## 2 CFD Numerical Model
### CFD Validation  
In order to validate the accuracy and reliability of CFD simulation, the train aerodynamic coefficients are compared with the results of a 1/30 scaled moving wind tunnel model carried out by [PERSON] [42] and [PERSON] et al. [16] on account of the same shape of train and bridge model in the simulation. The scaled model experiment was conducted in the XNJD-3 wind tunnel with dimensions of 36.0 \(\times\) 22.5 \(\times\) 4.5 m, and the entire test system is composed of a train model, bridge model and driving system. Figure 4 displays the arrangements and details associated with the wind tunnel test, where the train consisting of three cars (head, middle and tail) is connected to the moving slider on the guideway by the bias connector to run on a bridge with the use of the motor driving system, and two wireless force transducers are placed inside the head and middle cars to collect the aerodynamic force time history of the train. In the experiment, the train steadily travels 15 m on the bridge at a constant speed ranging from 0 to 8 m/s, and the wind speed varies from 0 to 10 m/s. All test settings in the wind tunnel are identically applied in the validation.  
Figure 4: Diagram of a moving train wind tunnel test: (**a**) a moving train model arrangement; (**b**) side view of model details; (**c**) general layout of the test system.  
Figure 3: Overview of overset mesh.  
A great number of related works have demonstrated that the aerodynamic coefficient of a moving train can be determined by the resultant wind speed and wind yaw angle. As seen in Figure 5, through the geometric relation, the resultant wind speed \(V_{R}\) and wind yaw angle \(\beta\) on a moving train are able to be given by the speed vectors:  
\[V_{R}=\sqrt{\left(V+U\cos\alpha\right)^{2}+\left(U\sin\alpha\right)^{2}} \tag{3}\]  
\[\beta=\arctan\frac{U\sin\alpha}{V+U\cos\alpha} \tag{4}\]  
where \(U\) and \(V\) are the wind speed and train speed, respectively; \(\alpha\) is the angle between the cross wind and traveling line. Thus, the key aerodynamic coefficients of a moving train associated with crosswind stability can be defined as follows:  
\[C_{S}=F_{y}/\left(\frac{1}{2}\rho A_{y}V_{R}^{2}\right) \tag{5}\]  
\[C_{L}=F_{z}/\left(\frac{1}{2}\rho A_{z}V_{R}^{2}\right) \tag{6}\]  
\[C_{R}=M_{x}/\left(\frac{1}{2}\rho A_{z}hV_{R}^{2}\right) \tag{7}\]  
where \(C_{S}\), \(C_{L}\) and \(C_{R}\) are the train aerodynamic coefficients of the side force \(F_{y}\), lift force \(F_{z}\) and rolling moment \(M_{x}\), respectively; \(\rho\) is the air density; \(A_{y}\) and \(A_{z}\) are the train area in the \(y\) and \(z\) direction, respectively; \(h\) is the train height.  
Figure 6 shows the comparison results of the train's aerodynamic coefficients in the simulation and test. It should be noted that only side force results are given for the consideration that the lift force can be easily affected by the turbulence characteristics and complex structures underneath the train, and the rolling moment is usually determined by the side force. It can be seen from Figure 6 that the experimental and numerical results of the head car in the various yaw angles are in a good level of agreement, while several individual data in the middle car between the numerical calculation and wind tunnel test are slightly different. As a matter of fact, it cannot be expected to obtain exactly identical agreement in the comparison results owing to the turbulent flow. The maximum error between the simulation and test is about 7%, usually which is acceptable in CFD calculation. Consequently, the comparison results indicate the numerical model in this study can sufficiently fulfill the simulation of a moving train in a crosswind.  
Figure 5: Diagram of speed vectors and aerodynamic forces on a moving train.