Abstract
This paper investigates the sloshing phenomena in a spherical liquid tank using the moving particle semi-implicit (MPS) method, a crucial study in fluid dynamics. Distinct from previous research focused on rectangular or LNG tanks, this work explores the unique motion patterns inherent to spherical geometries. The accuracy of our in-house MPS solver MLParticle-SJTU is validated against experimental data and finite volume method (FVM). And the MPS method reveals a closer alignment with experimental outcomes, which suggests that MPS method is particularly effective for modeling complex, non-linear fluid behaviors. Then the fluid’s response to excitation at its natural frequency is simulated, showcasing vigorous sloshing and rotational motion. Detailed analyses of the fluid motion are conducted by drawing streamline diagrams, velocity vector diagrams, and vorticity maps. The fluid’s motion response is explored using both time-domain and frequency-domain curves of the fluid centroid, as well as the sloshing force.
Similar content being viewed by others
References
Lu Y., Yue B. Z., Ma B. L. et al. Moving pulsating ball equivalent model and its validation experiment for large amplitude liquid slosh in gravity environment [J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2543–2551.
Ding S. L., Bao G. W. Modal analysis and equivalent mechanical model of liquid sloshing in arbitrary 3D container [J]. Chinese Quarterly of Mechanics, 2004, 25(1): 62–68.
Liu Z., Yuan K., Liu Y. et al. Fluid sloshing hydrodynamics in a cryogenic fuel storage tank under different order natural frequencies [J]. Journal of Energy Storage, 2022, 52: 104830.
Furuichi Y., Himeno T., Watanabe T. et al. Evaluation of sloshing effect on a tank during landing phases of spacecrafts in a micro-gravity environment [C]. ASCEND 2022, Las Vegas, Nevada, USA, 2022.
Hari M. D., Sarigul-Klijn N. Sloshing behavior in rigid and flexible propellant tanks: computations and experimental validation [J]. Journal of Spacecraft and Rockets, 2021, 58(1): 100–109.
Yang H. Q., Peugeot J. Propellant sloshing parameter extraction from computational-fluid-dynamics analysis [J]. Journal of Spacecraft and Rockets, 2014, 51(3): 908–916.
Chiba M., Motoyama N., Shigematsu S. Theoretical and experimental study on the effect of plane diaphragm tension on dynamic stability of liquid in a hemispherical tank under vertical excitation [J]. Journal of Fluids and Structures, 2023, 120: 103905.
Li D., Xiao H., Jin Y. Design optimization of sloshing tank using weakly compressible mesh free model [J]. Ocean Engineering, 2023, 284: 115218.
Martinez-Carrascal J., Pizzoli M., Saltari F. et al. Sloshing reduced-order model trained with Smoothed Particle Hydrodynamics simulations [J]. Nonlinear Dynamics, 2023, 111: 21099–21115.
Green M. D., Zhou Y., Dominguez J. M. et al. Smooth particle hydrodynamics simulations of long-duration violent three-dimensional sloshing in tanks [J]. Ocean Engineering, 2021, 229: 108925.
Kotsarinis K., Green M. D., Simonini A. et al. Modeling sloshing damping for spacecraft: A smoothed particle hydrodynamics application [J]. Aerospace Science and Technology, 2023, 133: 108090.
Koshizuka S., Oka Y., Tamako H. A particle method for calculating splashing of incompressible viscous fluid [C]. International Conference, Mathematics and Computations, Reactor Physics, and Environmental Analyses, Portland, 1995, 1514–1521.
Zhang G., Zha R., Wan D. MPS–FEM coupled method for 3D dam-break flows with elastic gate structures [J]. European Journal of Mechanics/B Fluids, 2022, 94: 171–189.
Chen X., Wan D. Numerical simulation of three-dimensional violent free surface flows by GPU-Based MPS method [J]. International Journal of Computational Methods, 2019, 16(4), 1843012.
Zhang Y., Wan D. MPS-FEM coupled method for fluid–structure interaction in 3D dam-break flows [J]. International Journal of Computational Methods, 2019, 16(2): 1846009.
Zha R., Zhao W., Wan D. Numerical study on water entry of projectiles with various head shapes by a multiphase moving particle semi-implicit method [J]. International Journal of Offshore and Polar Engineering, 2022, 32(4): 402–410.
Huang C. Y., Zhang G. Y., Wan D. C. Hydroelastic responses of an elastic cylinder impacting on the free surface by MPS-FEM coupled method [J]. Acta Mechanica Sinica, 2022, 38(11): 322057.
Zhang Y., Wan D. MPS-FEM coupled method for sloshing flows in an elastic tank [J]. Ocean Engineering, 2018, 152: 416–427.
Xie F. Z., Meng Q. J., Wan D. C. Numerical simulations of liquid-solid flows in a vertical pipe by MPS-DEM coupling method [J]. China Ocean Engineering, 2022, 36: 542–552.
Zhang G., Zhao W., Wan D. moving particle semi-implicit method coupled with Finite Element Method for hydroelastic responses of floating structures in waves [J]. European Journal of Mechanics /B Fluids, 2022, 95: 63–82.
Pan X. J., Xie F. Z., Wan D. C. Numerical analysis of influence of liquid velocity on characteristics of vertical pipe transportation by MPS-DEM method [J]. Chinese Journal of Hydrodynamics, 2021, 36(6): 835–842 (in Chinese).
Zha R., Zhao W., Wan D. Numerical study of wave-ice floe interactions and overwash by a meshfree particle method [J]. Ocean Engineering, 2023, 286: 115681.
Huang C. Y., Zhao W. W., Wan D. C. Simulation of the motion of an elastic hull in regular waves based on MPS-FEM method [J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3319–3332.
Wen X., Zhao W., Wan D. Multi-phase moving particle semi-implicit method for violent sloshing flows [J] European Journal of Mechanics /B Fluids, 2022, 95: 1–22.
Wen X., Zhao W. W., Wan D. C. Numerical simulations of multi-layer-liquid sloshing by multiphase MPS method [J]. Journal of Hydrodynamics, 2021, 33(5): 938–949.
Xie F., Zhao W., Wan D. MPS-DEM coupling method for interaction between fluid and thin elastic structures [J]. Ocean Engineering, 2021, 236: 109449.
Zhang G. Y., Zhao W. W., Wan D. C. Numerical simulations of sloshing waves in vertically excited square tank by improved MPS method [J]. Journal of Hydrodynamics, 2022, 34(1): 76–84.
Huang C. Y., Zhao W. W., Wan D. C. Numerical simulations of faraday waves in cylindrical and hexagonal tanks based on MPS method [J]. Journal of Hydrodynamics, 2023, 35(2): 278–286.
Tanaka M., Masunaga T. Stabilization and smoothing of pressure in MPS method by quasi-compressibility [J]. Journal of Computational Physics, 2010, 229(11): 4279–4290.
Lee B., Park J., Kim M. et al. Step-by-step improvement of MPS method in simulating violent free-surface motions and impact-loads [J]. Computer Methods in Applied Mechanics and Engineering, 2011, 200(9–12): 1113–1125.
Acknowledgement
(This research received other funding agency in the public, commercial, or not-for-profit sectors.)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest: The authors declare that they have no conflict of interest. De-cheng Wan is editorial board member for the Journal of Hydrodynamics and was not involved in the editorial review, or the decision to publish this article. All authors declare that there are no other competing interests.
Ethical approval: This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent: Not application.
Additional information
Project supported by the National Natural Science Foundation of China (Grant No. 52131102), the National Key Research and Development Program of China (Grant No. 2022YFC2806705).
Biography: Cong-yi Huang (1998-), Female, Ph. D.
Rights and permissions
About this article
Cite this article
Huang, Cy., Wang, Jf., Zhao, Ww. et al. Numerical simulation of liquid sloshing in a spherical tank by MPS method. J Hydrodyn (2024). https://doi.org/10.1007/s42241-024-0018-6
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s42241-024-0018-6