Three-dimensional nonlinear vortex-induced vibrations of risers under internal gas-liquid and external shear flows

A novel three-dimensional (3D) dynamic model is proposed to explore the nonlinear vortex-induced vibration (VIV) characteristics of top-tension risers under the combined action of internal gas-liquid two-phase flow and external shear flow. The van der Pol equation is used to evaluate the interaction between the riser and the external shear flow. The nonlinear governing equations are established through Hamilton's principle, and they are discretized by the Galerkin method and solved via the Runge-Kutta method. The VIV responses calculated by the proposed nonlinear dynamic model are compared with the previously experimental and computational fluid dynamics (CFD) results, demonstrating the effectiveness and accuracy of the present theoretical method. The influences of the internal flow effect, the tension and the shear parameter of the external flow on the VIV responses of the riser are analyzed. The results show that when the internal flow effect is not considered, the transition of the external flow from uniform flow to shear flow leads to an increase in excited modes and a decrease in resonance responses of the riser in the cross-flow (CF) direction. Furthermore, with the increase of the external shear flow velocity, resonances at different positions of the riser are not synchronized, which is different from that of the riser in uniform flow. In the case of the riser conveying gas-liquid two-phase flow and being subjected to external uniform or shear flow, the increase in the velocity of the liquid phase leads to an increase in the maximum response amplitudes of the riser in the in-line (IL) and axial directions. When the internal flow changes from single-phase to gas-liquid two-phase, the maximum VIV responses of the riser in the IL and axial directions tend to decrease regardless of whether the riser is in uniform flow or shear flow.