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Resonant sloshing in an upright annular tank

Published online by Cambridge University Press:  13 September 2016

Odd M. Faltinsen ,
Ivan A. Lukovsky  and
Alexander N. Timokha
Odd M. Faltinsen*
Affiliation:
Centre for Autonomous Marine Operations and Systems and Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Ivan A. Lukovsky
Affiliation:
Institute of Mathematics, National Academy of Sciences of Ukraine, 01601 Kiev, Ukraine
Alexander N. Timokha
Affiliation:
Centre for Autonomous Marine Operations and Systems and Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway Institute of Mathematics, National Academy of Sciences of Ukraine, 01601 Kiev, Ukraine
*
†Email address for correspondence: [email protected]
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Abstract

Resonant sloshing in an upright annular tank is studied by using a new nonlinear modal theory, which is complete within the framework of the Narimanov–Moiseev asymptotics. The applicability is justified for a fairly deep liquid (the liquid-depth-to-outer-tank-radius ratio $1.5\lesssim h=\bar{h}/\bar{r}_{2}$) and away from the non-dimensional inner radii $r_{1}=\bar{r}_{1}/\bar{r}_{2}=0.08546$, 0.17618, 0.27826, 0.31323, 0.31855, 0.43444, 0.46015, 0.48434, 0.68655, 0.70118. The theory is used to describe steady-state (stable and unstable) resonant waves due to a harmonic excitation with the forcing frequency close to the lowest natural sloshing frequency. We show that the surge-sway-pitch-roll excitation is always of either longitudinal or elliptic type. Existing experimental results on the horizontally excited steady-state wave regimes in an upright circular tank ($r_{1}=0$) are utilised for validation. Inserting an inner pole with the radii $r_{1}\approx 0.25$ and 0.35 ($1.5\lesssim h$) causes that no stable swirling and/or irregular waves exist. The response curves for an elliptic-type excitation are examined versus the minor-axis forcing-amplitude component. Stable swirling is then expected being co- and counter-directed to the angular forcing direction. Passage to the rotary (circular) excitation keeps the co-directed swirling stable for all resonant forcing frequencies but the stable counter-directed swirling disappears.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 804 , 10 October 2016 , pp. 608 - 645
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© 2016 Cambridge University Press 

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