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An inviscid analysis of the Prandtl azimuthal mass transport during swirl-type sloshing

Published online by Cambridge University Press:  27 February 2019

Odd M. Faltinsen Open the ORCID record for Odd M. Faltinsen [Opens in a new window]  and
Alexander N. Timokha Open the ORCID record for Alexander N. Timokha [Opens in a new window]
Odd M. Faltinsen*
Affiliation:
Centre for Autonomous Marine Operations and Systems & Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
Alexander N. Timokha
Affiliation:
Centre for Autonomous Marine Operations and Systems & Department of Marine Technology, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway Institute of Mathematics, National Academy of Sciences of Ukraine, 01004 Kiev, Ukraine
*
†Email address for correspondence: odd.faltinsen@ntnu.no
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Abstract

An inviscid analytical theory of a slow steady liquid mass rotation during the swirl-type sloshing in a vertical circular cylindrical tank with a fairly deep depth is proposed by utilising the asymptotic steady-state wave solution by Faltinsen et al. (J. Fluid Mech., vol. 804, 2016, pp. 608–645). The tank performs a periodic horizontal motion with the forcing frequency close to the lowest natural sloshing frequency. The azimuthal mass transport (first observed in experiments by Prandtl (Z. Angew. Math. Mech., vol. 29(1/2), 1949, pp. 8–9)) is associated with the summarised effect of a vortical Eulerian-mean flow, which, as we show, is governed by the inviscid Craik–Leibovich equation, and an azimuthal non-Eulerian mean. Suggesting the mass-transport velocity tends to zero when approaching the vertical wall (supported by existing experiments) leads to a unique non-trivial solution of the Craik–Leibovich boundary problem and, thereby, gives an analytical expression for the summarised mass-transport velocity within the framework of the inviscid hydrodynamic model. The analytical solution is validated by comparing it with suitable experimental data.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 884 - 903
Copyright
© 2019 Cambridge University Press 

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