Abstract
A simple theoretical dynamic model with a linearized damping coefficient is proposed for the gap resonance problem, as often referred to as the piston mode wave motion in a narrow gap formed by floating bodies. The relationship among the resonant response amplitude and frequency, the reflection and transmission coefficients, the gap width, and the damping coefficient is obtained. A quantitative link between the damping coefficient of the theoretical dynamic model (ε) and that devised for the modified potential flow model (u p) is established, namely, u p=3πεωn)/8 (where ωn is the natural frequency). This link clarifies the physical meaning of the damping term introduced into the modified potential flow model. A new explicit approach to determine the damping coefficient for the modified potential model is proposed, without resorting to numerically tuning the damping coefficient by trial and error tests. The effects of the body breadth ratio on the characteristics of the gap resonance are numerically investigated by using both the modified potential flow model and the viscous RNG turbulent model. It is found that the body breadth ratio has a significant nonlinear influence on the resonant wave amplitude and the resonant frequency. With the modified potential flow model with the explicit damping coefficient, reasonable predictions are made in good agreement with the numerical solutions of the viscous fluid model.
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Saitoh T., Miao G. P., Ishida H. Experimental study on resonant phenomena in narrow gaps between modules of very large floating structures [C]. Proceedings of International Symposium on Naval Architecture and Ocean Engineering. Shanghai, China, 2003, 39: 1–8.
Saitoh T., Miao G. P., Ishida H. Theoretical analysis on appearance condition of fluid resonance in a narrow gap between two modules of very large floating structure [C]. Proceedings of the 3rd Asia-Pacific Workshop on Marine Hydrodynamics. Shanghai, China, 2006, 170-175.
Molin B. On the piston and sloshing modes in moonpools [J]. Journal of Fluid Mechanics, 2001, 430: 27–50.
Faltinsen O. M., Rognebakke O. F., Timokha A. N. Two-dimensional resonant piston-like sloshing in a moonpool [J]. Journal of Fluid Mechanics, 2007, 575: 359–397.
Yeung R. W., Seah R. K. M. On Helmholtz and higher-order resonance of twin floating bodies [J]. Journal of Engineering Mathematics, 2007, 58(1–4): 251–265.
Liu Y., Li H. J. A new semi-analytical solution for gap resonance between twin rectangular boxes [J]. Proceedings Institution of Mechanical Engineers, Part M, 2014, 228(1): 3–16.
Miao G. P., Ishida H., Saitoh T. Influence of gaps between multiple floating bodies on wave forces [J]. China Ocean Engneering, 2000, 14(4): 407–422.
Miao G. P., Saitoh T., Ishida H. Water wave interaction of twin large scale caissons with a small gap between [J]. Coastal Engineering Journal, 2001, 43(1): 39–58.
Li B., Cheng L., Deeks A. J. et al. A modified scaled boundary finite element method for problems with parallel side-faces. Part II. Application and evaluation [J]. Applied Ocean Research, 2005, 27(4–5): 224–234.
Zhu H. R., Zhu R. C., Miao G. P. A time domain investigation on the hydrodynamic resonance phenomena of 3-D multiple floating structures [J]. Journal of Hydrodynamics, 2008, 20: 611–616.
Sun L., Eatock Taylor R., Taylor P. H. First- and second-order analysis of resonant waves between adjacent barges [J]. Journal of Fluids Structures, 2010, 26(6): 954–978.
Chen X. B. Hydrodynamics in offshore and naval applications [C]. The 6th International Conference on Hydrodynamics. Perth, Australia, 2004.
Pauw W. H., Huijsmans R., Voogt A. Advanced in the hydrodynamics of side-by-side moored vessels [C]. Proceedings of the 26th Conference on Ocean, Offshore Mechanics and Arctic Engineering (OMAE2007). San Diego, California, USA, 2007, OMAE2007-29374.
Molin B., Remy F., Camhi A. et al. Experimental and numerical study of the gap resonance in-between two rectangular barges [C]. Proceedings of the 13th Congress of the International Maritime Association of the Mediterranean (IMAM 2009). Istanbul, Turkey, 2009, 689–696.
Lu L., Teng B., Cheng L. et al. Modelling of multi-bodies in close proximity under water waves–Fluid resonance in narrow gaps [J]. Science China Physics Mechanics and Astronomy, 2011, 54(1): 16–25.
Lu L., Teng B., Sun L. et al. Modelling of multi- bodies in close proximity under water waves–Fluid forces on floating bodies [J]. Ocean Engineering, 2011, 38(13): 1403–1416.
Faltinsen O. M., Timokha A. N. On damping of two-dimensional piston-mode sloshing in a rectangular moonpool under forced heave motions [J]. Journal of Fluid Mechanics, 2015, 772: R1, 1–11.
Lu L., Cheng L., Teng B. et al. Numerical simulation and comparison of potential flow and viscous fluid models in near trapping of narrow gaps [J]. Journal of Hydrodynamics, 2010, 22(5): 120–125.
Lu L., Chen X. B. Dissipation in the gap resonance between two bodies [C]. Proceedings of the 27th International Workshop on Water Waves and Floating Bodies (IWWWFB 2012). Copenhagen, Denmark, 2012.
Kristiansen T., Sauder T., Firoozkoohi R. Validation of a hybrid code combining potential and viscous flow with application to 3D moonpool [C]. Proceedings 32nd International Conference on Ocean, Offshore Mechanics and Arctic Engineering. Nantes, France, 2013.
Fredriksen A. G., Kristiansen T., Faltinsen O. M. Wave-induced response of a floating two-dimensional body with a moonpool [J]. Philosophical Transactions of the Royal Society London A, 2015, 373(2033): 20140109.
Moradi N., Zhou T. M., Cheng L. Effect of inlet configuration on wave resonance in the narrow gap of two fixed bodies in close proximity [J]. Ocean Engineering, 2015, 103: 88–102.
Moradi N., Zhou T. M., Cheng L. Two-dimensional numerical study on the effect of water depth on resonance behaviour of the fluid trapped between two side-by-side bodies [J]. Applied Ocean Research, 2016, 58: 218–231.
Mei C. C., Stiassnie M., Yue D. K. P. Theory and applications of ocean surface waves, Part 1: Linear aspects [M]. Singapore: World Scientific, 2005, 6: 285–286.
Hirt C. W., Nichols B. D. Volume of fluid (VOF) method for the dynamics of free boundaries [J]. Journal of Computational Physics, 1981, 39(1): 201–225.
Wang B. L., Liu H. Higher order Boussmesq-type equations for water waves on uneven bottom [J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(6): 714–722.
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Project supported by the National Natural Science Foundation of China (Grant Nos. 51490673, 51479025 and 51279029).
Biography: Lei Tan (1989-), Male, Ph. D. Candidate
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Tan, L., Tang, Gq., Zhou, Zb. et al. Theoretical and numerical investigations of wave resonance between two floating bodies in close proximity. J Hydrodyn 29, 805–816 (2017). https://doi.org/10.1016/S1001-6058(16)60792-8
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DOI: https://doi.org/10.1016/S1001-6058(16)60792-8