Abstract
The sloshing free vibrations and the Equivalent Mechanical Model (EMM) parameters are determined for 2D multi-baffled containers under low-gravity conditions using Boundary Element Method (BEM) and potential flow model of the fluid. The presented model is applicable to any values of the acceleration of gravity and surface tension and to constant cross-section containers with arbitrary geometry, and baffle arrangement and shape. The results for a simple rectangular container are validated compared to the analytical values and very good agreement is achieved. Some baffled containers are also analyzed and their sloshing natural frequencies and EMM parameters are presented under low and zero-gravity conditions. Moreover, the effect of baffle characteristics on these parameters is investigated in a wide range of the acceleration of gravity and some conclusions are outlined.
Similar content being viewed by others
References
Bauer, H.F., Eidel, W.: Small amplitude liquid oscillations in a rectangular container under zero-gravity. Aeronaut. J. 93(930), 379–386 (1989)
Bauer, H.F., Eidel, W.: Frictionless liquid sloshing in circular cylindrical container configurations. Aerosp. Sci. Technol. 3(5), 301–311 (1999)
Bauer, H.F., Eidel, W.: Hydroelastic vibrations in a two-dimensional rectangular container filled with frictionless liquid and a partly elastically covered free surface. J. Fluid Struct. 19(2), 209–220 (2004)
Chu, W.-H.: Low-gravity fuel sloshing in an arbitrary axisymmetric rigid tank. J. Appl. Mech. 37(3), 828–837 (1970)
Dalmon, A., Lepilliez, M., Tanguy, S., Alis, R., Popescu, E.R., Roumiguié, R., Miquel, T., Busset, B., Bavestrello, H., Mignot, J.: Comparison between the fluidics experiment and direct numerical simulations of fluid sloshing in spherical tanks under microgravity conditions. Microgravity Sci. Technol. 31(1), 123–138 (2019)
Dodge, F.T., Garza, L.R.: Experimental and theoretical studies of liquid sloshing at simulated low gravity (1967)
Dodge, F.T., Garza, L.R.: Simulated low-gravity sloshing in spherical, ellipsoidal, and cylindrical tanks. J. Spacecr. Rockets 7(2), 204–206 (1970)
Ebrahimian, M., Noorian, M.A., Haddadpour, H.: A successive boundary element model for investigation of sloshing frequencies in axisymmetric multi baffled containers. Eng. Anal. Bound. Elem. 37(2), 383–392 (2013)
Ebrahimian, M., Noorian, M.A., Haddadpour, H.: Equivalent mechanical model of liquid sloshing in multi-baffled containers. Eng. Anal. Bound. Elem. 47, 82–95 (2014)
Ebrahimian, M., Noorian, M.A., Haddadpour, H.: Free vibration sloshing analysis in axisymmetric baffled containers under low-gravity condition. Microgravity Sci. Technol. 27(2), 97–106 (2015)
El-Kamali, M., Schott e, J.-S., Ohayon, R.: Three-dimensional modal analysis of sloshing under surface tension. Int. J. Numer. Meth. Fl. 65(1-3), 87–105 (2011)
El-Kamali, M., Schotté, J.-S., Ohayon, R.: Computation of the equilibrium position of a liquid with surface tension inside a tank of complex geometry and extension to sloshing dynamic cases. Comput. Mech. 46 (1), 169–184 (2010)
Firouz-Abadi, R.D., Haddadpour, H., Ghasemi, M.: Reduced order modeling of liquid sloshing in 3d tanks using boundary element method. Eng. Anal. Bound. Elem. 33(6), 750–761 (2009)
Gedikli, A., Ergüven, M.E.: Seismic analysis of a liquid storage tank with a baffle. J. Sound Vib. 223(1), 141–155 (1999)
Graham, E.W., Rodriquez, A.M.: The characteristics of fuel motion which affect airplane dynamics. Technical report, Douglas Aircraft Co Inc Santa Monica Ca (1951)
Ibrahim, R.A.: Liquid Sloshing Dynamics: Theory and Applications. Cambridge University Press, Cambridge (2005)
Li, J.-C., Lin, H., Zhao, J.-F., Li, K., Hu, W.-R.: Dynamic behaviors of liquid in partially filled tank in short-term microgravity. Microgravity Sci. Technol. 30(6), 849–856 (2018). https://doi.org/10.1007/s12217-018-9642-5
Marcus, M., Minc, H.: Introduction to Linear Algebra. Dover Publication Inc., New York (1988)
Neu, J.T., Good, R.J.: Equilibrium behavior of fluids in containers at zero gravity. AIAA J. 1(4), 814–819 (1963)
Noorian, M.A., Firouz-Abadi, R.D., Haddadpour, H.: A reduced order model for liquid sloshing in tanks with flexible baffles using boundary element method. Int. J. Numer. Meth. Eng. 89(13), 1652–1664 (2012)
Noorian, M.A., Haddadpour, H., Ebrahimian, M.: Stability analysis of elastic launch vehicles with fuel sloshing in planar flight using a bem-fem model. Aerosp. Sci. Technol. 53, 74–84 (2016)
Roberts, J.R., Chen, P.-Y.: Slosh design handbook I, vol. 406. National Aeronautics and Space Administration (1966)
Satterlee, H.M., Reynolds, W.C.: Dynamics of the free liquid surface in cylindrical containers under strong capillary and weak gravity conditions (1964)
Utsumi, M.: Low-gravity propellant slosh analysis using spherical coordinates. J. Fluids Struct. 12(1), 57–83 (1998)
Utsumi, M.: Development of mechanical models for propellant sloshing in teardrop tanks. J Spacecr. Rockets 37(5), 597–603 (2000)
Utsumi, M.: A mechanical model for low-gravity sloshing in an axisymmetric tank. J. Appl. Mech. 71(5), 724–730 (2004)
Utsumi, M.: Mechanical models of low-gravity sloshing taking into account viscous damping. J. Vib. Acoust. 136(1), 011007 (2014)
Veldman, A.E.P., Vogels, M.E.S.: Axisymmetric liquid sloshing under low-gravity conditions. Acta Astronaut. 11(10-11), 641–649 (1984)
Yuanjun, H., Xingrui, M., Pingping, W., Benli, W.: Low-gravity liquid nonlinear sloshing analysis in a tank under pitching excitation. J. Sound Vib. 299(1-2), 164–177 (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ebrahimian, M., Noorian, M.A. & Javadi, M. Sloshing Dynamics in 2D Multi-Baffled Containers Under Low-Gravity Conditions. Microgravity Sci. Technol. 32, 983–998 (2020). https://doi.org/10.1007/s12217-020-09825-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12217-020-09825-9