Numerical study of vortex-induced vibration in rough cylinders based on the Runge-Kutta method

In this study, a numerical program is developed to investigate the vortex-induced vibration (VIV) and analyze the dynamic responses of cylinders with varying surface roughness. A two-degree-of-freedom (2-DOF) fluid-structure interaction model is first established, incorporating the SST k-ω turbulence model and the classical fourth-order Runge-Kutta method. The accuracy of the numerical method and the reliability of the model are validated by comparison with available experimental data. Subsequently, within a velocity range of 2.0 to 14.0, the frequency-domain responses, VIV characteristics, wake vortex patterns, and trajectory behaviors of three cylinders with varying surface roughness are investigated and compared with those of a smooth cylinder. The results demonstrate that the proposed numerical method effectively captures the transitions of VIV in rough cylinders across different response branches and vortex shedding regimes. The motion trajectories of rough cylinders primarily exhibit “figure-eight” and chaotic patterns. Compared to smooth cylinders, rough cylinders show a narrower range of chaotic motion at low velocities but a significantly wider range at higher velocities, indicating that surface roughness intensifies chaotic behavior in cylindrical structures. This research not only provides a reliable computational framework for studying VIV in cylindrical systems but also offers theoretical guidance for the optimization of pipeline design.