SPH simulation of three-dimensional resonant viscous sloshing flows

Three-dimensional resonant sloshing flows in a square-base tank is analysed to investigate swirling instability. To this aim a tank is harmonically forced along the horizontal x-component with frequency equal to the first resonant mode. Specifically, the influence of the viscosity on the inception of this flow instability is studied. Four different liquids characterized by different viscosity are considered: water, sunflower oil, castor oil and glycerin. In order to model these flows, an enhanced version of the SPH model called delta-LES-SPH [2] is chosen as some of the considered flows are turbulent. The adopted numerical scheme correctly reproduces the swirling regimes as theoretically predicted and experimentally observed by [16]. The particle nature of SPH allows for a straightforward and explicit analysis of energy terms during the flow evolution. The sloshing related energy damping, therefore, can be directly measured. Further, the considered phenomenon requires the simulation of several tens of periods. In this respect, the adoption of SPH is an advantage thanks to the exact mass conservation and the accurate modelling of the complex free-surface deformations. The present investigation underlines the strict relation between the energy dissipation and the swirling instability, showing that more energy is dissipated when swirling motion is activated and wave breaking events occur. It is also shown that liquids characterized by lower viscosity are more prone to develop a swirling instability.