Simple analytical method for predicting the sloshing motion in a rectangular pool

  • Received : 2019.03.06
  • Accepted : 2019.10.31
  • Published : 2020.05.25


Predicting the sloshing motion of a coolant during a seismic assessment of a rectangular spent fuel pool is of critical concern. Linear theory, which provides a simple analytical method, has been used to predict the sloshing motion in rectangular pools and tanks. However, this theory is not suitable for the high-frequency excitation problem. In this study, the authors developed a simple analytical method for predicting the sloshing motion in a rectangular pool for a wide range of excitation frequencies. The correlation among the linear theory parameters, influencing on excitation and convective waves, and the excitation frequency is investigated. Sloshing waves in a rectangular pool with several liquid heights are predicted using the original linear theory, a modified linear theory and computational fluid dynamics analysis. The results demonstrate that the developed method can predict sloshing motion over a wide range of excitation frequencies. However, the developed method has the limitations of linear solutions since it neglects the nonlinear features of sloshing motion. Despite these limitations, the authors believe that the developed method can be useful as a simple analytical method for predicting the sloshing motion in a rectangular pool under various external excitations.


  1. M. Baba, Fukushima accident: what happened? Radiat. Meas. 55 (2013) 17-21.
  2. K. Shozugawa, N. Nogawa, M. Matsuo, Deposition of fission and activation products after the Fukushima Dai-ichi nuclear power plant accident, Environ. Pollut. 163 (2012) 243-247.
  3. H. Wang, L. Ge, J. Shan, J. Gou, B. Zhang, Safety analysis of CPR1000 spent fuel pool in case of loss of heat sink, in: Int. Conf. Nucl. Eng. Proceedings, ICONE, 2013.
  4. U.S.N.R. Commission, Standard Technical Specifications, Westinghouse Advanced Passive 1000 (AP1000) Plants, vol. 1, U.S. Nuclear Regulatory Commission, Washington, 2016.
  5. G.X. Wu, Q.W. Ma, R. Eatock Taylor, Numerical simulation of sloshing waves in a 3D tank based on a finite element method, Appl. Ocean Res. 20 (1998) 337-355.
  6. S. Zama, H. Nishi, M. Yamada, K. Hatayama, Damage of oil storage tanks caused by liquid sloshing in the 2003 Tokachi oki earthquake and revision of design spectra in the long-period range, in: 14 Th World Conf. Earthq. Eng, 2008.
  7. M.A. Goudarzi, S.R. Sabbagh-Yazdi, W. Marx, Seismic analysis of hydrodynamic sloshing force on storage tank roofs, Earthq. Spectra 26 (2010) 131-152.
  8. M. Ali Goudarzi, S. Reza Sabbagh-Yazdi, Investigation of nonlinear sloshing effects in seismically excited tanks, Soil Dyn. Earthq. Eng. 43 (2012) 355-365.
  9. P.K. Malhotra, Sloshing loads in liquid-storage tanks with insufficient freeboard, Earthq. Spectra 21 (2005) 1185-1192.
  10. T.M. Shin, Safety review of severe accident senario for wet spent fuel storage facility, J. Korean Radioact. Waste Soc. 9 (2011), 231-2326.
  11. G.W. Housner, The dynamic behavior of water tanks, Bull. Seismol. Soc. Am. 53 (1963) 381-387.
  12. I. Howard, Epstein, Seismic design of liquid storage tanks, ASCE J. Struct. Div. 102 (1976) 1659-1673.
  13. O.M. Faltinsen, A numerical nonlinear method of sloshing in tanks with twodimensional flow, J. Ship Res. 22 (1978) 193-202.
  14. W. Chen, M.A. Haroun, F. Liu, Large amplitude liquid sloshing in seismically excited tanks, Earthq. Eng. Struct. Dyn. 25 (1996) 653-669.<653::AID-EQE513>3.0.CO;2-H
  15. T. Okamoto, M. Kawahara, Two-dimensional sloshing analysis by Lagrangian finite element method, Int. J. Numer. Methods Fluids 11 (1990) 453-477.
  16. S. Aus der Wiesche, Computational slosh dynamics: theory and industrial application, Comput. Mech. 30 (2003) 374-387.
  17. S. Nicolici, R.M. Bilegan, Fluid structure interaction modeling of liquid sloshing phenomena in flexible tanks, Nucl. Eng. Des. 258 (2013) 51-56.
  18. L. Hou, F. Li, C. Wu, A numerical study of liquid sloshing in a two-dimensional tank under external excitations, J. Mar. Sci. Appl. 11 (2012) 305-310.
  19. Y. Su, Z.Y. Liu, Numerical model of sloshing in rectangular tank based on Boussinesq-type equations, Ocean Eng. 121 (2016) 166-173.
  20. J.H. Jung, H.S. Yoon, C.Y. Lee, Effect of natural frequency modes on sloshing phenomenon in a rectangular tank, Int. J. Nav. Archit. Ocean Eng. 7 (2015) 580-594.
  21. H. Akyildiz, N. Erdem Unal, Sloshing in a three-dimensional rectangular tank: numerical simulation and experimental validation, Ocean Eng. 33 (2006) 2135-2149.
  22. U.S.N.R. Commission, Consequence study of a beyond-design-basis earthquake affecting the spent fuel pool for a U.S. Mark I boiling water reactor, NUREG 2161 (2014).