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Identifying linear and nonlinear coupling between fluid sloshing in tanks, roll of a barge and external free-surface waves

Published online by Cambridge University Press:  04 April 2018

W. Zhao Open the ORCID record for W. Zhao [Opens in a new window] ,
P. H. Taylor ,
H. A. Wolgamot  and
R. Eatock Taylor
W. Zhao*
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
P. H. Taylor
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia Keble College, University of Oxford, OxfordOX1 3PJ, UK
H. A. Wolgamot
Affiliation:
Faculty of Engineering and Mathematical Sciences, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
R. Eatock Taylor
Affiliation:
Department of Engineering Science, University of Oxford, OxfordOX1 3PJ, UK
*
†Email address for correspondence: wenhua.zhao@uwa.edu.au
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Abstract

Wave-induced roll motions of liquefied natural gas carriers with partially filled spherical tanks are of practical concern. The fluid within the tanks may be excited into resonance and thus strong sloshing motion may occur at certain frequencies. However, the nature of the coupling between internal sloshing and global roll motions, possibly via higher harmonics, is uncertain. A NewWave-type approach, based on the average shape of large waves, is used to examine nonlinearity of the roll response with and without liquid cargo motion. A phase-combination method based on weakly nonlinear theory is adopted to extract the components of the high frequency signals coupled to the low frequency signals. A significant contribution is observed from the higher harmonics of the main roll response, which are coupled to the liquid cargo sloshing motion. This coupling between higher harmonics of the main roll resonance and internal sloshing appears to be linear, despite the internal sloshing being coupled nonlinearly to the low frequency roll.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 403 - 434
Copyright
© 2018 Cambridge University Press 

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References

Bhattacharyya, R. 1978 Dynamics of Marine Vehicles. Wiley.Google Scholar
Boccotti, P. 1983 Some new results on statistical properties of wind waves. Appl. Ocean Res. 5 (3), 134–140.10.1016/0141-1187(83)90067-6Google Scholar
van Dijk, R. R. T., Quiniou-Ramus, V. & Le-Marechal, G. 2003 Comparison of full-scale measurements with calculated motion characteristics of a West of Africa FPSO. In Proceedings of the 22nd International Conference on Offshore Mechanics and Arctic Engineering. OMAE2003-37182, June 8–13, Cancun, Mexico.Google Scholar
Downie, M. J., Bearman, P. W. & Graham, J. M. R. 1988 Effect of vortex shedding on the coupled roll response of bodies in waves. J. Fluid Mech. 189, 243–261.10.1017/S0022112088000990Google Scholar
Faltinsen, O. M., Rognebakke, O. F., Lukovsky, I. A. & Timokha, A. N. 2000 Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J. Fluid Mech. 407, 201–234.10.1017/S0022112099007569Google Scholar
Faltinsen, O. M., Rognebakke, O. F. & Timokha, A. N. 2003 Resonant three-dimensional nonlinear sloshing in a square-base basin. J. Fluid Mech. 487, 1–42.10.1017/S0022112003004816Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2009 Sloshing. Cambridge University Press.Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2012 Analytically approximate natural sloshing modes for a spherical tank shape. J. Fluid Mech. 703, 391–401.10.1017/jfm.2012.237Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2013a Multimodal analysis of weakly nonlinear sloshing in a spherical tank. J. Fluid Mech. 719, 129–164.10.1017/jfm.2012.635Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2013b Nonlinear sloshing in a spherical tank. In Proceedings of the 32nd International Conference on Offshore Mechanics and Arctic Engineering. OMAE2013-10036, June 9–14, Nantes, France.Google Scholar
Fitzgerald, C. J., Taylor, P. H., Eatock Taylor, R., Grice, J. & Zang, J. 2014 Phase manipulation and the harmonic components of ringing forces on a surface-piercing column. Proc. R. Soc. Lond. A 470 (2168), 20130847.10.1098/rspa.2013.0847Google Scholar
Grice, J. R., Taylor, P. H. & Eatock Taylor, R. 2013 Near-trapping effects for multi-column structures in deterministic and random waves. Ocean Engng 58, 60–77.10.1016/j.oceaneng.2012.09.021Google Scholar
Himeno, Y.1981 Prediction of ship roll damping-a state of the art. Tech. Rep. University of Michigan.Google Scholar
Ikeda, Y., Himeno, Y. & Tanaka, N.1978 A prediction method for ship roll damping. Report of the Department of Naval Architecture, University of Osaka Prefecture, Report No. 00405.Google Scholar
Jonathan, P. & Taylor, P. H. 1997 On irregular, nonlinear waves in a spread sea. J. Offshore Mech. Arctic Engng 119 (1), 37–41.10.1115/1.2829043Google Scholar
Kim, Y. 2007 Experimental and numerical analyses of sloshing flows. J. Engng Maths 58 (1), 191–210.10.1007/s10665-006-9124-4Google Scholar
Lee, S. J. & Kim, M. H. 2010 The effects of inner-liquid motion on LNG vessel responses. J. Offshore Mech. Arctic Engng 132 (2), 021101.Google Scholar
Lindgren, G. 1970 Some properties of a normal process near a local maximum. Ann. Math. Statist. 41, 1870–1883.10.1214/aoms/1177696688Google Scholar
Malenica, S., Zalar, M. & Chen, X. B. 2003 Dynamic coupling of seakeeping and sloshing. In Proceedings of the 13th International Offshore and Polar Engineering Conference, May 25–30, Honolulu, Hawaii, USA.Google Scholar
McIver, P. 1989 Sloshing frequencies for cylindrical and spherical containers filled to an arbitrary depth. J. Fluid Mech. 201, 243–257.10.1017/S0022112089000923Google Scholar
Mitra, S., Wang, C. Z., Reddy, J. N. & Khoo, B. C. 2012 A 3D fully coupled analysis of nonlinear sloshing and ship motion. Ocean Engng 39, 1–13.10.1016/j.oceaneng.2011.09.015Google Scholar
Molin, B., Remy, F., Rigaud, S. & De Jouette, C. 2002 LNG FPSOs: frequency domain, coupled analysis of support and liquid cargo motion. In Proceedings of the 10th International Maritime Association of the Mediterranean (IMAM) Conference, Rethymnon, Greece.Google Scholar
Nam, B. W. & Kim, Y. 2007 Effects of sloshing on the motion response of LNG-FPSO in waves. In Proceedings of the 22nd International Workshop on Water Waves and Floating Bodies. April 15–18, Plitvice, Croatia, http://www.iwwwfb.org/Abstracts/iwwwfb22/iwwwfb22_39.pdf.Google Scholar
Nasar, T., Sannasiraj, S. A. & Sundar, V. 2008 Experimental study of liquid sloshing dynamics in a barge carrying tank. Fluid Dyn. Res. 40 (6), 427–458.10.1016/j.fluiddyn.2008.02.001Google Scholar
Nasar, T., Sannasiraj, S. A. & Sundar, V. 2010 Motion responses of barge carrying liquid tank. Ocean Engng 37 (10), 935–946.10.1016/j.oceaneng.2010.03.006Google Scholar
Newman, J. N. 2005 Wave effects on vessels with internal tanks. In Proceedings of the 20th Workshop on Water Waves and Floating Bodies, May 15–June 1, Spitsbergen, Norway, http://www.iwwwfb.org/Abstracts/iwwwfb20/iwwwfb20_46.pdf.Google Scholar
Ohl, C. O. G., Eatock Taylor, R., Taylor, P. H. & Borthwick, A. G. L. 2001 Water wave diffraction by a cylinder array. Part 1. Regular waves. J. Fluid Mech. 442, 1–32.10.1017/S0022112001004931Google Scholar
Santo, H., Taylor, P. H., Eatock Taylor, R. & Choo, Y. S. 2013 Average properties of the largest waves in Hurricane Camille. J. Offshore Mech. Arctic Engng 135 (1), 011602.Google Scholar
Santo, H., Taylor, P. H., Moreno, E. C., Stansby, P., Eatock Taylor, R., Sun, L. & Zang, J. 2017 Extreme motion and response statistics for survival of the three-float wave energy converter M4 in intermediate water depth. J. Fluid Mech. 813, 175–204.10.1017/jfm.2016.872Google Scholar
Taylor, P. H. & Williams, B. A. 2004 Wave statistics for intermediate depth water-NewWaves and symmetry. J. Offshore Mech. Arctic Engng 126 (1), 54–59.10.1115/1.1641796Google Scholar
Tromans, P. S., Anaturk, A. R. & Hagemeijer, P. 1991 A new model for the kinematics of large ocean waves - application as a design wave. In Proceedings of the 1st International Offshore and Polar Engineering Conference, Aug 11–16, Edinburgh, UK.Google Scholar
Walker, D. A. G., Taylor, P. H. & Eatock Taylor, R. 2004 The shape of large surface waves on the open sea and the Draupner New Year wave. Appl. Ocean Res. 26 (3), 73–83.10.1016/j.apor.2005.02.001Google Scholar
Zhao, W. & McPhail, F. 2017 Roll response of an LNG carrier considering the liquid cargo flow. Ocean Engng 129, 83–91.10.1016/j.oceaneng.2016.11.023Google Scholar
Zhao, W., Taylor, P. H., Wolgamot, H. A. & Eatock Taylor, R. 2018 Linear viscous damping in random wave excited gap resonance at laboratory scale – new wave analysis and reciprocity. J. Fluids Struct. (in press).10.1016/j.jfluidstructs.2018.03.002Google Scholar
Zhao, W., Wolgamot, H. A., Taylor, P. H. & Eatock Taylor, R. 2017 Gap resonance and higher harmonics driven by focused transient wave groups. J. Fluid Mech. 812, 905–939.10.1017/jfm.2016.824Google Scholar
Zhao, W., Yang, J., Hu, Z. & Tao, L. 2014 Coupling between roll motions of an FLNG vessel and internal sloshing. J. Offshore Mech. Arctic Engng 136 (2), 021102.Google Scholar