Numerical Simulation of Liquid Sloshing in Tanks

  • Zuhal OzdemirEmail author
  • Yasin M. Fahjan
  • Mhamed Souli
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 44)


Sloshing waves induced by long-period components of earthquake ground motions may generate high magnitude hydrodynamic forces on liquid storage tanks. Past earthquake experience has shown that the forces generated by the sloshing waves may affect the overall safety of tanks by causing extensive damage on the tank wall and roof. Therefore, the accurate description of these forces is vital for reducing the potential risk of tank failure during an earthquake. Appropriate numerical simulation methods can be used to predict response of liquid storage tanks, as they offer a concise way of accurate consideration of all nonlinearities associated with fluid, tank and soil response in the same model. This chapter is, therefore, devoted to the Finite Element (FE) analysis of the sloshing phenomenon occurring in liquid storage tanks under external excitations. The governing equations for the fluid and structure and their solution methodologies are clarified. Current nonlinear FE modelling strategies for interactions between liquid, tank and soil are presented in great detail. The presented numerical modelling schemes are applied to analyze sloshing response of rectangular and cylindrical tanks when subjected to external excitations. Strong correlation between experimental and numerical results is obtained in terms of sloshing wave height for a rectangular tank model under resonant harmonic motion. Numerical simulations on cylindrical tanks have indicated that tank material, boundary conditions at the base and the presence of a second horizontal component in addition to one horizontal component have negligible effect on the sloshing response of cylindrical tanks when subjected to earthquake motions.


Liquid storage tanks Earthquake Numerical methods Fluid-structure interaction (FSI) 


  1. 1.
    Jacobsen LS (1949) Impulsive hydrodynamics of fluid inside a cylindrical tank and of fluid surrounding a cylindrical pier. Bull Seismol Soc Am 39(3):189–204MathSciNetGoogle Scholar
  2. 2.
    Housner GW (1954) Earthquake pressures on fluid containers. In: The 8th technical report under office of naval research. California Institute of Technology, Pasadena, CaliforniaGoogle Scholar
  3. 3.
    Housner GW (1957) Dynamic pressures on accelerated fluid containers. Bull Seismol Soc Am 47(1):15–35Google Scholar
  4. 4.
    Housner GW (1963) The dynamic behavior of water tanks. Bull Seismol Soc Am 53(2):381–387Google Scholar
  5. 5.
    Veletsos AS, Yang JY (1977) Earthquake response of liquid storage tanks. Advances in civil engineering through engineering mechanics. In: Proceedings of the engineering mechanics division specialty conferences. ASCE, Raleigh, North Carolina, pp 1–24Google Scholar
  6. 6.
    Faltinsen OM (1978) A numerical nonlinear method of sloshing in tanks with two-dimensional flow. J Ship Res 22:193–202Google Scholar
  7. 7.
    Fischer FD, Rammerstorfer FG (1999) A refined analysis of sloshing effects in seismically excited tanks. Int J Press Vessels Pip 76:693–709CrossRefGoogle Scholar
  8. 8.
    El-Zeiny A (1995) Nonlinear time-dependent seismic response of unanchored liquid storage tanks. PhD Dissertation, Department of Civil and Environmental Engineering, University of California, IrvineGoogle Scholar
  9. 9.
    Chen BF, Chiang HW (1999) Complete 2D and fully nonlinear analysis of ideal fluid in tanks. J Eng Mech ASCE 125(1):70–78CrossRefGoogle Scholar
  10. 10.
    Chen BF (2005) Viscous fluid in tank under coupled surge, heave, and pitch motions. J Waterw Port Coast Ocean Eng ASCE 131(5):239–256CrossRefGoogle Scholar
  11. 11.
    Souli M, Ouahsine A, Lewin L (2000) ALE formulation for fluid-structure interaction problems. Comput Methods Appl Mech Eng 190:659–675CrossRefzbMATHGoogle Scholar
  12. 12.
    Souli M, Zolesio JP (2001) Arbitrary Lagrangian-Eulerian and free surface methods in fluids mechanics. Comput Methods Appl Mech Eng 191:451–466CrossRefzbMATHGoogle Scholar
  13. 13.
    Longatte E, Benddjedou Z, Souli M (2003) Methods for numerical study of tube bundle vibrations in cross-flows. J Fluids Struct 18(5):513–528CrossRefGoogle Scholar
  14. 14.
    Longatte E, Bendjeddou Z, Souli M (2003) Application of Arbitrary Lagrange Euler formulations to flow-induced vibration problems. J Press Vessel Technol 125:411–417CrossRefGoogle Scholar
  15. 15.
    Aquelet N, Souli M, Olovson L (2005) Euler Lagrange coupling with damping effects: application to slamming problems. Comput Methods Appl Mech Eng 195:110–132MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Chen YH, Hwang WS, Ko CH (2007) Sloshing behaviours of rectangular and cylindrical liquid tanks subjected to harmonic and seismic excitations. Earthq Eng Struct Dyn 36:1701–1717CrossRefGoogle Scholar
  17. 17.
    Liu D, Lin P (2008) A numerical study of three-dimensional liquid sloshing in tanks. J Comput Phys 227:3921–3939CrossRefzbMATHGoogle Scholar
  18. 18.
    Mitra S, Upadhyay PP, Sinhamahapatra KP (2008) Slosh dynamics of inviscid fluids in two-dimensional tanks of various geometry using finite element method. Int J Numer Meth Fluids 56:1625–1651CrossRefzbMATHGoogle Scholar
  19. 19.
    Kana DD (1979) Seismic response of flexible cylindrical liquid storage tanks. Nucl Eng Des 52:185–199CrossRefGoogle Scholar
  20. 20.
    Manos GC (1986) Dynamic response of a broad storage tank model under a variety of simulated earthquake motions. In: Proceedings of the 3rd U.S. National Conference on Earthquake Engrg. Earthquake Engineering Research Institute, E1 Cerrito, CA, pp 2131–2142Google Scholar
  21. 21.
    Ibrahim RA (2005) Liquid sloshing dynamics: theory and applications. Cambridge University Press, New York, USACrossRefzbMATHGoogle Scholar
  22. 22.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, New YorkzbMATHGoogle Scholar
  23. 23.
    Hughes TJR, Liu WK, Zimmerman TK (1981) Lagrangian Eulerian finite element formulation for viscous flows. J Comput Methods Appl Mech Eng 29:329–349MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Benson DJ (1992) Computational methods in Lagrangian and Eulerian Hydrocodes. Comput Methods Appl Mech Eng 99:235–394MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Van Leer B (1977) Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J Comput Phys 23:276–299CrossRefzbMATHGoogle Scholar
  26. 26.
    Reid JD, Hiser NR (2004) Friction modelling between solid elements. Int J Crashworthiness 9(1):65–72CrossRefGoogle Scholar
  27. 27.
    Hallquist JO (2005) LS-DYNA theoretical manual. Livermore Software Technology Corporation, Livermore, CAGoogle Scholar
  28. 28.
    Ozdemir Z, Moatamedi M, Fahjan YM, Souli M (2009) ALE and fluid structure interaction for sloshing analysis. Int J Multiphys 3(3)Google Scholar
  29. 29.
    Ozdemir Z, Souli M, Fahjan YM (2010) FSI methods for seismic analysis of sloshing tank problems. Mécanique et Industries 11(2):133–147CrossRefGoogle Scholar
  30. 30.
    Ozdemir Z, Fahjan YM, Souli M (2012) Numerical evaluation of non-linear response of broad cylindrical steel tanks under multi-dimensional earthquake motion. Earthq Spectra 28(1):217–238CrossRefGoogle Scholar
  31. 31.
    Ozdemir Z, Souli M, Fahjan YM (2010) Application of nonlinear fluid-structure interaction methods to seismic analysis of anchored and unanchored tanks. Eng Struct 32:409–423CrossRefGoogle Scholar
  32. 32.
    TSDC (Turkish Seismic Design Code) (2007) Specification for buildings to be built in seismic zones (TSC). Earthquake Research Department, Ministry of Public Works and Settlement, Government of Republic of Turkey, Ankara. (in Turkish)
  33. 33.
    Fahjan YM (2008) Selection and scaling of real earthquake accelerograms to fit the Turkish design spectra. Teknik Dergi Tech J Turk Chamber Civ Eng (TCCE) Digest 19, 1231–1250Google Scholar
  34. 34.
    PEER (Pacific Earthquake Engineering Research Center) (2006) PEER strong motion database.
  35. 35.
    Abrahamson NA (1993) Non-stationary spectral matching. Seismol Res Lett 63:30Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Civil and Structural EngineeringUniversity of SheffieldSheffieldUK
  2. 2.Department of Earthquake and Structural EngineeringGebze Institute of TechnologyKocaeliTurkey
  3. 3.Laboratoire de Mécanique de LilleUniversité de LilleVilleneuve D’AscqFrance

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