Large-scale amplitude liquid sloshing in container under pitching excitation

Large-scale amplitude liquid sloshing in container under pitching excitation is numerically studied in this paper. Firstly, the kinematics of the ALE description is introduced and the fluid dynamics equations are revised in the ALE form. Secondly, the boundary condition about free-surface tension is represented in the form of weak integration that can be computed by the differential geometry method derived in the present paper and the normal vector on free surface is calculated using accurate formulas presented in this paper. Then the numerical discretized equations of fractional step finite element method are developed by Galerkin weighted residual method. Furthermore, the numerical simulation of large-scale amplitude sloshing of the liquid both in rectangular container and cylindrical container is carried out. The computed time evolution of the wave height, and free surface profiles at different time are obtained. Comparisons among the present numerical results with other published numerical results and experimental data confirm the effectiveness and validity of the method developed in this paper.