Predicting the Second-Order Resonant Roll Motions of an FPSO

This paper aims at summarizing the results obtained in a recent research project concerning the prediction of wave-induced resonant behavior of new FPSO concepts. The analysis was based on a conceptual hull designed to operate in deep water fields off the Brazilian coast. Throughout this project, several configurations of the hull were proposed, some of them leading to relatively large natural periods. As a consequence, the resonant behavior of roll motions induced by second-order wave effects was clearly observed in small-scale model tests performed with some of these configurations, providing also good results for the verification and validation of numerical models that aim at predicting such wave forces. From the numerical standpoint, the hydrodynamic excitation forces can be estimated using well-established techniques for solving the second order diffraction problem, usually adopting a BEM approach. In terms of the computational time required for this analysis, however, this procedure is not so trivial since, in principle, the contribution of all pair of frequencies used to represent the wave spectrum must be computed. In face of the large computational effort tha is required and depending on the characteristics of the resonant problem, some approximations are consolidated and largely used by designers. One example is the approximation used to model the horizontal drift of the vessel, based on the very low natural frequencies that characterize the problem. Taking advantage of the asymptotic behavior of the second order horizontal force, good results can be obtained by computing the QTF (Quadratic Transfer Function) only in zero frequency. For the present case, however, this kind of approximation is not so effective. Even though the roll natural frequency of the FPSO is certainly lower than the usual values, it is not low enough for considering this asymptotic behavior. On the other hand, some other approximations can be envisaged and tested aiming at reducing the computational burden. In fact, the low viscous damping leads to a narrow-band transfer function for the roll motion and therefore enables modeling the resonant roll dynamics by means of an white-noise approach. In this case, the second order force spectrum needs to be computed only for one particular difference frequency, which is equal to the natural period of roll. This approach was investigated for different waves and draft conditions and the numerical results compared to those measured in the wave basin. Important aspects such as the influence of the viscous damping on the computation of the second-order wave forces and the change in the bandwidth of the response spectrum with the vessel draft are also discussed in the analysis, in view of the experimental results.