The paper is based on adaptive mesh refinement (AMR) to numerically simulate the multilayer liquid sloshing in a three-dimensional rectangular vessel with different external excitations. The numerical simulation is carried out in a numerical tank controlled by the Navier-Stokes equation solved by STAR-CCM+ (a commercial software based on the finite volume method). In order to verify the accuracy of the AMR method, the qualitative and quantitative results including waveform, interface height and dynamic pressure are compared with the experimental data and other theoretical numerical results. The results show that the two are in good agreement. In particular, the evolution of free surface and phase interface is compared, and it is found that there are obvious differences between them. It is found that when the external excitation frequency is near the natural frequency of the system, the oil-water interface will also appear the phenomenon of beat frequency like the free surface. In addition, different phase interface states were observed at different excitation frequencies. The key factors of the dominant phase interface motion are analyzed, which provides a theoretical basis for suppressing the sloshing of stratified liquid in the FPSO oil storage tank.
The problem of stratified liquid sloshing is widespread in the industry and the environment. In the industrial sector, there are food, oil extraction and transportation, aerospace and nuclear industries. This motion refers to the forced motion of two or more immiscible fluids in a finite container. The study of stratified liquid sloshing can be traced back to the latter part of the last century. For example, in the oil industry, the typical feature of the oil industry is the transportation of oil-water mixtures in pipelines. When mining, especially offshore mining, this part of the liquid often has both oil and water, so it is a stratified fluid and usually needs to be transported to processing facilities or offshore refineries. Many scholars have carried out in-depth research on this issue, especially Faltinsen (2009) published a monograph on liquid sloshing in ship engineering. It is found in industry that stratified liquid sloshing is different from single-layer liquid sloshing. Density stratification will change the nature of sloshing, especially in the field of oil exploitation and transportation, which has attracted the attention of many scholars. Compared with single-layer liquid sloshing, there is not only a free surface in layered liquid sloshing, but also an internal interface between fluids of different densities. Moreover, the period and wavelength of phase interface wave are often quite different from those of surface waves.