Nonlinear coupled dynamics of a liquid-filled spherical container in microgravity are investigated. The governing equations of the low-gravity liquid sloshing in a convex axisymmetrical container subjected to lateral excitation is obtained by the variational principle and solved with a modal analysis method. The variational formulas are transformed into a frequency equation in the form of a standard eigenvalue problem by the Galerkin method, in which admissible functions for the velocity potential and the liquid flee surface displacement are determined analytically in terms of the Gaussian hypergeometric series. The coupled dynamic equations of the liquid-filled container are derived using the Lagrange＇s method and are numerically solved. The time histories of the modal solutions are obtained in numerical simulations.
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.
