Pitch Motion Analysis of a Submerged Cylindrical Structure in a Two-layer Fluid

Abstract

This study investigates the effects of radiation force due to the rotational pitch motion of a wave energy device, which comprises a coaxial bottom-mounted cylindrical caisson in a two-layer fluid, along with a submerged cylindrical buoy. The system is modeled as a two-layer fluid with infinite horizontal extent and finite depth. The radiation problem is analyzed in the context of linear water waves. The fluid domain is divided into outer and inner zones, and mathematical solutions for the pitch radiating potential are derived for the corresponding boundary valve problem in these zones using the separation of variables approach. Using the matching eigenfunction expansion method, the unknown coefficients in the analytical expression of the radiation potentials are evaluated. The resulting radiation potential is then used to compute the added mass and damping coefficients. Several numerical results for the added mass and damping coefficients are investigated for numerous parameters, particularly the effects of the cylinder radius, the draft of the submerged cylinder, and the density proportion between the two fluid layers across different frequency ranges. The major findings are presented and discussed.

Keywords

Pitch radiation / Eigenfunction expansion / Two-layer / Hydrodynamic coefficients / Submerged cylinder / Bottom-mounted cylinder

References

[1] Abbas Z, Altaf I, Hasnain J, Ali A. Theoretical analysis of two-layer fluids with continuity of stresses at interface and slip at the walls of an inclined channel. Ain Shams Engineering Journal, 2021, 12(1): 761-774

[2] Baines PG. Topographic effects in stratified flows, 1995

[3] Barman KK, Chanda A, Tsai CC. A mathematical study of a two-layer fluid flow system in the presence of a floating breakwater in front of VLFS. Applied Mathematical Modelling, 2023, 122: 706-730

[4] Bhatta DD, Rahman M. On scattering and radiation problem for a cylinder in water of finite depth. International Journal of Engineering Science, 2003, 41(9): 931-967

[5] Cadby JR, Linton CM. Three-dimensional water-wave scattering in two-layer fluids. Journal of Fluid Mech, 2000, 423: 155-173

[6] Das D. Construction of wave-free potentials and multipoles in a two-layer fluid having free-surface boundary condition with higher-order derivatives. J. Marine Sci. Appl, 2015, 14(3): 270-282

[7] Das D, Mandal BN. Wave scattering by a horizontal circular cylinder in a two-layer fluid with an ice-cover. International Journal of Engineering Science, 2007, 45(10): 842-872

[8] Das D, Mandal BN. Wave radiation by a sphere submerged in a two-layer ocean with an ice-cover. Applied Ocean Research, 2010, 32(3): 358-366

[9] Du T, Wu W. The generation and distribution of ocean internal waves. MARINE SCI.-QING.-CHIN. ED., 2001, 25(4): 25-27

[10] Koo W. Free surface simulation of a two-layer fluid by boundary element method. International Journal of Naval Architecture and Ocean Engineering, 2010, 2(3): 127-131

[11] Linton CM, McIver M. The interaction of waves with horizontal cylinders in two-layer fluids. Journal of Fluid Mech, 1995, 304: 213-229

[12] Linton CM, McIver P. Handbook of mathematical techniques for wave/structure interactions, 2001

[13] Martha SC, Bora S. Reflection and transmission coefficients for water wave scattering by a sea-bed with small undulation. ZAMM- Journal of Applied Mathematics and Mechanics/ Zeitschrift für Ange-wandte Mathematik und Mechanik, 2007, 87(4): 314-321

[14] Mohapatra S, Bora SN. Radiation of water waves by a sphere in an ice-covered two-layer fluid of finite depth. Journal of Advance Research in Applied Mathematics, 2010, 2(1): 46-63

[15] Mohapatra S, Bora SN. Reflection and transmission of water waves in a two-layer fluid flowing through a channel with undulating bed. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 2011, 91(1): 46-56

[16] Mohapatra SC, Da Silva Bispo IB, Guo Y, Guedes SC. Analysis of Wave-Induced forces on a floating rectangular box with analytical and numerical approaches. Journal of Marine Science and Application, 2024, 23(1): 113-126

[17] Mondal R, Sahoo T. Wave structure interaction problems for two-layer fluids in three dimensions. Wave Motion, 2012, 49(5): 501-524

[18] Neog CK, Hassan M. Evaluation of exciting force and moment by a vertical floating cylinder in appearance of a coaxial cylindrical obstacle in two-layer fluid. Journal of Engineering Mathematics, 2023, 141(1): 5

[19] Neog CK, Hassan M. Hydrodynamic of surge radiation by a floating cylinder in the presence of bottom-mounted cylindrical obstacle in a two-layer fluid system. Journal of Engineering Mathematics, 2024, 145(11-26

[20] Shah KS, Pegler SS, Minchew BM. Two-layer fluid flows on inclined surfaces. Journal of Fluid Mechanics, 2021, 917: A54

[21] Shen YM, Zheng YH, You YG. On the radiation and diffraction of linear water waves by a rectangular structure over a sill. Part I. Infinite domain of finite water depth. Ocean Engineering, 2005, 32(8–9): 1073-1097

[22] Sherief HH, Faltas MS, Saad EI. Forced gravity waves in two-layered fluids with the upper fluid having a free surface. Canadian Journal of Physics, 2003, 81(4675-689

[23] Shi Q, You YX, Miao GP. Diffraction of water waves by a vertically floating cylinder in a two-layer fluid. China Ocean Engineering, 2008, 22(2): 181-193

[24] Shi Q, You YX, Miao GP. Radiation of vertically floating cylinder in two-layer fluid. Journal of Shanghai Jiaotong University, 2009, 43(2): 187-192

[25] Shi Q, You YX, Wei G, Miao GP. The interaction of water waves with a floating rectangular box in a two-layer fluid. Progress in Natural Science, 2006, 16(8): 992-1001

[26] Sturova IV. Problems of radiation and diffraction for a circular cylinder in a stratified fluid. Fluid dynamics, 1999, 34(4): 521-533

[27] Ten I, Kashiwagi M. Hydrodynamics of a body floating in a two-layer fluid of finite depth. Part 1. Radiation problem. Journal of Marine Science and Technolgy, 2004, 9: 127-141

[28] Wu BJ, Zheng YH, You YG, Jie DS, Chen Y. On diffraction and radiation problem for two cylinders in water of finite depth. Ocean Engineering, 2006, 33(5–6): 679-704

[29] Wu BJ, Zheng YH, You YG, Sun XY, Chen Y. On diffraction and radiation problem for a cylinder over a caisson in water of finite depth. International Journal of Engineering Science, 2004, 42(11–12): 1193-1213

[30] Xu F, Lu DQ. Wave scattering by a thin elastic plate floating on a two-layer fluid. International Journal of Engineering Science, 2010, 48(9): 809-819

[31] You YX, Shi Q, Miao GP. The hydrodynamic forces on a large diameter cylinder in Two-Laver fluid. Shanghai Jiaotong Daxue Xuebao (J. Shang. Jiaotong Uni.) (China), 2005, 39(5): 695-700

[32] You YX, Shi Q, Miao GP. The radiation and diffraction of water waves by a bottom-mounted circular cylinder in a two-layer fluid. Journal of Hydrodynamics, 2007, 19(1): 1-8

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