Wave impact in sloshing flows: Hydroelasticity in shallow water condition

The hydroelastic interaction between a fluid (sloshing flow) and a flexible metal structure, as a consequence of a gravitational wave impact, has been investigated. When hydroelasticity occurs, the real stresses which the structure must overcome, may be underestimate if only the hydrodynamic pressure is taken in account. The knowledge of the stresses acting on the structure, as well as, the physical mechanisms which are able to trigger this kind of phenomena, are fundamental for a right design and the safety of a marine structures. The investigation has been performed following both the experimental and mathematical approach. An experimental set-up has been designed for the reproduction of the impact, during a two dimensional sloshing flow in low filling condition, against a flexible structure(, as well as, a rigid one). Two specific typologies of wave impacts have been considered, both of them, characterized by hydrodynamic loads which may activate hydroelastic effects on the structure: a) Flip-Through type wave impact b) Single Air-Bubble entrapment wave impact for the last one, the investigation has been extended also at the influence of the Euler number on the structural stress. The influence of the ullage pressure is an important topic related to the scaling procedure when model scale experiments are performed. For a better identification of the major physical features which play an active role in the hydroelastic phenomena, an hybrid “weak” hydroelastic and a fully hydroelastic methods have been developed. The three different sub-problems, that have been individuated from the experimental activities: 1a) sloshing stage with single phase flow, 1b) sloshing stage with two phase flow and 2) structural problem, have been modelled with a proper mathematical models, where the physical assumptions adopted, have been inspired by the experimental finding and also by the literature. The hybrid model combines a numerical model for the structural problem with hydrodynamic loads estimated during experimental tests with a fully rigid structure. More in detail, the Euler beam theory together with a model for the added mass have been used to describe the behavior of the structure. The hybrid model highlights how the added mass effect influence both the natural frequencies and the displacement of the structure. Anyway some differences on the structure displacement have been observed, especially on the higher peaks just after the impact, this suggests that a stronger hydroelastic interaction is present. For the fully hydroelastic model, also the sloshing sub-problem, which can be considered both as single phase of two phase flow, depending on the impact type, has been solved numerically. In particular, a mixed Eulerian-Lagrangian method has been applied for the evolution of the free surface, where for the liquid phase the hypotheses of incompressible and irrotational fluid have been considered. In that cases where the air cavity is present, the pressure inside the cavity has been modelled with ad-hoc semi-analytical model, such as the “lumped” model. The dynamic behaviour of the structure has been approximated as in the hybrid method. The coupling, during the numerical time integration scheme, of the cited sub-models gives the fully hydroelastic method.