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A multimodal method for liquid sloshing in a two-dimensional circular tank

Published online by Cambridge University Press:  22 October 2010

ODD M. FALTINSEN  and
ALEXANDER N. TIMOKHA
ODD M. FALTINSEN*
Affiliation:
Centre for Ships and Ocean Structures and Department of Marine Technology, Norwegian University of Science and Technology, NO-7091 Trondheim, Norway
ALEXANDER N. TIMOKHA
Affiliation:
Centre for Ships and Ocean Structures and Department of Marine Technology, Norwegian University of Science and Technology, NO-7091 Trondheim, Norway
*
†Email address for correspondence: [email protected]
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Abstract

Two-dimensional forced liquid sloshing in a circular tank is studied by the multimodal method which uses an expansion in terms of the natural modes of free oscillations in the unforced tank. Incompressible inviscid liquid, irrotational flow and linear free-surface conditions are assumed. Accurate natural sloshing modes are constructed in an analytical form. Based on these modes, the ‘multimodal’ velocity potential of both steady-state and transient forced liquid motions exactly satisfies the body-boundary condition, captures the corner-point behaviour between the mean free surface and the tank wall and accurately approximates the free-surface conditions. The constructed multimodal solution provides an accurate description of the linear forced liquid sloshing. Surface wave elevations and hydrodynamic loads are compared with known experimental and nonlinear computational fluid dynamics results. The linear multimodal sloshing solution demonstrates good agreement in transient conditions of small duration, but fails in steady-state nearly-resonant conditions. Importance of the free-surface nonlinearity with increasing tank filling is explained.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 457 - 479
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Aliabadi, S., Johnson, A. & Abedi, J. 2003 Comparison of finite element and pendulum models for simulating of sloshing. Comput. Fluids 32, 535–545.CrossRefGoogle Scholar
Bogomaz, G. I. & Sirota, S. A. 2002 Oscillations of a Liquid in Containers: Methods and Results of Experimental Studies (in Russian). National Space Agency of Ukraine.Google Scholar
Djavareshkian, M. H. & Khalili, M. 2006 Simulation of sloshing with the volume of fluid method. Fluid Dyn. Mater. Process. 2 (4), 299–307.Google Scholar
Eastham, M. 1962 An eigenvalue problem with the parameter in the boundary condition. Q. J. Math. 13, 304–320.CrossRefGoogle Scholar
Faltinsen, O. M., Rognebakke, O. F., Lukovsky, I. A. & Timokha, A. N. 2000 Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J. Fluid Mech. 407, 201–234.CrossRefGoogle Scholar
Faltinsen, O. M. & Timokha, A. N. 2001 Adaptive multimodal approach to nonlinear sloshing in a rectangular tank. J. Fluid Mech. 432, 167–200.CrossRefGoogle Scholar
Faltinsen, O. M. & Timokha, A. N. 2009 Sloshing. Cambridge University Press.Google Scholar
Karamanos, S. A., Papaprokopiou, D. & Platyrrachos, M. A. 2009 Finite element analysis of externally-induced sloshing in horizontal-cylindrical and axisymmetric liquid vessels. J. Press. Vessel Technol. 131, 051301.CrossRefGoogle Scholar
Keulegan, G. 1959 Energy dissipation in standing waves in rectangular basins. J. Fluid Mech. 6 (1), 33–50.CrossRefGoogle Scholar
Kobayashi, N., Mieda, T., Shiba, H. & Shinozaki, Y. 1989 A study of the liquid slosh response in horizontal cylindrical tanks. Trans. ASME J. Press. Vessel Technol. 111, 32–38.CrossRefGoogle Scholar
Komarenko, A. 1980 Asymptotic expansion of eigenfunctions of a problem with a parameter in the boundary conditions in a neighborhood of angular boundary points. Ukrainian Math. J. 32 (5), 433–437.CrossRefGoogle Scholar
Kulczycki, T. & Kuznetsov, N. 2009 ‘High spots’ theorems for sloshing problems. Bull. Lond. Math. Soc. 41, 495–505.CrossRefGoogle Scholar
Lukovsky, I. A. 1990 Introduction to Nonlinear Dynamics of Rigid Bodies with the Cavities Partially Filled by a Fluid (in Russian). Naukova Dumka.Google Scholar
Lukovsky, I. A., Barnyak, M. Y. & Komarenko, A. N. 1984 Approximate Methods of Solving the Problems of the Dynamics of a Limited Liquid Volume (in Russian). Naukova Dumka.Google Scholar
McIver, P. 1989 Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth. J. Fluid Mech. 201, 243–257.CrossRefGoogle Scholar
Moderassi-Tehrani, K., Rakheja, S. & Sedaghati, R. 2006 Analysis of the overturning moment caused by transient liquid slosh inside a partly filled moving tank. Proc. Inst. Mech. Engrs, Part D: J. Automob. Engng 220, 289–301.CrossRefGoogle Scholar
Morand, J.-P. & Ohayon, R. 1995 Fluid Structure Interaction: Applied Numerical Methods. Wiley.Google Scholar
Navarrete, J. A. R., Cano, O. R., Romero, J. M. F., Hildebrand, R. & Madrid, M. M. 2003 Caracterización experimental del oleaje en tanques. Tech. Rep. 219. Instituto Mexicano del Transporte (IMT), Secretaria de Comunicaciones Y Transportes (SCT).Google Scholar
Strandberg, L. 1978 Lateral sloshing of road tankers, vol. 1: main report. Tech. Rep. 138A-1978. National Road & Traffic Research Institute, S-58101, Linköping, Sweden.Google Scholar
Vekua, I. N. 1953 On completeness of a system of harmonic polynomials in space. Doklady Akad. Nauk SSSR (NS) 90, 495–498.Google Scholar
Vekua, I. N. 1967 New Methods for Solving Elliptic Equations. Wiley.Google Scholar
Wigley, N. M. 1964 Asymptotic expansions at a corner of solutions of mixed boundary value problems. J. Math. Mech. 13, 549–576.Google Scholar
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