A numerical study of the effects of the T-shaped baffles on liquid sloshing in horizontal elliptical tanks

A semi-analytical scaled boundary finite-element method (SBFEM) is firstly extended to study the effects of the T-shaped baffle on liquid sloshing in horizontal elliptical tanks. The proposed method is based on the finite-element technology and gains the advantages of the boundary element method as well. Only the boundary is discretized reducing the spatial discretization by one, no fundamental solution is required and singularity problems can be modeled rigorously. Based on linear potential theory, the formulations (using new variational principle formulation) and the solutions of SBFEM equations for the sloshing problems are derived in details. As a key point, the solution for the inclusion of flow velocity along the baffles, which is called the side-faces of bounded domain in SBFEM, is also expressed in details. The accuracy, simplicity and convergence of the present method are demonstrated via numerical examples, and excellent agreement with the other method is observed. Meanwhile, three T-shaped baffled configurations are considered including surface-piercing baffle, bottom-mounted baffle and their combination form, and Y-shaped baffled configuration evolved from that of T-shaped baffle has been taken into consideration as well. The effects of liquid fill level, baffled arrangement and length of those baffles upon the sloshing frequencies, the associated sloshing mode shapes and sloshing wave height are investigated in details. The results also show that the present method has strong ability to resolve singularity problems analytically by choosing the scaling center at the tip of the baffles and allows for the simulation of complex sloshing phenomena using a very small number of degrees of freedom while the mesh consists of one-dimensional elements only.