Numerical simulation of two-layered liquid sloshing in tanks under horizontal excitations

A numerical model NEWTANK has been developed to study two-layered liquid sloshing under horizontal external excitations. The model solves spatially averaged NSEs on a non-inertial coordinate for external excitations. The two-step projection method is employed in numerical solutions, and the Poisson equation for pressure field is solved by Bi-CGSTAB technique. A multi-layered volume-of-fluid method is proposed to track both free surface and interface between layered liquids simultaneously. In order to validate the accuracy of the model, the simulated results of sloshing responses are compared with linear analytical solutions and experimental data. Good agreements are obtained when response amplitude is within linear regime. However, when nonlinearity becomes strong, deviation from analytical solution will be large due to nonlinear energy transfer from the primary mode to higher modes. Further investigation reveals that for two-layered liquid sloshing, there exist two natural frequencies with the smaller one related to response of lower layer liquid and the larger one upper layer. Therefore, different external excitation frequencies may induce upper-layer resonance, lower-layer resonance or resonances of both layers, each of which exhibits very different patterns of energy transport between modes and layers. Finally, a violent 3-D sloshing with broken free surface and interface is simulated and discussed.