## 3 Aeroelasticity and Aerodynamics of Cable-Supported Bridges
### Flutter-Aeroelasticity of the Deck
#### 3.1.3 CFD Studies of Flutter
In the ALE-VMS method, the turbulence is computed similarly to that in LES, where large-scale eddies are fully resolved, and subgrid eddies are modelled. Hence, the turbulence behaviour can be reflected with satisfactory accuracy. However, their computational domain is a slice of the wind tunnel they are comparing and only contains a limited number of cells in the transverse direction. While this saves on computational power, it is arguable whether it is accurate enough in terms of the spatial discretisation since they did not provide any sensitivity study to justify their choice of the computational domain and mesh. Combined with nonpenetration boundary conditions configured at walls, their computational domain might limit the development of the flow in the transverse direction, which could possibly influence the accuracy of the results of the 3D simulations. [PERSON], [PERSON] and [PERSON] [68] performed a flutter analysis using forced vibration numerical simulations on twin-box girders. Two-dimensional URANS simulations were conducted with the k-\(\omega\) SST turbulence model. Flutter derivatives were determined for girders with three different slot widths under different mean angles of attack. It was found that under zero mean angle of attack, the larger central slot width can effectively increase the critical flutter velocity. However, when considering the larger mean angle of attack, the presence of the central slot will significantly reduce the critical flutter velocity for torsional flutter. Increasing the slot width will further reduce the critical flutter velocity, making the deck more prone to torsional flutter. However, the simulations are only 2D and use URANS with an eddy-viscosity model and validation was only performed for a stationary bridge deck with steady-state wind tunnel tests in terms of mean streamwise velocity field. Comparisons between numerical results with flutter derivatives derived from aeroelastic wind tunnel tests were not presented which makes the findings potentially unreliable. Free vibration simulations [PERSON] and [PERSON] [61] appear to be the first to incorporate the free vibration method into CFD simulations. They performed 2D URANS simulations with the k-\(\omega\) SST turbulence model on three different geometries--an idealised thin-plate deck, a trapezoidal deck and a streamlined deck with lateral cantilevers. The simulation results of the thin-plate deck agree well with the analytical solution. However, when comparing the results of the other two geometries with the corresponding forced vibration tests, moderate discrepancies were found at high velocities. For the trapezoidal deck, the discrepancies were found in the flutter derivatives related to the heaving motions. It was suggested that this could be due to the larger mean angle of attack in the free vibration simulation due to high torsional moment coefficients at high wind velocities, which supports the findings of [PERSON] et al. [66]. For the streamlined deck, the discrepancies were mainly found in the flutter derivatives that are related to the coupling effect between torsional vibrations and vertical vibrations. It was suggested that this was due to the nonlinear nature of the aeroelastic forces which cannot be fully reflected in the commonly used linearised flutter theory. [PERSON], [PERSON] and [PERSON] [69] present frameworks for bridge aeroelasticity with a strong focus on nonlinearity. Their simulations were based on a 2D mesh although it is widely accepted that by its nature, turbulence tends to develop in three dimensions. Using a 3D turbulence model in 2D simulations will significantly influence the accuracy of the results [70].