## 3 Aeroelasticity and Aerodynamics of Cable-Supported Bridges
### Flutter-Aeroelasticity of the Deck
#### 3.1.3 CFD Studies of Flutter  
Wind tunnel studies have constituted the bedrock for research of flutter instability. Great achievements have been made in revealing the underlying mechanism and providing valid frameworks to predict the onset of flutter. However, limitations caused by apparatus have been witnessed, especially in the identification of flutter derivatives at high wind velocities. Therefore, numerical simulations that inherit the frameworks of the wind tunnel tests have gained research interest in this area. (1) Forced vibration simulations  
The first attempt to combine experimental wind tunnel methods and modern numerical simulations in the study of flutter on bridge deck was made by [PERSON], [PERSON] and [PERSON] [62]. They extracted eight flutter derivatives of a 2-DOF airfoil section by conducting URANS simulations using the standard k-\(\epsilon\) turbulence model and the finite element method. The bridge surface was treated as a no-slip wall where the near-wall treatment was fulfilled by applying a wall function on the thick near-wall elements that contained the viscous and transitional sublayers. Compared with currently available computational capacity, these simulations would be considered nascent for using a 2D coarse mesh and approximating the near-wall behaviour using wall functions. This turbulence model has been demonstrated to poorly represent the near-wall regions and the numerical scheme only offers first order of accuracy. Nonetheless, the results are shown to agree well with analytical results even in the high-Reynolds number condition where the flow becomes turbulent. Additionally, applying the no-slip wall condition at the bridge surface has become a common practice in the study of bridge aerodynamics. [PERSON], [PERSON] and [PERSON] [63] identified eight flutter derivatives from a 2-DOF system using 2D URANS simulations. The standard k-\(\epsilon\) turbulence model was used, although the configuration of the near-wall region was not specified. A dynamic mesh was used so that the sectional model could move in vertical and torsional directions. Compared to results of a forced vibration wind tunnel test and analytical results, their simulations give similar results when estimating the self-excited forces, structural motions and the flutter derivatives. Furthermore, a 3D fluid-structure-interaction (FSI) simulation was performed to determine the critical flutter velocity. While the results have shown agreement with those from the wind tunnel test, there are some limitations to the work. The geometry was an idealised thin-plate section without handrails and barriers. A \"much coarser mesh\" was used than that in the 2D simulation, which could potentially compromise the accuracy of the results. Additionally, the wind field was conducted using a URANS simulation with the k-\(\epsilon\) turbulence model, which represents a compromise of accuracy in favour of simulation efficiency. [PERSON], [PERSON] and [PERSON] [64] suggest that the use of the k-\(\epsilon\) turbulence model could create excessive turbulent kinematic energy as wind makes contact with the bridge deck, which could substantially compromise the flow. It was also suggested that the k-\(\omega\) model and its variants are better for URANS simulations of flutter because the energy dissipation frequency \(\omega\) can maintain a nonzero value in the near-wall region which allows for direct integration in the viscous sublayer. A 2D URANS simulation was conducted on a rectangular cylinder with the standard k-\(\omega\) turbulence model. Instead of using wall functions at the boundary layer, they adopted a fine mesh that resolves the viscous sublayer. The 18 flutter derivatives of the 3-DOF system were derived from the simulations using the forced vibration method and good agreement was found compared to the wind tunnel results. [PERSON], [PERSON] and [PERSON] [65] emphasise that the application of an appropriate turbulence model is essential to the accurate estimation of aeroelastic forces.