Analysis Of Hydrodynamic Loads And Coupled Heave-pitch Motion For Spar Platform

The objectives of this study are to obtain wave loads and hydrodynamic coefficients for Spar platform and to evaluate heave-pitch coupling motion and Mathieu instability, which are referable in design and fabrication of spar platform.According to the characteristic of Spar, the pitch restoring coefficient can be represented by a function of the displaced volume and the metacentric height of Spar. Due to heave motion, the displaced volume and the metacentric height of Spar platform change in time and this heave-pitch coupling can be represented by parameter excited equation. Mathieu instability for a Spar platform arises when there is large heave motion and the period of the heave motion is half of the pitch natural. In the process, kinetic energy is transferred from heave mode to pitch and the amplitude of pitch is magnified considerably.For wave exciting force, the main body of the Spar platform is simplified as an isolated truncated float vertical cylinder. An exact semi-analytical method is described to solve one order diffraction problem of Spar platform and a computer program is developed for obtaining surge, heave wave exciting force and pitch wave exciting moment in different wave heading. For hydrodynamic coefficients, using the same simplified model, one order radiation problem of Spar platform is in detail deduced by using semi-analytical method in theory and also a computer program is developed for obtaining the added mass and damping coefficients of surge, heave and pitch respectively. The two Calculation program ware compiled using Matlab software. Comparisons between the numerical results given in the paper and those obtained from MOSES and WAMIT show excellent agreement. The results can be used for calculating motion of Spar. The mooring is simulated by lumped mass model and coupled with the hull of Spar to evaluate the motion of Spar by a coupled program.The results in this paper show that the wave elevation effect is the main reason for inducing heave motion and the pitch damping coefficient significantly affects the Mathieu instability. The results also show that mooring effect can suppress the Mathieu instability by reducing the heave amplitude but not directly function on pitch.