces of the interconnecting sub-domains. The dynamic response equation is derived using the mode superposition method with the damping term for swaying excitation. The obtained solution is validated by comparing it with a numerical model, demonstrating excellent accuracy and efficiency. Parametric studies are performed to determine the effect of the baffle on liquid sloshing, indicating that the baffle can considerably reduce the liquid sloshing when considering an optimal baffle position and width. This technique can be extended to investigate the sloshing reduction in vertical containers with arbitrary cross-sections.