A semi-analytical study of the three-dimensional liquid sloshing in a horizontal cylindrical tank with an arbitrary liquid depth

In this paper, a semi-analytical study is presented to solve the linear liquid sloshing frequencies and mode shapes of a three-dimensional partially filled horizontal cylindrical container. The internal liquid of the tank is regarded as the incompressible, inviscid fluid, whose velocity potential function satisfies the Laplace function and the free surface gravity wave function. According to the sloshing modal shapes, the velocity potential function is expressed as symmetric and antisymmetric modes, respectively. The normal velocities of the fluid are set to be zero to model the rigid boundary condition on the fluid-structure interface of the container. Two coordinate systems are introduced in the model. The fluid field coordinate system is set at the midpoint of the free liquid surface. The other coordinate system, the structure coordinate system, is established at the geometric center of the tank cross-section. Through the coordinate transformation and the continuous boundary condition, the motion equation of the system could be obtained. The Galerkin method is employed to solve the governing equation and acquire the sloshing frequencies. Simultaneously, a series of experiments are carried out to investigate the sloshing movement with different liquid depths, and the low-order sloshing frequencies and mode shapes are obtained through the experiments. The accuracy of the semi-analytical method is verified by comparing the results with the published results, the finite element results, and the experimental results. The effects of the liquid depths and the tank length on the sloshing motion are investigated as well.