# Effects of Tunnel and Its Ventilation Modes on the Aerodynamic Drag of a Subway Train
## 4 Discussion  
### Effects of Tunnel and Tunnel Ventilation Modes on \(\tau_{uu}\)  
Figure 10 compares \(\tau_{uu}\) inside the tunnel with that in the open air for both recirculation and free-cooling modes. The maximum \(V\) in the open air was about 15 m/s; thus, the measured \(\tau_{uu}\) in the open air is only available below this speed. The second order curve fit to the data in the open air is extrapolated to \(V=22\) m/s for comparison, as shown by the dashed line. The presence of the tunnel increases \(\tau_{uu}\), especially at a higher \(V\). At \(V=11.5\)m/s, \(\tau_{uu}\) in the tunnel exceeds that in the open air by 13.3% and 53.3% for the free-cooling and recirculation modes, respectively, and by 30.2% and 62.0%, respectively, at \(V=20.5\) m/s. [PERSON] [14] suggested for a high-speed train at \(V\approx 70\) m/s (250 km/h) that the presence of the tunnel increases the wall shear stress by a factor of \(1+2.21R\). If we take \(R=0.6\), the averaged blockage ratio along the present tunnel, the corresponding increase in \(\tau_{uu}\) should be 133%. An extrapolation of the data in Figure 9 to \(V=70\) m/s (not shown here) predicts the increase in \(\tau_{uu}\) by about 118% and 179% for the free-cooling and recirculation modes, respectively, which agrees with [PERSON]'s formula. Interestingly, the tunnel ventilation mode also has a remarkable effect on \(\tau_{uu}\). The \(\tau_{uu}\) in the recirculation mode is significantly larger than that in the free-cooling mode; for example, the former exceeds the latter by 35.2% and 27% at \(V=11.5\) m/s and 20.5 m/s, respectively. Several previous investigations on a fully developed turbulent boundary layer [27; 28; 29] unveiled that the wall shear stress grew with the increasing free-stream turbulence intensity \(Ti\) (\(=u_{rms}/U_{\infty}\), where \(u_{rms}\) is the root mean square value of the fluctuating streamwise velocity and \(U_{\infty}\) is free-stream velocity). This observation is linked  
Figure 10: Averaged wall shear stress \(\tau_{uu}\) in the two ventilation modes and in the open air. to the fact that the increased turbulence intensity promotes lateral momentum transport, and the random fluctuation carries more fast-moving fluid from the outer layers into the near wall region, thus increasing the velocity gradient at the wall. [PERSON] (1983) pointed out that a 6% increase in the nominal turbulence intensity resulted in as much as a 20% increase in the wall shear stress, compared to that in smooth flow. In the present measurement, _Ti_ in the tunnel at the recirculation mode was obviously higher than in the free-cooling mode, because the lateral injection of cooled air enhanced flow disturbance inside the tunnel. Therefore, the increase in \(\tau_{uu}\) in the recirculation mode (Figure 10) is essentially caused by the enhanced _Ti_ inside the tunnel. Figure 11 presents the dependence of the friction coefficient \(C_{f}\) on \(V\) in the two ventilation modes and the open air. The data in the open air are extrapolated to \(V=22\) m/s, as indicated by the dashed line. For the range of \(V\) examined, \(C_{f}\) falls in the range of 0.001 to 0.006, as proposed by [PERSON] [2]. In all cases, \(C_{f}\) drops with increasing \(V\) and approaches gradually its asymptotic value. The observation is qualitatively similar to the well-known skin friction law for an incompressible turbulent boundary layer. Compared with the open-air case, \(C_{f}\) in the tunnel increases by 30.2 % and 66.2 % at \(V=11.5\) m/s and 27.9% and 76.5% at \(V=20.5\) m/s for the free-cooling and recirculation modes, respectively. Note that the difference in \(C_{f}\) between the free-cooling mode and the open air shrinks with decreasing \(V\), down to approximately zero at \(V\leq 5\) m/s. That is, the tunnel effect on \(C_{f}\) completely vanishes at low \(V\) if no additional turbulence is introduced. On the other hand, the recirculation mode, which introduces additional turbulence, has a considerable effect on \(C_{f}\) even at low \(V\).