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Research Papers: Flows in Complex Systems

Numerical and Experimental Evaluation of Sloshing Wave Force Caused by Dynamic Loads in Liquid Tanks

[+] Author and Article Information
Mohammad Mahdi Kabiri, Mohammad Reza Nikoomanesh

Department of Lifeline Earthquake Engineering,
Structural Engineering Research Center,
International Institute of Earthquake
Engineering and Seismology,
Tehran 19537-14453, Iran

Pouya Nouraei Danesh

Department of Lifeline Earthquake Engineering,
Structural Engineering Research Center,
International Institute of Earthquake
Engineering and Seismology,
Tehran 19537-14453, Iran

Mohammad Ali Goudarzi

Department of Lifeline Earthquake Engineering,
Structural Engineering Research Center,
International Institute of Earthquake
Engineering and Seismology,
No. 21, Arghavan Street,
North Dibajee, Farmanieh,
Tehran 19537-14453, Iran
e-mail: m.a.goodarzi@iiees.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 15, 2019; final manuscript received May 17, 2019; published online June 20, 2019. Assoc. Editor: Kevin R. Anderson.

J. Fluids Eng 141(11), 111112 (Jun 20, 2019) (24 pages) Paper No: FE-19-1029; doi: 10.1115/1.4043855 History: Received January 15, 2019; Revised May 17, 2019

Proper evaluation of forces exerted on a solid boundary by liquid sloshing is difficult. If the free board in a liquid storage tank is insufficient, the sloshing waves caused by seismic excitation will collide with the tank roof and may cause major damage. The current study investigated the sloshing wave impact force (SWIF) in full-scale liquid storage tanks using numerical simulation based on the lattice Boltzmann method (LBM). Several shaking table tests have been conducted on a small-scale rectangular tank to validate the numerical model. The results of a standard dam break test have been used to express the validity of the proposed numerical model. This comparison confirms the validity of the numerical strategy for simulating the effect of sloshing. After validating the numerical model, it has been applied to a practical parametric study of SWIF in full-scale liquid tanks. The results of numerical simulation indicate that the simplified method recommended by related codes and standards for calculating SWIF in liquid tanks significantly underestimates the sloshing force. This confirms that the dynamic nature of sloshing should be considered in the design process of liquid storage tanks.

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References

Milgram, J. H. , 1969, “ The Motion of a Fluid in a Cylindrical Container With a Free Surface Following Vertical Impact,” J. Fluid Mech., 37(3), pp. 435–448. [CrossRef]
Minowa, C. , Ogawa, N. , Harada, I. , and Ma, D. C. , 1994, “ Sloshing Roof Impact Tests of a Rectangular Tank,” Argonne National Laboratory, Lemont, IL, Report No. ANL/RE/CP-82360. https://inis.iaea.org/search/search.aspx?orig_q=RN:25069948
Minowa, C. , 1997, “ Sloshing Impact of a Rectangular Water Tank (Water Tank Damage Caused by the Kobe Earthquake),” Nippon Kikai Gakkai Ronbunshu, C-Hen, 63(612), pp. 2643–2649.
Ibrahim, R. A. , 2005, Liquid Sloshing Dynamics: Theory and Applications, Cambridge University Press, New York.
Faltinsen, O. M. , and Timokha, A. N. , 2009, Sloshing, Cambridge University Press, Cambridge, UK.
Yi, W. , and Natsiavas, S. , 1992, “ Seismic Response of Unanchored Fluid-Filled Tanks Using Finite Elements,” ASME J. Pressure Vessel Technol., 114(1), pp. 74–79. [CrossRef]
Wu, G. X. , Ma, Q. W. , and Eatock Taylor, R. , 1998, “ Numerical Simulation of Sloshing Waves in a 3D Tank Based on a Finite Element Method,” Appl. Ocean Res., 20(6), pp. 337–355. [CrossRef]
Mitra, S. , Upadhyay, P. P. , and Sinhamahapatra, K. P. , 2008, “ Slosh Dynamics of Inviscid Fluids in Two‐Dimensional Tanks of Various Geometry Using Finite Element Method,” Int. J. Numer. Methods Fluids, 56(9), pp. 1625–1651. [CrossRef]
Faltinsen, O. M. , and Timokha, A. N. , 2001, “ An Adaptive Multimodal Approach to Nonlinear Sloshing in a Rectangular Tank,” J. Fluid Mech., 432, pp. 167–200. https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/an-adaptive-multimodal-approach-to-nonlinear-sloshing-in-a-rectangular-tank/D520FD5608316B33C3B778922EAF0FFC
Chen, B.-F. , and Nokes, R. , 2005, “ Time-Independent Finite Difference Analysis of Fully Non-Linear and Viscous Fluid Sloshing in a Rectangular Tank,” J. Comput. Phys., 209(1), pp. 47–81. [CrossRef]
Chen, B.-F. , and Chiang, H.-W. , 2000, “ Complete Two-Dimensional Analysis of Sea-Wave-Induced Fully Non-Linear Sloshing Fluid in a Rigid Floating Tank,” Ocean Eng., 27(9), pp. 953–977. [CrossRef]
Dodge, F. T. , 2000, The New Dynamic Behavior of Liquids in Moving Containers, Southwest Research Institute, San Antonio, TX, pp. 111–116.
Kim, Y. , 2001, “ Numerical Simulation of Sloshing Flows With Impact Load,” Appl. Ocean Res., 23(1), pp. 53–62. [CrossRef]
Akyildiz, H. , and Serdar Çelebi, M. , 2001, “ Numerical Computation of Pressure in a Rigid Rectangular Tank Due to Large Amplitude Liquid Sloshing,” Turk. J. Eng. Environ. Sci., 25(6), pp. 659–674
Eswaran, M. , Saha, U. K. , and Maity, D. , 2009, “ Effect of Baffles on a Partially Filled Cubic Tank: Numerical Simulation and Experimental Validation,” Comput. Struct., 87(3–4), pp. 198–205. [CrossRef]
aus der Wiesche, S. , 2008, “ Sloshing Dynamics of a Viscous Liquid in a Spinning Horizontal Cylindrical Tank,” Aerosp. Sci. Technol., 12(6), pp. 448–456. [CrossRef]
Veldman, A. E. , Gerrits, J. , Luppes, R. , Helder, J. A. , and Vreeburg, J. P. B. , 2007, “ The Numerical Simulation of Liquid Sloshing on Board Spacecraft,” J. Comput. Phys., 224(1), pp. 82–99. [CrossRef]
Fang, Z.-Y. , Duan, M.-Y. , and Zhu, R.-Q. , 2007, “ Numerical Simulation of Liquid Sloshing in a Liquid Tank Based on Level-Set Method,” J. Ship Mech., 11(1), pp. 62–67. http://en.cnki.com.cn/Article_en/CJFDTOTAL-CBLX200701007.htm
Arai, M. , Cheng, L.-Y. , and Inoue, Y. , 1995, “ A Computing Method for the Analysis of Water Impact of Arbitrary Shaped Bodies (2nd Report),” J. Soc. Nav. Archit. Jpn., 1995(177), pp. 91–99. [CrossRef]
Arai, M. , Cheng, L.-Y. , and Inoue, Y. , 1992, “ 3D Numerical Simulation of Impact Load Due to Liquid Cargo Sloshing,” J. Soc. Nav. Archit. Jpn., 1992(171), pp. 177–184. [CrossRef]
Rhee, S. H. , 2005, “ Unstructured Grid Based Reynolds-Averaged Navier-Stokes Method for Liquid Tank Sloshing,” ASME J. Fluids Eng., 127(3), pp. 572–582. [CrossRef]
Sames, P. C. , Marcouly, D. , and Schellin, T. E. , 2002, “ Sloshing in Rectangular and Cylindrical Tanks,” J. Ship Res., 46(3), pp. 186–200. https://www.ingentaconnect.com/content/sname/jsr/2002/00000046/00000003/art00004
Price, W. G. , and Chen, Y. G. , 2006, “ A Simulation of Free Surface Waves for Incompressible Two‐Phase Flows Using a Curvilinear Level Set Formulation,” Int. J. Numer. Methods Fluids, 51(3), pp. 305–330. [CrossRef]
Chen, Y. G. , Djidjeli, K. , and Price, W. G. , 2009, “ Numerical Simulation of Liquid Sloshing Phenomena in Partially Filled Containers,” Comput. Fluids, 38(4), pp. 830–842. [CrossRef]
Battaglia, L. , Cruchaga, M. , Storti, M. , D'Elía, J. , Núñez Aedo, J. , and Reinoso, R. , 2018, “ Numerical Modelling of 3D Sloshing Experiments in Rectangular Tanks,” Appl. Math. Modell., 59, pp. 357–378. [CrossRef]
Shao, S. , and Lo, E. Y. , 2003, “ Incompressible SPH Method for Simulating Newtonian and Non-Newtonian Flows With a Free Surface,” Adv. Water Resour., 26(7), pp. 787–800. [CrossRef]
Colagrossi, A. , and Landrini, M. , 2003, “ Numerical Simulation of Interfacial Flows by Smoothed Particle Hydrodynamics,” J. Comput. Phys., 191(2), pp. 448–475. [CrossRef]
Souto-Iglesias, A. , Delorme, L. , Pérez-Rojas, L. , and Abril-Pérez, S. , 2006, “ Liquid Moment Amplitude Assessment in Sloshing Type Problems With Smooth Particle Hydrodynamics,” Ocean Eng., 33(11–12), pp. 1462–1484. [CrossRef]
Fang, J. , Parriaux, A. , Rentschler, M. , and Ancey, C. , 2009, “ Improved SPH Methods for Simulating Free Surface Flows of Viscous Fluids,” Appl. Numer. Math., 59(2), pp. 251–271. [CrossRef]
Koh, C. G. , Luo, M. , Gao, M. , and Bai, W. , 2013, “ Modelling of Liquid Sloshing With Constrained Floating Baffle,” Comput. Struct., 122, pp. 270–279. [CrossRef]
Chen, Z. , Zong, Z. , Li, H. T. , and Li, J. , 2013, “ An Investigation Into the Pressure on Solid Walls in 2D Sloshing Using SPH Method,” Ocean Eng., 59, pp. 129–141. [CrossRef]
Cao Cao, X. Y. , Ming, F. R. , and Zhang, A. M. , 2014, “ Sloshing in a Rectangular Tank Based on SPH Simulation,” Appl. Ocean Res., 47, pp. 241–254. [CrossRef]
Li, J. G. , Hamamoto, Y. , Liu, Y. , and Zhang, X. , 2014, “ Sloshing Impact Simulation With Material Point Method and Its Experimental Validations,” Comput. Fluids, 103, pp. 86–99. [CrossRef]
You, S. , and Bathe, K.-J. , 2015, “ Transient Solution of 3D Free Surface Flows Using Large Time Steps,” Comput. Struct., 158, pp. 346–354. [CrossRef]
Tadashi, W. , 2016, “ Numerical Simulation of Liquid Sloshing Using Arbitrary Lagrangian-Eulerian Level Set Method,” Int. J. Multiphys., 5(4), pp. 339–352.
Zuhal, O. , Fahjan, Y. M. , and Souli, M. , 2017, “ Numerical Simulation of Liquid Sloshing in Tanks,” Computational Methods in Earthquake Engineering, Springer, Cham, Switzerland, pp. 49–79.
Zhang, Y. L. , Tang, Z. Y. , and Wan, D. C. , 2016, “ MPS-FEM Coupled Method for Interaction Between Sloshing Flow and Elastic Structure in Rolling Tanks,” Seventh International Conference on Computational Methods (ICCM), Berkeley, CA, Aug. 1–4, pp. 1–4. http://dcwan.sjtu.edu.cn/userfiles/1493-6106-1-PB.pdf
Zhang, Y. , Chen, X. , and Wan, D. , 2017, “ Sloshing Flows in an Elastic Tank With High Filling Liquid by MPS-FEM Coupled Method,” 27th International Ocean and Polar Engineering Conference, San Francisco, CA, June 25–30, Paper No. ISOPE-I-17-040. https://www.onepetro.org/conference-paper/ISOPE-I-17-040
Hejazi, F. S. , Akhavan, M. K. , and Mohammadi , 2019, “ Investigation on Sloshing Response of Water Rectangular Tanks Under Horizontal and Vertical Near Fault Seismic Excitations,” Soil Dyn. Earthquake Eng., 116, pp. 637–653. [CrossRef]
Zhou, J. G. , 2004, Lattice Boltzmann Methods for Shallow Water Flows, Vol. 4, Springer, Berlin.
CS Product, 2016, “ ProLB,” CS Product, Le Plessis Robinson, France, accessed June 3, 2019, http://www.prolb-cfd.com/products/solver/
SIMULIA, 2018, “ PowerFLOW,” SIMULIA, Waltham, MA.
ANSYS, 2018, “ CFX,” ANSYS® Academic Research Mechanical, Release 18.1, ANSYS, Canonsburg, PA.
ANSYS, 2018, “ Fluent,” ANSYS® Academic Research Mechanical, Release 18.1,” ANSYS, Canonsburg, PA.
Next Limit Technologies, 2013, “ XFlow,” Next Limit Technologies, Madrid, Spain.
He, X. , and Luo, L.-S. , 1997, “ A Priori Derivation of the Lattice Boltzmann Equation,” Phys. Rev. E, 55(6), p. R6333. [CrossRef]
Owen, D. R. J. , Leonardi, C. R. , and Feng, Y. T. , 2011, “ An Efficient Framework for Fluid–Structure Interaction Using the Lattice Boltzmann Method and Immersed Moving Boundaries,” Int. J. Numer. Methods Eng., 87(1–5), pp. 66–95. [CrossRef]
Nourgaliev, R. R. , Dinh, T.-N. , Theofanous, T. G. , and Joseph, D. , 2003, “ The Lattice Boltzmann Equation Method: Theoretical Interpretation, Numerics and Implications,” Int. J. Multiphase Flow, 29(1), pp. 117–169. [CrossRef]
Martys, N. S. , and Chen, H. , 1996, “ Simulation of Multicomponent Fluids in Complex Three-Dimensional Geometries by the Lattice Boltzmann Method,” Phys. Rev. E, 53(1), p. 743. [CrossRef]
Luan, H.-B. , Xu, H. , Chen, L. , Sun, D.-L. , He, Y.-L. , and Tao, W.-Q. , 2011, “ Evaluation of the Coupling Scheme of FVM and LBM for Fluid Flows Around Complex Geometries,” Int. J. Heat Mass Transfer, 54(9–10), pp. 1975–1985. [CrossRef]
Sterling, J. D. , and Chen, S. , 1996, “ Stability Analysis of Lattice Boltzmann Methods,” J. Comput. Phys., 123(1), pp. 196–206. [CrossRef]
Junk, M. , Klar, A. , and Luo, L.-S. , 2005, “ Asymptotic Analysis of the Lattice Boltzmann Equation,” J. Comput. Phys., 210(2), pp. 676–704. [CrossRef]
Bouzidi, M. , Firdaouss, M. , and Lallemand, P. , 2001, “ Momentum Transfer of a Boltzmann-Lattice Fluid With Boundaries,” Phys. Fluids, 13(11), pp. 3452–3459. [CrossRef]
Rothman, D. H. , and Keller, J. M. , 1988, “ Immiscible Cellular-Automaton Fluids,” J. Stat. Phys., 52(3–4), pp. 1119–1127. [CrossRef]
Shan, X. , and Doolen, G. , 1995, “ Multicomponent Lattice-Boltzmann Model With Interparticle Interaction,” J. Stat. Phys., 81(1–2), pp. 379–393. [CrossRef]
Enright, D. , Fedkiw, R. , Ferziger, J. , and Mitchell, I. , 2002, “ A Hybrid Particle Level Set Method for Improved Interface Capturing,” J. Comput. Phys., 183(1), pp. 83–116. [CrossRef]
Ginzburg, I. , 2002, “ A Free-Surface Lattice Boltzmann Method for Modelling the Filling of Expanding Cavities by Bingham Fluids,” Philos. Trans. R. Soc., A, 360(1792), pp. 453–466. [CrossRef]
Krafczyk, M. , Lehmann, P. , Filippova, O. , Hänel, D. , and Lantermann, U. , 2000, “ Lattice Boltzmann Simulations of Complex Multiphase Flows,” Multifield Problems, Springer, Berlin, pp. 50–57.
Janssen, C. , and Krafczyk, M. , 2010, “ A Lattice Boltzmann Approach for Free-Surface-Flow Simulations on Non-Uniform Block-Structured Grids,” Comput. Math. Appl., 59(7), pp. 2215–2235. [CrossRef]
Körner, C. , and Singer, R. F. , 1999, “ Numerical Simulation of Foam Formation and Evolution With Modified Cellular Automata,” Metal Foams and Porous Metal Structures, MIT Publication, Bermen, Germany.
Kleefsman, K. M. T. , Fekken, G. , Veldman, A. E. P. , Iwanowski, B. , and Buchner, B. , 2005, “ A Volume-of-Fluid Based Simulation Method for Wave Impact Problems,” J. Comput. Phys., 206(1), pp. 363–393. [CrossRef]
Akkerman, I. , Bazilevs, Y. , Kees, C. E. , and Farthing, M. W. , 2011, “ Isogeometric Analysis of Free-Surface Flow,” J. Comput. Phys., 230(11), pp. 4137–4152. [CrossRef]
Xie, B. , Jin, P. , and Xiao, F. , 2017, “ An Unstructured-Grid Numerical Model for Interfacial Multiphase Fluids Based on Multi-Moment Finite Volume Formulation and THINC Method,” Int. J. Multiphase Flow, 89, pp. 375–398. [CrossRef]
SPHERIC, 2005, “ SPHERIC, SPH European Research Interest Community, SIG, Test-Case 2, 3D Dam Breaking, Release 1.1, March 2006, by Réza ISSA and Damien VIOLEAU, Electricité De France, Laboratoire National d'Hydraulique et Environnement,” accessed June 3, 2019, http://spheric-sph.org/tests/test-2
Danesh, P. N. , Kabiri, M. , and Goudarzi, M. A. , 2016, “ Experimental Investigation of Sloshing Wave Effects on a Fixed Roof Rectangular Storage Tank,” J. Seismol. Earthquake Eng., 18(1), pp. 23–32. http://jsee.ir/index.php/jsee/article/view/429
Jaiswal, O. R. , Rai, D. C. , and Jain, S. K. , 2007, “ Review of Seismic Codes on Liquid-Containing Tanks,” Earthquake Spectra, 23(1), pp. 239–260. [CrossRef]
Malhotra, P. K. , 2005, “ Sloshing Loads in Liquid-Storage Tanks With Insufficient Freeboard,” Earthquake Spectra, 21(4), pp. 1185–1192. [CrossRef]

Figures

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Fig. 2

Example of bounce-back algorithm

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Fig. 3

Example of VOF free-surface algorithm

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Fig. 4

Multicore desktop personal computer scalability

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Fig. 5

Maritime dam-break experimental setup [61]

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Fig. 6

Snapshots of surface generated from numerical results

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Fig. 7

Comparison of numerical and experimental fluid motion

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Fig. 8

Pressure gages 1, 2, 7 with 0.05 m lattice size

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Fig. 9

Pressure time history (roof to bottom) for pressure gages 1, 2, and 7 for 0.02 m lattice size

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Fig. 10

Time history of pressure (roof to bottom) for pressure gages 1, 2, and 7 (0.007 m lattice size)

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Fig. 11

Pressure time histories at P1, P3, P5, and P7

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Fig. 12

Water height time histories H1, H2, H3, and H4

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Fig. 13

Snapshots of spatial distribution of pressure field

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Fig. 14

Location of pressure gages and loadcells mounted on tank

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Fig. 15

Location of load cells and pressure gages

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Fig. 16

Pressure field in fluid domain for case 50-5-1

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Fig. 17

Comparision of time history of liquid pressure from numerical simulation and experimental measurments for point P1 (test case 50-5-1)

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Fig. 18

Comparision of Fourier transform of liquid pressure from numerical simulation and experimental measurements for point P1 (test case 50-5-1)

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Fig. 19

Comparision of time history of liquid pressure from numerical simulation and experimental measurments for point P1 (test case 50-5-3)

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Fig. 20

Comparision of time history of liquid pressure from numerical simulation and experimental measurments for point P2 (test case 50-5-3)

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Fig. 21

Comparision of Fourier transform of liquid pressure from numerical simulation and experimental measurements for point P2 (test case 50-5-3)

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Fig. 22

Comparison of snapshots of liquid free surface before liquid-roof impact and corresponding numerical results (test case 50-10-3)

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Fig. 23

Comparison of snapshots of liquid free surface before liquid-roof impact and corresponding numerical results (test case 50-10-3)

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Fig. 24

Comparision of time history of liquid pressure from numerical simulation and experimental measurments for point P1 (test case 50-10-3)

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Fig. 25

Comparision of time history of liquid pressure from numerical simulation and experimental measurments for point P2 (test case 50-10-3)

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Fig. 26

Comparision of time history of total pure liquid impact force on tank roof from numerical simulation and experimental measurments (test case 50-10-3)

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Fig. 27

Comparision of fourier transform of liquid pressure from numerical simulation and experimental measurments for point P1 (test case 50-10-3)

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Fig. 28

Comparision of fourier transform of liquid pressure from numerical simulation and experimental measurments for point P2 (test case 50-10-3)

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Fig. 29

Comparision of fourier transform of total pure liquid impact force on tank roof from numerical simulation and experimental measurments (test case 50-10-3)

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Fig. 30

Comparision of time history of liquid pressure from numerical simulation and experimental measurments on point P1 (liquid height: 20 cm, without roof, 1 cm amplitude of excitation)

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Fig. 31

Comparision of fourier transform of liquid pressure from numerical simulation and experimental measurments on point P1 (liquid height: 20 cm, without roof, 1 cm amplitude of excitation)

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Fig. 32

Linear accelerated tank parameters

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Fig. 33

Time history of total sloshing impact force (Fr = free board height; Fr(ACI) = free board height in ACI code)

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Fig. 34

Maximum sloshing force versus tank aspect ratio and free board height

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Fig. 35

(a) Decrease in relative sloshing force for (H/L); (b) increase in convective weight of liquid for (H/L)

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Fig. 36

Schematic view of the numerical model for single sloshing collision

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Fig. 37

Schematic of time history of single-sloshing collision force

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Fig. 38

Comparison of results of numerical analysis and simplified method

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