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Numerical simulations of sloshing waves in vertically excited square tank by improved MPS method

Abstract

Faraday wave is a phenomenon of sloshing due to a heave motion of a partially filled tank, which is also called parametric instability or parametric resonance. In the present paper, the phenomenon of faraday wave in a pure heave excited square tank is numerically simulated through the moving particle semi-implicit (MPS) method. The surface tension effect and a new Dirichlet boundary condition for the pressure Poisson equation are considered to avert unphysical fragmentation and clustering of particles in splash simulation. In the numerical simulation, the evolution of wave motion, and the non-linearity together with breaking phenomenon of faraday wave can be observed. The agreement is good in general, both amplitude and phase. Besides, the parameter studies including the excitation frequency and the forcing amplitude are carried out to analyses the mechanism of resonances response.

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References

  1. Faraday M. On the forms and states assumed by fluids in contact with vibrating elastic surfaces [J]. Philosophical Transactions, 1831, 121(52): 319–340.

    Google Scholar 

  2. Benjamin T. B., Ursell F. J. The stability of the plane free surface of a liquid in vertical periodic motion [J]. Proceedings of the Royal Society of London, 1954, 225(1163): 505–515.

    MathSciNet  MATH  Google Scholar 

  3. Frandsen J. B. Sloshing motions in excited tanks [J]. Journal of Computational Physics, 2004, 196(1): 53–87.

    Article  Google Scholar 

  4. Frandsen J. B., Peng W. Experimental sloshing studies in sway and heave base excited square tanks [C]. Sixth International Conference on Civil Engineering in the Oceans, Baltimore, USA, 2006, 504–512.

  5. Zhuang Y., Wan D. Numerical study on ship motion fully coupled with LNG tank sloshing in CFD Method [J]. International Journal of Computational Methods, 2019, 16(6): 1840022.

    MathSciNet  Article  Google Scholar 

  6. Jin X., Xue M. A., Lin P. Experimental and numerical study of nonlinear modal characteristics of Faraday waves [J]. Ocean Engineering, 2021, 221: 108554.

    Article  Google Scholar 

  7. Liu D., Lin P., Xue M. A. et al. Numerical simulation of two-layered liquid sloshing in tanks under horizontal excitations [J]. Ocean Engineering, 2021, 224: 108768.

    Article  Google Scholar 

  8. Koshizuka S., Oka Y. Moving-particle semi-implicit method for fragmentation of incompressible fluid [J]. Nuclear Science and Engineering, 1996, 123(3): 421–434.

    Article  Google Scholar 

  9. Tang Z., Zhang Y., Wan D. Multi-resolution MPS method for free surface flows [J]. International Journal of Computational Methods, 2016, 13(4): 1641018.

    MathSciNet  Article  Google Scholar 

  10. Chen X., Wan D. GPU accelerated MPS method for large-scale 3-D violent free surface flows [J]. Ocean Engineering, 2019, 171: 677–694.

    Article  Google Scholar 

  11. Tang Z., Wan D., Chen G. et al. Numerical simulation of 3D violent free-surface flows by multi-resolution MPS method [J]. Journal of Ocean Engineering and Marine Energy, 2016, 2(3): 355–364.

    Article  Google Scholar 

  12. Zhang Y. X., Wan D. C., Hino T. Comparative study of MPS method and level-set method for sloshing flows [J]. Journal of Hydrodynamics, 2014, 26(4): 577–585.

    Article  Google Scholar 

  13. Xie F. Z., Zhao W. W., Wan D. C. CFD simulations of three-dimensional violent sloshing flows in tanks based on MPS and GPU [J]. Journal of Hydrodynamics, 2020, 32(5): 672–683.

    Article  Google Scholar 

  14. Shibata K., Koshizuka S., Sakai M. et al. Lagrangian simulations of ship wave interactions in rough seas [J]. Ocean Engineering, 2012, 42: 13–25.

    Article  Google Scholar 

  15. Wen X., Wan D. Numerical simulation of three-layer-liquid sloshing by multiphase MPS method [C]. Proceedings of the ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering, (OMAE2018), Madrid, Spain, 2018.

  16. Wen X., Zhao W., Wan D. An improved moving particle semi-implicit method for interfacial flows [J]. Applied Ocean Research, 2021, 117: 102963.

    Article  Google Scholar 

  17. Wen X., Zhao W. W., Wan D. C. A multiphase MPS method for bubbly flows with complex interfaces [J]. Ocean Engineering, 2021, 238: 109743.

    Article  Google Scholar 

  18. Chen X., Zhang Y., Wan D. Numerical study of 3-D liquid sloshing in an elastic tank by MPS-FEM coupled method [J]. Journal of Ship Research, 2019, 63(3): 143–153.

    Article  Google Scholar 

  19. Zhang G., Chen X., Wan D. MPS-FEM coupled method for study of wave-structure interaction [J]. Journal of Marine Science and Application, 2019, 18(4): 387–399.

    Article  Google Scholar 

  20. Khayyer A., Gotoh H., Falahaty H. et al. Towards development of a reliable fully-Lagrangian MPS-based FSI solver for simulation of 2D hydroelastic slamming [J]. Ocean Systems Engineering, 2017, 7(3): 299–318.

    Google Scholar 

  21. Zhang G., Zhao W., Wan D. Partitioned MPS-FEM method for free-surface flows interacting with deformable structures [J]. Applied Ocean Research, 2021, 114: 102775.

    Article  Google Scholar 

  22. Xie F., Zhao W., Wan D. MPS-DEM coupling method for interaction between fluid and thin elastic structures [J]. Ocean Engineering, 2021, 236: 109449.

    Article  Google Scholar 

  23. Brackbill J. U., Kothe D. B., Zemach C. A continuum method for modeling surface tension [J]. Journal of Computational Physics, 1992, 100(2): 335–354.

    MathSciNet  Article  Google Scholar 

  24. Alam A., Kai H., Suzuki K. Two-dimensional numerical simulation of water splash phenomena with and without surface tension [J]. Journal of Marine Science and Technology, 2007, 12(2): 59–71.

    Article  Google Scholar 

  25. Khayyer A., Gotoh H., Tsuruta N. A new surface tension model for particle methods with enhanced splash computation [J]. Journal of Japan Society of Civil Engineers, Ser. B2 (Coastal Engineering), 2014, 70(2): 26–30.

    Article  Google Scholar 

  26. Chen X., Xi G., Sun Z. G. Improving stability of MPS method by a computational scheme based on conceptual particles [J]. Computer Methods in Applied Mechanics and Engineering, 2014, 278(1): 254–271.

    MathSciNet  Article  Google Scholar 

  27. Shibata K., Masaie I., Kondo M. et al. Improved pressure calculation for the moving particle semi-implicit method [J]. Computational Particle Mechanics, 2015, 2(1): 91–108.

    Article  Google Scholar 

  28. Zhu Y., Jiang S. Y., Yang X. T. et al. Study on pressure oscillation in particle method [J]. Chinese Journal of Computational Mechanics, 2018, 035(005): 574–581(in Chinese).

    Google Scholar 

  29. 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.

    Article  Google Scholar 

  30. Lee B. H., Park J. C., Kim M. H. 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.

    Article  Google Scholar 

  31. Khayyer A., Gotoh H., Shao S. D. Enhanced predictions of wave impact pressure by improved incompressible SPH methods [J]. Applied Ocean Research, 2009, 31(2): 111–131.

    Article  Google Scholar 

  32. Duan G., Koshizuka S., Chen B. A contoured continuum surface force model for particle methods [J]. Journal of Computational Physics, 2015, 298: 280–304.

    MathSciNet  Article  Google Scholar 

  33. 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.

    Article  Google Scholar 

  34. Lei J., Perlin M., Schultz W. W. Period tripling and energy dissipation of breaking standing waves [J]. Journal of Fluid Mechanics, 1998, 369: 273–299.

    MathSciNet  Article  Google Scholar 

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Authors and Affiliations

Authors

Corresponding author

Correspondence to De-cheng Wan.

Additional information

Project supported by the National Natural Science Foundation of China (Grant Nos. 52131102, 51909160 and 51879159), the National Key Research and Development Program of China (Grant No. 2019YFB1704200).

Biography

Guan-yu Zhang (1994-), Female, Ph. D., E-mail: yugagaga@sina.com

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Zhang, Gy., Zhao, Ww. & Wan, Dc. Numerical simulations of sloshing waves in vertically excited square tank by improved MPS method. J Hydrodyn 34, 76–84 (2022). https://doi.org/10.1007/s42241-022-0008-5

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  • DOI: https://doi.org/10.1007/s42241-022-0008-5

Key words

  • Liquid sloshing
  • faraday wave
  • moving particle semi-implicit (MPS) method
  • surface tension
  • MLParticle-SJTU solver