Browse > Article
http://dx.doi.org/10.1016/j.ijnaoe.2019.04.006

New analytical solutions to water wave diffraction by vertical truncated cylinders  

Li, Ai-jun (College of Engineering, Ocean University of China)
Liu, Yong (College of Engineering, Ocean University of China)
Publication Information
International Journal of Naval Architecture and Ocean Engineering / v.11, no.2, 2019 , pp. 952-969 More about this Journal
Abstract
This study develops new analytical solutions to water wave diffraction by vertical truncated cylinders in the context of linear potential theory. Three typical truncated surface-piercing cylinders, a submerged bottom-standing cylinder and a submerged floating cylinder are examined. The analytical solutions utilize the multi-term Galerkin method, which is able to model the cube-root singularity of fluid velocity near the edges of the truncated cylinders by expanding the fluid velocity into a set of basis function involving the Gegenbauer polynomials. The convergence of the present analytical solution is rapid, and a few truncated numbers in the series of the basis function can yield results of six-figure accuracy for wave forces and moments. The present solutions are in good agreement with those by a higher-order BEM (boundary element method) model. Comparisons between present results and experimental results in literature and results by Froude-Krylov theory are conducted. The variation of wave forces and moments with different parameters are presented. This study not only gives a new analytical approach to wave diffraction by truncated cylinders but also provides a reliable benchmark for numerical investigations of wave diffraction by structures.
Keywords
Wave diffraction; Truncated cylinders; Multi-term galerkin method; Cube-root singularity; Wave forces;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Eatock Taylor, R., Huang, J.B., 1997. Semi-analytical formulation for second-order diffraction by a vertical cylinder in bichromatic waves. J. Fluids Struct. 11 (5), 465-484. https://doi.org/10.1006/jfls.1997.0091.   DOI
2 Evans, D.V., Porter, R., 1997. Efficient calculation of hydrodynamic properties of OWC-Type devices. J. Offshore Mech. Arct. Eng. 119 (4), 210-218. https://doi.org/10.1115/1.2829098.   DOI
3 Finnegan,W., Meere, M., Goggins, J., 2013. The wave excitation forces on a truncated vertical cylinder in water of infinite depth. J. Fluids Struct. 40 (40), 201-213. https://doi.org/10.1016/j.jfluidstructs.2013.04.007.   DOI
4 Garrett, C.J.R., 1971. Wave forces on a circular dock. J. Fluid Mech. 46 (1), 129-139. https://doi.org/10.1017/S0022112071000430.   DOI
5 Gradshteyn, I.S., Ryzhik, I.M., 2007. Table of Integrals, Series, and Products, th edition, vol. 7. Academic Press, New York.
6 Havelock, T.H., 1940. The pressure of water waves upon a fixed obstacle. Proc. Roy. Soc. Lond. 175, 409-421. https://doi.org/10.1098/rspa.1940.0066.
7 Hogben, N., Standing, R.G., 1975. Experience in Computing Wave Loads on Large Bodies. Seventh Offshore Technology Conference, Houston, pp. 413-431. Paper No. OTC 2189. https://doi.org/10.4043/2189-MS.
8 Isaacson, M., 1975.Wave forces on compound cylinder. In: Proc. Civil Engineering in the Ocean, pp. 518-530.
9 Jiang, S.C., Gou, Y., Teng, B., Ning, D.Z., 2014. An analytical solution of wave diffraction problem on a submerged cylinder. J. Eng. Mech. 140 (1), 225-232. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000637.   DOI
10 Kanoria, M., Dolai, D.P., Mandal, B.N., 1999. Water-wave scattering by thick vertical barriers. J. Eng. Math. 35 (4), 361-384. https://doi.org/10.1023/A:1004392622976.   DOI
11 Mandal, B.N., Kanoria, M., 2000. Oblique wave-scattering by thick horizontal barriers. J. Offshore Mech. Arct. Eng. 122, 100-108. https://doi.org/10.1115/1.533731.   DOI
12 Kanoria, M., 2001.Water wave scattering by thick rectangular slotted barriers. Appl. Ocean Res. 23 (5), 285-298. https://doi.org/10.1016/S0141-1187(01)00018-9.   DOI
13 Linton, C.M., 2009. Accurate solution to scattering by a semi-circular groove. Wave Motion 46, 200-209. https://doi.org/10.1016/j.wavemoti.2008.11.001.   DOI
14 Linton, C.M., McIver, P., 2001. Handbook of Mathematical Techniques for Wave/structure Interactions. Chapman & Hall/CRC, Boca Raton.
15 Martins-Rivas, H., Mei, C.C., 2009. Wave power extraction from an oscillating water column at the tip of a breakwater. J. Fluid Mech. 626, 395-414. https://doi.org/10.1017/S0022112009005990.   DOI
16 Porter, R., Evans, D.V., 1995. Complementary approximations to wave scattering by vertical barriers. J. Fluid Mech. 294, 155-180. https://doi.org/10.1017/S0022112095002849.   DOI
17 Otsuka, K., Ikeda, Y., 1996. Estimation of inertia forces on a horizontal circular cylinder in regular and irregular waves at low Keulegan-Carpenter numbers. Appl. Ocean Res. 18 (2-3), 145-156. https://doi.org/10.1016/0141-1187(96)00023-5.   DOI
18 Porter, R., 1995. Complementary Methods and Bounds in Linear Water Waves. Doctoral thesis. University of Bristol.
19 Porter, R., 2002. Surface wave scattering by submerged cylinders of arbitrary crosssection. Proceedings Mathematical Physical & Engineering Sciences 458, 581-606. https://doi.org/10.1098/rspa.2001.0885.   DOI
20 Roy, R., Chakraborty, R., Mandal, B.N., 2017. Propagation of water waves over an asymmetrical rectangular trench. Q. J. Mech. Appl. Math. 70 (1), 49-64. https://doi.org/10.1093/qjmam/hbw015.
21 Eatock Taylor, R., Hung, S.M., 1987. Second order diffraction forces on a vertical cylinder in regular waves. Appl. Ocean Res. 9 (1), 19-30. https://doi.org/10.1016/0141-1187(87)90028-9.   DOI
22 Banerjea, S., Kanoria, M., Dolai, D.P., Mandal, B.N., 1996. Oblique wave scattering by submerged thin wall with gap in finite-depth water. Appl. Ocean Res. 18 (6), 319-327. https://doi.org/10.1016/S0141-1187(97)00002-3.   DOI
23 Bhatta, D.D., Rahman, M., 1995. Wave loadings on a vertical cylinder due to heave motion. Int. J. Math. Math. Sci. 18 (1), 151-170. https://doi.org/10.1155/S0161171295000202.   DOI
24 Chang, K.H., Tsaur, D.H., Huang, L.H., 2012. Accurate solution to diffraction around a modified V-shaped breakwater. Coast Eng. 68 (10), 56-66. https://doi.org/10.1016/j.coastaleng.2012.05.002.   DOI
25 Ursell, F., 1949. On the heaving motion of a circular cylinder on the surface of a fluid. Q. J. Mech. Appl. Math. 2 (2), 218-231.   DOI
26 Rumpa, C., Mandal, B.N., 2015. Oblique wave scattering by a rectangular submerged trench. ANZIAM J. 56 (3), 286-298. https://doi.org/10.1017/S1446181115000024.   DOI
27 Teng, B., Gou, Y., 2017a. BEM for wave interaction with structures and low storage accelerated methods for large scale computation. J. Hydrodyn. 29 (5), 748-762.   DOI
28 Teng, B., Gou, Y., 2017b. Instruction forWAFDUT1.6 Program. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian (In Chinese with English abstract).
29 Teng, B., Ning, D., 2004. A fast multipole boundary element method for threedimensional potential flow problems. Acta Oceanol. Sin. 23 (4), 747-756.
30 Teng, B., Eatock Taylor, R., 1995. New higher-order boundary element methods for wave diffraction/radiation. Appl. Ocean Res. 17 (2), 71-77. https://doi.org/10.1016/0141-1187(95)00007-N.   DOI
31 Williams, A.N., Demirbilek, Z., 1988. Hydrodynamic interactions in floating cylinder arraysdI. Wave scattering. Ocean Eng. 15 (6), 549-583. https://doi.org/10.1016/0029-8018(88)90002-9.   DOI
32 Yeung, R.W., 1981. Added mass and damping of a vertical cylinder in finite-depth waters. Appl. Ocean Res. 3 (3), 119-133. https://doi.org/10.1016/0141-1187(81)90101-2.   DOI
33 Zhao, H.T., Teng, B., Li, G.W., Lin, Y.Z., 2003. An experimental study of first-harmonic wave force on vertical truncated cylinder. China Offshore Platform 4 (18), 12-17 (In Chinese with English abstract).