Cross-flow vortex-induced vibration of a flexible riser transporting an internal flow from subcritical to supercritical

This study aims to model and explore the IFE (Internal Flow Effect) on the CF (Cross-Flow) VIV (Vortex Induced Vibration) of a flexible riser transporting an axial single-phase internal flow. The simulation model employs the nonlinear equations describing the coupling of axial and transverse vibrations of a fluid-conveying pipe as the structural model, and adopts a distribution of van der Pol oscillators to create the VIV effect. The governing equations can be solved via a Galerkin-based multi-mode approach combined with the Houbolt's finite difference scheme. The developed code has been validated for VIV effect and IFE from subcritical to supercritical region. The Argand diagram of a flexible riser is plotted at first, and the varying natural frequencies with the increase of internal flow velocity and the critical internal flow velocity can be obtained. Then simulations of the flexible riser at two uniform currents with the increase of internal flow velocity in a transition range from being subcritical to supercritical are conducted. The IFE on CF VIVs are examined by the space-time modifications of riser responses and dominant vibration frequency for which the mode switching and sharing can be identified. It has demonstrated that internal flow influences the vibration amplitude and the dominant vibration frequency. Internal flow can trigger new natural modes and switch the role of the most predominant one. Moreover, a buckling-flutter coupled instability is captured where the riser is experiencing a static divergence and a Hopf bifurcation via the first natural mode.