Summary
The numerical simulation of three-dimensional large amplitude liquid sloshing under low gravity environment is discussed in this paper. The ALE (Arbitary Lagrange-Euler) kinematics description is introduced into the finite element fractional step method. The corresponding discrete numerical equations are developed by Galerkin weighted residual method afterwards. The formulations to calculate the free-surface tension are derived. Three-dimensional large amplitude fuel sloshing under low gravity environment in a cylindrical tank is simulated and some important nonlinear characteristics of three-dimensional nonlinear liquid sloshing are obtained. The numerical results are compared with experimental results and the effectiveness of the method conducted in this paper is demonstrated.
Similar content being viewed by others
References
Weatherburn, C. E.: Differential geometry of three dimensions. Cambridge: Cambridge University Press 1955.
Dodge, F. T., Carza, L. R.: Experimental and theoretical studies of liquid sloshing at simulated low gravities. J. Appl. Mech.34, 555–562 (1967).
Abramson, H. N., Chu, W. H., Kara, D. D.: Some studies of nonlinear lateral sloshing in rigid containers. J. Appl. Mech.33, 777–784 (1966).
Szabo, P., Hassager, O.: Simulation of free surfaces in 3D with the arbitrary Lagrange-Euler method. Int. J. Numer. Methods Eng.38, 717–734 (1995).
Hauashi, M., Hatanaka, K.: Lagrange finite element method for free surface Navier-Stokes flow using fractional step methods. Int. J. Numer. Methods Fluids.13, 805–840 (1991).
Ramasuwamy, B., Kawahara, M.: Arbitrary Lagrangian-Eulerian finite element method for unsteady convective incompressible viscous free surface fluid flow. Int. J. Numer. Methods fluids7, 1053–1075 (1987).
Hughes, T. J. R., Liu, W. K., Zimmerman, T. K.: Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput. Methods Appl. Mech. Engrg.29, 329–349 (1981).
Yue, B.: Numerical simulation of three-dimensional large-scale amplitude liquid sloshing and study of hydroelastic coupling dynamics. Ph. D. Diss., Tsinghua University, China, April 1998 (in Chinese).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yue, B., Liu, Y. & Wang, Z. Simulation of nonlinear liquid sloshing under low-gravity environment. Acta Mechanica 148, 231–237 (2001). https://doi.org/10.1007/BF01183680
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01183680