## Abstract

[Truncated] The present work deals with the hydrodynamic behaviour of structures oscillating in an infinite fluid at varying free surface proximities. This is of interest for the offshore industry for applications including subsea structure installation. For this study a circular plate with negligible thickness was chosen due to its axisymmetric shape. The focus of the study is to understand the hydrodynamic forces when the plate porosity and free surface proximities are varied. The aim is to understand the physics of a hydrodynamic problem involving fluid structure interaction by studying added mass and damping behaviour. The work has also enhanced the hydrodynamic literature archive by providing information about hydrodynamic coefficients obtained using mathematical analysis and experimental techniques.

The study commences with an analysis of variation of added mass and damping coefficients with (i) Keulegan Carpenter (KC)number, (ii) frequency parameter (β), and proceeds to the hydrodynamic study of (iii) structure porosity (τ) and (iv) submergence level of oscillating plate. Mathematical analysis of hydrodynamic forces over the horizontally submerged plate is simulated using potential theory. The fluid domain is divided into three virtual subregions. The harmonic expressions of the velocity potential in three subregions are obtained in terms of unknown coefficients, Bessel functions and trigonometric functions using suitable boundary conditions. The unknowns in the expressions are obtained using boundary conditions and the method of matching Eigen function expansions at the virtual boundaries. The complex hydrodynamic force is evaluated from the velocity potentials, which gives added mass and damping forces by separating the real and imaginary parts. The same methodology is also applied for the porous plates, where the velocity potentials are redefined to include the pressure drop due the porosity of the plate. A number of porous models for discharge of flow through the porous plate were tested before choosing the one used here.

The study commences with an analysis of variation of added mass and damping coefficients with (i) Keulegan Carpenter (KC)number, (ii) frequency parameter (β), and proceeds to the hydrodynamic study of (iii) structure porosity (τ) and (iv) submergence level of oscillating plate. Mathematical analysis of hydrodynamic forces over the horizontally submerged plate is simulated using potential theory. The fluid domain is divided into three virtual subregions. The harmonic expressions of the velocity potential in three subregions are obtained in terms of unknown coefficients, Bessel functions and trigonometric functions using suitable boundary conditions. The unknowns in the expressions are obtained using boundary conditions and the method of matching Eigen function expansions at the virtual boundaries. The complex hydrodynamic force is evaluated from the velocity potentials, which gives added mass and damping forces by separating the real and imaginary parts. The same methodology is also applied for the porous plates, where the velocity potentials are redefined to include the pressure drop due the porosity of the plate. A number of porous models for discharge of flow through the porous plate were tested before choosing the one used here.

Original language | English |
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Qualification | Doctor of Philosophy |

Publication status | Unpublished - 2011 |