Thèse de doctorat en Mécanique
Sous la direction de Roger Ohayon.
Soutenue en 2010
à Paris, CNAM .
Pas de résumé disponible.
Sloshing of liquids with surface tension : static and dynamic studies
The aim of this thesis is to model the linear vibrations of liquids (sloshing) in low gravity or microgravity environments. The dynamic study of spacecrafts containing liquids is one of the possible applications of this work. Due to the low gravity level, surface tension phenomena (capillarity) at the liquid free surface are preponderant. Their effects introduce, on the one hand, additional forces proportional to the curvature of the free surface, and on the other hand, a contact angle condition to be satisfied between the free surface of the liquid and the tank internal wall. The first part of this document addresses the problem of finding the equilibrium position of the liquid inside the tank, i. E. To determine the shape of the meniscus formed by the free surface of the liquid at equilibrium. The second part is dedicated to the study of liquid sloshing near this equilibrium position. The originality of this work is to treat these two problems (static and dynamic) in a tree dimensional point on view, using variational formulations that avoid the explicit computation of the free surface curvatures. In both parts, the discretization was then performed using the Finite Elements method with standard linear elements. Furthermore, the spectral problem established in the dynamic part is symmetric. The results obtained in the static and dynamic cases have been validated on simple cases where analytical or semi-analytical solutions are available.