## 3 Aeroelasticity and Aerodynamics of Cable-Supported Bridges
### Rain-Wind-Induced Vibration--Aeroelasticity of the Cable System
#### 3.3.3 CFD Studies of Rain-Wind-Induced Vibrations  
Despite the progress achieved using wind tunnel tests to reproduce RWIVs, the underlying mechanism of RWIVs is still not fully understood, and so validation of numerical models of RWIVs is challenging. However, there have been some attempts to apply CFD simulations to investigate RWIV. One of the most significant merits of using CFD simulations is that the rainwater can be fully controlled and parameters such as the size, velocity and pressure of the raindrop can be simulated. [PERSON], [PERSON] and [PERSON] [96] developed a 2D numerical model based on lubrication theory in fluid mechanics, in which rainwater forms a thin film on the surface of the stay cable. They have performed two numerical simulations based on their water film model to study the effects of friction and pressure on the formation of the water rivulets. These showed that the friction has a significant influence on the generation of water rivulets, which is in good agreement with the result of a prior wind tunnel test. [PERSON] et al. [97] tried to develop the water-film model into a 3D model. However, they neglected the wind effect on the water flowing in the z-direction and the change of water film geometry, which indicates that their study is still 2D. Additionally, this water film model, which is based on lubrication theory, is not ideal for the study of RWIVs since it assumes the thickness of the water on the cable is very small. Using such an assumption might lead to an underestimation of the effect of geometry change in thickness direction on RWIVs. [PERSON] et al. [98] developed a theoretical model based on a quasi-steady assumption and suggested the onset of RWIV might be related to the initial position of water rivulets. However, [PERSON] et al. [99] suggest that applying the quasi-steady assumption in simulations of RWIV will lead to poor estimation of aerodynamic effect on the structure due to the neglection of unsteadiness of the fluid. To solve such problems, they used results of wind tunnel tests to modify the quasi-steady simulation and developed a semiempirical model that can linearise the unsteady characteristics of fluid motions. To save computational power, [PERSON] et al. [100] applied a hybrid method of free oscillation wind tunnel tests and CFD simulations, in which structural motions were recorded from the wind tunnel test and configured as boundary conditions for the simulation. Three-dimensional URANS simulations with the k-\(\omega\) SST turbulence model were performed to determine the aerodynamic forces acting on the cable. The study showed good agreement in terms of the displacement of vibrations with experimental results. However, since the water rivulet was treated as a solid attachment in the simulation, large discrepancies with experimental results were found in results of cable responses under specific wind conditions, which indicated the importance of considering the shape effect of the water rivulet. [PERSON] and [PERSON] [101] investigated the effect of the rivulet position on RWIVs using 3D FSI simulations. The motions of the solid and fluid were coupled by a multistage numerical scheme. A dynamic mesh was configured with the spring-damper-mass model that enables linear oscillation of the cable. The fluid part of the FSI simulation was solved by LES with the Smagorinsky subgrid model. The geometry used in the simulations was a cylindrical cable. To save computational power, the upper rivulet was simplified into solid arc attachments on the surface of the cable. A baseline simulation without the rivulet attachment was conducted and compared with a wind tunnel test. The comparison showed good agreement between computational results and experimental results in terms of aerodynamic forces acting on the cable surface. The attachment of the rivulet was placed in multiple positions defined by position angles on the cable surface. It was found that the 45\({}^{\circ}\) position angle triggered an RWIV with the largest amplitude.