Hydrodynamic coefficients for a floating semi-porous compound cylinder in finite ocean depth
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ORIGINAL PAPER
Hydrodynamic coefficients for a floating semi‑porous compound cylinder in finite ocean depth Abhijit Sarkar1 · Swaroop Nandan Bora1 Received: 18 December 2019 / Accepted: 24 August 2020 © Sociedade Brasileira de Engenharia Naval 2020
Abstract Employing the methods of separation of variables and matched eigenfunction expansions for velocity potential, analytical solutions are proposed for a water wave radiation problem of a floating semi-porous compound cylinder in finite ocean depth. The configuration of the semi-porous compound cylinder is such that it consists of an impermeable inner cylinder rising above the free surface and a coaxial truncated porous cylinder around the lower part of the inner cylinder with the top of the porous cylinder being impermeable. The condition on the porous boundary is defined by applying Darcy’s law as in Williams et al. (Ocean Eng 27:1–28, 2000) . The translational motions in the x- and z-directions, i.e., surge and heave motions, are investigated. A mathematical model is developed which can be considered as an extension of a number of the earlier works, e.g., Kokkinowrachos et al. (Ocean Eng 13:505–538, 1986) and Calisal and Subancu (Ocean Eng 11(5):529–542, 1984), in which significance of porosity of the structure was neglected. Numerical investigation is taken up here in order to examine the influence of submerged depth, radii, porous coefficient, and water depth on added mass and radiation damping, two most important entities in radiation problems, with respect to surge and heave motions. It is found that the variation of porous coefficient, radii, and depth has a significant influence on the added mass and damping coefficients for the semi-porous compound cylinder. The added mass is found not sufficiently affected by lower values of porous coefficient G, but exhibits significant variation corresponding to higher values of G. Another important observation is that the damping coefficients oscillate alternately between negative and positive values which can be attributed to coupled behavior between different motions. The results establish that an appropriate optimal ratio of various parameters may be considered in designing ocean structures with minimum adverse hydrodynamic effect. The effectiveness of the present model is validated by comparing it with an available result which shows an excellent agreement. Keywords Semi-porous · Compound cylinder · Darcy’s law · Porous coefficient · Added mass · Damping coefficient
1 Introduction Porous media concept naturally occurs in a number of areas of applied science and engineering such as filtration, mechanics, petroleum engineering, construction engineering, hydrogeology, geophysics, biology, biophysics, material science, etc. Porous structures reduce the waveloads and wave run-up, and they are found to be very useful in the construction of floating airports, bridges, piers, docks, * Swaroop Nandan Bora [email protected] Abhijit Sarkar [email protected] 1
Department of Mathematics, Indian Institute of Te
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