Navier–Stokes simulations of vertical sloshing with time-periodic excitation

An in-house Navier–Stokes multiphase VOF (Volume-Of-Fluid) solver is used to study sloshing phenomena in a partially filled rectangular tank subjected to vertical sinusoidal excitation, with the main goal of characterizing the effects of vertical acceleration and excitation frequency on the flow dynamics. The solver is validated through comparison with analytical solutions and with available experiments of vertical sloshing. We find that the computed forces acting on the tank walls are well predicted, both in two- and three-dimensional numerical simulations. The flow dynamics is found to be significantly affected by the forcing parameters, and to exhibit more chaotic and three-dimensional nature in cases with strong acceleration and low forcing frequency. As a consequence, certain properties such as the energy dissipation and the mixing efficiency of the system are poorly predicted by two-dimensional simulations in that range of parameters, necessitating the use of more expensive three-dimensional simulations. The time history of the sloshing force and instantaneous flow visualizations are used to analyze the effects of liquid impacting on the walls on energy exchanges between the fluid and the tank. Finally, the evolution of mixing efficiency and its influence on the energy losses are discussed.