Evaluation Of Wave And Current Loads On Offloading FPSOS

The offloading operation of a FPSO system composed of two floating units under action of waves and current is considered. The multi-body analysis is performed to take account of hydrodynamic interactions between the FPSO and offloading vessel. The method based on the consistent formulation to evaluate the second-order wave and current loads is extended to the case of multiple bodies. Further to obtaining usual linear outputs like first-order wave loads and motion RAOs, the quadratic transfer function of drift loads is evaluated for a system of a FPSO and a shuttle in tandem. The comparison with experimental measurements is presented. Introduction We consider the offloading operation of a FPSO system composed of two floating units, i.e. a FPSO and a shuttle, under the action of a regular wave and a uniform current. The fluid is assumed to be inviscid and flow irrotational. The problem is classified as that of wave diffraction and radiation around floating bodies. This wave-current-body interaction problem is formulated following the way presented in Chen & Malenica (1998) for a single body. Due to the flow symmetry, the wave diffraction-radiation at low forward speed is equivalent to the interaction of waves with a current in the opposite direction. The decomposition of the time-harmonic potential into linear and interaction components is presented then where terms of order O(τ) and higher are neglected. The Strouhal number τ = Uω/g is associated with the current speed U , the encounter frequency ω and gravity acceleration g. Applying the Green theorem to the time-harmonic potentials and the Green function, integral equations are established. The source method is adopted to numerical evaluation of the unknown velocity potentials. Expressions for first and second-order wave loadings, including the radiation coefficients, are given. The difficulty to evaluate accurately the double derivatives of the linear steady potential (to obtain the mj terms) on the body surface and the double derivative with respect to z on the free surface is solved by the method inspired from Wu (1991) and presented in Chen & Malenica (1998). The way to evaluate accurately the free-surface integrals is the same as that presented in Chen & Malenica (1998). The new middle-field formulation to evaluate the second-order drift loads is presented further on. The formulation is shown, in Chen (2004), to be more robust than the near-field formulation. The usual far-field formulation is not applicable to obtain the second-order loads on an individual body. Numerical implementation in our in-house program HydroStar, and results for a half-immersed sphere and a system of FPSO with a shuttle in tandem are presented furthermore. Interaction effects of the local steady flow on global first and second-order loadings and radiation coefficients are analyzed. Wave-current-body interaction problem A moving system of coordinates (x, y, z) in steady translation with the current speed is defined such that the x-axis points in the opposite direction of the current, the z-axis points vertically upward and z = 0 is the mean free-surface plane. Based on the assumptions of perfect fluid, irrotational flow and small wave steepness, the velocity potential is written, in Malenica (1994), as the sum of a steady φ(x, y, z), a time-harmonic unsteady φ(x, y, z) potentials and a constant second-order potential φ Φ(x, y, z, t) = U(φ−x) + R { φ exp(−iωt) } + φ (1) The second-order time-dependent potential φ is discussed in Finne & Grue (1998) and affect the second-order yaw moment. For the sake of space, we neglect in the following this term which can be added in the same way as Finne & Grue (1998). Both the steady φ and unsteady φ potentials satisfy the Laplace equation in the fluid domain and an appropriate radiation condition at infinity. In particular, assuming small forward speed, the steady potential φ satisfies : φz |z=0 = 0 and φn|SB = n1 (2)