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Multimodal analysis of weakly nonlinear sloshing in a spherical tank

Published online by Cambridge University Press:  19 February 2013

Odd M. Faltinsen  and
Alexander N. Timokha
Odd M. Faltinsen*
Affiliation:
Centre for Ships and Ocean Structures and Department of Marine Technology, Centre for Autonomous Marine Operations and Systems, 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, Centre for Autonomous Marine Operations and Systems, Norwegian University of Science and Technology, NO-7091, Trondheim, Norway
*
†Email address for correspondence: oddfal@marin.ntnu.no
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Abstract

Sloshing in a spherical tank due to horizontal excitation is studied by using the nonlinear multimodal method which involves the analytically approximate sloshing modes by Faltinsen & Timokha (J. Fluid Mech., vol. 703, 2012, pp. 391–401). General fully and weakly nonlinear modal equations are derived but an emphasis is on the Moiseev–Narimanov asymptotic modal system which implies that the forcing frequency is close to the lowest natural sloshing frequency and there are no secondary resonances in the forcing frequency range leading to a nonlinear resonant amplification of double and triple harmonics in higher modes. The Moiseev–Narimanov modal system is used to construct an asymptotic time-periodic solution and, thereby, classify the corresponding steady-state wave regimes appearing as stable and unstable planar waves and swirling. The results on the stability boundaries are compared with experiments by Sumner & Stofan (1963, Tech. Rep. TN D-1991, NASA Technical Note) and Sumner (1966, Tech. Rep. TN D-3210, NASA). A good agreement is established for $0. 2\leq h\lesssim 1$. Discrepancy for higher liquid depths $1\lesssim h\lt 2$ are explained by secondary resonance.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 129 - 164
Copyright
©2013 Cambridge University Press

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