# High-Speed Vehicles in Low-Pressure Tunnels--Influence of Choked Flows
## 2 Base Case
### Pressure  
Figure 2a shows pressure histories at key locations along the tunnel during and shortly after the vehicle journey. The chosen locations are at \(x/L_{tun}\) = 0, 0.25, 0.50, 0.75 and 1, where \(x\) denotes distance along the tunnel of length \(L_{tun}\). As is the usual practice for graphs of pressure variations in tunnels, the displayed values are expressed relative to ambient conditions. That is, unless the context implies otherwise, the word \"pressure\" is used herein to imply \((p_{abs}-p_{amb})\), where \(p_{abs}\) denotes the instantaneous, absolute, thermodynamic pressure and \(p_{amb}\) is the corresponding pressure in the initial, undisturbed conditions. The principal reason for this almost universal practice is that the focus of the study is usually on _changes_ in pressure caused by vehicle movements, not on absolute values per se. Consider first the pressure at \(x/L_{tun}\) = 0.25. This increases slowly at first and then at an ever-increasing rate until the vehicle passes by after approximately 43 s. This event is very short-lived (just over a quarter of a second). Thereafter, the pressure at this location is smaller than the original ambient pressure and it does not differ strongly from that at \(x/L_{tun}\) = 0. This illustrates an overall effect during most of the journey, namely to compress air ahead of the vehicle and to decompress air behind it. Similar behaviour is seen at \(x/L_{tun}\) = 0.50 and at \(x/L_{tun}\) = 0.75 except that, at the latter location, the later parts of the increase occur more slowly--because the vehicle begins to decelerate after 75 s. The pressure at the far end of the tunnel shows a seemingly different behaviour, but this does not imply any conflict. Indeed, the pressure begins to increase in much the same manner as at \(x/L_{tun}\) = 0.75 before, after reaching a peak at which it exceeds twice the ambient pressure, it falls atan even greater rate than the preceding increase. The root cause of the decrease is, of course, the deceleration of the vehicle. However, as at \(x/L_{tun}\) = 0.75, the early consequence of this is only a reduction in the rate of increase. In practice, the extra rapid decrease occurs because of a sudden change from choked to un-choked flow at the tail of the vehicle. That enables a strong backflow past the vehicle and into the region of much lower pressure behind it. This sudden release is easily seen at all locations behind the vehicle, albeit at successively later times (NB: waves travelling at sonic speed need over 45 s to traverse the whole tunnel). Figure 2b shows corresponding pressures at the nose (N) and tail (T) of the vehicle. In both locations, the suffix \"ann\" denotes the annulus alongside the vehicle and \"tun\" denotes the open tunnel ahead of and behind the vehicle. In 1-D simulations such as those used exclusively herein, these locations are on opposite sides of abrupt geometrical discontinuities, whereas, in physical reality, strong 3-D behaviour exists, and the transition is more gradual. When comparing \"ann\" values with physical measurements, it is common to locate measurement instruments a small distance from the ends of the vehicle. They should be in locations where it is believed that the flows will be approximately one  
Figure 2: Pressure histories in the tunnel and alongside the vehicle (base case), (**a**) tunnel, (**b**) vehicle. (\(x/L\) = proportional distance along tunnel. \(N_{tun}\), \(T_{tun}\) = small distances ahead of the nose and behind the tail. \(N_{sum}\), \(T_{ann}\) = in the annulus, small distances from the nose and tail). -dimensional or, at least, where plane pressure conditions will prevail. Typically, the smallest reasonable distances are in the order of one vehicle diameter from the geometrical ends of the vehicle. It is not normal to be able to have corresponding instruments at similar distances ahead of and behind vehicles. Instead, conditions are usually inferred from sensors located on the tunnel itself.