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Hydrodynamic coefficients in surge for a radiating hollow cylinder placed above a coaxial cylinder at finite ocean depth

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Abstract

Hydrodynamic coefficients due to horizontal oscillation in surge motion for a floating, hollow cylinder placed above a fixed, coaxial, bottom-mounted cylinder are investigated within the framework of linear, water wave theory. This problem of radiation by this specific pair of two cylinders can be considered as a wave energy device consisting of two coaxial cylinders: the upper one hollow and the lower one solid. The energy that is created and transferred by this device finds use in a number of practical applications. We use the method of separation of variables to obtain the analytical expressions for the corresponding radiated potentials in clearly identified regions. By using the matching conditions which ensure the continuity of velocity and pressure along the virtual vertical boundaries of the regions, a system of linear equations for the unknown coefficients is derived and solved. The analytical expressions of the radiated potentials allow us to obtain the hydrodynamic coefficients, namely, the added mass and damping coefficients, which play a vital role for a structure in motion, however small. A set of values of added mass and damping coefficients is obtained for different radii of the fixed cylinder and for different gaps between the cylinders (i.e., also for different drafts of the floating cylinder) for the same fixed radii of the cylinders. It is observed that changes in values in radius and the gap have significant effect on the hydrodynamic coefficients. We also compute the coefficients due to different gaps between the cylinders with the radii of both taken to be different. The behaviour of both the added mass and damping coefficients is observed to be steady in the lower frequency range. However, fluctuations are observed for both coefficients due to resonance in the neighbourhood of a specific frequency. These results are depicted graphically and compared with available results. Comparison is carried out with numerical data presented by other investigators by considering the case of a hollow cylinder floating over an even sea bottom, i.e., without the coaxial cylindrical caisson underneath. Good agreement is observed from this comparison. A numerical verification is also carried out for the body boundary condition satisfied at the boundary of both the cylinders.

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Acknowledgments

The first author wishes to thank Indian Institute of Technology Guwahati for providing him graduate fellowship to pursue Ph.D. The authors are very much indebted to the reviewers whose comments and suggestions allowed the revised version of the manuscript reach a much better form in terms of content and presentation.

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  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, 781039, India

    M. Hassan & S. N. Bora

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  1. M. Hassan
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  2. S. N. Bora
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Correspondence to S. N. Bora.

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Hassan, M., Bora, S.N. Hydrodynamic coefficients in surge for a radiating hollow cylinder placed above a coaxial cylinder at finite ocean depth. J Mar Sci Technol 19, 450–461 (2014). https://doi.org/10.1007/s00773-014-0280-3

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  • DOI: https://doi.org/10.1007/s00773-014-0280-3

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