# Investigation on Numerical Simulation of VIV of Deep-Sea Flexible Risers
## 5 Conclusions  
In this paper, based on the slice method, through a self-compiled UDF program in the Fluent solver, a 3D riser structure vibration program and 2D Fluent flow field calculation were combined to achieve fluid-structure coupling, and the numerical simulation of the vortex-induced vibration of a flexible riser with different slenderness ratios and different flow velocities was carried out. The following conclusions may be drawn:  
(1) Uniform flow did not result in smooth or regular sine or cosine curves for displacement-time history curves in the IL and CF directions but rather approximated to the vibration trace of a two-dimensional cylinder when multi-frequency flapping occurred. The maximum point of the riser's IL displacement balance was between 2% and 4% below the riser's midpoint;  
(2) With an increase in the slenderness ratio, the equilibrium position of the vibration of the riser in the IL direction continuously increased, but the position of the maximum value of the average value of the IL displacement in the axial direction of the riser remained unchanged. The \"8\"-shaped vibration track of the riser became increasingly vague and chaotic while being limited to a certain range. The vibration frequencies and vibration  
Figure 20: Vortex shedding diagram at different axial positions of riser. (a) C4, U = 0.10 m/s, L/D = 700. (b) C5, U = 0.15 m/s, L/D = 700. (c) C6, U = 0.25 m/s, L/D = 700.  
modes in the IL and CF directions continued to increase gradually, shifting from single-mode vibration to multi-modal vibration. At the same time, the order of the natural frequency of the vibration frequency continued to rise, and the number of vibration modes continued to increase. Furthermore, the phenomena of multi-frequency vibration and wide-frequency vibration became more apparent;  
(3) With an increase in flow velocity, the equilibrium position of the vibration of the riser in the IL direction continuously increased, but the position of the maximum value of the average value of the IL displacement in the axial direction of the riser remained unchanged. The vibration frequency increased with increasing flow velocity; however, the natural frequency remained constant. Therefore, the order of the natural frequency at which the vibration frequency was located continuously increased, leading to an increase in the number of vibration modes. This phenomenon also displayed a shift from a lower-order standing wave to a higher-order traveling wave (the standing wave response gradually disappeared, and the traveling wave response gradually dominated);  
(4) The 2S vortex shedding mode primarily occurred at the two ends of the riser and near the vibration stagnation point where the amplitude was relatively small. The P + S and 2P vortex shedding modes mainly occurred at places with relatively large amplitudes.  
Conceptualization, L.J.; methodology, L.J. and S.S.; software, F.S.; investigation, X.S.; resources, X.S.; data curation, L.J. and F.S.; writing--original draft preparation, L.J.; writing--review and editing, S.S. and L.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the NSFC and Shandong Province (U2106223); the Major Science and Technology Innovation Project in Shandong Province (2021 CXGC010707); and the Natural Science Foundation of Shandong Province (ZR2022 ME092).  
Not applicable.  
Thanks to [PERSON] to help in papers.  
The authors declare no conflict of interest.