Developing New Numerical Modeling for Sloshing Behavior in Two-Dimensional Tanks Based on Nonlinear Finite-Element Method
Publication: Journal of Engineering Mechanics
Volume 145, Issue 12
Abstract
In this paper, the nonlinear sloshing behavior of a liquid in a partially filled tank is studied using the finite-element method (FEM) based on new spherical Hankel shape functions. The liquid free surface is one of the important parameters in the modeling of the sloshing problems. The main aim of this study is the determination of the free surface location using a new finite-element technique. In this new method, the finite-element method with new shape functions is developed and reformulated. These shape functions are derived using the first and second kind of Bessel functions and have properties such as piecewise continuity. Using these new functions, the number of elements can be reduced, while the accuracy of the results can be increased. The application and accuracy of the proposed method are investigated by several problems related to the sloshing behavior of the liquid. The obtained results indicate that the new method is capable of computing the free surface elevation with a lower number of elements with good accuracy.
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References
Aslam, M. 1981. “Finite element analysis of earthquake-induced sloshing in axisymmetric tanks.” Int. J. Numer. Methods Eng. 17 (2): 159–170. https://doi.org/10.1002/nme.1620170202.
Battaglia, L., M. Cruchaga, M. Storti, J. D’Elia, J. N. Aedo, and R. Reinoso. 2018. “Numerical modelling of 3D sloshing experiments in rectangular tanks.” Appl. Math. Modell. 59 (Jul): 357–378. https://doi.org/10.1016/j.apm.2018.01.033.
Bodard, N., and M. O. Deville. 2006. “Fluid-structure interaction by the spectral element method.” J. Sci. Comput. 27 (1–3): 123–136. https://doi.org/10.1007/s10915-005-9031-2.
Buhmann, M. D. 2003. Radial basis functions: Theory and implementations. Cambridge, UK: Cambridge University Press.
Chen, Y. H., W. S. Hwang, and W. H. Tsao. 2017. “Nonlinear sloshing analysis by regularized boundary integral method.” J. Eng. Mech. 143 (8): 04017046. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001255.
Cho, J. R., and H. W. Lee. 2004. “Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank.” Int. J. Numer. Methods Eng. 61 (4): 514–531. https://doi.org/10.1002/nme.1078.
Faltinsen, O. M. 1978. “A numerical nonlinear method of sloshing in tanks with two-dimensional flow.” J. Ship. Res. 22 (3): 193–202.
Faltinsen, O. M., O. F. Rognebakke, I. A. Lukovsky, and A. N. Timokha. 2000. “Multidimensional modal of nonlinear sloshing in a rectangular tank with finite water depth.” J. Fluid Mech. 407 (Mar): 201–234. https://doi.org/10.1017/S0022112099007569.
Farmani, S., M. Ghaeini-Hessaroeyeh, and S. Hamzehei Javaran. 2018. “The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions.” Int. J. Numer. Methods Fluids 87 (2): 70–89. https://doi.org/10.1002/fld.4482.
Frandsen, J. B. 2004. “Sloshing motions in excited tanks.” J. Comput. Phys. 196 (1): 53–87. https://doi.org/10.1016/j.jcp.2003.10.031.
Hamzehei Javaran, S., and S. Shojaee. 2017. “The solution of elasto static and dynamic problems using the boundary element method based on spherical Hankel element framework.” Int. J. Numer. Methods Eng. 112 (13): 2067–2086. https://doi.org/10.1002/nme.5595.
Hu, Z., X. Zhang, X. Li, and Y. Li. 2018. “On natural frequencies of liquid sloshing in 2-D tanks using boundary element method.” Ocean Eng. 153 (Apr): 88–103. https://doi.org/10.1016/j.oceaneng.2018.01.062.
Javaran, S. H., and N. Khaji. 2012. “Inverse multiquadric (IMQ) function as radial basis function for plane dynamic analysis using dual reciprocity boundary element method.” In Proc., 15th World Conf. on Earthquake Engineering. Tehran, Iran: Tarbiat Modares University.
Javaran, S. H., and N. Khaji. 2014. “Dynamic analysis of plane elasticity with new complex Fourier radial basis functions in the dual reciprocity boundary element method.” Appl. Math. Modell. 38 (14): 3641–3651. https://doi.org/10.1016/j.apm.2013.12.010.
Javaran, S. H., N. Khaji, and H. Moharrami. 2011a. “A dual reciprocity BEM approach using new Fourier radial basis functions applied to 2D elastodynamic transient analysis.” Eng. Anal. Boundary Elem. 35 (1): 85–95. https://doi.org/10.1016/j.enganabound.2010.05.014.
Javaran, S. H., N. Khaji, and A. Noorzad. 2011b. “First kind Bessel function (J-Bessel) as radial basis function for plane dynamic analysis using dual reciprocity boundary element method.” Acta Mech. 218 (3–4): 247–258. https://doi.org/10.1007/s00707-010-0421-7.
Jena, D., and K. C. Biswal. 2018. “Violent sloshing and wave impact in a seismically excited liquid-filled tank: Meshfree particle approach.” J. Eng. Mech. 144 (3): 04017182. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001364.
Khaji, N., and S. H. Javaran. 2013. “New complex Fourier shape functions for the analysis of two-dimensional potential problems using boundary element method.” Eng. Anal. Boundary Elem. 37 (2): 260–272. https://doi.org/10.1016/j.enganabound.2012.11.001.
Kolukula, S. S., and P. Chellapandi. 2013a. “Finite element simulation of dynamic stability of plan free-surface of a liquid under vertical excitation.” Modell. Simul. Eng. 2013: 252760. https://doi.org/10.1155/2013/252760.
Kolukula, S. S., and P. Chellapandi. 2013b. “Nonlinear finite element analysis of sloshing.” Adv. Numer. Anal. 2013: 571528. https://doi.org/10.1155/2013/571528.
Longuet-Higgins, M. S., and E. D. Cokelet. 1976. “The deformation of steep surface waves on water. I: A numerical method of computation.” Proc. R. Soc. London, Ser. A. 350 (1660): 1–26. https://doi.org/10.1098/rspa.1976.0092.
Nukulchai, W. K., and B. T. Tam. 1999. “Structure-fluid interaction model of tuned liquid dampers.” Int. J. Numer. Methods Eng. 46 (9): 1541–1558. https://doi.org/10.1002/(SICI)1097-0207(19991130)46:9%3C1541::AID-NME711%3E3.0.CO;2-Y.
Pal, P. 2012. “Slosh dynamics of liquid-filled rigid containers: Two-dimensional meshless local Petrove-Galerkin approach.” J. Eng. Mech. 138 (6): 567–581. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000367.
Patera, A. T. 1984. “A spectral element method for fluid dynamics: Laminar flow in a channel expansion.” J. Comput. Phys. 54 (3): 468–488. https://doi.org/10.1016/0021-9991(84)90128-1.
Ramaswamy, B., M. Kawahara, and T. Nakayama. 1986. “Lagrangian finite element method for the analysis of two-dimensional sloshing problems.” Int. J. Numer. Methods Fluids 6 (9): 659–670. https://doi.org/10.1002/fld.1650060907.
Reddy, J. N. 2010. The finite element method in heat transfer and fluid dynamics. 3rd ed. Boca Raton, FL: CRC Press.
Sriram, V., S. A. Sannasiraj, and V. Sundar. 2006a. “Numerical simulation of 2D sloshing waves due to horizontal and vertical random excitation.” Appl. Ocean Res. 28 (1): 19–32. https://doi.org/10.1016/j.apor.2006.01.002.
Sriram, V., S. A. Sannasiraj, and V. Sundar. 2006b. “Simulation of 2-D nonlinear waves using finite element method with cubic spline approximation.” J. Fluids Struct. 22 (5): 663–681. https://doi.org/10.1016/j.jfluidstructs.2006.02.007.
Tosun, U., R. Aghazadeh, C. Sert, and M. B. Ozer. 2017. “Tracking free surface and estimating sloshing force using image processing.” Exp. Therm. Fluid Sci. 88 (Nov): 423–433. https://doi.org/10.1016/j.expthermflusci.2017.06.016.
Wang, J. G., and G. R. Liu. 2002. “On the optimal shape parameters of radial basis functions used for 2-D meshless methods.” Comput. Methods Appl. Mech. Eng. 191 (23–24): 2611–2630. https://doi.org/10.1016/S0045-7825(01)00419-4.
Wu, G. X., G. W. Ma, and R. E. Taylor. 1998. “Numerical simulation of sloshing waves in a 3D tank on a finite element method.” Appl. Ocean Res. 20 (6): 337–355. https://doi.org/10.1016/S0141-1187(98)00030-3.
Wu, G. X., and R. E. Taylor. 1994. “Finite element analysis of two-dimensional non-linear transient water waves.” Appl. Ocean Res. 16 (6): 363–372. https://doi.org/10.1016/0141-1187(94)00029-8.
Wu, G. X., and R. E. Taylor. 1995. “Time stepping solutions of the two-dimensional nonlinear wave radiation problem.” Ocean Eng. 22 (8): 785–798. https://doi.org/10.1016/0029-8018(95)00014-C.
Zhang, Y., and D. Wan. 2018. “MPS-FEM coupled method for sloshing flows in an elastic tank.” Ocean Eng. 152 (Mar): 416–427. https://doi.org/10.1016/j.oceaneng.2017.12.008.
Zhao, D., Z. Hu, G. Chen, S. Lim, and S. Wang. 2018. “Nonlinear sloshing in rectangular tanks under forced excitation.” Int. J. Nav. Archit. Ocean Eng. 10 (5): 545–565. https://doi.org/10.1016/j.ijnaoe.2017.10.005.
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Published In
Journal of Engineering Mechanics
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Apr 17, 2018
Accepted: Apr 22, 2019
Published online: Sep 30, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 29, 2020
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