A Numerical Method for the Analysis of Nonlinear Sloshing in Circular Cylindrical Containers

  • Tsukasa Nakayama
  • Hiroaki Tanaka

Summary

A new computational method has been developed for the analysis of three-dimensional large-amplitude motion of liquids with free surfaces in moving containers. The problem is formulated mathematically as a nonlinear initial-boundary value problem under the assumption of irrotational flow of an inviscid fluid. Basic equations of the problem are discretized spacewise by the boundary element method based on Green’s second identity and timewise by a forward-time Taylor series expansion. The size of a time increment is determined every time step so that the remainder of truncated Taylor series should be equal to a given small value. This variable time-stepping technique has made a great contribution to numerically stable computations. As a numerical example, swirl motion of a liquid free surface in a circular cylindrical container undergoing horizontal excitation has been analyzed.

Keywords

Assure 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramson, H. N. (editor): The dynamic behavior of liquids in moving containers. NASA SP-106, 1966.Google Scholar
  2. 2.
    Nakayama, T.: Numerical simulation of large-amplitude liquid sloshing in horizontally excited tanks. Proc. 7th Int. Conf. on Finite Element Methods in Flow Problems, Huntsville, Alabama, 1989, 659-664.Google Scholar
  3. 3.
    Nakayama, T.: A computational method for simulating transient motions of an incompressible inviscid fluid with a free surface. Int. J. Num. Meth. Fluids, 10 (1990) 683–695.MATHCrossRefGoogle Scholar
  4. 4.
    Sudo, S. and Hashimoto, H.: Dynamic behavior of a liquid in a cylindrical container subject to horizontal vibration (On nonlinear response of liquid surface)(in Japanese). Trans. Japan Soc. Mech. Engng., 52 (1986) 3655–3659.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1991

Authors and Affiliations

  • Tsukasa Nakayama
    • 1
  • Hiroaki Tanaka
    • 1
  1. 1.Department of Precision Mechanical EngineeringChuo UniversityTokyoJapan

Personalised recommendations