## 3 Aeroelasticity and Aerodynamics of Cable-Supported Bridges
### Vortex-Induced Vibration
#### 3.2.3 CFD Studies of Vortex-Induced Vibrations  
In an attempt to overcome some of the shortcomings of wind tunnel tests, in recent years, there has been a move to investigate VIVs using CFD. Similar to the wind tunnel studies, the focus of these numerical studies can also be categorised into two groups: studies that investigate effect of various factors on VIVs and studies that test the efficiency of aerodynamic countermeasures to VIVs. Investigations of factors that affect VIVs  
The effect of incident turbulence on VIVs was systematically investigated by [PERSON], [PERSON] and [PERSON] (2017). Three-dimensional LESs were performed on a rectangular cylinder geometry with an aspect ratio of four. Four different integral length scales of the incident turbulence were considered--B/6, B/3, 2B/3 and 4/3B (where B is the width the section), and three levels of turbulence intensities--3%, 6% and 12%. Results indicated that increases in turbulence intensity reduce the VIV amplitude, whereas the increases in integral length scales of the eddies would moderately increase the VIV amplitude. It was highlighted that the range of turbulence length scales used in the simulations was in the same order of magnitude of the section width. It was suggested that eddies of an integral length scale exceeding this range might stimulate a significantly larger VIV amplitude. Similarly, [PERSON] et al. (2018) also studied the VIV of a 4:1 rectangular cylinder using 3D LESs. They investigated the effects of the grid resolution on the VIV amplitudes determined from free oscillation simulations. Simulation results were found to be sensitive to the spanwise mesh density. Finer spatial discretisation in the spanwise direction would derive results of VIV amplitudes that are closer to the experimental results. However, these simulations were only performed in smooth-flow conditions. Further future studies that consider incident turbulence will provide greater insights into the application of LESs in this area. [PERSON] et al. (2018) simulated the formation of a VIV on a streamlined box girder. The simulations were based on the ALE-VMS method in which turbulence was computed using a multiscale approach similar to the LES method. The simulations applied a full-scale sectional geometry of the bridge girder while the corresponding wind tunnel tests use a 1:50 scaled model. Compared to the wind tunnel results, the simulations significantly underestimated the magnitude of the VIV by approximately 50%. This discrepancy was the result of the incompatibility of the nonpenetration boundary condition at the transverse walls with the domain width, which suggested the significance of physical boundary conditions when deriving accurate model results. However, considering that the geometry used in the wind tunnel tests is 50 times smaller than the one used in the simulations, the Reynolds number scaling effect might also contribute to the discrepancy. [PERSON], [PERSON] and [PERSON] (2018) performed 3D LESs with the standard Smagorinsky subgrid model on a streamlined box girder without any nonstructural elements. The turbulence intensity was set to be 1%, creating a rather smooth free-stream flow. The angle of attack ranged from \(-10^{\circ}\) to \(10^{\circ}\). This is the first study that the authors are aware of that estimates VIV amplitudes using a forced oscillation method which was computationally more efficient than the conventional free oscillation simulations due to the prescribed motions of the geometry. Nonetheless, compared to wind tunnel results, the simulations drew a substantially larger value of the VIV amplitude. The reasons for such discrepancies were twofold. Firstly, the simulations adopted a computational domain that had a small spanwise size. Through a comparison of different spanwise sizes, it was found that aerodynamic damping was sensitive to this value and a larger domain size in the spanwise direction would deliver more accurate estimations of the VIV amplitude.