# High-Speed Vehicles in Low-Pressure Tunnels--Influence of Choked Flows
## 2 Base Case  
The primary purpose of the base case is to investigate the overall aerodynamic behaviour of a possible configuration. Although the system necessarily satisfies the same laws of physics as conventional trains in tunnels, the actual outcomes in these two applications differ strongly. This is primarily because of the choking caused by the combination of high vehicle speed and a closed system. In real applications, the choked flow condition will exist for most of the journey unless significant compromises are made in addition to optimising vehicle shapes to delay the onset of choking--e.g., increased tunnel cross-section, reduced maximum speed, on-board compressors. The base case values of the key parameters of the tunnel and vehicle are listed in Table 1. Several of these are idealistic, but that can be rather helpful for base case specifications. Alternative values are considered in Section 3, the primary purpose of which is to clarify the relative importance of the many factors that designers need to consider. The tunnel is closed at both ends to enable low-pressure conditions to persist. The vehicle accelerates to maximum speed at a constant rate in 5 km, travels at this speed for 5 km, and decelerates to a halt at a constant rate in 5 km. The durations of these three periods are 50 s, 25 s and 50 s, respectively. In real histories, the early and late stages of acceleration and deceleration would need to be more gradual because rapid _rates of change in_ acceleration cause discomfort and disruption. Nevertheless, the chosen idealised history is broadly indicative of likely histories, and it has the advantage of being easy to use. Figure 1: Base case configuration: A single vehicle in a simple, closed tunnel. The vehicle nose is initially 250 m from one end of the tunnel, and, after travel, it is 150 m from the other end. The corresponding positions of the tail depend on the vehicle length. To accommodate these end regions, the tunnel length (15.4 km) is slightly longer than the total distance of travel (15 km). The listed numerical values of the skin friction coefficients of the tunnel and vehicle surfaces are nominal values at very large Reynolds numbers and the software automatically adjusts them to reflect actual flow states. The values are greater than those corresponding to totally smooth surfaces for which, at large Reynolds numbers, values of about \(f\approx 0.0015\) (\(\lambda\approx 0.006\)) would pertain. The relevance of the implied quasi-steady representation of skin friction is discussed in Section 3.1. The vehicle nose coefficient (zero) implies perfect streamlining and the tail coefficient is 0.4 \(\beta_{vth}\)\({}^{2}\), where \(\beta_{vth}\) is the vehicle:tunnel area blockage ratio. For the chosen blockage ratio of 0.5, the tail coefficient is equal to 0.1. Together, the chosen blockage ratio and maximum vehicle speed are responsible for the development of choked flow conditions that are the focus of this study. Other values of these parameters are considered later. Most other parameters in the Table are self-explanatory, but particular attention is drawn to heat transfer coefficients because some large changes in air temperature are inevitable. In a nutshell, large, rapid _proportional_ changes in absolute air pressure necessarily imply large, rapid proportional changes in absolute temperature. Heat transfer processes at the vehicle and wall surfaces influence the consequences of this effect. The rates of such processes depend upon the balance between (i) convection in the air and (ii) conduction in the walls. Special attention to this effect is reserved until Section 3.2, in which (i) the heat transfer processes at the tunnel and vehicle surfaces are described and (ii) comparisons are made with outcomes based on adiabatic conditions at these surfaces. In the base case, heat transfers exist at both surfaces.