Improvement for modeling the damping of the wake oscillator based on the Van der Pol scheme

Given the importance of risers and umbilical cables in the exploitation of deep-sea resources, the vortex induced vibration (VIV) of long flexible cylinders has been systematically studied, and it is acknowledged that the wake oscillator is a satisfactory tool in practically predicting the VIV for offshore engineering applications. Based on the conventional wake oscillator with different damping term formulations, the present study systematically explores the influences of the coefficients and the maximum order of a polynomial damping term within the Van der Pol type wake oscillator. More specifically, the coefficients of the second-order polynomial are adjusted to vary inside a reasonable range, and the polynomial order is increased from the conventional specification of 2-4, 6, and 8. The vibrations of the flexible cylinder predicted by the revised wake oscillator are compared to the measurements taken from an experiment reported in the literature. The comparison indicates that increasing polynomial coefficients generally reduce VIV dominant mode numbers. In addition, increasing the polynomial order aligns the dominant mode more closely with experimental data, although this effect diminishes when the polynomial order exceeds 4. It is argued that the gradual change in phase differences along the cylinder induced by increasing either polynomial coefficient or maximum order could be the reason. The present study sheds light into the mechanism for the damping effect observed in hydrodynamic forces observed in VIVs and lays the foundation for suggesting an optimal formulation of the damping terms as 0.45q(2) + 0.6q - 0.3 compared to the conventional formulation of 0.3q(2) - 0.3.