Long term extreme analysis of moored FPSO with emphasis on the effect of hydrodynamic drag coefficient

One of the key coupling mechanisms between the FPSO and the mooring/riser, which remains to be a challenging topic, is the damping contribution from the mooring lines. The mooring line damping especially from hydrodynamic drag forces is of vital importance to FPSO's low frequency motion in deep water and its associated maximum mooring line tension and the maximum offset. The coupled analysis can take the mooring line damping into account automatically, but it suffers from the extremely high computational cost. Some methods use a linear damping coefficient to represent the damping effect but that estimate may not be accurate due to the line damping depending on several factors such as the wave frequencies, the response and offset position. An efficient and accurate analysis method is required to balance accuracy and efficiency. Morison's equation with a drag coefficient is often employed to calculate the hydrodynamic drag loads of mooring lines. The drag coefficient is not easily determined, particularly for chain, with its complex shape. The variation of hydrodynamic drag coefficient would alter the level of line damping. That means the drag coefficient is important to the damping and the ensuing extreme offset and maximum line tension. Therefore, it is worthwhile to investigate the effects of the hydrodynamic drag coefficient on the damping contribution to the extreme low frequency FPSO motion and the maximum mooring line tension. To begin with, a hybrid time and frequency domain method is developed for dynamic analysis of moored FPSO. The time domain simulation with a large time step is performed for low frequency motion of the FPSO, whilst the wave frequency response of the mooring lines at a given mean offset position will be conducted in the frequency domain.;The frequency domain analysis will be based upon a specific linearization approach where the damping to the low frequency FPSO motion from the wave frequency response of the mooring line can be accounted for in the form of an increased mean tension. Comparison is made of the tension/motion results with that of the dynamically coupled time-domain analysis, as well as the computational efficiency. Next, the methodologies for the long term extreme analysis are validated. The all sea state method for the long term extreme analysis is performed by use of Kriging metamodel (Simpson et al., 1998; Wang and Shan, 2006). The Monte Carlo simulation is applied for the long term probability integral based on the Kriging metamodel.;The improved method based on the environmental contour method and accurate distribution tail extrapolation method is proposed. The contour line method assumes that the short term variability could be accounted for separately. This method evaluates the extreme response based on limited sea states along a well-defined environmental contour line with a given return period. Then the short term variability is considered by selecting a high fractile. The distribution of the response is evaluated by the average conditional exceedance rates (ACER) method. The ACER method, which can accurately capture the effect of statistical dependence for the extreme value prediction problem, is less restrictive and more flexible than the one based on asymptotic theory. Finally, the reliability analysis for the extreme response considering the uncertainty influence of the drag coefficient is performed. The conditional distribution for the long term extreme response with given the drag coefficient is estimated by contour line method and ACER method. The perturbation method based on 4th-order expansion is developed. The asymptotic approximation method based on the Laplace's method is also employed for the approximation of probability integral . The asymptotic evaluation is based on the assertion that the greatest contribution to an integral derives from the locations where the integrand is a maximum point.One of the key coupling mechanisms between the FPSO and the mooring/riser, which remains to be a challenging topic, is the damping contribution from the mooring lines. The mooring line damping especially from hydrodynamic drag forces is of vital importance to FPSO's low frequency motion in deep water and its associated maximum mooring line tension and the maximum offset. The coupled analysis can take the mooring line damping into account automatically, but it suffers from the extremely high computational cost. Some methods use a linear damping coefficient to represent the damping effect but that estimate may not be accurate due to the line damping depending on several factors such as the wave frequencies, the response and offset position. An efficient and accurate analysis method is required to balance accuracy and efficiency. Morison's equation with a drag coefficient is often employed to calculate the hydrodynamic drag loads of mooring lines. The drag coefficient is not easily determined, particularly for chain, with its complex shape. The variation of hydrodynamic drag coefficient would alter the level of line damping. That means the drag coefficient is important to the damping and the ensuing extreme offset and maximum line tension. Therefore, it is worthwhile to investigate the effects of the hydrodynamic drag coefficient on the damping contribution to the extreme low frequency FPSO motion and the maximum mooring line tension. To begin with, a hybrid time and frequency domain method is developed for dynamic analysis of moored FPSO. The time domain simulation with a large time step is performed for low frequency motion of the FPSO, whilst the wave frequency response of the mooring lines at a given mean offset position will be conducted in the frequency domain.;The frequency domain analysis will be based upon a specific linearization approach where the damping to the low frequency FPSO motion from the wave frequency response of the mooring line can be accounted for in the form of an increased mean tension. Comparison is made of the tension/motion results with that of the dynamically coupled time-domain analysis, as well as the computational efficiency. Next, the methodologies for the long term extreme analysis are validated. The all sea state method for the long term extreme analysis is performed by use of Kriging metamodel (Simpson et al., 1998; Wang and Shan, 2006). The Monte Carlo simulation is applied for the long term probability integral based on the Kriging metamodel.;The improved method based on the environmental contour method and accurate distribution tail extrapolation method is proposed. The contour line method assumes that the short term variability could be accounted for separately. This method evaluates the extreme response based on limited sea states along a well-defined environmental contour line with a given return period. Then the short term variability is considered by selecting a high fractile. The distribution of the response is evaluated by the average conditional exceedance rates (ACER) method. The ACER method, which can accurately capture the effect of statistical dependence for the extreme value prediction problem, is less restrictive and more flexible than the one based on asymptotic theory. Finally, the reliability analysis for the extreme response considering the uncertainty influence of the drag coefficient is performed. The conditional distribution for the long term extreme response with given the drag coefficient is estimated by contour line method and ACER method. The perturbation method based on 4th-order expansion is developed. The asymptotic approximation method based on the Laplace's method is also employed for the approximation of probability integral . The asymptotic evaluation is based on the assertion that the greatest contribution to an integral derives from the locations where the integrand is a maximum point