## 3 Unsteady Flow Analysis  
Figure 6 shows the snap-shot of velocity magnitude contours at the central vertical plane for both cases. In both cases, results can be seen a significant reduction in the velocity magnitude is induced in the first bogie under the body and the separated flows cover the downstream coaches behind the TC-car. However, the flow pattern upstream and downstream of the train is slightly different between the two cases: disturbed velocity fluctuations exist in more upstream and downstream directions for the tunnel case. These results can be understood as the disturbances occurring around the vehicle body are more trapped in the tunnel than in the open field. Figure 7 shows the instantaneous static pressure field on the same plane for both cases as Figure 6. It can be seen in Figure 7a for the open-field case that the compressible acoustic pressure waves propagate from the train bodies, and the primary aeroacoustic sources are the bogies, pantographs, inter-coach gaps, and roof fairings. However, for the tunnel case in Figure 7b, the acoustic pressure waves generated from the train are confined by the tunnel and seem to form a more complex pattern due to their interaction with the hydrodynamic fluctuation. These differences are more highlighted in Figure 8, which shows the instantaneous iso-contours of pressure fluctuations \(p^{\prime}\) defined as \(p-\overline{p}\) on the horizontal plane at the height of 1.5 m from the ground and at the central vertical plane. The circular radiation patterns of the compressible acoustic pressure waves from the well-known aerodynamic noise sources, such as bogies, pantographs, and inter-coaches were more clearly visible in the open-field case. However, in the tunnel case, those patterns seemed to be more complex due to the interaction of acoustic pressure waves with the tunnel wall and the hydrodynamic field. Figure 6: Snap-shot of iso-contours of flow velocity magnitude for a train (**a**) in open-field at t = 1.12 s and (**b**) in tunnel at t = 1.22 s.  
For more quantitative analysis, the pressure coefficient defined as  
\[C_{p}=\frac{p_{\infty}-\overline{p}}{\frac{1}{2}\rho U^{2}} \tag{11}\]  
where \(p_{\infty}\) is the upstream pressure, \(\overline{p}\) is the time-averaged static pressure, \(\rho\) is the air density, and \(U\) is the train speed, is computed on the train surface. Figure 9a,b show the distributions of the computed pressure coefficient on the lines where the train surface meets the planes of y = 0 and z = 1.107 m, respectively, for the train in the open field. The monitored lines are also depicted using the red- and blue-colored lines and the black-colored lines on the train surface. There is the most significant variation in the pressure  
Figure 8: Instantaneous pressure fluctuation contours of (**a**) open field at t = 1.12 s and (**b**) tunnel cases at t = 1.22 s.  
Figure 7: Snap-shot of iso-contours of static gauge pressure for a train (**a**) in open field at t = 1.12 s and (**b**) in tunnel at t = 1.22 s.  
distribution around the train head because the flow decelerates in the vicinity of the stagnation point of the train head nose and again accelerates in the downstream direction along the surface of the train head. The process is reversed for the flow around the train tail, with a negative peak followed by a positive peak. It can also be seen that the parts where the significant pressure variation occurs match the vital source regions, as shown in Figure 8a. In the upper side of the train, as shown in Figure 9a, the substantial variations in the pressure coefficient occur around the following parts: the front nose and HVAC boxes of the TC-car, the pantograph and the HVAC box of the M1-car, the HVAC box and pantograph of the M'3-car, and the HVAC boxes of the TC2-car. Significantly, the pressure variation on the rear part of the M'3-car is as high as that of the train head because the pantograph goes up, thereby manifesting the most contributing aerodynamic noise source.