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This paper describes a simplified analytical procedure to predict the hydrodynamic radiation damping coefficients. In the formulation of the wave damping force due to oscillatory rigid-body motion, the use of the wave radiation component is made. At the initial stage of the development a rectangular barge form was used and the formulation is based on the strip theory. The simplified numerical procedure developed was used to predict the hydrodynamic characteristics of a prismatic barge. The hydrodynamic coefficients are developed using the Haskind- Newman relation together with the 2D energy conservation principle in the frequency domain and numerical results from the radiation damping coefficient and force calculations are compared with Vughts' experimental results. INTRODUCTION In order to predict the ship motion in a seaway, we need to determine wave excitation forces and hydrodynamic coefficients. The influence of viscosity and surface tension is of minor importance compared to forces due to incident and diffracted waves. Presently this statement has not been disproved by model tests or full scale measurements; at least as far as ship motion problem is concerned. On the other hand, the viscous effects should be considered in the maneuvering problem. Currently many commercial programs based on various numerical procedures are used to predict the hydrodynamic coefficients. However the use of commercial programs usually requires special knowledge and skills to model the ship geometry for accurate results. This paper presents a simplified numerical procedure to predict the hydrodynamic damping coefficients. The coefficients are derived using Haskind-Newman relation together with the 3D energy conservation principle in the frequency domain.
Derivation of CALM Buoy Coupled Motion RAOs In Frequency Domain And Experimental Validation
Le Cunff, C. (Principia R.D.) | Ryu, Sam (SOFEC Inc) | Duggal, Arun (SOFEC Inc) | Ricbourg, C. (Principia R.D.) | Heurtier, J-M (Principia R.D.) | Heyl, Caspar (SOFEC Inc) | Liu, Yonghui (SOFEC Inc) | Beauclair, Olivier (Principia R.D.)
Frequency domain analysis is used to solve a complete catenary anchor leg mooring (CALM) buoy system comprised of the buoy, its moorings lines and the export lines. The advantage of such an approach is that it is very fast to run and allows large parametric studies in relatively short times. The underlying assumption of the frequency analysis is that the coupling is essentially linear. Therefore, calculations are performed taking into account first order waves loads on the floater. Added mass and radiation damping terms are frequency dependent and can be easily handled in this formulation. The main source of non-linearity comes from the viscous damping both on lines and buoy. Classical methods are employed to linearize the drag force on the lines and are similarly used for the buoy. Time domain simulations remain necessary when higher order loads, or drift forces are imposed. But for first order waves, frequency analysis is a powerful and accurate tool to predict buoys motions and evaluate the fatigue life of mooring and export lines submitted to first order excitations. Comparisons are made between numerical simulations and model test results. Good agreement is found between the experimental data and the frequency-domain analysis for the coupled CALM buoy motion response. INTRODUCTION Deepwater offloading buoys are being extensively used in West Africa to allow efficient loading of spread-moored FPSOs (Ryu et al., 2006). Some of the current projects of the offloading buoys include Agbami (Nigeria, 1435m water depth), Akpo (Nigeria, 1285m), Bonga (Nigeria, 1000m), Dalia (Angola, 1341m), Erha (Nigeria, 1190m), Girassol (Angola, 1320m), Greater Plutonio (Angola, 1310m), and Kizomba A & B (Angola, 1200m, 1000m). Compared to other floating systems such as TLP, SPAR, and FPSO, the deepwater offloading buoy system has relatively small displacement and inertia so that the mass, damping, and stiffness of the mooring lines and oil offloading lines (OOLs) can be considerable compared to the inertia, radiation damping, and hydrostatic stiffness of the buoy.
The Motion Analysis Program Suite (MAPS) has been developed at Memorial University of Newfoundland based on the panel-free method for the accurate computation of wave-body interactions in the frequency domain. In the panel-free method, the desingularized integral equation in terms of source strength distribution is developed by removing the singularity due to the Rankine term in the Green function. NURBS surfaces are adopted to describe the exact body geometry mathematically. The integral equations are discretized over the body surface by Gaussian quadratures. In this work, computations by the panel-free method have been extended to floating bodies with complex geometry. Validation studies are presented for a Liquefied Natural Gas (LNG) carrier in shallow water and a Floating Production Storage and Offloading (FPSO) vessel in deep water. Results are compared with experimental data and those by the panel method. INTRODUCTION The panel method has been widely used in the computation of ship and offshore structure responses in waves. Hess and Smith (1964) pioneered the panel method in which the body surface was subdivided into flat quadrilaterals. The integration of the singular 1/r term over a panel was obtained by assuming that the panel is planar quadrilateral or triangle with the constant source strength distribution. It is often referred as the constant-source-flat-panel method or a lower-order panel method. Normally, a large number of panels are required to achieve accurate results. For bodies with complex geometry, it is challenging to develop a panel generator for practical applications. Higher-order panel methods have been developed in various degrees to overcome the deficiencies of the constant-source-flat-panel method. Most higher-order methods allow for linear or quadratic panels and first- or second-degree polynomial distribution of source strength over a panel. It normally requires more computational effort than the lower-order panel method.