Frequency‑domain prediction method for wake‑induced vibrations of a downstream flexible riser

The riser bundle system is an important equipment to explore oil and gas in ocean engineering. Under ocean flows， upstream and downstream risers in tandem will experience vortex‑induced vibrations and wake‑induced vibrations， respectively， which seriously threatens the structural fatigue life. To predict the vibration responses of a downstream flexible riser， this paper develops a semi‑empirical frequency‑domain prediction method for wake‑induced vibrations based on the classical vortex‑induced vibration prediction method of a single flexible riser. Considering the wake shielding effect on the downstream riser due to the existence of the upstream riser， the reductive wake velocity becomes the flow velocity to excite the vibrations of the downstream riser. Then， the upstream‑to‑downstream diameter ratio is utilized to determine whether the frequency capture occurs. The added mass coefficient of the downstream riser will be adjusted when the frequency capture occurs， otherwise it is 1 constantly. Subsequently， the prediction is based on the resonance condition. The excitation coefficients from a series of forced oscillation tests of a rigid cylinder are approximate to be the wake‑induced force coefficients. According to the balance between the modal structural damping force and the modal hydrodynamic force amplitudes， the modal amplitude can be non‑iteratively solved. Afterwards， the wake‑induced vibration displacements can be calculated based on the mode superposition method. By comparing prediction results with the experimental results， the proposed method can basically correctly predict the dominant frequency， displacement， strain and fatigue damage of the wake‑induced vibration for the downstream flexible riser. Therefore， the present method is conducive to the multiple‑riser system design in practical engineering.