Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-011-1237-7 A numerical simulation of train-induced unsteady airflow in a tunnel of Seoul subway Yuandong Huang 1,3, Tae Hyub Hong 2 and Chang Nyung Kim 3,4,* 1 Department of Environmental Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China 2 Department of Mechanical Engineering, Graduate School, Kyung Hee University, Yongin 449-701, Korea 3 College of Engineering, Kyung Hee University, Yongin 449-701, Korea 4 Industrial Liaison Research Institute, Kyung Hee University, Yongin 449-701, Korea (Manuscript Received January 8, 2011; Revised September 26, 2011; Accepted December 20, 2011) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract This study has been conducted to investigate numerically the characteristics of train-induced unsteady airflow in a subway tunnel. A three-dimensional numerical model using the dynamic layering method for the moving boundary of a train is applied. The validation of the present study has been carried out against the experimental data obtained by Kim and Kim [1] in a model tunnel. After this, for the geometries of the tunnel and subway train which are very similar to those of the Seoul subway, a three-dimensional unsteady tunnel flow is simulated. The predicted distributions of pressure and air velocity in the tunnel as well as the time series of mass flow rate at natural ventilation ducts reveal that the maximum exhaust mass flow rate of air through the duct occurs just before the frontal face of a train reaches the ventilation duct, while the suction mass flow rate through the duct reaches the maximum value just after the rear face of a train passes the ventilation duct. The results of this study can be utilized as basic data for optimizing the design of tunnel ventilation systems. Keywords: Dynamic layering method; Moving boundaries; Numerical simulation; Train-induced flow; Tunnel ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Investigation of train-induced unsteady airflow in a subway tunnel is essential for optimizing the design of both natural and mechanical ventilation systems. With the development of computational fluid dynamics (CFD) and with the advent of ever increasing computer power, it has already been possible to utilize CFD technology to analyze problems involved in airflow in subways. For example, Yuan and Yu carried out a CFD simulation, through simplifying the transient airflow to steady process, to evaluate the time-averaged velocity and temperature in a side-platform station [2]. Ke et al. combined the SES (subway environmental simulation) program with the PHOENICS to carry out simulations for optimizing the design of subway environmental control system, and they examined specifically the influence of train velocities on the pressure distribution in a station area [3]. Kim and Kim performed a numerical analysis on the train-induced airflow in their experimental model tunnel [1]. One of the main difficulties in developing the numerical This paper was recommended for publication in revised form by Associate Editor Jun Sang Park * Corresponding author. Tel.: +82 31 201 2578, Fax.: +82 31 202 8106 E-mail address: cnkim@khu.ac.kr KSME & Springer 2012 method for simulating train-induced airflow in a subway tunnel is how to model the moving boundaries of a train (an immersed solid). There have been two methods developed to model the moving boundaries of an immersed solid: the moving grid method and the fixed grid method. The application of moving grid method is closely related to the formation of a grid system. For the analysis of a flow field with a train moving in a tunnel, the chimera grid system, the patched grid system, and the adaptive remeshing grid system were used [3]. The fixed grid method can be divided into the diffuse interface method and the sharp interface method [4, 5]. Using the sharp interface method, Kim and Kim have recently carried out a numerical analysis of train-induced unsteady airflow inside their experimental model tunnel [1]. In a subway, the airflow in a ventilation duct is greatly influenced by the train-induced tunnel flow. If a ventilation opening is located at an appropriate position, the natural ventilation can be accomplished by the piston effect caused by the moving train in the subway tunnel. Although there have been studies on underground tunnel ventilation associated with the piston effects caused by train motion, yet the conditions such as the geometric dimensions of tunnels and subway train as well as the train run schedules are different from those in Seoul subway [6]. Especially, there has not been any research
786 Y. Huang et al. / Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 report on analyzing quantitatively the train-induced unsteady airflow in tunnel space with a natural ventilation duct in a real situation. Therefore, it is necessary to conduct research on the three-dimensional unsteady airflow in a tunnel so as to provide basic data for optimizing the design of tunnel ventilation system and for the analysis of other environmental issues related to the train-induced flows (such as the evaluation of particle movement and the distribution in a tunnel, and the determination of appropriate position for dust control filters in a tunnel). The aim of the present work is to investigate numerically the characteristics of train-induced unsteady airflow in a tunnel in a real situation. In the present study, a numerical model using the dynamic layering method for the moving boundary of a train is firstly developed, and then is validated against the experimental data obtained from Kim and Kim in a model tunnel [1]. After this, for the geometries of the tunnel and subway train which are very similar to the Seoul subway, a three-dimensional unsteady airflow is simulated. The numerical results are analyzed to elucidate the tunnel flow features mainly in terms of pressure and air velocity distributions in the tunnel space near a natural ventilation duct as well as to reveal the impacts of train motion on the suction and exhaust of airflow in a natural ventilation duct. 2. Problem formulation and numerical simulation setup 2.1 Numerical model The computational models are constructed based on the geometries of Seoul subway and the velocity and pressure are solved using the CFD code FLUENT6.3.26. The governing equations for unsteady airflow are the continuity equation, Reynolds-averaged Navier-Stokes (RANS) equations, and standard κ ε model. The governing equations are discretized on finite-volumes. The PISO algorithm is applied to solve the pressure-velocity coupling. The second-order upwind scheme is employed for the discretization of convection-diffusion terms. As to the pressure corrective equation, the PRESTO scheme is used. This is a method of pressure interpolation which is similar to that used in the staggered grid schemes used with structural mesh [7]. The PRESTO scheme provides improved pressure interpolation in situations where the large pressure gradients exist. For unsteady analysis, the time derivatives are discretized using the first-order implicit scheme. For modeling the moving boundaries of the train, the dynamic mesh model is adopted. In FLUENT6.3.26, three groups of mesh motion methods are available to update the volume mesh in the deforming regions subject to the motion defined at the boundaries: smoothing methods, dynamic layering, and local remeshing methods (see FLUENT 6.3 User s Guide). Considering the characteristics of train motion in a subway tunnel, the dynamic layering method is employed in this study. With the dynamic layering method layers of cells Fig. 1. Schematic diagram of experimental layout (Kim and Kim, 2007). Fig. 2. Schedule of train run (Kim and Kim, 2007). adjacent to the boundaries of a computational domain can be created or removed based on the size of the layer adjacent to the above boundaries in association with the motion of a movable block of grids. Therefore, with the motion of a train the update of the volume meshes is handled by the FLUENT at each time step. 2.2 Model validation The validation of the present CFD calculation has been performed against the experimental study in the model tunnel carried out by Kim and Kim [1]. Fig. 1 shows a schematic diagram of the experimental layout. The model tunnel was built to be 1/20th scale of a subway tunnel. The model tunnel is 39 m long, 250 mm high and 210 mm wide. The train is 3 m long, 225 mm high and 156 mm wide. The blockage ratio of the train to the tunnel is approximately 0.67. The train is connected by the cable to the front and the back, and moves on the guide rail forwards or backwards. The speed of train is controlled by a drive motor equipped with an electrical inverter. The distance of the train run is 33 m. Two velocity transducers are installed 0.5 m inside the tunnel inlet and outlet,and four pressure transducers are installed at 8.5 m, 15.5 m, 23.5 m, and 30.5 m, respectively, from the tunnel inlet located in the left along the center line of the model tunnel roof. Both the velocity and pressure measurements are recorded at the time interval of 0.1 s. The velocity of the model train run is shown in Fig. 2. After the train velocity is increased to 3.0 m/s at the rate of the acceleration of 1.0 m/s 2, it runs at a constant speed of 3.0 m/s for 8 seconds. Then the train velocity is decreased to stop at the rate of the acceleration of 1.0 m/s 2. The maximum train speed U T_MAX is 3.0 m/s, and the Reynolds number based on the hydraulic diameter of the model tunnel and U T_MAX is 4.9 10 4. Employing the geometric configurations and train-run velocity used in the experimental test, Kim and Kim also con-
Y. Huang et al. / Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 787 Fig. 3. Comparison of C p variations between experimental and numerical results at position of PT1. Fig. 4. Cross sections of the tunnel and of subway train for a Seoul subway (not in scale). ducted a numerical analysis on the train-induced unsteady airflow inside the model tunnel [1]. In their numerical simulation, the air velocity and pressure were solved using the commercially available CFD software CFX4, and the sharp interface method in a fixed grid system was adopted to model the moving boundaries of the train. To evaluate the accuracy and applicability of the current numerical method, we also performed a numerical simulation on the case with the same geometric configurations and trainrun schedule as those of the model tunnel experiment. In the calculation of this test case, the time step is set to be 0.005 s. The grid size in the longitudinal direction (x axis) in the tunnel is set to be 0.03 m. In the cross-section of the tunnel (i.e., the y-z plane), the grid size is set to be 0.02 m in both y and z directions except for in the narrow gap between the surface of train and the tunnel walls, where fine grids are distributed. Initially, the entire computational domain consists of 334,400 hexahedral cells. The current numerical method is quite different from that used by Kim and Kim in modeling the moving boundaries in association with the train motion [1]. In the numerical method proposed by Kim and Kim, the grid system is fixed during the whole computation process and the moving boundary is modeled by the shape interface method, which represents the effect of train motion through changing the grid feature of the fluid into that of solid in the front of the train and changing reversely in the rear of the train in association with the train motion [1]. In the current numerical method, however, a block of grids including a train is sliding on non-moving blocks of grids at each time step based on the actual motion of the train. Thus, the moving boundaries of the train (i.e., the train surface) can be accurately tracked during the simulation by using the current numerical method. Fig. 3 shows the comparison among the numerical and experimental results obtained by Kim and Kim and the current numerical results of the variations of pressure coefficient C p 1 2 ( Cp = p/ ρut MAX where p is the pressure) with time at 2 the position of the first pressure transducer (PT1) [1]. The qualitative behaviors of the numerical results obtained by Kim and Kim agree well generally with those of the experimental Fig. 5. Geometry of the ventilation ducts connected to the tunnels (side view, not in scale). results [1]. However, there are large discrepancies in C p variations during the period of constant train speed after the train passes the transducers. From this figure, it can be seen clearly that the present numerical results of C p variations with time are in a good agreement with the experimental data through the whole time period (0-20 s). At the other positions of the pressure transducers, and at the two positions of the velocity transducers the current numerical results are quite agreeable with the experimental results. Obviously, it can be revealed from the comparisons between the current numerical and experimental results that the current numerical method is applicable for modeling the traininduced unsteady airflow inside a subway tunnel. 2.3 Numerical simulation setup We use the above validated CFD model to investigate the characteristics of train-induced unsteady airflow in a tunnel of Seoul subway. The subway line selected for the present case study is of two-way tunnel. The cross sections of the tunnel and of the subway train are illustrated in Fig. 4. The tunnel is divided into two ways and the ventilation ducts are connected to the tunnel ceiling (see Fig. 5). In this simulation, we only consider the case where a train is running in one way and there is no train in another way. As is shown in Figs. 6 and 7, the three dimensional computational domain includes both the station zones (excluding the station platform over the platform-screen doors installed in the station
788 Y. Huang et al. / Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 250m 1 370m 500m (Inlet part for grid sensitivity analysis) 1 Fig. 9. Zone for grid sensitivity tests (not in scale). Fig. 6. The 3D computational domain (the red block represents a train). Fig. 7. Front-view of the station zones and the tunnel (not in scale). Fig. 10. Velocity profile of train run for grid sensitivity tests. As for the boundary conditions, the pressure is given to be zero at the ground openings of the six ventilation ducts and at the left and right side of the tunnel zone. The air velocity is set to zero at the walls of the tunnel and ventilation ducts. Also, the velocity of air in contact with the train surface is the same as that of the train. Fig. 8. Variations of train velocity with time. platform) and the tunnel zone. The length of the two-way tunnel is 1.14 km. The station zones located at the both ends of the tunnel are 120 m long, respectively, and the cross section of each station zone is the same as that of the tunnel zone (see Fig. 7). In the simulation, the train moves for 75 seconds with the velocity profile depicted in Fig. 8, which can be expressed as tπ π UT = 10 sin + 1 25 2 m/s for 0 s < t 25 s U = 20 m/s T for 25 s < t 50 s ( t 50) π π UT = 10 sin + + 1 m/s 2 25 for 50 s < t 75 s where U T is the train velocity and is the time. 3. Results and discussion 3.1 Grid independence In order to get grid independent numerical results, a comprehensive grid sensitivity test is performed. Considering the piston effects caused by a train motion, attention is focused on the effects of grid size ( Δ x ) in the train-running direction. Since it takes much time to calculate the whole geometry, we only check the grid independency for the first part of 500 m in the tunnel (Fig. 9). The simulations for grid sensitivity analysis are conducted for two grid sizes ( Δ x = 0.3 m and 0.6 m, respectively) in the first part of the tunnel with the grids of Δ x = 0.6 m in the rest part of the tunnel, while applying the same boundary and initial conditions, the same velocities of train run and the same time step size ( Δ t = 0.01 s) in the two cases with different grid sizes. In the grid independency test the train moves for 20 seconds with the velocity profile depicted in Fig. 10, and passes completely the ventilation duct 1. Here, the train velocity profile shown in Fig. 8 is not used in order to investigate the grid independency with higher train velocity. The results of the grid sensitivity analysis are shown in terms of the velocity distribution along the train-running direction of the tunnel in the front of the moving train. When the
Y. Huang et al. / Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 789 (a) Pressure contour Fig. 11. Comparison of velocity profiles in front of the moving train for two different grid sizes. frontal face of the train reaches the point of x = 368 m adjacent to the ventilation duct1, the distributions of axial velocity for two grid systems with different grid sizes ( Δ x = 0.3 m and 0.6 m) in front of the moving train along the central axial line (for 368 m < x < 468 m with y = 2.05 m and z = 2.1 m) of the tunnel are shown Fig. 11, which reveals that the velocity decreases with the increase of the distance away from the frontal face of the train. From this figure, it is apparent that the velocity distributions, which reflect the characteristics of piston effects caused by the train motion, are almost insensitive to the grid size in the train-running direction when the grid size Δ x is in the range of 0.3 to 0.6 m. This figure shows that a large amount of air in front of a train in motion with a cruising speed is moving in the same direction, which is well known as a piston effect caused by a moving train. Furthermore, the Courant number CFL = UT MAXΔt / Δ x (Here, UT MAX = 20 m / s is the maximum velocity of the train) is obtained to be 0.67 and 0.33 for the two grid sizes of Δ x = 0.3 m and Δ x = 0.6 m, respectively. One of the most limiting factors in performing three dimensional CFD simulations for real engineering problems is the mesh size, which directly affects the overall cost of the simulation. On the basis of this grid sensitivity analysis, the grid size is set to be 0.6 m in the current numerical simulations so as to reduce the required computing time, while the grid sizes Δ y and Δ z are 0.3 m and 0.4 m, respectively, except in the narrow gap between the surfaces of moving train and the tunnel walls, where finer grids are adopted in order to resolve the high gradients of flow variables that are expected to occur in those regions. 3.2 Numerical results and discussion Numerical analysis has been carried out for flow field in the tunnel as described in Chapter 2. Fig. 12 gives the pressure contour and velocity vectors in the middle section (y = 2.05 m) of a one way of the tunnel when the train approaches the ventilation duct 1 at t = 24.42 s, which displays that the air pushed ahead of the train causes a pressure increase in front of (b) Velocity vector field Fig. 12. Pressure contour and velocity vectors in the middle section (y = 2.05 m) of a one way of the tunnel when the train approach the ventilation duct 1 at time t = 24.42 s. the train, and that some part of the pushed air is flowing to the train-running direction to move forward in the tunnel and to get into the ventilation duct and some other part is flowing over the roof of the train in the direction opposite to the train motion in the upper part of the region between the ceiling of the tunnel and the top surface of the moving train. Near the top surface of the train the air velocity is in the same direction as the train motion because of the viscous effect. In the region between the floor of the tunnel and the bottom surface of a moving train, velocity in the direction of train run is generally observed. Fig. 13 shows the pressure contour and velocity vectors in the middle section of a one way of the tunnel when the train moves to the right under the ventilation duct 1 at t = 27.22 s. As can be seen, low pressure is observed in the region between the ceiling of the tunnel and the top surface of a moving train, which slightly sucks the air through the ventilation duct. Here, the general air velocity pattern in the region between the ceiling of the tunnel and the top surface of the train is similar to that shown in Fig. 12. Fig. 14 shows the pressure contour and velocity vectors in the middle section of a one way of the tunnel just after the train passes the ventilation duct1 at t = 30.42 s. Here, it can be observed clearly that air is pulled into the tunnel through the ventilation duct 1 since a negative pressure occurs in a region under the duct 1 just after the rear face of the train passes the ventilation duct 1. Also, it is seen that there is a region of high velocity in the train-running direction near the rear face of the train. The air flow in the direction opposite to the train motion observed in the upper part of the
790 Y. Huang et al. / Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 (a) Pressure contour Fig. 15. Mass flow rates of the airflow through the different ducts with time. (b) Velocity vector field Fig. 13. Pressure contour and velocity vectors in the middle section (y = 2.05 m) of a one way of the tunnel when the train moves under the ventilation duct 1 at time t = 27.22 s. (a) Pressure contour (b) Velocity vector field Fig. 14. Pressure contour and velocity vector field in the middle section (y = 2.05 m) of tunnel 1 after the train passes through the ventilation duct 1 at time t = 30.42 s. region between the tunnel ceiling and the top surface of a moving train is entrained to the air flow in the train-running direction near the rear face of the train, which is induced by train motion. Fig. 15 illustrates the variations of mass flow rate with time at the six ventilation ducts, which reveal clearly the influence of train movement on the suction and exhaust of airflow in the ventilation ducts. Here, the positive and negative values of mass flow rate represent the suction and exhaust of the air through the ducts, respectively. Since the duct 1 and duct 4, the duct 2 and duct 5, the duct 3 and duct 6 are located in a pair along the direction of train motion (Fig. 6), the flow patterns in each pair of the ducts are very similar to each other. As the train moves towards the ventilation duct 1, the mass flow rate of air exhausted out of the tunnel through the duct 1 increases with time and reaches its peak value just before the frontal face of a train passes the opening of the duct 1 at t = 24.86-24.90 s. As the train passes the ventilation duct 1, the pattern of exhaust flow in the duct is changed very quickly to the suction flow, and the mass flow rate of air sucked into the tunnel through the duct 1 increases with time and reaches its peak value just after the rear face of a train passes the opening of the duct 1 at t = 30.10-30.14 s. After the train passes through the ventilation duct 1, the mass flow rate of air pulled into the tunnel through the duct 1 decreases with time since the pressure at the opening of the duct 1 is recovered as time goes on. Generally, very similar flow patterns are observed in the duct 2 and duct 3 in association with the train motion passing each opening of the duct 2 and duct 3. However, during the period when the mass flow rate of the suction flow through the duct 1 is quite large (that is, approximately for 26 s < t < 32 s), the mass flow rate of the exhaust flow through the duct 2 is shown to be larger. The same trend is observed in the mass flow rate of the exhaust flow through the duct 3 for the above period of the time. Again, during the period when the mass flow rate of the suction flow through the duct 2 is quite large (that is, approximately for 36 s < t < 42 s) the mass flow rate of the suction flow through the duct 1 is reduced and that of the exhaust flow through the duct 3 is increased. Since the distance be-
Y. Huang et al. / Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 791 tween the duct 1 and duct 2 is the same as that between the duct 2 and duct 3, the larger mass flow rate through the duct 2 for the above period of the time may affect the flows in the duct 1 and the duct 3 to a similar degree. Also, during the period when the mass flow rate of the suction flow through the duct 3 is quite large (that is, approximately for 46 s < t < 52 s) the mass flow rates of the suction flows through the duct 1 and duct 2 are reduced. The reduction in the mass flow rate in the duct 2 is more notable compared with the duct 1 since the distance between the duct 2 and duct 3 is smaller than that between the duct 1 and duct 3. And when the train velocity is quite reduced near the right station, the exhaust airflows through the duct 2 (for 72.84 s < t < 75 s) and the duct 3 (for 67.18 s < t < 75 s) are observed, which is caused by the fact that usually the air in the front and the rear of the train is moving together with the train, and when the train velocity is quite reduced the air following the train near the rear of the train is blocked by the train so that some part of the air following the train is pushed out through the ducts. Since the distance between the right station and the duct 3 is smaller than the distance between the right station and the duct 2, the mass flow rate (absolute value) at the duct 3 is larger. When the train approaches each pairs of ducts 1, 2 and 3, the exhaustive volumetric air flow rates through the ducts 1, 2 and 3 are slightly larger than those of ducts 4, 5 and 6 since the piston effect is stronger in a track where a train runs. Just after the fontal face of the train passes each pairs of the ducts, higher horizontal velocities of the air between the train roof and tunnel ceiling in a direction opposite to the train motion, observed near these ducts, have a stronger tendency to suppress the air flow through the ducts 1, 2 and 3 compared with the air flow through the ducts 4, 5 and 6 (Please see the velocity distribution near the opening in Fig 13(b)). This causes slightly higher suction flow rates through the ducts 4, 5 and 6 compared to those through the ducts 1, 2 and 3 just after the fontal face of the train passes each pair of ventilation ducts. In Fig. 16 the mass flow rate through the left side is given. Here, for 0 s < t < 25 s, during which the exhaust flow rate through the duct 1 is increasing (Fig. 15), the incoming flow rate through the left side is also increasing, with a peak around t = 25 s when the exhaust flow rate through the duct 1 gets the maximum value. Again, another local peak of the mass flow rate is observed around t = 35 s when the exhaust flow rate through the duct 2 has the maximum value. And, the mass flow rate through the right side is shown in Fig. 17, where the flow rate for around 0 s < t < 50 s is increasing with time, during which the train is accelerating and cruising with high speed. The peak value is observed around at t = 50 s when the train is starting to decelerate. From this time on the flow rate is decreasing. Also, it is notable that the large mass flow rate through the right side for around 45 s < t < 60 s is observed together with a large mass flow rate of the air suction through the duct 3. In Table 1, shown are the total mass flows of air through the Table 1. Mass flow of air through the six ventilation ducts and the left and right sides for 0 < t < 75 s. t (sec) when mass flow rate is zero Mass flowout (kg) Mass flowin (kg) Net mass flow-in (kg) Duct 1 26.06 207.842 331.758 123.916 Duct 2 Duct 3 35.50 72.84 45.30 67.18 279.602 0.742 292.999 18.538 311.364 31.020 215.228-96.309 Duct 4 26.06 202.622 338.062 135.440 Duct 5 Duct 6 35.50 73.56 45.30 67.32 273.716 0.391 305.811 19.575 316.978 42.871 237.413-87.973 Left side 5094.743 5094.743 Right side 5201.084-5201.084 Fig. 16. Mass flow rate of the air through the left boundary. Fig. 17. Mass flow rate of the air through the right boundary. six ventilation ducts and across the left and right sides for the period of 0 s < t < 75 s, together with the time points when the mass flow rate through a duct is zero. The duct 2 (and duct 5) and duct 3 (and duct 6) have two time points, respectively, when the mass flow rate through the duct is zero, which yields the two periods of air exhaust through the duct. The net mass flow into the given computational domain is shown to be 42.624 kg, which shows the size of the error in the current numerical calculation. The ratio of the above value to the mass
792 Y. Huang et al. / Journal of Mechanical Science and Technology 26 (3) (2012) 785~792 flow through the right side is 0.00837, expressing that the current calculation turns out to be very accurate. As can be seen in Table 1, at the duct 1 (and duct 4) the mass flow-out is fairly smaller than the mass flow-in, while at the duct 3 (and duct 6) the mass flow-out is quite larger than the mass flow-in. The current numerical calculation is started with the initial condition that the air velocity in the computational domain is zero. However, as can be seen in Fig. 17, the mass flow rate at t = 75 when the train just stops at the right station is around 70 kg/s, which corresponds to the air velocity of 4.09 m/s in the region between the tunnel wall and the surface of the train. Though this velocity would be decreasing while the train is stopping at a station, this type of air velocity that can be observed when the train is stopping in the left station is not considered in the current study. If the above velocity is considered at t = 0 when the train starts from the left station and if it is noted that the air velocity in the front of the train (say, at 20 m ahead of the front of the train) is not very small as can be seen in Fig. 16 given for the grid-size independency, then it could be presumed that in a real situation the mass flow-out through the duct 1 (and duct 4) is larger than the value given in the Table 1 and it is also the case of the duct 2 (and duct 5) and that the mass flow-out through the duct 3 (and duct 6) is smaller than the value given in the Table 1 in consideration of the mass balance in the computational domain. 4. Conclusions A three-dimensional numerical analysis using the dynamic layering method for the moving boundary of an immersed body is firstly performed for simulating train-induced unsteady airflow in a subway tunnel. With a validation of the current numerical analysis against the experimental data obtained from the experimental study conducted by Kim and Kim in a model tunnel, a three-dimensional unsteady tunnel flow is simulated with a comprehensive grid sensitivity analysis for the geometries of a subway tunnel and a subway train which are very similar to those of a real subway system of Seoul [1]. The distributions of pressure and air velocity in the tunnel as well as the time series of mass flow rates at natural ventilation ducts are numerically analyzed. The numerical results reveal that the suction and exhaust of airflow in a natural ventilation duct is strongly affected by the train motion. When the train approaches a ventilation duct, the air is pushed out of the tunnel through the ventilation duct. The maximum mass flow rate of the air exhaust through the duct occurs when the frontal face of a train reaches the ventilation duct. When the train runs under the ventilation duct, the exhaust flow in the duct is changed very quickly to the suction flow and the mass flow rate of air pulled into the tunnel through the duct reaches the maximum value just after the rear face of train passes the ventilation duct. Also, a drastic change in the mass flow rate at a ventilation duct occurring when a train passes the corresponding ventilation duct affects a change in the mass flow rate at other ventilation ducts. This study can be applicable in the design of ventilation ducts in a subway system. Acknowledgment This work was supported partly by the Seoul R and BD program (CS070160) and partly by Leading Academic Discipline Project of Shanghai Municipal Education Commission (J50502). Any opinion, findings, and conclusions or recommendations expressed in this article are those of the authors, and do not necessarily reflect the view of the Seoul R and BD program. References [1] J. Y. Kim and K. Y. Kim, Experimental and numerical analyses of train-induced unsteady tunnel flow in subway, Tunn. Undergr. Space Technol., 22 (2) (2007) 166-172. [2] F. D. Yuan and S. J. You, CFD simulation and optimization of the ventilation for subway side-platform, Tunn. Undergr. Space Technol., 22 (4) (2007) 474-482. [3] M. T. Ke, T. C. Cheng and W. P. Wang, Numerical simulation for optimizing the design of subway environmental control system, Build. Environ., 37 (1) (2002) 1139-1152. [4] D. M. Anderson, G. B. Mcfadden and A. A. Wheeler, Diffuse interface methods in fluid mechanics, Annu. Rev. Fluid Mech., 30 (1) (1998) 139-165. [5] H. S. Udaykumar, R. Mittal, P. Rampunggoon and A. Khanna, A sharp interface Cartesian grid method for simulating flows with complex moving boundaries, J. Comput. Phys., 174 (1) (2001) 345-380. [6] C. J. Lin, Y. K. Chauh and C. W. Liu, A study on underground tunnel ventilation for piston effects influenced by draught relief shaft in subway system, Appl. Therm. Eng., 28 (5-6) (2008) 372-379. [7] V. Yakhot, S. A. Orszag, S. Thangam, T. B. Gatski and C. G. Speziale, Development of turbulence models for shear flows by a double expansion technique, Phys. Fluids A, 4 (7) (1992) 1510-1520. Chang Nyung Kim is a Professor of the Department of Mechanical Engineering, College of Engineering, Kyung Hee University, Republic of Korea. He received his Ph.D degree in Mechanical Engineering at the University of California, Los Angeles. His research area includes micro-fluid dynamics and environmental fluid dynamics.