el-kamali08-SEMINAIRE

Spatial structures, like satellites, probes or space stations, can contain a large amount of liquid. Their sloshing may hamper critical manoeuvres in space such as the docking of liquid-cargo vehicles, the pointing of observational satellites or the stabilization of the International Space Station (which is essential when experiments are in progress). In order to predict the dynamic behaviour of such structures, the motion of onboard liquids must be taken into account. In addition, surface tension phenomena can no longer be neglected because of the low gravity environment. To study the vibrations of liquids in tanks, ONERA has developed a formulation for linearized liquid-structure interaction with a lagrangian approach. To extend its domain of application to a microgravity environment, we first need to find the equilibrium position of the liquid inside the tank (meniscus). We solve this problem by computing the position of the liquid free surface minimizing the total potential energy of the fluid (which contains a capillarity term proportional to the free surface area). Whereas many authors consider particular cases with simple geometries of tanks, we propose, in this work, a nonlinear finite-element formulation which can be applied to threedimensional tanks with complex geometries. This approach by form finding presents a singularity with respect to the tangential position of the finite-element nodes. For two-dimensional examples, we can regularize the problem by introducing an additional stiffness. However, because of the geometric complexity of the three-dimensional formulation, we propose instead to adapt the URS (Updated Reference Strategy) homotopy method proposed by Bletzinger. Once the initial static configuration is determined, the dynamic equations of the Newtonian fluid are linearized with respect to this reference position to establish the equations of small amplitude sloshing in microgravity.