Prediction model for multidirectional vortex-induced vibrations of catenary riser in convex/concave and perpendicular flows

This study presents an advanced numerical prediction model based on nonlinear wake oscillators for the investigation of multidirectional vortex-induced vibration (VIV) responses of a long catenary riser depending on the structural curved configuration versus the incoming flow direction. By considering a uniform free-stream flow aligned with the initial curvature plane of the catenary riser in a convex or concave shape, the normal flow velocity component is nonlinearly sheared owing to the spanwise variation of inclination angles. This is different from the perpendicular flow case in which the normal flow velocity is spatially constant. To capture the influence of flow direction on the three-dimensionally coupled cross-flow and in-line VIV, distributed wake oscillators are introduced and applied to simulate the fluctuating hydrodynamic lift and drag forces that account for the important effects of cylinder inclination, variable vortex excitation frequencies, global–local​ displacement relationships, and relative flow-cylinder velocities. The amplified mean drag force and the axial force depending on the tangential flow velocity are also considered. These empirical hydrodynamic effects are nonlinearly coupled with the equations of riser three-dimensional motion, and the overall governing equations are numerically solved to assess the multimode, multi-frequency and multi-degree-of-freedom responses. Validation of the model is carried out for VIV of flexible straight and curved cylinders based on experimental results in the literature. Parametric investigations are performed by varying the incoming flow velocities in perpendicular, convex and concave configurations for a long catenary riser with a low mass-damping ratio. In-plane (horizontal and vertical) and out-of-plane VIV features are presented and discussed in terms of space–time varying amplitudes, drag-amplified shape reconfigurations, oscillation frequencies, lock-in occurrences, dual resonances, orbital motion trajectories, fluid–structure energy transfer, and multimodal contributions. Overall prediction results highlight the influence of the cylinder geometric configuration versus the incoming flow orientation on multidirectional VIV characteristics that should be recognised and incorporated into practical analysis tools.