Liquid sloshing in an upright circular tank under periodic and transient excitations


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.

Liquid sloshing in an upright circular tank under periodic and transient excitations - Advances in Engineering

Liquid sloshing in an upright circular tank under periodic and transient excitations - Advances in Engineering

Liquid sloshing in an upright circular tank under periodic and transient excitations - Advances in Engineering

About the author

Hui Liang conducted his PhD research on marine hydrodynamics at Dalian University of Technology and Norwegian University of Science and Technology under a joint-cultivation programme. Since 2018, he has been a Research Scientist at Technology Centre for Offshore and Marine, Singapore (TCOMS). Prior to his current appointment, he was a research engineer at Bureau Veritas working on the development of ship seakeeping software.

Hui’s research is mainly concerned with analytical and numerical modelling of water waves and their interactions with marine structures, including: ships, offshore platforms, aquaculture structures, offshore renewable energy devices, etc. This ranges from the fundamental understanding of physical mechanism to the development of useful tools for practical applications. Hui collaborates widely with industrial and academic partners, and has authored more than 20 peer-review journal articles.

About the author

Harrif Santo received both his B. Eng (1st Class Hons) in Civil Engineering and Ph.D. in Offshore Engineering from the National University of Singapore (NUS) in 2010 and 2014, respectively. Since 2018, he has been a scientist in Technology Centre for Offshore & Marine, Singapore (TCOMS). He is currently co-leading a research programme funded by Agency for Science, Technology and Research (A*STAR) to TCOMS and research partners from A*STAR Research Institutes and Institutes of Higher Learning to co-create knowledge and co-develop solutions with industry partners to enhance productivity, integrity and survivability of offshore systems in extreme environment through structural digital twin. Prior to his current appointment, he was a postdoctoral research assistant in University of Oxford working on renewable energy, and a research fellow in NUS working on extreme fluid loading on space-frame structures.

Dr Santo’s current research interests lie on the predictability of hydrodynamic environment and the associated response of systems for applications ranging from marine & offshore, maritime, renewable energy to aquaculture. He has authored more than 20 scientific journal publications.

About the author

Yanlin Shao received his Ph.D. in marine hydrodynamics from the Norwegian University of Science and Technology (NTNU) in 2010. Since 2018, he has been an associate professor at the Technical University of Denmark. He was a visiting associate professor at NTNU in 2019, and has been an adjunct professor at Harbin Engineering University since 2017. He became a new associate editor for ASME Journal of Offshore Mechanics and Arctic Engineering in 2019, and served as a guest editor for MDPI journal Water on Research on Marine Hydrodynamics in 2020. Before returning to academia, he has worked as a senior engineer in DNVGL and Sevan Marine (now Sevan SSP) on hydrodynamic analysis and mooring design.

His research has been funded by Independent Research Fund Denmark, Research Council of Norway, COWI Fonden, DNVGL Technology Leadership, etc. Dr. Shao’s current research interests lie in the modelling of ocean waves and their interaction with marine structures, e.g. ships, offshore structures, floating offshore wind turbines, floating bridges, and aquaculture structures, etc. He has authored more than 40 scientific publications.

About the author

Yun Zhi Law received his bachelor in Physics from National University for Singapore (NUS) in 2012. After graduation, he joined Center For Quantum Technologies (CQT) as a research assistant and worked on the extraction of intrinsic randomness. Later in 2014 he joined Faculty of Engineering in NUS as a research engineer. The work there involves the investigation of Vortex-Induced Vibration (VIV) on various surface geometry of a riser via CFD. After the project is completed in 2018, he moved to Technology Centre for Offshore and Marine Singapore (TCOMS) as a research engineer. His current work is on the prediction of surface elevation using High-Order Spectral (HOS) method, as well as Artificial Neural Network (ANN) to assist the operation on a vessel or an offshore platform.

About the author

Eng Soon Chan received his Doctor of Science degree from the Massachusetts Institute of Technology in 1986. He is the Chief Executive Officer of Technology Centre for Offshore and Marine, Singapore (TCOMS).

Prior to his current appointment, he held several key positions in NUS, including the Vice Provost (Special Duties) in the Provost Office, Keppel Chair Professor in the Department of Civil and Environmental Engineering, Dean of Engineering, Head of the Civil Engineering Department, Director of the Tropical Marine Science Institute and Executive Director of the Centre for Offshore Research and Engineering. He was also a Provost’s Chair Professor at the Faculty of Engineering, National University of Singapore (NUS).

Professor Chan was also on the management board of several institutions and research facilities, such as the Centre for Remote Imaging, Sensing and Processing (CRISP), Institute for Mathematical Sciences, Temasek Laboratories, Temasek Defence Systems Institute and Tropical Marine Science Institute. He is currently a member of the Workplace Safety and Health Council. He also serves on the PUB Board and the Board of the DSO National Laboratories.

Professor Chan’s research interests and activities are focused on marine processes, including marine hydrodynamics, wave-structure interactions, sediment transport and coastal protection. Professor Chan is a Fellow of the Singapore Academy of Engineering, Institute of Marine Engineering, Science and Technology, and the Institution of Engineers, Singapore.


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.

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