A numerical analysis of sloshing dynamics of two-layer liquid with a free surface

A numerical study on the two-layer liquid sloshing with a free surface in a rectangular tank under horizontal sinusoidal excitation is investigated in this work. It is observed that the interface displacement is mainly influenced by the lower liquid depth, while the free surface displacement primarily depends on the total liquid depth. Using dimensional analysis of the numerical results, we obtained a fitting curve in the S-model expression, which relates the displacements of both liquids to the forcing amplitude, forcing frequency and liquid depth. Furthermore, distinct from the phenomena for a single-layer liquid, we find that the sum and difference frequencies play significant roles in the power spectral density curves. There are similar power spectral density curve shapes and energy concentration locations with a fixed type of excitation independent of the liquid filling depth and layer depths ratio.