## 3 Aeroelasticity and Aerodynamics of Cable-Supported Bridges
### Flutter-Aeroelasticity of the Deck
#### 3.1.3 CFD Studies of Flutter
Three-dimensional LESs were conducted using the dynamic Smagorinsky subgrid model and 2D URANS simulations were conducted based on the k-\(\omega\) SST turbulence model to study how different turbulence modelling techniques can affect the results of flutter derivatives derived from numerical simulations. In general, results of both the 2D URANS simulations and the 3D LESs were in good agreement with the experimental data, although the LESs provided a closer match to the experimental results. However, compared to the experimental data, discrepancies were found in two damping-related flutter derivatives derived from both the LESs and the URANS simulations. By studying the distribution of pressure amplitudes and pressure phase angles, large differences between URANS results and experimental results were found to be caused by the limitation of the URANS method in the representation of flow separation. This finding suggests that the use of 2D URANS simulations with the k-\(\omega\) SST turbulence model might not be suitable to accurately identify flutter derivatives. However, the comparison was not extended to include the application of other eddy-viscosity models and Reynolds stress models in the URANS method, which might provide some insights into the topic. It was also found that the discrepancies between the LES results and the experimental results were caused by the larger separation bubbles in the simulations, which is suggested to be a result of the smooth incident flow condition used in the LESs. Furthermore, it was shown that the LESs consumed more than 10 times the CPU hours of the 2D URANS simulations. In addition, 3D URANS simulations were not conducted which might be more computationally affordable than LESs and provides better results than 2D URANS simulations. [PERSON], [PERSON] and [PERSON] [66] performed a series of 2D URANS simulations to study the dependence of flutter derivatives on various factors. A comparison was made between an eddy-viscosity model, the one-equation Spalart-Allmaras model, and a Reynolds stress model, the linearised explicit algebraic (LEA) model. It was found that the Reynolds stress model delivered slightly better results than the Spalart-Allmaras model. By comparing these results to the experimental results from a free vibration test, large discrepancies were found at high velocities in the values of the two flutter derivatives related to aerodynamic damping. These discrepancies were caused by the difference in the mean angles of attack used in the simulations and in the wind tunnel tests. After replacing the mean angle of attack in the simulations by the value used in wind tunnel tests, the discrepancies were almost eliminated. The study was further extended to compare two different configurations of the bridge deck section--a smooth edge with a rounded shape and a sharp edge that had a higher bluffness. By incorporating both geometries into the simulations, it was found that the smooth-edge geometry with a large mean angle of attack had similar flutter derivatives to the section of the sharp-edge geometry. The author also emphasised the important role of the Reynolds number on flutter derivatives and found that bridge decks might have a dramatic change in flutter derivatives within Reynolds number range of \(1\times 10^{6}\) to \(5\times 10^{6}\). When increasing the Reynolds number up to \(1\times 10^{8}\), the effect of negative aerodynamic damping tended to decrease. Therefore, it was necessary to include high-Reynolds number wind tunnel tests in the experimental measurement of flutter derivatives. Similarly, [PERSON] et al. [67] identified flutter derivatives through a series of 3D forced vibration simulations based on the ArbitraryLagrangian-Eulerian Variational Multiscale (ALE-VMS) formulation of the Navier-Stokes equations for incompressible flows, which offers a convenient FSI framework based on the finite element approach.