# Train-Induced Unsteady Airflow in a Metro Tunnel with a Ventilation Shaft
###### Abstract  
To ensure only one train operates in each ventilation section within an extra-long tunnel, a ventilation shaft was typically installed to divide the entire tunnel into multiple sections. Given the crucial role of piston wind in the metro tunnel environment and ventilation, a deeper understanding of train-induced unsteady airflow in a metro tunnel with a ventilation shaft is desirable. This study uses the unsteady flow theory of the Bernoulli equation to mathematically model piston wind in metro tunnels both with and without ventilation shafts. The influence of various shaft parameters on piston wind development is systematically analyzed. The results indicate that the shaft significantly impacts the piston wind. The maximum piston wind speed and ventilation rate in tunnels with ventilation shafts surpass those in tunnels without them. Moreover, shaft location and the cross-sectional area notably affect the maximum piston wind speed, ventilation rate, and airflow in the shaft, whereas shaft height has no significant effect. It is found that a ventilation shaft with a larger cross-sectional area positioned in the middle of the tunnel enhances the performance of piston ventilation. piston effect; ventilation shaft; theoretical model; piston wind speed; ventilation rate +
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piston wind by establishing theoretical models for the calculation of piston wind. With the development of computational fluid dynamics (CFD) technology, the CFD technique has become more and more popular with scholars to help analyse the piston wind induced by train motion [15; 16]. [PERSON] et al. [17; 18] used a CFD simulation to explore piston winds in subway tunnels with natural ventilation ducts. The ventilation performance of various ventilation strategies (with different ventilation duct structures and partition geometries) is compared and analyzed [19]. [PERSON] et al. [20] conducted numerical simulations to investigate the airflow dynamics induced by train movement in single- or double-track tunnels. Their study revealed that the airflow velocity in narrow single-track tunnels was significantly higher than that in double-track tunnels. [PERSON] et al. [21] employed a CFD model incorporating dynamic grid technology to numerically simulate the airflow induced by a train in a subway station. The findings indicated that air circulation escalated with the augmentation of both the blockage rate and train speed. Using CFD simulations, [PERSON] et al. [22] found that the ventilation airflow induced by train movement inside the tunnel significantly increased with the increase in the blockage ratio. Furthermore, the effects of piston wind on the environment and energy consumption of subway tunnels [23], the performance of jet fans [24], and smoke propagation characteristics [25; 26] are also addressed by some other researchers. The above studies mainly focus on the piston wind generated by the train in the tunnel without ventilation shafts. Ventilation shafts are usually installed in some long tunnels, which possibly have an important impact on the ventilation performance of the tunnel. With respect to this regard, [PERSON] et al. [27] measured the periodic airflow induced by the piston effect in ventilation shafts of a subway station in Taipei, China. They found that the piston effect causes some air exchanges inside the tunnel through the ventilation shafts. However, the cross-sectional area of the shaft was found to be less important in enhancement of the piston effect and air exchange. [PERSON] et al. [28] used three-dimensional numerical simulation to explore the influence of the shaft position on the ventilation performance of subway tunnels. Through the analysis of the ventilation flow rate through the shaft and the flow field in the tunnel nearby the shaft, the results suggested that the ventilation shaft be installed near the station. [PERSON] et al. [29] studied the energy-saving effect of natural ventilation by utilizing the newly built shafts in a super-long highway tunnel.