SIMULATION OF SECOND-ORDER ROLL MOTIONS OF A FPSO Fl´ avia Rezende Research Department Bureau Veritas (France) Xiao-Bo Chen Research Department Bureau Veritas (France) Professorship, HEU (China) Marcos D. Ferreira CENPES PETROBRAS (Brazil) ABSTRACT The roll motions are a key parameter on the design of FPSOs that operate in moderate and severe environmental conditions. To reduce the magnitude of roll motions, some techniques based on changing the vertical position of gravity center are used to put the roll natural period outside of the frequency range of the linear waves. However, recent model tests and also numerical calculations have shown that the vessel may still experience large roll motions which are considered to be induced by second-order wave loads. Further to the work in Rezende et al. (2007) to compute the roll response in frequency domain, new developments to per- form simulations in time domain are presented here. In this new method, variations of second-order roll moments dependent on the roll and heave motions are taken into account consistently. It is shown that, unlike the horizontal loads, the quadratic transfer functions of the vertical loads depend on the instantaneous po- sition of the vessel. The variation of the roll moment with the heave position of the vessel has been considered more important than the variation obtained only with the inclination of the vessel. Furthermore, numerical results of roll simulations are compared with model tests results and presented in the paper. NOMENCLATURE FPSO Floating Production Storage and Offloading Unit QTF Quadratic Transfer Function INTRODUCTION It is observed that several FPSOs operating in different ar- eas around the world experience large roll motions, resulting in delays and production down time. For the new constructions, the optimization of the hull geometry in order to achieve good motions characteristics has been an issue of major concern. One technique used to limit the roll response is to design the unit such that the roll natural period is outside of the range of linear wave energy (roughly from 3s to 20s). However, recent tests for FPSOs with roll resonant periods larger than the maximal linear wave period have demonstrated the presence of roll response at their natural periods, what is attributed to non-linear mechanisms. We consider the theory of second-order wave diffraction and radiation within which the wave loads occurring at the differ- ence of wave frequencies can be evaluated. These low-frequency wave loads are considered to be the main source of large pe- riod roll motion. Much work has been done for the prediction of the horizontal components of second-order loads and two classes of theories have been developed: far-field formulation based on the momentum principle and the near-field based on the direct second-order pressure integration on the hull surface. The fruit- ful results have been obtained in the application to the design of mooring system. However, few works as in Pinkster et Dijk (1985) and in Chen et Molin (1989) have been pursued on the computation of the vertical components of second-order loads due to two critical issues associated with their numerical evalua- tion. One concerns the accurate prediction of second-order wave moments and another, the coupling of linear and second-order motions. Concerning the vertical components (force in the ver- tical direction and moments around the horizontal axis), the far- 1 Copyright c  2008 by ASME Proceedings of the ASME 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE2008 June 15-20, 2008, Estoril, Portugal OMAE2008-57405