Eirini Anastasiou | National Technical University of Athens (original) (raw)
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Introduction The main objective of this study is to develop a semi-analytical formulation for the... more Introduction The main objective of this study is to develop a semi-analytical formulation for the hydrodynamic diffraction and radiation problems of a fully submerged spheroid. The term “spheroid” refers here to the oblate geometry of arbitrary eccentricity and to the axisymmetric configuration, i.e. the spheroid’s axis of symmetry is oriented perpendicular to the undisturbed free surface. The spheroid is assumed to be immersed below the free surface and subjected to harmonic incident waves, while the examined water depth is assumed to be infinite. The proposed approach is based on using the method of the image singularity system which, for the case of a spheroid, contains multipole expansions in terms of external spheroidal harmonics, allocated lengthwise the major axis of the spheroid between its two foci. The method of the image singularities, developed initially for a prolate spheroid, was suggested for the first time without a proof by Havelock (1952). The proof was later obtai...
In this paper, we instigate numerically the performance of an oblate spheroidal heaving Wave Ener... more In this paper, we instigate numerically the performance of an oblate spheroidal heaving Wave Energy Converter (WEC). The diffraction/radiation problems are solved in the frequency domain by utilizing the conventional boundary integral equation method. This method is, initially, compared against an analytical method that utilizes the image singularity system to manipulate the underlying Green’s function. Next, extended results are presented focusing on the comparison of the oblate spheroidal WEC with other WEC geometries as well as on the effect of various design parameters (i.e. equatorial and polar radius, distance from a bottom-mounted vertical wall) on the performance of the oblate spheroidal WEC.
Applied Ocean Research, 2021
Fluids
The main objective of this study is to develop a semi-analytical formulation for the radiation pr... more The main objective of this study is to develop a semi-analytical formulation for the radiation problem of a fully immersed spheroid in a liquid field of infinite depth. The term “spheroid” refers herein to the oblate geometry of arbitrary eccentricity and to the axisymmetric case, where the axis of symmetry is normal to the free surface. The proposed numerical approach is based on the method of image singularities, and it enables the accurate and fast calculation of the hydrodynamic coefficients for the translational degrees of freedom of the oblate spheroid. The excellent agreement of the results, with those of other investigators for the limiting case of the sphere and with those obtained using a respected boundary integral equation code, demonstrates the accuracy of the proposed methodology. Finally, extensive calculations are presented, illustrating the direct impact of the immersion depth and the slenderness of the spheroid on the hydrodynamic coefficients.
Journal of Marine Science and Engineering
This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamic... more This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamical applications. The theorem provides explicit relations that express the oblate spheroidal harmonics, given in terms of the fundamental solutions of the Laplace equation. Here, the theorem is employed to transform the underlying Green’s function into the relevant coordinate system and, consequently, to formulate the diffraction potential. The case considered refers to the axisymmetric placement of the spheroid, namely, symmetrical axis perpendicular to the free surface. The mathematical formulations have been implemented numerically providing exceptionally accurate computations, which manifests the consistency and robustness of the relevant formulas.
Journal of Marine Science and Engineering
This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamic... more This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamical applications. The theorem provides explicit relations that express the oblate spheroidal harmonics, given in terms of the fundamental solutions of the Laplace equation. Here, the theorem is employed to transform the underlying Green’s function into the relevant coordinate system and, consequently, to formulate the diffraction potential. The case considered refers to the axisymmetric placement of the spheroid, namely, symmetrical axis perpendicular to the free surface. The mathematical formulations have been implemented numerically providing exceptionally accurate computations, which manifests the consistency and robustness of the relevant formulas.
Introduction The main objective of this study is to develop a semi-analytical formulation for the... more Introduction The main objective of this study is to develop a semi-analytical formulation for the hydrodynamic diffraction and radiation problems of a fully submerged spheroid. The term “spheroid” refers here to the oblate geometry of arbitrary eccentricity and to the axisymmetric configuration, i.e. the spheroid’s axis of symmetry is oriented perpendicular to the undisturbed free surface. The spheroid is assumed to be immersed below the free surface and subjected to harmonic incident waves, while the examined water depth is assumed to be infinite. The proposed approach is based on using the method of the image singularity system which, for the case of a spheroid, contains multipole expansions in terms of external spheroidal harmonics, allocated lengthwise the major axis of the spheroid between its two foci. The method of the image singularities, developed initially for a prolate spheroid, was suggested for the first time without a proof by Havelock (1952). The proof was later obtai...
In this paper, we instigate numerically the performance of an oblate spheroidal heaving Wave Ener... more In this paper, we instigate numerically the performance of an oblate spheroidal heaving Wave Energy Converter (WEC). The diffraction/radiation problems are solved in the frequency domain by utilizing the conventional boundary integral equation method. This method is, initially, compared against an analytical method that utilizes the image singularity system to manipulate the underlying Green’s function. Next, extended results are presented focusing on the comparison of the oblate spheroidal WEC with other WEC geometries as well as on the effect of various design parameters (i.e. equatorial and polar radius, distance from a bottom-mounted vertical wall) on the performance of the oblate spheroidal WEC.
Applied Ocean Research, 2021
Fluids
The main objective of this study is to develop a semi-analytical formulation for the radiation pr... more The main objective of this study is to develop a semi-analytical formulation for the radiation problem of a fully immersed spheroid in a liquid field of infinite depth. The term “spheroid” refers herein to the oblate geometry of arbitrary eccentricity and to the axisymmetric case, where the axis of symmetry is normal to the free surface. The proposed numerical approach is based on the method of image singularities, and it enables the accurate and fast calculation of the hydrodynamic coefficients for the translational degrees of freedom of the oblate spheroid. The excellent agreement of the results, with those of other investigators for the limiting case of the sphere and with those obtained using a respected boundary integral equation code, demonstrates the accuracy of the proposed methodology. Finally, extensive calculations are presented, illustrating the direct impact of the immersion depth and the slenderness of the spheroid on the hydrodynamic coefficients.
Journal of Marine Science and Engineering
This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamic... more This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamical applications. The theorem provides explicit relations that express the oblate spheroidal harmonics, given in terms of the fundamental solutions of the Laplace equation. Here, the theorem is employed to transform the underlying Green’s function into the relevant coordinate system and, consequently, to formulate the diffraction potential. The case considered refers to the axisymmetric placement of the spheroid, namely, symmetrical axis perpendicular to the free surface. The mathematical formulations have been implemented numerically providing exceptionally accurate computations, which manifests the consistency and robustness of the relevant formulas.
Journal of Marine Science and Engineering
This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamic... more This study exploits the Touvia Miloh oblate spheroid theorem with a special focus on hydrodynamical applications. The theorem provides explicit relations that express the oblate spheroidal harmonics, given in terms of the fundamental solutions of the Laplace equation. Here, the theorem is employed to transform the underlying Green’s function into the relevant coordinate system and, consequently, to formulate the diffraction potential. The case considered refers to the axisymmetric placement of the spheroid, namely, symmetrical axis perpendicular to the free surface. The mathematical formulations have been implemented numerically providing exceptionally accurate computations, which manifests the consistency and robustness of the relevant formulas.