Slosh Dynamics of Liquid-Filled Rigid Containers: Two-Dimensional Meshless Local Petrov-Galerkin Approach
Publication: Journal of Engineering Mechanics
Volume 138, Issue 6
Abstract
This paper presents some of the interesting effects arising from the nonlinear motion of the liquid-free surface, due to sloshing, in a partially filled rigid container subjected to forced excitation. A two-dimensional meshless local Petrov-Galerkin method is used for the numerical simulation of the problem. A local symmetric weak form (LSWF) for nonlinear sloshing of liquid is developed, and a truly meshless method, based on LSWF and moving least squares (MLS) approximation, is presented for the solution of the Laplace equation with the requisite time-dependent boundary conditions. The MLS approximation with linear basis as well as Gaussian type weight function is employed in the computation. At every instant of time, velocity potential is computed at each node and the nodal positions are updated. The choice of a suitable scaling parameter value in the MLS approximation is discussed in this study. The effectiveness of the developed algorithm is demonstrated through a few numerical examples. The accuracy and stability of the numerical method introduced are verified from the comparison with the existing reference solutions.
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Acknowledgments
The author acknowledges the support of Prof. S. K. Bhattacharyya from the Department of Civil Engineering at the Indian Institute of Technology Kharagpur for his encouragement in performing this research work.
References
Abramson, H. N. (1963). “The dynamic behaviour of liquids in moving containers.” Appl. Mech. Rev.AMREAD, 16(7), 501–506.
Abramson, H. N. (1966). “The dynamic behavior of liquids in moving containers.” NASA Rep. SP-106, National Aeronautics and Space Administration, Washington, DC.
Atluri, S. N., and Shen, S. (2002a). The meshless local Petrov—Galerkin (MLPG) method, Technical Science Press, Encino, CA, 382.
Atluri, S. N., and Shen, S. (2002b). “The meshless local Petrov-Galerkin (MLPG) method: A simple and less-costly alternative to the finite element and boundary element methods.” Comput. Model. Eng. Sci.CMESCE, 3(1), 11–51.
Atluri, S. N., and Zhu, T. (1998). “A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics.” Comput. Mech., 22(2), 117–127.
Biswal, K. C., Bhattacharyya, S. K., and Sinha, P. K. (2006). “Non-linear sloshing in partially liquid filled containers with baffles.” Int. J. Numer. Methods Eng.IJNMBH, 68(3), 317–337.
Choun, S. Y., and Yun, C. B. (1999). “Sloshing analysis of rectangular tanks with a submerged structure by using small-amplitude water wave theory.” Earthquake Eng. Struct. Dyn.IJEEBG, 28(7), 763–783.
Delorme, L., Colagrossi, A., Souto-Iglesias, A., Zamora-Rodriguez, R., and Botia-Vera, E. (2009). “A set of canonical problems in sloshing. Part I: Pressure field in forced roll—Comparison between experimental results and SPH.” Ocean Eng.OCENBQ, 36(2), 168–178.
Faltinsen, O. M. (1974). “A nonlinear theory of sloshing in rectangular tanks.” J. Ship Res.JSRHAR, 18(4), 224–241.
Faltinsen, O. M., and Timokha, A. N. (2001). “An adaptive multimodal approach to nonlinear sloshing in a rectangular tank.” J. Fluid Mech.JFLSA7, 432, 167–200.
Faltinsen, O. M., and Timokha, A. N. (2009). Sloshing, Cambridge Univ. Press, New York.
Faltinsen, O. M., and Timokha, A. N. (2010). “A multimodal method for liquid sloshing in a two-dimensional circular tank.” J. Fluid Mech.JFLSA7, 665, 457–479.
Frandsen, J. B. (2004). “Sloshing motions in excited tanks.” J. Comput. Phys.JCTPAH, 196(1), 53–87.
Ibrahim, R. A. (2005). Liquid sloshing dynamics: Theory and applications, Cambridge Univ. Press, New York.
Li, Q., Shen, S., Han, Z. D., and Atluri, S. N. (2003). “Application of meshless local Petrov-Galerkin (MLPG) to problems with singularities and material discontinuities in 3-D elasticity.” Comput. Model. Eng. Sci.CMESCE, 4(5), 571–585.
Liu, G. R., and Gu, Y. T. (2005). An introduction to meshfree methods and their programming, Springer, New York.
Ma, Q. W. (2005). “Meshless local Petrov–Galerkin method for two-dimensional nonlinear water wave problems.” J. Comput. Phys.JCTPAH, 205(2), 611–625.
Miles, J. W. (1958). “On the sloshing of liquid in a flexible tank.” J. Appl. Mech.JAMCAV, 28, 277–283.
Nie, Y. F., Atluri, S. N., and Zuo, C. W. (2006). “The optimal radius of the support of radial weights used in moving least squares approximation.” Comput. Model. Eng. Sci.CMESCE, 12(2), 137–147.
Pal, P., and Bhattacharyya, S. K. (2010). “Sloshing in partially filled liquid containers—Numerical and experimental study for 2-D problems.” J. Sound Vib.JSVIAG, 329(21), 4466–4485.
Pal, N. C., Bhattacharyya, S. K., and Sinha, P. K. (2001). “Experimental investigation of slosh dynamics of liquid-filled containers.” Exp. Mech.EXMCAZ, 41(1), 63–69.
Pal, N. C., Bhattacharyya, S. K., and Sinha, P. K. (2003). “Nonlinear coupled slosh dynamics of liquid-filled laminated composite containers: A two dimensional finite element approach.” J. Sound Vib.JSVIAG, 261(4), 729–749.
Rafiee, A., Thiagarajan, K. P., and Monaghan, J. J. (2009). “SPH simulation of 2D sloshing flow in a rectangular tank.” 19th Int. Offshore (Ocean) and Polar Engineering Conf., ISOPE, Cupertino, CA, 205–212.
Souto-Iglesias, A., Delorme, L., Rojas, P. L., and Abril, S. (2006). “Liquid moment amplitude assessment in sloshing type problems with SPH.” Ocean Eng.OCENBQ, 33(11-12), 1462–1484.
Souto-Iglesias, A., Rojas, P. L., and Rodríguez, Z. R. (2004). “Simulation of anti-roll tanks and sloshing type problems with smoothed particle hydrodynamics.” Ocean Eng.OCENBQ, 31(8-9), 1169–1192.
Washizu, K., Nakayama, T., Ikegawa, M., Tanaka, Y., and Adachi, T. (1984). “Some finite element techniques for the analysis of non-linear sloshing problems.” Chap. 17, Finite elements in fluids, 5, Gallaghar, R. H., Oden, J. T., Zenkiewicz, O. C., Kawai, T., and Kawahara, M., eds., Wiley, New York, 357–376.
Wu, G. X., Ma, Q. W., and Eatock, T. R. (1998). “Numerical simulation of sloshing waves in a 3D tank based on finite element method.” Appl. Ocean Res.AOCRDS, 20(6), 337–355.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 138 • Issue 6 • June 2012
Pages: 567 - 581
Copyright
© 2012. American Society of Civil Engineers.
History
Received: May 14, 2010
Accepted: Dec 8, 2011
Published online: May 15, 2012
Published in print: Jun 1, 2012
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