Advertisement

Liquid Sloshing in Circular Toroidal and Coaxial Cylindrical Shells

Conference paper
  • 251 Downloads
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

Free liquid vibrations in circular toroidal and coaxial cylindrical shells are considered. The liquid is supposed to be an ideal and incompressible one, and its flow inside the reservoirs is irrotational. In these assumptions, there exists a velocity potential that satisfies the Laplace equation. The mixed boundary value problem to determine this potential and liquid pressure are formulated for the Laplace equation and further reduced to solving the system of one-dimensional singular integral equations. For its numerical implementation, the boundary element method is used taking into account the ring shape of the free surface. The effective numerical procedures are proposed to accurate calculations of singular integrals containing elliptical integrals in their kernels. Numerical simulations are provided for both circular toroidal and coaxial cylindrical shells for different filling levels and various widths of gaps. The analytical solution is received for coaxial cylindrical shells, including a limit case of the infinitesimal gap. This solution can be considered as a benchmark test and allows us to validate the proposed numerical method.

Keywords

Free liquid vibrations Circular toroidal and coaxial cylindrical shells Boundary element method 

Notes

Acknowledgments

Financial support for Joint Ukraine-Indian Republic R&D Projects is gratefully acknowledged. The authors would also like to thank our foreign collaborator, Professor Alexander Cheng, University of Mississippi, USA, for his constant support and interest to our research.

References

  1. 1.
    Ibrahim, R.A.: Liquid Sloshing Dynamics. Theory and Applications. Cambridge University Press, Cambridge (2005)CrossRefGoogle Scholar
  2. 2.
    Zingoni, A.: Liquid-containment shells of revolution. A review of recent studies on strength, stability and dynamic. Thin-Walled Struct. 87, 102–114 (2015)CrossRefGoogle Scholar
  3. 3.
    Gnitko, V., Degtyariov, K., Naumenko, V., Strelnikova, E.: BEM and FEM analysis of the fluid-structure Interaction in tanks with baffles. Int. J. Comput. Methods Exp. Meas. 5(3), 317–328 (2017)Google Scholar
  4. 4.
    Spyros, A.K., Papaprokopiou, D., Platyrracho, M.A.: Finite element analysis of sloshing in horizontal-cylindrical industrial vessels under earthquake. J. Press. Vessel Technol. Trans. ASME 131, 05130101–05130111 (2009)Google Scholar
  5. 5.
    Gnitko, V., Marchenko, U., Naumenko, V., Strelnikova, E.: Forced vibrations of tanks partially filled with the liquid under seismic load. In: Proceedings of XXXIII Conference Boundary elements and other mesh reduction methods, WITPress, Transaction on Modeling and Simulation, vol. 52, pp. 285−296 (2011)Google Scholar
  6. 6.
    Wang, X.H., Redekop, D.: Natural frequencies analysis of moderately-thick and thick toroidal shells. Procedia Eng. 14, 636–640 (2011)CrossRefGoogle Scholar
  7. 7.
    Enoma, N., Egware, H.O., Itoje, H.J., Unueroh, U.G.: Membrane solutions for circular toroidal shells under internal hydrostatic pressure. J. Multidiscip. Eng. Sci. Technol. 2(10), 2895–2901 (2015)Google Scholar
  8. 8.
    Zua, L., Koussiosb, S., Beukersb, A.: A novel design solution for improving the performance of composite toroidal hydrogen storage tanks. Int. J. Hydrog. Energy 37, 14343–14350 (2012)CrossRefGoogle Scholar
  9. 9.
    Zingoni, A., Mokhothu, B., Enoma, N.: A theoretical formulation for the stress analysis of multi-segmented spherical shells for high-volume liquid containment. Eng. Struct. 87, 21–31 (2015)CrossRefGoogle Scholar
  10. 10.
    Jeong, K.-H.: Natural frequencies and mode shapes of two coaxial cylindrical shells coupled with bounded fluid. J. Sound Vib. 215(1), 105–124 (1998)CrossRefGoogle Scholar
  11. 11.
    Bochkarev, S.A., Lekomtsev, S.V., Matveenko, V.P.: Numerical modeling of spatial vibrations of cylindrical shells partially filled by liquid. Comput. Technol. 18(2), 12–24 (2013)Google Scholar
  12. 12.
    Mikilyan, M., Marzocca, P.: Vibration and stability of coaxial cylindrical shells with a gap partially filled with liquid. J. Aerosp. Eng. 32(6), 12–26 (2019)CrossRefGoogle Scholar
  13. 13.
    McIver, P.: Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth. J. Fluid Mech. 201, 243–250 (1989)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Faltinsen, O.M., Timokha, A.N.: Sloshing. Cambridge University Press, Cambridge (2009)zbMATHGoogle Scholar
  15. 15.
    Curadelli, O., Ambrosini, D., Mirasso, A., Amani, M.: Resonant frequencies in an elevated spherical container partially filled with water: FEM and measurement. J. Fluids Struct. 26(1), 148–159 (2010)CrossRefGoogle Scholar
  16. 16.
    Kulczycki, T., Kwaśnicki, M., Siudeja, B.: The shape of the fundamental sloshing mode in axisymmetric containers. J. Eng. Math. 99(1), 157–193 (2016)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Budiansky, B.: Sloshing of liquid in circular canals and spherical tanks. J. Aerosp. Sci. 27(3), 161–172 (1960)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Gnitko, V.V., Degtyariov, K.G., Naumenko, V.V., Strelnikova, E.A.: Coupled BEM and FEM analysis of fluid-structure interaction in dual compartment tanks. Int. J. Comput. Methods Exp. Meas. 6(6), 976–988 (2018)zbMATHGoogle Scholar
  19. 19.
    Landau, L.D., Lifshits, E.M.: Fluid Dynamics. Pergamon Press, Oxford (1987)Google Scholar
  20. 20.
    Brebbia, C.A., Telles, J.C.F., Wrobel, L.C.: Boundary Element Techniques. Springer, Heidelberg and New York (1984).  https://doi.org/10.1007/978-3-642-48860-3CrossRefzbMATHGoogle Scholar
  21. 21.
    Gnitko, V.I., Degtyariov, K.G., Karaiev, A.O., Strelnikova, E.A.: Singular boundary method in a free vibration analysis of compound liquid-filled shells. WIT Trans. Eng. Sci. 126, 189–200 (2019)CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.V.N. Karazin, Kharkiv National UniversityKharkivUkraine
  2. 2.A. Pidgorny Institute of Mechanical Engineering Problems of the National Academy of Sciences of UkraineKharkivUkraine

Personalised recommendations