Coupled in-line and cross-flow vortex-induced vibration responses of a fluid-conveying riser with a variable tension

When seawater flows around a riser, it induces vortex-induced vibrations (VIV), which occur in two forms: in-line (IL) and cross-flow (CF), and these two forms influence each other. Accurate prediction of the coupled IL and CF VIV behavior is crucial for riser design. Therefore, a coupled VIV model with variable tension considering internal flow was established to analyze the coupled VIV behavior of a vertical riser in a linear shear flow. The riser is modeled as an Euler–Bernoulli beam, using two van der Pol wake oscillators to simulate the drag and lift coefficients, with the equations of motion in the IL and CF directions coupled by fluid forces. The generalized integral transform technique (GITT) is used to transform the coupled nonlinear partial differential equations into a set of nonlinear ordinary differential equations for numerical solution. The model is first validated by comparing numerical results with existing reference data, and then the differences between the IL and CF coupled model and with one-direction CF only VIV model are analyzed. The effects of uniform flow, linear shear flow, and three different tension models on coupled VIV are analyzed. Finally, a parametric analysis of the impact of external and internal flow velocities on riser coupled VIV is conducted. The results show that the vibration response in the IL direction is more complex than in the CF direction. Compared to uniform flow, shear flow mainly affects the vibration in the IL direction, and variable tension impacts the mean displacement peak position in the IL direction as well as the vibration modes in both IL and CF directions. The external flow velocity affects the power-in region in the IL direction, while the internal flow velocity affects that in the CF direction. As the internal flow velocity increases, the characteristics of the traveling waves become more pronounced. The study finds that an appropriate internal flow velocity can stabilize the vibration of the VIV of the riser.