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Time-Independent Finite Difference and Ghost Cell Method to Study Sloshing Liquid in 2D and 3D Tanks with Internal Structures

Published online by Cambridge University Press:  03 June 2015

C. H. Wu ,
O. M. Faltinsen  and
B. F. Chen
C. H. Wu
Affiliation:
Department of Marine Environment and Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
O. M. Faltinsen
Affiliation:
Certrefor Ships and Ocean Structures & Department of Marine Technology, NTNU, Trondheim 7491, Norway
B. F. Chen*
Affiliation:
Department of Marine Environment and Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
*
*Corresponding author.Email:[email protected]
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Abstract

A finite difference scheme with ghost cell technique is used to study viscous fluid sloshing in 2D and 3D tanks with internal structures. The Navier-Stokes equations in a moving coordinate system are derived and they are mapped onto a time-independent and stretched domain. The staggered grid is used and the revised SIMPLEC iteration algorithm is performed. The developed numerical model is rigorously validated by extensive comparisons with reported analytical, numerical and experimental results. The present numerical results were also validated through an experiment setup with a tank excited by an inclined horizontal excitation or a tank mounted by a vertical baffle. The method is then applied to a number of problems including sloshing fluid in a 2D tank with a bottom-mounted baffle and in a 3D tank with a vertical plate. The phenomena of diagonal sloshing waves affected by a vertical plate are investigated in detail in this work. The effects of internal structures on the resonant frequency of a tank with liquid are discussed and the present developed numerical method can successfully analyze the sloshing phenomenon in 2D or 3D tanks with internal structures.

Keywords

65M0676B1049L2535Q3574F10Liquid sloshingbaffleplatetime-independent finite differenceghost cell
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 3 , March 2013 , pp. 780 - 800
Copyright
Copyright © Global Science Press Limited 2013

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References

[1]Abramson, H. N., The dynamics of liquids in moving containers, NASA Rep, (1966), SP 106.Google Scholar
[2]Faltinsen, O. M., Rognebakke, O. F. and Timokha, A. N., Resonance three-dimensional nonlinear sloshing in a square-base basin, J. Fluid Mech., 487 (2003), 1–42.Google Scholar
[3]Faltinsen, O. M., Rognebakke, O. F. and Timokha, A. N., Classification of three-dimensional nonlinear sloshing in a square-base tank with finite depth, J. Fluids Structures., 20 (2005), 81–103.CrossRefGoogle Scholar
[4]Faltinsen, O. M., Rognebakke, O. F. and Timokha, A. N., Resonant three-dimensional nonlinear sloshing in a square-base basin: part 2. effect of higher modes, J. Fluid Mech., 523 (2005), 199–218.CrossRefGoogle Scholar
[5]Chen, B. F. and Chiang, S. W., Complete 2D and fully nonlinear analysis of sloshing fluid in a rigid tank, J. Eng. Mech., 125(1) (1999),70–78.Google Scholar
[6]Sames, P. C., Marcouly, D. and Schellin, T., Sloshing in rectangular and cylindrical tank, J. Ship Res., 46 (2002), 186–200.CrossRefGoogle Scholar
[7]Frandsen, J. B., Sloshing motions in excited tanks, J. Comput. Phys., 196 (2004), 53–87.Google Scholar
[8]Chen, B. F., Viscous fluid in tank under coupled surge, heave and pitch motions, J. Waterway. Port Coastal Ocean Eng., 131(5) (2005), 239–256.CrossRefGoogle Scholar
[9]Chen, B. F. and Nokes, R., Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular tank, J. Comput. Phys., 209 (2005), 47–81.Google Scholar
[10]Akyildiz, H. and Unal, N. E., Experimental investigation of pressure distribution on a rectan-gular tank due to the liquid sloshing, Ocean Eng., 32 (2005), 1503–1516.CrossRefGoogle Scholar
[11]Akyildiz, H. and Ujnal, N. E., Sloshing in a three-dimensional rectangular tank: numerical simulation and experimental validation, Ocean Eng., 33 (2006), 2135–2149.Google Scholar
[12]Liu, D. and Lin, P., A numerical study of three-dimensional liquid sloshing in tanks, J. Comput. Phys., 227 (2008), 3921–3939.Google Scholar
[13]Wu, C. H. and Chen, B. F., Sloshing waves and resonance modes of fluid in a 3D tank by a time-independent finite difference method, Ocean Eng., 36 (2009), 500–510.Google Scholar
[14]Chen, B. F. and Wu, C. H., Effects of excitation angle and coupled heave-surge-sway motion on fluid sloshing in a three-dimensional tank, J. Mar. Sci. Tech., 16 (2011), 22–50.Google Scholar
[15]Faltinsen, O. M. and Timokha, A. N., Sloshing, Cambridge University Press, 2009.Google Scholar
[16]Warnitchai, P. and Pinkaew, T., Modelling of liquid sloshing in rectangular tanks with flow-damping devices, Eng. Struct., 20 (1998), 593–600.Google Scholar
[17]Isaacson, M. and Premasiri, S., Hydrodynamic damping due to baffles in a rectangular tank, Can. J. Civ. Eng., 28 (2001), 608–616.CrossRefGoogle Scholar
[18]Biswal, K. C., Bhattacharyya, S. K. and Sinha, P. K., Non-linear sloshing in partially liquid filled containers with baffles, Int. J. Numer. Meth. Eng., 68 (2006), 317–337.CrossRefGoogle Scholar
[19] R. D. Firouz-Abadi, Haddadpour, H., Noorian, M. A. and Ghasemi, M., A 3D BEM model for liquid sloshing in baffled tanks, Int. J. Numer. Meth. Eng., 76 (2008), 1419–1433.Google Scholar
[20]Kim, Y., Numerical simulation of sloshing flows with impact loads, Appl. Ocean Res., 23 (2001), 53–62.Google Scholar
[21]Kim, Y., Shin, Y. S. and Lee, K. H., Numerical study on sloshing-induced impact pressures on three-dimensional prismatic tanks, Appl. Ocean Res., 26 (2004), 213–226.Google Scholar
[22]Liu, D. and Lin, P., Three-dimensional liquid sloshing in a tank with baffles, Ocean Eng., 36(2) (2009), 202–212.CrossRefGoogle Scholar
[23]Panigrahy, P. K., Saha, U. K. and Maity, D.,Experimental studies on sloshing behavior due to horizontal movement of liquids in baffled tanks, Ocean Eng., 36 (2009), 213–222.Google Scholar
[24]Berthelsen, P. A. and Faltinsen, O. M., A local directional ghost cell approach for incompressible viscous flow problems with irregular boundaries, J. Comput. Phys., 227 (2008), 43544397.Google Scholar
[25]Hirt, C. W., Nicholas, B. D. and Romero, N. C., SOLA-a numerical solution algorithm for transient fluid flows, Los Alamos Scientific Laboratory, Report LA-5852,1975.Google Scholar
[26]Hung, T. K. and Wang, M. H., Nonlinear hydrodynamic pressure on rigid dams motion, J. Eng. Mech. ASCE, 113(4) (1987), 482–499.Google Scholar
[27]Hung, T. K. and Chen, B. F., Nonlinear hydrodynamic pressure on dams during earthquake, J. Eng. Mech., ASCE 116(6) (1990), 1372–1391.CrossRefGoogle Scholar
[28]Faltinsen, O. M., Rognebakke, O. F. and Timokha, A. N., Resonant three-dimensional nonlinear sloshing in a square-base basin: part 3. base ratio perturbations, J. Fluid Mech., 551 (2006), 93–116.Google Scholar
[29]Faltinsen, O. M., A numerical non-linear method of sloshing in tanks with two dimensional flow, J. Ship Res., 22(3) (1978), 193–202.CrossRefGoogle Scholar