# High-Speed Vehicles in Low-Pressure Tunnels--Influence of Choked Flows
## 2 Base Case
### Pressure
In the case of the extended wake region behind the tail, relevant distances are greater, typically a tunnel diameter in unchoked cases and potentially much greater in choked flow cases. It is constructive to consider first the continuous lines denoting pressures at \(N_{tun}\) and \(T_{tun}\), because these can be compared directly with values in Figure 2a as the vehicle passes \(x/L_{tun}=0.25\), \(0.50\) and \(0.75\). Values just before vehicle-passing correspond to pressures just ahead of the vehicle and values just after passing correspond to pressures just behind it. Although these _quantitative_ comparisons can be made from these figures only at the times of vehicle passing, some _qualitative_ comparisons are also possible. In particular, the pressure history at \(T_{tun}\) exhibits a loose family resemblance to histories in the tunnel after vehicle passing. Likewise, the history at \(N_{tun}\) loosely resembles that at the closed end of the tunnel. Attention is drawn to this because, in part, it is a consequence of the semi-independent behaviour of flows upstream and downstream of the choked section at the tail of the vehicle. Next, consider the broken lines showing pressures in the annulus alongside the vehicle. At the front of the vehicle, the history mimics the pressure just ahead of it, except for a strong reduction caused by the venturi-like behaviour of flows relative to the vehicle. Since the nose loss coefficient in the base case is zero, the stagnation pressure relative to the vehicle does not change across the nose and so variations in the differences between these two graphs give an approximate indication of the rate of flow (relative to the vehicle). By inspection, the changes occur quite slowly. A very different outcome is seen at the tail of the vehicle. Although some trends during early and late stages of the journey are consistent with those at the nose, the behaviour during a large part of the journey is fundamentally different. Indeed, for a considerable period of time, the pressure in the annulus at the tail actually exceeds that behind the vehicle. This seemingly anomalous behaviour occurs during the period when the flow is choked (approx. 28 s to 108 s). Before and after this period, all flow parameters vary continuously when considered from a 3-D standpoint even though, in the 1-D representation, the tail is treated as a geometrical discontinuity. In contrast, during the period of choked flow, even 3-D interpretations involve a discontinuity that, in the base case, is a normal shock at the rear of the annulus. Across this, the mass flow rate and stagnation temperature are continuous, but the specific entropy and stagnation pressure are discontinuous. After choking occurs, further increases in the vehicle speed have only a small influence on velocities relative to the vehicle at the rear of the annulus, but the pressure increases strongly. For moderate increases in speed, the wake region behind the vehicle is broadly similar to wakes behind unchoked vehicles, but sufficiently large increases cause the wake to behave as a succession of oblique shocks forming a diamond-like pattern. These changes might be of little consequence in tunnels with very small ambient pressures, but they can be important in less fully evacuated tunnels because they cause strong increases in aerodynamic drag. One consequence of this is that the maximum acceptable speeds in higher pressure tunnels tend to be smaller than those in more strongly evacuated tunnels. For completeness, it is noted that the onset of choking can be delayed by ducting flow through the vehicle itself, using a compressor--e.g., [PERSON] et al. (2019) [2], [PERSON] et al. (2021) [3]. Compressors can also be used to promote lift forces by enhancing flow rates beneath the vehicles. However, no consideration is given to these possibilities herein.