# Effects of Tunnel and Its Ventilation Modes on the Aerodynamic Drag of a Subway Train
As such, the averaged pressure on the forward surface was linearly related to the front stagnation pressure (\(P_{p}\)). They further noted that the pressure magnitude on the forward surface was much larger than that on the backward surface, implying that \(D_{p}\) could be estimated from the pressure on the forward surface. [PERSON] ascribed this observation to the very large length-to-width ratio of a train, pointing out that the tail end was completely immersed in the thick boundary layer developing along the train [2]. The direct measurement of \(\tau_{w}\) is more challenging than \(D_{p}\). The boundary layer over a train develops; it is highly three-dimensional with an increasing thickness along the train [8]. The \(\tau_{w}\) can be determined from the mean velocity profile based on a Clauser chart, which assumes a logarithmic mean velocity distribution in the boundary layer [9]. [PERSON] and [PERSON] [10] measured the velocity distribution in the boundary layer on a 1:75 scale train model using hot film anemometry. Their estimated \(\tau_{w}\) based on a Clauser chart gave a local wall friction coefficient C\({}_{f}\)(\(\equiv\tau_{w}/0.5\rho V^{2}\), where \(\rho\) is density of air) of 0.0039. The measurement of the velocity distribution on a full-scale train during routine operation is more difficult. Using a Preston tube [11; 12], which is essentially a Pitot tube placed on the wall facing the flow, [PERSON] and [PERSON] [10] measured C\({}_{f}\) for a full-scale passenger train and obtained a C\({}_{f}\) range of 0.002-0.004. It is worth mentioning that C\({}_{f}\) may vary remarkably depending on the train surface conditions and the gaps between carriages. [PERSON] [2] summarized the reported \(C_{f}\), suggesting a range of 0.001-0.006. However, [PERSON] and [PERSON] [13] suggested that \(C_{f}\) could reach 0.01 for a freight train with irregularly arranged carriages. The present railway system involves more and more tunnels for various reasons, such as environmental considerations, scarcity of free flat space in urban areas and the desire for straighter tracks for high-speed operation [1; 2]. Aerodynamic drag on a train in a tunnel can significantly exceed its counterpart in open air. Consequently, a train in a tunnel requires much more power and incurs more traction energy consumption than in the open air. The tunnel effects on the aerodynamic drag on a train depend primarily on the ratio of the cross-sectional area of the train to that of the tunnel, i.e., the blockage ratio (\(R\)), the lengths of the tunnel and the train, and the presence of air shafts. [PERSON] [14] suggested that \(D_{f}\) rose in a tunnel, compared to that in the open air, by a factor of 1 + 2.21 \(R\) for a high-speed train with \(V\) > 34.7 m/s (\(\approx\)125 km/hr). [PERSON] [8] found that this factor decreased with an increasing train length and was almost independent of the train speed for \(R\approx\) 0.1-0.2. However, [PERSON] [3; 4] cautioned that the tunnel effects might not be conclusively determined because many factors could contribute to the drag on a train in the tunnel. Most previous investigations of the tunnel effects on the aerodynamic drag were performed for high-speed trains, since aerodynamic drag on a train is approximately proportional to the square of train speed (\(V\)) and accounts for 75-80% of its total resistance for \(V\) = 250-300 km/h [5]. Most of these studies focused on the pressure waves induced by a high-speed train when it passes through a tunnel [15], which may deteriorate the comfort of passengers and cause additional load on the tunnel and its appurtenances, e.g., catenary system, cables, etc. Due to an increase in the subway train speeds and a large blockage ratio, the aerodynamic issues of the tunnels in subway systems attracted more and more attention [16; 17; 18]. A number of investigations, including field test, moving model experiments and numerical simulations, have been conducted on the pressure load on platform screen doors (PSDs) imposed by passing subway trains [17; 18; 19].