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Diffraction and radiation loads on open cylinders of thin and arbitrary shapes

Published online by Cambridge University Press:  07 May 2015

Mohamed Hariri Nokob  and
Ronald W. Yeung
Mohamed Hariri Nokob
Affiliation:
Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1740, USA
Ronald W. Yeung*
Affiliation:
Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720-1740, USA
*
†Email address for correspondence: [email protected]
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Abstract

We study the effects of having an opening in a vertical cylinder of an arbitrary cross-sectional shape when subjected to incident waves from the outside field. Both the diffraction and radiation problems of linear potential-flow theory are addressed. The cylinders considered are bottom-mounted with vanishing thickness and the problem is formulated as a hypersingular boundary-integral method. A simple higher-order procedure is presented to handle the strong singularity. Comparisons are made between the hydrodynamic properties of open and closed cylinders, and the effects of increasing the opening size are discussed and explained. Results for square, circular and elliptical open cylindrical shells, presented as examples, indicate that wave loads on the structures could be dramatically decreased to zero (effectively) at certain frequencies and opening sizes. This leads to the surprising conclusion that directing an open structure into the incident-wave field results in lower loads on the structure. A model of an open harbour with a frontal breakwater in a wave field, inspired by the idea of the Portunus Project, is also analysed.

JFM classification

Mathematical Foundations: Computational methods Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 772 , 10 June 2015 , pp. 649 - 677
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Copyright
© 2015 Cambridge University Press 

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References

Burton, A. J. & Miller, G. F. 1971 The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc. R. Soc. Lond. A 323 (1553), 201–210.Google Scholar
Farina, L. & Martin, P. A. 1998 Scattering of water waves by a submerged disc using a hypersingular integral equation. Appl. Ocean Res. 20 (3), 121–134.Google Scholar
Garrett, C. J. R. 1970 Bottomless harbours. J. Fluid Mech. 43 (3), 433–449.Google Scholar
Guiggiani, M. 1995 Hypersingular boundary integral equations have an additional free term. Comput. Mech. 16 (4), 245–248.Google Scholar
Hadavinia, H., Travis, R. P. & Fenner, R. T. 2000 $C^{1}$ -continuous generalised parabolic blending elements in the boundary element method. Math. Comput. Model. 31 (8–9), 17–34.Google Scholar
Hariri Nokob, M. & Yeung, R. W.2014a Computation of arbitrary thin-shell vertical cylinders in a wavefield by a hyper-singular integral-equation method. In Proceedings of the ASME 33rd International Conference on Ocean, Offshore and Arctic Engineering, San Francisco, CA.Google Scholar
Hariri Nokob, M. & Yeung, R. W.2014b Hypersingular integral-equation method for wave diffraction about arbitrary, shell-like vertical cylinders in finite-depth waters. In The 29th International Workshop on Water Waves and Floating Bodies, Osaka, Japan.Google Scholar
Kinsler, L. E., Frey, A., Coppens, A. & Sanders, J. 2000 Fundamentals of Acoustics. Wiley.Google Scholar
Krishnasamy, G., Schmerr, L. W., Rudolphi, T. J. & Rizzo, F. J. 1990 Hypersingular boundary integral equations: some applications in acoustic and elastic wave scattering. Trans. ASME: J. Appl. Mech. 57 (2), 404–414.Google Scholar
Lee, C.-H. & Sclavounos, P. D. 1989 Removing the irregular frequencies from integral equations in wave–body interactions. J. Fluid Mech. 207, 393–418.CrossRefGoogle Scholar
Linton, C. M. & Evans, D. V. 1993 Hydrodynamic characteristics of bodies in channels. J. Fluid Mech. 252, 647–666.Google Scholar
Manolis, G. D. & Banerjee, P. K. 1986 Conforming versus non-conforming boundary elements in three-dimensional elastostatics. Intl J. Numer. Meth. Engng 23 (10), 1885–1904.Google Scholar
Martin, P. A. 1991 End-point behaviour of solutions to hypersingular integral equations. Proc. R. Soc. Lond. A 432 (1885), 301–320.Google Scholar
Martin, P. A. & Farina, L. 1997 Radiation of water waves by a heaving submerged horizontal disc. J. Fluid Mech. 337, 365–379.Google Scholar
Martin, P. A. & Rizzo, F. J. 1989 On boundary integral equations for crack problems. Proc. R. Soc. Lond. A 421 (1861), 341–355.Google Scholar
Martin, P. A. & Rizzo, F. J. 1996 Hypersingular integrals: how smooth must the density be? Intl J. Numer. Meth. Engng 39 (4), 687–704.Google Scholar
Mavrakos, S. A. 1988 Hydrodynamic coefficients for a thick-walled bottomless cylindrical body floating in water of finite depth. Ocean Engng 15 (3), 213–229.Google Scholar
Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005a Theory and Applications of Ocean Surface Waves: Linear Aspects. World Scientific.Google Scholar
Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005b Theory and Applications of Ocean Surface Waves: Nonlinear Aspects. World Scientific.Google Scholar
Miles, J. W. & Lee, Y. K. 1975 Helmholtz resonance of harbours. J. Fluid Mech. 67 (3), 445–464.Google Scholar
Newman, J. N. 1977 Marine Hydrodynamics. MIT Press.Google Scholar
de Oliveira, A. C., Vilameá, E. M., Figueiredo, S. R. & Malta, E. B. 2013 Hydrodynamic moonpool behavior in a monocolumn hub platform with an internal dock. In Proceedings of the ASME 32nd International Conference on Ocean, Offshore and Arctic Engineering, OMAE 2013, June 9–14, Nantes, France, Paper Number: OMAE2013-10709 ASME.Google Scholar
Parsons, N. F. & Martin, P. A. 1992 Scattering of water waves by submerged plates using hypersingular integral equations. Appl. Ocean Res. 14 (5), 313–321.Google Scholar
Parsons, N. F. & Martin, P. A. 1994 Scattering of water waves by submerged curved plates and by surface-piercing flat plates. Appl. Ocean Res. 16 (3), 129–139.Google Scholar
Renzi, E. & Dias, F. 2012 Resonant behavior of an oscillating wave energy converter in a channel. J. Fluid Mech. 701, 482–510.CrossRefGoogle Scholar
Sarkar, D., Renzi, E. & Dias, F. 2014 Wave farm modelling of oscillating wave surge converters. Proc. R. Soc. Lond. A 470 (2167), 20140118.Google Scholar
Sladek, V. & Sladek, J. 1998 Singular Integrals in Boundary Element Methods. WIT Press/ Computational Mechanics.Google Scholar
Wampler, S.2010 Plan floated to ship cargo inspection offshore (newsline.llnl.gov).Google Scholar
Wehausen, J. V. & Laitone, E. V. 1960 Surface waves. In Encyclopedia of Physics, vol. 9, pp. 446–778. Springer.Google Scholar
Yeung, R. W. 1981 Added mass and damping of a vertical cylinder in finite-depth waters. Appl. Ocean Res. 3 (3), 119–133.Google Scholar
Yeung, R. W. 1982 Numerical methods in free-surface flows. Annu. Rev. Fluid Mech. 14 (1), 395–442.Google Scholar
Yeung, R. W. & Hariri Nokob, M.2013 Hypersingular integral-equation solution for a finite-draft surface-piercing cylindrical shell at high- and low-frequency. In The 28th International Workshop on Water Waves and Floating Bodies, L’Isle sur la Sorgue, France (ed. B. Molin, O. Kimmoun & F. Remy).Google Scholar
Yeung, R. W. & Seah, R. K. M. 2007 On Helmholtz and higher-order resonance of twin floating bodies. J. Engng Maths 58 (1–4), 251–265.Google Scholar
Yeung, R. W. & Sphaier, S. H. 1989a Wave-interference effects on a floating body in a towing tank. In Proceedings, 4th International Symposium on Practical Design of Ships and Mobile Units (PRADS-89), Varna, Bulgaria, p. 23. Bulgaria Ship Hydrodynamics Center, Paper 95.Google Scholar
Yeung, R. W. & Sphaier, S. H. 1989b Wave-interference effects on a truncated cylinder in a channel. J. Engng Maths 23 (2), 95–117.Google Scholar