DOI QR코드

DOI QR Code

Arbitrary Lagrangian-Eulerian 기법에 의한 원통형 유체저장구조물 내부유체의 비선형 슬러싱 해석

Nonlinear Liquid Sloshing Analysis in a Cylindrical Container by Arbitrary Lagrangian-Eulerian Approach

  • 권형오 (연세대학교 사회환경시스템공학부) ;
  • 조경환 (연세대학교 사회환경시스템공학부) ;
  • 김문겸 (연세대학교 사회환경시스템공학부) ;
  • 임윤묵 (연세대학교 사회환경시스템공학부)
  • 발행 : 2005.04.01

초록

유체자유수면의 동적거동을 합리적으로 예측하기 위해서는 비선형 특성을 보이는 자유수면의 동역학적 경계조건을 고려해야할 뿐만 아니라 시간에 따라 변화하는 자유수면의 위치변화에 따른 운동학적 경계조건을 고려하여야 한다. 이러한 문제는 대상구조물이 3차원이 될 경우 더욱 복잡해지므로 3차원 비선형 유체자유수면의 해석은 이론해의 도출이 어려우며 수치해석 방법을 이용하는 것이 효과적이다. 본 연구에서는 수치해석 안정성이 높고 3차원 문제에서도 하나의 변수로 유체거동을 모사할 수 있는 arbitrary Lagrangian-Eulerian approach 를 경계요소에 적용하여 효율적이며 안정적인 유체 대변형 해석기법을 개발하였다. 개발된 기법은 향후 자유수면의 비선형 효과를 고려한 유체-구조물 상호작용 해석에 효과적으로 적용할 수 있을 것으로 판단된다.

The solution to a liquid sloshing problem is challenge to the field of engineering. This is not only because the dynamic boundary condition at the free surface is nonlinear, but also because the position of the free surface varies with time in a manner not known a priori. Therefore, this nonlinear phenomenon, which is characterized by the oscillation of the unrestrained free surface of the fluid, is a difficult mathematical problem to solve numerically and analytically. In this study, three-dimensional boundary element method(BEM), which is based on the so-called an arbitrary Lagrangian-Eulerian(ALE) approach for the fluid flow problems with a free surface, was formulated to solve the behavior of the nonlinear free surface motion. An ALE-BEM has the advantage to track the free surface along any prescribed paths by using only one displacement variable, even for a three-dimensional problem. Also, some numerical examples were presented to demonstrate the validity and the applicability of the developed procedure.

키워드

참고문헌

  1. Chen, W., Haroun, M.A. and Liu, F., 'Large amplitude liquid sloshing in seismically excited tanks,' Earthquake Engineering and Structural Dynamics, Vol.25, 1996, pp. 653-669 https://doi.org/10.1002/(SICI)1096-9845(199607)25:7<653::AID-EQE513>3.0.CO;2-H
  2. Nakayama, T. and Washizu, K., 'The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problem,' International Journal for Numerical Methods in Engineering, Vol.17, 1981, pp. 1631-1646 https://doi.org/10.1002/nme.1620171105
  3. Okamoto, T. and Kawahara, M., 'Two-dimen sional sloshing analysis by the arbitrary Lagrangian-Eulerian finite element method,' Proceedings of JSCE, Structural Engineering/Earthquake Engineering, Vol.18, No.4, 1992, pp.207-216
  4. Wu, G.X., Ma, Q.W. and Taylor, R.E., 'Numerical simulation of sloshing waves in a 3D tank based on a finite element method,' Applied Oceans Research, Vol. 20, 1998, pp.337-355 https://doi.org/10.1016/S0141-1187(98)00030-3
  5. Kasuga, L., Sugino, R. and Tosaka, N., 'Sloshing motion in a cylindrical container by boundary element method,' Boundary Element Methods, Eds. M. Tanata, Q. Du and T. Honma, Elsevier, 1993, pp.315-324
  6. Ushijima, S., 'Three-dimensional arbitrary Lagrangian-Eulerian numerical prediction method for non-linear free surface oscillation,' International Journal for Numerical Methods in Fluids, Vol.26, 1998, pp.605-623 https://doi.org/10.1002/(SICI)1097-0363(19980315)26:5<605::AID-FLD668>3.0.CO;2-W
  7. Kim, M.K., Lim, Y.M., Cho, K.H., Cho, S.Y. and Lee, S.M., 'Three Dimensional Analysis of Large Sloshing Motion in a Fluid Container with nonlinear Boundary Conditions,' Journal of KSCE, Vol.22, No.5-A, 2002, pp.1093-1103
  8. Cho, J.R. and Lee, H.W., 'Numerical Study on Liquid Sloshing in Baffled Tank by Nonlinear Finite Element Method,' Computer Methods in Applied Mechanics and Engineering, Vol.193, 2004, pp.2581-2598 https://doi.org/10.1016/j.cma.2004.01.009
  9. Brebbia, C.A, Telles, J.C.F. and Wrobel, L.C., Boundary Element Technique: Theory and Applications in Engineering, Springer-Verlag, New York, 1984
  10. Stoker, J.J., Water Waves, Interscience Publishers, New York, 1954
  11. Hirt, C.W., Amsden, A.A. and Cook, J.L., 'An arbitrary Lagrangian-Eulerian computing method for all flow speeds,' International Journal of Computational Physics, Vol.14, 1974, pp.227-253 https://doi.org/10.1016/0021-9991(74)90051-5
  12. Beskos, D.E., Computational Methods in Mechanics 3: Boundary Element Methods in Mechanics, Amsterdam, Elsevier, 1987, pp.400-401
  13. Takayama, T., 'Theory of Transient Fluid Waves in a Vibrated Storage Tank,' Report of the Port & Harbour Research Institute, Vol.15, No.2, 1976, pp.3-53