Computation of the equilibrium position of a liquid with surface tension inside a tank of complex geometry and extension to sloshing dynamic cases

摘要

To study the vibrations of a tank partially filled with a liquid in low-gravity environment, we first have to find the static position of the liquid. In this paper, we present a three-dimensional finite element approach to find this equilibrium configuration for any tank geometry. Both gravity and capillary effects are taken into account. The nonlinear equations of this problem are derived from the differentiation of the total potential energy of the system, then the problem is transformed into a liquid free surface form-finding. The well-known singularity of this kind of problems is regularized using the updated reference strategy. The equations of the regularized problem are discretized using the finite element method and solved by the Newton–Raphson algorithm. Several examples illustrate the effectiveness of this method, even for complex cases, and two validation tests are presented. The linear sloshing vibrations of the liquid are finally studied near this equilibrium position and two validation cases are proposed for the eigenvalue dynamic problem.