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Abstract
Frequencies of floating production, storage and offloading's (FPSO's) horizontal motions are much smaller than the natural frequencies of waves and thus 2nd-order difference-frequency wave drift forces could excite large response. In this paper, the 2nd-order wave drift forces and low-frequency (LF) horizontal motions of a multi-point moored FPSO are computed in bi-directional swell and wind-sea conditions offshore West Africa (WOA). Newman's approximation has been applied as the computation theory. Numerical approximation compares reasonably well with measured results of model tests. Under environmental conditions in WOA, it is concluded that swell induces larger drift loads than wind-sea at the surge/sway natural frequency, and they both are indispensable to the LF motion. However, the coupling interacting drift loads between different incident angles could be neglected due to the large peak period deviation between swell and wind-sea. Simplified approximation will be effective by superposition of drift force contributions from uni-directional long-crested swell and wind-sea. Newman's approximation provides a tool to accurately simulate drift loads on FPSO in the bi-directional waves in WOA. An important reference has been obtained for both LF motion prediction and mooring system design in bi-directional swell and wind-sea WOA.
Acknowledgements
The model test is conducted in the State Key Laboratory of Ocean Engineering at Shanghai Jiao Tong University. Numerical tools in present paper are developed by Det Norske Veritas. This work is financially supported by the National Natural Science Foundation of China (Grant No. 50879045). All technical supports and contributions from above are truly appreciated.
Nomenclature
| Φ | = | Total velocity potential |
| m | = | FPSO mass matrix |
| A | = | FPSO added mass matrix |
| C | = | FPSO potential damping matrix |
| K | = | FPSO restoring stiffness matrix |
| x | = | Displacement vector |
| x | = | Velocity vector |
| x | = | Acceleration vector |
| fwave | = | Wave exciting force in frequency |
| A∞ | = | FPSO added mass at frequency ∞ |
| C∞ | = | FPSO damping at frequency ∞ |
| q | = | Total external force and moment |
| D1, D2 | = | Linear and 2nd-order damping matrix |
| X(ω) | = | Complex of x in frequency domain |
| F(ω) | = | Complex of f(t) in frequency domain |
| h(τ) | = | Retardation function |
| RI | = | Inertia force vector |
| RD | = | Damping force vector |
| RS | = | Internal reaction force vector |
| RE | = | External load vector |
| qWI | = | Wind force |
| q1WA | = | 1st-order wave exciting force |
| q2WA | = | 2nd-order wave exciting force |
| qCU | = | Current force |
| qext | = | External force, e.g. mooring force |
| t | = | Time |
| M(x) | = | System mass matrix |
| Cd | = | System damping matrix |
| Δx | = | Incremental nodal displacements |
| Δx | = | Incremental nodal velocities |
| Δx | = | Incremental nodal accelerations |
| Δt | = | Incremental time |
| S(Δω) | = | Spectral density of 2nd-order wave forces |
| Δω | = | Difference frequency |
| ξ(μ) | = | Directional wave spectrum |
| H/ Hmn | = | QTF with different incident angles: m,n |
| ζm | = | Amplitude of wave component |
| Acronyms | = | |
| LF | = | Low frequency |
| DOF | = | Degree of freedoms |
| QTF | = | Quadratic transfer function |
| RAO | = | Response amplitude operator |
| FPSO | = | Floating production, storage and offloading |
| WOA | = | West of Africa/offshore West Africa |
| LNG | = | Liquefied natural gas |