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Surge Hydrodynamic Coefficients Due to a Floating Cylindrical Structure in Presence of a Bottom-Mounted Circular Plate in a Channel of Finite Depth

International Journal of Applied and Computational Mathematics volume 8, Article number: 193 (2022) Cite this article

Abstract

The current investigation aims to study the effect of radiation force by the floating hollow cylindrical structure in presence of bottom obstacle and channel walls of finite width. Since the hollow cylinder captures the essential features of an oscillating water column (OWL), therefore the proposed device consists of a floating vertical hollow cylinder placed above a fixed circular cylindrical obstacle in the presence of a channel having finite width and the floating cylinder allows to oscillate in surge mode of motion. This device can be considered as an oscillating water column (OWL) which is one kind of wave energy device. The linear water wave theory is used to formulate this radiation problem and the whole fluid domain is divided into three sub-domains, and then the boundary value problems are set up in each sub-domain. The methods of variables separation and channel multipoles are applied to solve such boundary value problems. However, the method of matched eigenfunction expansion is used to evaluate the unknown coefficients that are appearing in the obtained surge radiated velocity potentials. This radiated velocity potential allows us to evaluate the radiation force in terms of added mass and damping coefficients. A set of numerical results of added mass and damping coefficients are demonstrated through suitable graphs along with different parameters of the device. The obtained numerical results show the significant effect of the channel walls on the hydrodynamic coefficients, namely the added mass and damping coefficients. It is observed that as the draft of the floating cylinder increases the corresponding hydrodynamic coefficients also increase. At some particular values of wavenumber, the hydrodynamic coefficients exhibit huge fluctuations, which can be attributed to the phenomenon of resonance. The hydrodynamic coefficients are remarkable near the lower values of wavenumbers. The obtained results have compared with available established results, and it shows good agreement between both the results.

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Acknowledgements

The research scholar shows his gratefulness to North Eastern Regional Institute of Science and Technology, Itanagar for giving graduate fellowship to carry out research work. The authors are grateful to SERB, DST (Grant number YSS /14/ 000884), Govt. of India, for giving support during this research work. The authors are grateful to the esteemed editor and reviewers for their valuable comments that helped us to improve the quality of the paper.

Funding

This work was supported by [SERB DST] (Grant numbers [YSS /14/ 000884], author M. Hassan has received research support from SERB, DST, Govt. of India and P. Borah received GATE scholarship from Govt. of India.

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  1. Department of Mathematics, North Eastern Regional Institute of Science and Technology, Itanagar, 791 109, Arunachal Pradesh, India

    Mohammad Hassan & Pankaj Borah

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  1. Mohammad Hassan
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by both authors. The first draft of the manuscript was written by M. Hassan and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Mohammad Hassan.

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Author M. Hassan has received financial support from SERB DST, Govt of India and author P. Borah has received Gate scholarship from Govt. of India .

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Hassan, M., Borah, P. Surge Hydrodynamic Coefficients Due to a Floating Cylindrical Structure in Presence of a Bottom-Mounted Circular Plate in a Channel of Finite Depth. Int. J. Appl. Comput. Math 8, 193 (2022). https://doi.org/10.1007/s40819-022-01391-5

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  • DOI: https://doi.org/10.1007/s40819-022-01391-5

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