UBC Theses and Dissertations
Hydrodynamic coefficients of large vertical cylinders Mathai, Thomas
The evaluation of hydrodynamic loads on a large surface-piercing vertical cylinder of arbitrary section oscillating in water is addressed. By exploiting the restriction to the structure's geometry, the problem is formulated in the frequency domain as a series of two-dimensional linear radiation problems. Analytical solutions are first obtained for the special cases of circular and elliptic cylinders. A numerical solution based on the method of integral equations is then developed. This is initially applied to circular and elliptic cylinders, so that results may be compared with the corresponding closed-form solutions. Two extrapolation schemes to accelerate the convergence of the numerical results are evaluated. The occurrence of irregular frequencies in the method of integral equations is studied and available methods to eliminate them are summarized. To circumvent numerical difficulties in the integral equation method at high frequencies, alternative approaches to calculating the hydrodynamic coefficients are investigated. Two schemes for calculating damping coefficients are outlined: a short-wave approximation to the propagating mode potential, and a method based on geometrical optics. Of these, the former is found to be particularly suitable. Two different methods for calculating high frequency added masses are also proposed. One involves discarding the propagating mode and using only the evanescent modes, which are free of irregular frequencies. The other is based on an application of the Kramers- Kronig relations and is valid over the entire frequency range. The extension of the various methods to very high frequencies at which compressibility effects become significant is also examined. Of the four high frequency methods, damping coefficients may be obtained by the short-wave approximation, and added masses may be obtained by the evanescent mode approximation. As examples of the application of the various methods, results are presented for a square cylinder and a typical ocean engineering application is illustrated.
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