Bearing in mind recent experimental and theoretical results showing that viscous damping can qualitatively affect resonant sloshing in clean tanks, the Narimanov-Moiseev multimodal sloshing theory for an upright circular container is revised to analytically analyze steady-state surface waves when the container performs a small-amplitude sway/roll/pitch/surge prescribed periodic motion with the forcing frequency close to the lowest natural sloshing frequency. The revised theory is applicable for the radius-scaled mean liquid depths h > 1 providing the secondary resonance phenomenon does not occur at the primary resonance zone. A focus is on how the damping influences the phase lag as well as on the amplitude response curves versus the forcing type, which can in the lowest-order approximation be treated as if the container translatory moves along an elliptic orbit in the horizontal plane. The analytical results are compared with existing experiments for longitudinal and circular orbital tank excitations. Whereas a good agreement is found for longitudinal excitations, a discrepancy is detected for the circular orbital forcing. The discrepancy may, most probably, be explained by the wave breaking and mean angular mass-transport (Ludwig Prandtl, 1949) phenomena. Occurrence of the Prandtl phenomenon makes inapplicable the existing analytical inviscid sloshing theories, even if they are modified to account for damping.
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ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering
June 17–22, 2018
Madrid, Spain
Conference Sponsors:
- Ocean, Offshore and Arctic Engineering Division
ISBN:
978-0-7918-5130-2
PROCEEDINGS PAPER
Resonant Steady-State Sloshing in Upright Tanks: Effect of Three-Dimensional Excitations and Viscosity
Alexander N. Timokha,
Alexander N. Timokha
Norwegian University of Science and Technology, Trondheim, Norway
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Ihor A. Raynovskyy
Ihor A. Raynovskyy
National Academy of Sciences of Ukraine, Kiev, Ukraine
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Alexander N. Timokha
Norwegian University of Science and Technology, Trondheim, Norway
Ihor A. Raynovskyy
National Academy of Sciences of Ukraine, Kiev, Ukraine
Paper No:
OMAE2018-77534, V009T13A022; 10 pages
Published Online:
September 25, 2018
Citation
Timokha, AN, & Raynovskyy, IA. "Resonant Steady-State Sloshing in Upright Tanks: Effect of Three-Dimensional Excitations and Viscosity." Proceedings of the ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. Volume 9: Offshore Geotechnics; Honoring Symposium for Professor Bernard Molin on Marine and Offshore Hydrodynamics. Madrid, Spain. June 17–22, 2018. V009T13A022. ASME. https://doi.org/10.1115/OMAE2018-77534
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