3D numerical modeling of wave forces on tandem fixed cylinders using the BEM

Abstract

In this paper a 3D numerical model was developed to study the complicated interaction between waves and a set of tandem fixed cylinders. The fluid was considered to be inviscid and irrotational. Therefore, the Helmholtz equation was used as a governing equation. The boundary element method (BEM) was adopted to discretize the relevant equations. Open boundaries were used in far fields of the study domain. Linear waves were generated and propagated towards tandem fixed cylinders to estimate the forces applied on them. Special attention was paid to consideration of the effect on varying non-dimensional cylinder radius and distance between cylinders, ka and kd on forces and trapped modes. The middle cylinder wave forces and trapped modes in a set of nine tandem cylinders were validated utilizing analytical data. The comparisons confirm the accuracy of the model. The results of the inline wave force estimation on n tandem cylinders show that the critical cylinder in the row is the middle one for odd numbers of cylinders. Furthermore the results show that the critical trapped mode effect occurs for normalized cylinder radiuses close to 0.5 and 1.0. Finally the force estimation for n tandem cylinders confirms that force amplitude of the middle cylinder versus normalized separation distance fluctuates about that of a single cylinder.

Keywords

tandem cylinders / boundary element method (BEM) / wave force / diffraction / trapped mode / Henkel function

References

[1] Chen JT, Lee JW, Shyu WS. SH-wave scattering by a semi-elliptical hill using a null-field boundary integral equation method and a hybrid method. Geophysical Journal International, 2011, 188(1): 177-194

[2] Chen JT, Lee JW, Hsiao YC. Analysis of water wave problems containing single and multiple cylinders by using degenerate kernel method. International Journal of Offshore and Polar Engineering, 2011, 21(1): 13-21

[3] Duclos G, Clement AH. Wave propagation through arrays of unevenly spaced vertical piles. Journal of Ocean Engineering, 2004, 31: 1655-1668

[4] Evans DV, Porter R. Trapped modes about multiple cylinders in a channel. Journal of Fluid Mechanics, 1997, 339: 331-356

[5] Han KM, Ohkusu M. Wave force on groups of vertical circular cylinders. Research Papers, Ocean Resources Research Institute, Dong-A University, 1995, 8(1): 17-26

[6] Havelock TH. The pressure of water waves upon a fixed obstacle. Proc. Roy. Soc. A, 1940, 175: 409-421

[7] Kagemoto H, Yue DKP. Interactions among multiple three dimensional bodies in water waves: an exact algebraic method. Journal of Fluid Mechanics, 1986, 166: 189-209

[8] Kagemoto H, Murai M, Saito M, Molin B, Malenica S. Experimental and theoretical analysis of the wave decay along a long array of vertical cylinders. Journal of Fluid Mechanics, 2002, 456: 113-135

[9] Kim NH, Park MS, Yang SB. Wave force analysis of the vertical circular cylinder by boundary element method. KSCE Journal of Civil Engineering, 2007, 11(1): 31-35

[10] Kim NH, Cao T. Wave force analysis of the two vertical cylinders by boundary element method. KSCE Journal of Civil Engineering, 2008, 12(6): 359-366

[11] MacCamy RC, Fuchs RA. Wave forces on piles: a diffraction theory, 1954

[12] Maniar HD, Newman JN. Wave diffraction by a long array of cylinders. Journal of Fluid Mechanics, 1997, 339: 309-330

[13] Newman JN. Wave effect on multiple bodies. Conference on Hydrodynamics in Ship and Ocean Engineering, Hakozaki, 2005, 3-26

[14] Simon MJ. Multiple scattering in arrays of axisymmetric wave-energy devices. Part 1. A matrix method using a plane wave approximation. Journal of Fluid Mechanics, 1982, 120: 1-25

[15] Spring BH, Monkmeyer PL. Interaction of plane waves with vertical cylinders. Proceedings of the Fourteenth International Conference on Coastal Engineering, Copenhagen, Denmark, 1974, 1828-1847

[16] Twersky V. Multiple scattering of radiation by an arbitrary configuration of parallel cylinders. J. Acoust. Soc. Am., 1952, 24: 42-46

[17] Vos L, Frigaard P, Rouck JD. Wave run-up on cylindrical and cone shaped foundations for offshore wind turbines. Journal of Coastal Engineering, 2007, 54: 17-29

[18] Walker DAG, Taylor ER. Wave diffraction from linear arrays of cylinders. Journal of Ocean Engineering, 2005, 32: 2053-2078