The movement of a liquid inside another object is referred to as sloshing. Technically, the liquid must have a free surface to constitute a slosh dynamics problem, where the dynamics of the liquid can interact with the container to alter the system dynamics significantly. Specifically, sloshing in an upright circular tank is relevant for ship motions and floating storage facilities due to water waves in marine hydrodynamics, closed fish tanks in aquaculture – among other applications. Basically, the presence of sloshing flow has a strong influence on the motion and response behaviors of structures, and thus it is of both theoretical and practical importance. A review of literature reveals that with regard to sloshing in upright tanks, four kinds of responses: i.e. planar harmonic, swirling harmonic, periodically modulated sinusoid, and chaotically modulated sinusoid can be predicted. Further review reveals that in the weakly nonlinear multimodal theory, known to be capable of predicting sloshing behaviour analytically for a given tank shape and dimension, the first five natural modes are nonlinearly coupled. However, it is not limited to only five modes, as the higher modes can be included through linear modal equations. Besides the excitation of single degree of freedom, attention has also been paid to the mean mass transport of liquid in the tank induced by a rotary oscillation off resonance.
In general, this field has not been exhaustively explored. For instance, for the occurrence of swirling sloshing waves in the steady state, it takes long time to build up, and nonlinearity must be accounted for. Therefore, a time efficient, fully nonlinear solver is required. This is important particularly since most of the existing studies focus on the use of periodic excitation. However, transient-type excitation associated with an extreme event has seldom been considered in the literature, and therefore little is known about the underlying physics. On this account, researchers from Technology Centre for Offshore and Marine, Singapore (TCOMS) and Technical University of Denmark (DTU): Dr. Hui Liang, Dr. Harrif Santo, Dr. Yanlin Shao, Engineer Yun Zhi Law and Professor Eng Soon Chan developed a fully nonlinear time-domain harmonic polynomial cell (HPC) method based on overset mesh to delve into the flow physics of an upright circular tank undergoing an oscillation in surge motion. Their work is currently published in the research journal, Physical Review Fluids.
In their approach, a fully nonlinear HPC method incorporating the overset-mesh technique was developed. To begin with, basic equations together with the linear and weakly nonlinear multimodal theories were presented. Subsequently, a fully nonlinear time-domain HPC method incorporating the overset-mesh technique was developed. The accuracy on the Neumann-type boundaries was improved by introducing ghost nodes outside of the computational domain. Lastly, the developed numerical model was used to assess the flow physics of liquid sloshing in an upright circular tank. Comparison is made between the results predicted by the multimodal theories and the developed HPC model.
The authors found that when the tank was undergoing time-harmonic oscillation with a single degree of freedom near the lowest natural frequency, swirling waves were observed; which included time-harmonic swirling waves and periodically modulated swirling waves caused by mode interactions, resulting in lateral force and roll moment on the tank. Moreover, it was established that the swirling behavior was not dependent on initial conditions, but initial conditions could determine the swirling direction. Also, when a transient-type excitation was imposed, such as NewWave-type or focused-wave-type excitation was imposed, no swirling waves were observed in both fully nonlinear HPC results and weakly nonlinear multimodal analysis. Both transient-type excitations produce comparable sloshing response, however the hydrodynamic forces can be quite different. Based on the NewWave-type excitation, the concept of designer-wave-type excitation was applied to derive the largest sloshing response for a given sea-state. Through hydrodynamic force decomposition, it is reported that under a focused-wave-type excitation, the inertial component of the hydrodynamic forces, which is associated with the tank motion, was more dominant; while under a designer-wave-type excitation, the residual component, associated with the liquid sloshing response in the tank, dominated instead.
Hui Liang, Harrif Santo, Yanlin Shao, Yun Zhi Law, Eng Soon Chan. Liquid sloshing in an upright circular tank under periodic and transient excitations. Physical Review Fluids; volume 5, 084801.