Abstract Summary
The use of equivalent mechanical models, of the mass-spring or pendulum type, to represent the forces due to the sloshing of liquids in tanks on the dynamics of the main structure is a method still widely used today in many industrial fields (aeronautics, space, road transport, etc.). The determination of the parameters of these mechanical oscillators (mass, inertia, frequency, position) was initially established from analytical solutions of the linearized Euler equations of incompressible potential fluids in domains of simple shapes (parallelepipedic or axisymmetric), assuming that the axis of (apparent) gravity is aligned with one of the axes of symmetry of the volume considered. These restrictions are limiting for the use of these models because, if we are interested for example in a space launcher, its tanks have in practice sometimes more complex shapes (with internal equipments which break the axial symmetry) and are not necessarily aligned with the axis of the acceleration of the structure. This is why an approach based on a numerical resolution of the sloshing equations has been developed. It is based on a discretization by the Finite Element Method (FEM) or Boundary Element Method (BEM) in three dimensions, which allows to treat any fluid domain geometry. Although simpler to implement, FEM requires meshing the volume of the fluid which can be tedious for complex shaped tanks with internal equipment, especially if several filling levels are envisaged. The BEM more generally used for external potential fluids has been adapted for internal fluids with free surface. The resulting matrices are full but their construction requires only surface meshes of the fluid domain boundaries (fluid-structure interface and free surface). This approach is all the more interesting if we want to model the internal walls that exist inside the tanks (anti-slosh baffles): although they introduce numerical difficulties in the calculation of the operators, taking them into account in the meshing of the interfaces is much easier than with a volume mesh. The developments made around these methods will be illustrated by applications in the aerospace field, in particular for the piloting of reusable space launchers during their atmospheric re-entry phase.
