Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-13T01:41:50.723Z Has data issue: false hasContentIssue false
  • English
  • Français

FSI methods for seismic analysis of sloshing tankproblems

Published online by Cambridge University Press:  15 September 2010

Zuhal Ozdemir ,
Mhamed Souli  and
Yasin M. Fahjan
Zuhal Ozdemir*
Affiliation:
Bogazici University, Kandilli Observatory, Cengelkoy, Istanbul, Turkey Université de Lille, Laboratoire de Mécanique de Lille, CNRS 8107, Bd Paul Langevin, Villeneuve d'Ascq, France
Mhamed Souli
Affiliation:
Université de Lille, Laboratoire de Mécanique de Lille, CNRS 8107, Bd Paul Langevin, Villeneuve d'Ascq, France
Yasin M. Fahjan
Affiliation:
Gebze Institute of Technology (GYTE), Cayirova Campus, Kocaeli, Turkey
*
a Corresponding author:ozdemirzuhal@yahoo.com
Get access

Abstract

The long-period components in earthquake ground motions, which attenuate gradually withdistance, can induce sloshing waves in the liquid containment tanks although they arelocated far away from the seismic source. The resulting sloshing waves generate additionalforces impacting the wall and roof of the tanks and may cause extensive damage on the tankstructure. Numerous examples of tank damages due to sloshing of fluid have been observedduring many earthquakes. Nevertheless, the effect of sloshing is usually primitivelyconsidered in most of the seismic design codes of tanks. On the other hand, the derivationof an analytical solution for the sloshing response of a liquid storage tank subjected toharmonic excitation includes many assumptions and simplifications. Most of the analyticalsolutions in the recent literature assumed the containing liquid to be invicid,incompressible and irrotational, and the tank structure to be an isotropic elastic platewith uniform stiffness, mass and thickness. Even though, experimental works are necessaryto study the actual behavior of the system, they are time consuming, very costly andperformed only for specific boundary and excitation conditions. However, appropriatenumerical simulation using fluid structure interaction techniques can be used to predictthe hydrodynamic forces due to the high-speed impacts of sloshing liquid on a tank walland roof. These simulations can reduce the number of experimental tests. The nonlinearfinite element techniques with either Lagrangian and/or Eulerian formulations may beemployed as a numerical method to model sloshing problems. But, most of the Lagrangianformulations used to solve such problems have failed due to high mesh distortion of thefluid. The arbitrary Lagrangian Eulerian techniques are capable of keeping mesh integrityduring the motion of the tank. In this study, an explicit nonlinear finite elementanalysis method with ALE algorithm is developed and sloshing phenomenon is analyzed. Theanalysis capabilities of the method are explained on a technical level. Although, thedeveloped numerical procedure is applicable to deformable structures, the accuracy of themethod is validated with the existing analytical formulation derived from potential flowtheory as well as the experimental data carried out on rigid tanks when subjected toharmonic and earthquake ground motions. High consistency between numerical andexperimental results in terms of peak level timing, shape and amplitude of sloshing wavesis obtained not only for non-resonant excitation but also for resonant frequencymotion.

Keywords

Fluid-structure interactionarbitrary Lagrangian-Eulerian algorithm (ALE)sloshingearthquaketanksInteraction fluide structurealgorithme ALEballottementséismeréservoirs
Type
Research Article
Information
Mechanics & Industry , Volume 11 , Issue 2 , March 2010 , pp. 133 - 147
Copyright
© AFM, EDP Sciences 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Jacobsen, L.S., Impulsive hydrodynamics of fluid inside a cylindrical tank and of fluid surrounding a cylindrical pier, Bull. Seismological Soc. Amer. 39 (3) (1949) 189–204 Google Scholar
G.W. Housner, Earthquake pressures on fluid containers. 8th Technical Report under Office of Naval Research, California Institute of Technology, Pasadena, California, August, 1954
Housner, G.W., Dynamic pressures on accelerated fluid containers. Bull. Seismological Soc. Amer. 47 (1) (1957) 15–35 Google Scholar
Housner, G.W., The dynamic behavior of water tanks. Bull. Seismological Soc. Amer. 53 (2) (1963) 381–387 Google Scholar
A.S. Veletsos, J.Y. Yang, Earthquake response of liquid storage tanks. Advances in Civil Engineering Through Engineering Mechanics, Proceedings of the Engineering Mechanics Division Specialty Conferences, ASCE, Raleigh, North Carolina (1977) 1–24
Faltinsen, O.M., A numerical nonlinear method of sloshing in tanks with two-dimensional flow, J. Ship Res. 22 (1978) 193–202Google Scholar
Fischera, F.D., Rammerstorferb, F.G., A Refined Analysis of Sloshing Effects in Seismically Excited Tanks, Int. J. Press. Vessels Piping 76 (1999) 693–709CrossRefGoogle Scholar
Lay, K.S., Seismic Coupled Modeling of Axisymmetric Tanks Containing Liquid, J. Eng. Mech. 119 (1993) 1747–1761CrossRefGoogle Scholar
A. El-Zeiny, Nonlinear Time-Dependent Seismic Response of Unanchored Liquid Storage Tanks, Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Irvine, 1995
Chen, B.F., Chiang, H.W., Complete 2D and Fully Nonlinear Analysis of Ideal Fluid in Tanks, J. Eng. Mech. ASCE 125 (1999) 70–78CrossRefGoogle Scholar
Chen, B.F., Viscous Fluid in Tank under Coupled Surge, Heave, and Pitch Motions, Journal of Waterway, Port, Coastal, and Ocean Engineering ASCE 131 (2005) 239–256 CrossRefGoogle Scholar
Souli, M., Ouahsine, A., Lewin, L., ALE formulation for fluid-structure interaction problems, Comput. Methods Appl. Mech. Eng. 190 (2000) 659–675CrossRefGoogle Scholar
Souli, M., Zolesio, J.P., Arbitrary Lagrangian-Eulerian and free surface methods in fluids mechanics, Comput. Methods Appl. Mech. Eng. 191 (2001) 451–466CrossRefGoogle Scholar
Longatte, E., Benddjedou, Z., Souli, M., Methods for numerical study of tube bundle vibrations in cross-flows, J. Fluids Struct. 18 (2003) 513–528CrossRefGoogle Scholar
Longatte, E., Bendjeddou, Z., Souli, M., Application of Arbitrary Lagrange Euler Formulations to Flow-Induced Vibration problems, J. Press. Vessel Technology 125 (2003) 411–417CrossRefGoogle Scholar
Aquelet, N., Souli, M., Olovson, L., Euler Lagrange coupling with damping effects: Application to slamming problems, Comput. Methods Appl. Mech. Eng. 195 (2005) 110–132CrossRefGoogle Scholar
Chen, Y.H., Hwang, W.S., Ko, C.H., Sloshing Behaviours of Rectangular and Cylindrical Liquid Tanks Subjected to Harmonic and Seismic Excitations, Earthquake Engineering and Structural Dynamics 36 (2007) 1701–1717CrossRefGoogle Scholar
Liu, D., Lin, P., A numerical study of three-dimensional liquid sloshing in tanks, J. Comput. Phys. 227 (2008) 3921–3939CrossRefGoogle Scholar
Mitra, S., Upadhyay, P.P., Sinhamahapatra, K.P., Slosh Dynamics of Inviscid Fluids in Two-Dimensional Tanks of Various Geometry Using Finite Element Method, Int. J. Num. Methods Fluids 56 (2008) 1625–1651CrossRefGoogle Scholar
Kana, D.D., Seismic Response of Flexible Cylindrical Liquid Storage Tanks, Nuclear Engineering and Design 52 (1979) 185–199CrossRefGoogle Scholar
G.C. Manos, Dynamic response of a broad storage tank model under a variety of simulated earthquake motions. Proc. 3rd U.S. Nat. Conf. on Earthquake Engrg., Earthquake Engineering Research Institute, E1 Cerrito, Calif., 1986, pp. 2131–2142
Tanaka, Motoaki, Sakurai, Ishida, Tazuke, Akiyama, Kobayashi and Chiba, Proving Test of Analysis Method on Nonlinear Response of Cylindrical Storage Tank Under Severe Earthquakes, Proceedings of 12th World Conference on Earthquake Engineering (12 WCEE), Auckland, New Zealand, 2000
R.A. Ibrahim, Liquid Sloshing Dynamics: Theory and Applications, Cambridge University Press, New York, USA, 2005
T. Belytschko, W.K. Liu, B. Moran, Nonlinear finite elements for continua and structures, Wiley, New York, 2000
Benson, D.J., Computational Methods in Lagrangian and Eulerian Hydrocodes, Comput. Methods Appl. Mech. Eng. 99 (1992) 235–394CrossRefGoogle Scholar
Hughes, T.J.R., Liu, W.K., Zimmerman, T.K., Lagrangian Eulerian finite element formulation for viscous flows, J. Comput. Methods Appl. Mech. Eng. 29 (1981) 329–349CrossRefGoogle Scholar
Ghosh, S., Kikuchi, N., An arbitrary Lagrangian-Eulerian finite element method for large deformation analysis of elastic-viscoplastic solid, Comput. Meth. Appl. Mech. Engng. 86 (1991) 127–188CrossRefGoogle Scholar
J. Donea, Arbitrary Lagrangian-Eulerian Finite Element Methods, Computational methods four Transient Analysis, T. Belytschko, T.J.R. Hughes (eds.) Elsevier Sciences Publishers, B.V. 1983, pp. 473–513
Benson, D.J., A mixture theory for contact in multi-material eulerian formulations, Comput. Meth. Appl. Mech. Eng. 140 (1997) 59–86CrossRefGoogle Scholar
Flanagan, D.P., Belytschko, T., A Uniform Strain Hexahedron, Quadrilateral Orthogonal Hourglass Control, Int. J. Numer. Meths, Eng. 17 (1981) 679–706CrossRefGoogle Scholar
F. Erchiqui, M. Souli, R.B. Yedder, Nonisothermal Finite-Element Analysis of Thermoforming of Polyethylene Terephthalate Sheet: Incomplete Effect of the Forming Stage, Polymer Engineering and Science (2007) 2129–2144
Hirt, C.W., Nichols, B.D., Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 201–225CrossRefGoogle Scholar
Halow, F.H., Welch, J.E., Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface, Phys. Fluids 12 (1965) 2182 Google Scholar
Viecelli, J.A., A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique, J. Comput. Phys. 4 (1969) 543 CrossRefGoogle Scholar
D.L. Young, Time-dependent multi-material flow with large fluid distortion, Numerical Methods for Fluids Dynamics, K.W. Morton, M.J. Baines (eds.), Academic Press, New-York, 1982
Aquelet, N., Souli, M., Gabrys, J., Olovsson, L., A new ALE formulation for sloshing analysis, Struct. Eng. Mech. 16 (2003) 423–440CrossRefGoogle Scholar
Alia, A., Souli, M., High explosive simulation using multi-material formulations, Appl. Therm. Eng. 26 (2006) 1032–1042CrossRefGoogle Scholar
P.R. Woodward, P. Collela, The numerical simulation of two-dimensional fluid flow with strong shocks, Lawrence Livermore National Laboratory, UCRL-86952, 1982
Van Leer, B., Towards the Ultimate Conservative Difference Scheme. IV. A New Approach to Numerical Convection, J. Comput. Phys. 23 (1977) 276–299CrossRefGoogle Scholar
Benson, D.J., Eulerian finite element methods for the micromechanics of heterogenous materials: Dynamics prioritization of material interfaces, Comput. Methods Appl. Mech. Eng. 150 (1998) 343–360CrossRefGoogle Scholar
A.A. Amsden, C.W. Hirt, YAQUI: An Arbitrary Lagrangian-Eulerian Computer Program for Fluid Flow at All Speeds, Los Alamos Scientific Laboratory, LA-5100, 1973