All Title Author
Keywords Abstract

Publish in OALib Journal
ISSN: 2333-9721
APC: Only $99

ViewsDownloads

Relative Articles

More...

Nonlinear Finite Element Analysis of Sloshing

DOI: 10.1155/2013/571528

Full-Text   Cite this paper   Add to My Lib

Abstract:

The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed. 1. Introduction It is common everyday knowledge to each of us that any small container filled with liquid must be moved or carried very carefully to avoid spills. For example, one has to be careful while carrying a cup of coffee while moving, because the motion of the person makes coffee spill. Such a motion on the free surface of the liquid, due to external excitation in the liquid-filled containers, is called sloshing. Sloshing is likely to be seen whenever we have a liquid with a free surface in the presence of gravity. At equilibrium the free surface of the liquid is static and coincides with a gravitational equipotential surface. When the surface is perturbed, an oscillation is set up in which the energy oscillates between kinetic energy and gravitational potential energy. The phenomenon called sloshing occurs in a variety of engineering applications such as sloshing in liquid-propellant launch vehicles, sloshing in liquids used in industries to store oil, water, chemicals, liquefied natural gases, and so forth, and sloshing in the nuclear reactors of pool type, nuclear fuel storage tanks under earthquake. The liquid sloshing may cause huge loss of human, economic, and environmental resources owing to unexpected failure of the container; for example the spillage of toxic chemicals stored in tanks in industries can cause contamination of soil and the environment. Thus, understanding the dynamic behaviour of liquid free surface is essential. As a result, the problem of sloshing has attracted many researchers and engineers targeting to understand the complex behaviour of sloshing and to design the structures to withstand its effects. Abundant

References

[1]  H. N. Abramson, “The dynamic behaviour of liquid in moving containers,” NASA Report SP 106, 1996.
[2]  M. A. Haroun, “Dynamic analysis of liquid storage tanks,” Tech. Rep. EERL 80-4, California Institute of Technology, 1980.
[3]  O. M. Faltinsen, “A numerical non-linear method of sloshing in tanks with two dimensional flow,” Journal of Ship Research, vol. 22, no. 3, pp. 193–202, 1978.
[4]  O. M. Faltinsen, “A nonlinear theory of sloshing in rectangular tanks,” Journal of Ship Research, vol. 18, pp. 224–241, 1974.
[5]  T. Nakayama and K. Washizu, “The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems,” International Journal for Numerical Methods in Engineering, vol. 17, no. 11, pp. 1631–1646, 1981.
[6]  G. X. Wu and R. E. Taylor, “Finite element analysis of two-dimensional nonlinear transient water waves,” Applied Ocean Research, vol. 16, pp. 363–372, 1994.
[7]  G. X. Wu and R. E. Taylor, “Time stepping solutions of the two-dimensional nonlinear wave radiation problem,” Ocean Engineering, vol. 8, pp. 785–798, 1995.
[8]  W. Chen, M. A. Haroun, and F. Liu, “Large amplitude liquid sloshing in seismically excited tanks,” Journal of Earthquake Engineering and Structural Dynamics, vol. 25, pp. 653–669, 1996.
[9]  M. S. Turnbull, A. G. L. Borthwick, and R. Eatock Taylor, “Numerical wave tank based on a σ-transformed finite element inviscid flow solver,” International Journal for Numerical Methods in Fluids, vol. 42, no. 6, pp. 641–663, 2003.
[10]  J. B. Frandsen, “Sloshing motions in the excited tanks,” Journal of Computational Physics, vol. 196, no. 1, pp. 53–87, 2004.
[11]  J. R. Cho and H. W. Lee, “Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank,” International Journal for Numerical Methods in Engineering, vol. 61, no. 4, pp. 514–531, 2004.
[12]  C. Z. Wang and B. C. Khoo, “Finite element analysis of two-dimensional nonlinear sloshing problems in random excitations,” Ocean Engineering, vol. 32, no. 2, pp. 107–133, 2005.
[13]  V. Sriram, S. A. Sannasiraj, and V. Sundar, “Numerical simulation of 2D sloshing waves due to horizontal and vertical random excitation,” Applied Ocean Research, vol. 28, no. 1, pp. 19–32, 2006.
[14]  K. C. Biswal, S. K. Bhattacharyya, and P. K. Sinha, “Non-linear sloshing in partially liquid filled containers with baffles,” International Journal for Numerical Methods in Engineering, vol. 68, no. 3, pp. 317–337, 2006.
[15]  R. A. Ibrahim, V. N. Pilipchuk, and T. Ikeda, “Recent advances in liquid sloshing dynamics,” ASME Applied Mechanics Review, vol. 54, pp. 133–199, 2001.
[16]  M. S. Longuet-Higgins and E. D. Cokelet, “The deformation of steep surface waves on water. I. A numerical method of computation,” Proceedings of the Royal Society A, vol. 350, no. 1660, pp. 1–26, 1976.
[17]  O. C. Zienkiewicz and J. Z. Zhu, “The superconvergent patch recovery and a posteriori error estimates. I. The recovery technique,” International Journal for Numerical Methods in Engineering, vol. 33, no. 7, pp. 1331–1364, 1992.

Full-Text

Contact Us

[email protected]

QQ:3279437679

WhatsApp +8615387084133