The impact of ambient pressure and tunnel inclination angle on the smoke transport in a subway tunnel

: The subway tunnel will be built in the plateau where the pressure is relatively low, and the tunnel will tilt at a certain angle due to topographic factors. In order to investigate the smoke transport characteristics of moving subway trains caught fire under different ambient pressures and different tunnel inclination angles, three-dimensional full-scale calculation models of subway trains, two stations and one tunnel are established, and three different environmental pressures (50kPa, 75kPa, 100kPa) and three different tunnel inclination angles (- 1.5 °, 0 °, + 1.5 °) are simulated. The IDDES turbulence model based on k ω -sst RANS combined with the overset grid technology is used to simulate the subway train movement and the detailed flow field. The velocity and temperature distribution characteristics and smoke concentration field are studied in detail. The soot density of smoke and temperature increases with reduced ambient pressure due to the weakening of air entrainment and the decreased air density and the influence of ambient pressure on smoke diffusion decreases with the increase of pressure. The longitudinal airflow induced by the stack effect under the negative inclination angle of the tunnel is helpful to prevent the flowing back of smoke. the influence of train movement on the transport characteristics of smoke under different ambient pressure and tunnel inclination in detail, this paper establishes a model involving a 3-D full-scale subway train and the IDDES turbulence model based on k ω -sst RANS combined with the overset grid technology is used to simulate the subway train movement and the detailed flow field.


Introduction
With the continuous development of social economy, subway traffic has gradually become an indispensable part of urban traffic structure due to its characteristics of fast, large traffic volume, small pollution, and high efficiency. According to statistics, by the end of December 2019, there were 38 cities in China that had opened metro, with a total operating mileage of 5,480 kilometers (Liu and Li, 2020). Although the construction of subway line greatly alleviates the pressure of urban ground transportation and brings convenience to residents' life, the frequent operation of subway also brings a lot of safety problems. Fire, as the main form of disaster, attracts people's extensive attention. Due to the complex structure of subway system, the occurrence, development and development of fire have particularity. Once a fire occurs, the fire situation is complex, which can easily cause huge casualties and property losses. In the process of continuous operation, the heat and smoke generated by the fire accumulate and spread rapidly in the subway tunnel. The operation of the train makes the propagation behavior of fire smoke in the tunnel more complex N. Zhang et al., 2018a). So, it is urgent to carry out the research on the operation of train carrying fire sources and the law of fire smoke transport in subway tunnels and stations.
Subway is an underground enclosed building, and the occurrence of subway fire is the most harmful one in subway accidents, which can easily cause mass death and mass injury of people, and it is difficult to evacuate and rescue. Therefore, countries all over the world have invested plenty of manpower and material resources to conduct extensive research on the characteristics of subway fire smoke under the effect of various factors, mainly using the three methods of full-size fire test (Cafaro and Bertola, 2014;Hu et al., 2005;Lemaire and Kenyon, 2006;Tian et al., 2017;Wang et al., 2009;Weng et al., 2014;Yan et al., 2009), fire model test (Chaabat et al., 2020;Chow et al., 2017Chow et al., , 2011Ji et al., 2016;Oka and Atkinson, 1995;Vauquelin and Mégret, 2002;Vauquelin and Telle, 2005;Zhang et al., 2017Zhang et al., , 2016 and numerical simulation (Bai et al., 2016;Gannouni and Maad, 2015;Hu et al., 2013b;Ji et al., 2013;Ko and Hadjisophocleous, 2013;Lee and Ryou, 2006;Tang et al., 2017;Wang et al., 2020;N. Zhang et al., 2018a). With the continuous maturity of test conditions, test equipment and test technology, the development scope of full-size tunnel fire test is further expanded, the test content is constantly expanded, and the accumulated test data is more comprehensive, which provides a lot of valuable experience for the development of tunnel engineering.
However, due to the high cost of individual test, less measurable content, low repeatability and other factors, it is not easy to conduct a comprehensive study of tunnel fire.
Therefore, research methods such as model test and numerical simulation method are gradually derived. Compared with model test research, numerical calculation has the advantages of low cost, fast calculation speed and comprehensive output results, and can calculate all parameters in the whole calculation area. Therefore, many scholars use numerical simulation methods to simulate subway fire research. However, at present, scholars at home and abroad are studying and analyzing the static fire source utilization model test and CFD.
However, in the case of moving subway train on fire, the research on smoke transport and temperature distribution is relatively few. The fire characteristics of moving trains will be seriously affected by the piston wind induced by the train movement. X. Zhang et al. (2019) carried out numerical simulation with IDA Tunnel software, studied the four parameters of open and closed system, by-pass ducts, train intervals and adjustable vent, and analyzed the air inflow rate at the gate of the adjustable station. Zhong et al. (2015) numerically studied the smoke transport of subway fire under the effect of piston wind and put forward three methods to reduce the effect of the piston wind on smoke layer transport. The detailed analysis of the flow field, temperature field and velocity distribution shows that the piston wind produces a large range of eddy current and horizontal inertia force, which destroys the stratification of smoke layer. Xie et al.(2010) investigated the smoke transport of the moving train on fire using CFD and the research shows that the train piston wind plays a leading role in the transport of the smoke, and the flowing back phenomenon of the smoke almost does not exist. In the process of continuous operation and evacuation, the upstream compartment is basically unaffected, and the temperature and smoke concentration in the downstream compartment increase with time, and tend to be stable when the fire reaches the maximum scale. D. Zhou et al. (2015) used dynamic grid technology to study the distribution of smoke field in the tunnel when the subway head train catches fire at the bottom of the train. The results present the piston wind induced by train movement plays a decisive role in the transport of smoke in the tunnel. The direction of mechanical ventilation should be consistent with the running direction of the train to prevent smoke from continuing to spread upstream in the tunnel. N. Zhang et al.(2018) established a three-dimensional full-scale model and used the dynamic grid technology to study the effect of the blockage ratio and train speed on the transport of smoke and temperature distribution in the tunnel when the subway train caught fire. The smoke movement is basically the same as that of D. Zhou et al. (2015). when the train is running normally and decelerating, the smoke moves to the tail (upstream). The slipstream formed during the train moving plays a leading role in the smoke movement in the tunnel, which makes the smoke flow to the front region of the train (downstream). After the slipstream weakens until it disappears, the smoke will spread to the tail (upstream) again. In this paper, it is pointed out that the effect of block ratio on smoke movement is more significant than the speed of train.
At present, the research on the smoke transport of moving train on fire under different ambient pressure and tunnel inclination angle is not deep enough. The effects of ambient pressure and tunnel inclination on the smoke movement and temperature distribution of the static fire in tunnel have been studied by Jie Ji et al. (2017Ji et al. ( , 2019. In order to study the influence of train movement on the transport characteristics of smoke under different ambient pressure and tunnel inclination in detail, this paper establishes a model involving a 3-D full-scale subway train and the IDDES turbulence model based on kω-sst RANS combined with the overset grid technology is used to simulate the subway train movement and the detailed flow field.

Geometry model
To realistically simulate the blockage effect of a vehicle and realistically describe the smoke flow characteristics, a 1:1 3D subway train consisting of 6 cars is used in this study, as shown in Fig.1. The model train has a length of 140m (25 2+22.5 4) ×× , and the cross-sectional area of the subway train body is 9.5m 2 . Certain components, e.g., the bogie, apron, head, windshield, and equipment cabin, which have a strong influence on the flow of smoke, are modeled in detail. According to incomplete statistics of subway fire accidents(H. W. , approximately 46% of subway train fire accidents are due to equipment failure, such as electrical equipment and brakes, which are mostly located at the bottom of the train. As the fire source moves with the train, the smoke has the greatest influence on the rear carriages when the fire occurs in the first carriage. Therefore, the location of the fire source is set at the bottom of car 1, the dimension of the fire is 8m×2m×1m [3], as shown in Fig. 1. The profile and basic dimensions of the tunnel section used in the numerical simulation in this paper are shown in

Computational domain and boundary conditions
The physical model used in this paper consists of a 6-car subway train and two stations connected by a 1500 m long tunnel, as shown in

Meshing strategy
In this paper, it is necessary to carefully simulate the influence of slipstream on smoke transport caused by train movement. according to previous articles on slipstream Li et al., 2019;Liang et al., 2020), so the IDDES turbulence model based on the k ω − turbulence model is adopted in this paper. Mixed grids were used in the entire computation domain, which contained prism layers at the wall boundaries (train surface and tunnel wall) and hexahedral grids in the stationary region (SR) and polyhedral mesh in the moving region (MR), as shown in Fig. 4. Considering the effect of boundary layers on the surfaces of the tunnel and train body, the 16 prism grids with a growth rate of 1.1 around the tunnel wall and train body are generalized to resolve the near-wall flow structure. The thickness of the first boundary layer was approximately 2 mm, to ensure that the averaged Y+ was approximately 2, which met the demands of the k ω − turbulence model. To verify the grid independence, three different mesh numbers were compared. the details of the differences between the four grids are listed in Table   1. Three sets of grids, i.e., coarse, medium, and fine grids, containing 17.6 million cells, 27 million cells, and 38.7 million cells, respectively, were used to test the grid sensitivity of the simulation. The medium grid distribution around the train is shown in Fig. 4.

Fire source model
It is difficult to provide a model to describe the fire development process due to the complex combustion process, so the subway fire source is simplified to a fixed heat release rate (HRR) model. The most used unsteady HRR model is the 2 t -model applied in Star-CCM+ software. According to the user guide, there are four types of 2 t -model: slow, medium, fast, and ultra-fast, the corresponding fire growth factor, respectively 0.0029, 0.01127, 0.04689, where α is the fire growth factor. Taking the fast model as an example, the HRR requires nearly 3min to reach a maximum of 10MW, so we artificially crank up the value of α to 500000 in order to make the fire quickly reach a stable state and study the distribution of smoke and temperature in the tunnel when the fire source is stable. The fire size is set to 8m × 2m × 1m, and the fire heat release rate is 10MW according to the European UPTUN tunnel project (Migoya et al., 2011;N. Zhang et al., 2018b). The amount of soot released by burning one gram of fuel is 0.118 g . The smoke release rate is set according to the principle of oxygen

Radiation model
Radiative heat transfer is energy transferred through electromagnetic waves. The black body intensity is expressed as: Where h is Planck's constant, 0 c is speed of light, λ is the wavelength inside the medium, When the radiation passes through the simulation region, the transfer equation ( Where I λ is the radiative intensity at wavelength λ , b I λ is the black body intensity at wavelength λ , a k λ is the absorption coefficient at wavelength λ , s k λ is the scattering coefficient at wavelength λ and s is the distance in the Ω direction. The first term is the gained intensity for the heat emission and the second term is the lost intensity due to the absorption and scattering effect. Discrete Ordinate Method (DOM) in STAR CCM+ is used in this paper to simulate the radiation effect. The DOM is a numerical model for describing radiative heat transfer in a simulation region. Within the DOM module, the gray thermal radiation model makes it possible to simulate diffuse radiation independently of wavelength. In this model, the radiation characteristics of the region and the surface are the same for all wavelengths. The surface radiative properties are quantified in terms of emissivity, specular and diffuse reflectivity, transmissivity, and radiation temperature. And the Kirchhoff's law is used to enforce the sum of the emissivity, reflectivity, and transmissivity to be 1.0 at surfaces. The discrete ordinates method participating media radiation solver in the STAR-CCM+ code is used to compute the radiative heat flux to the tunnel region in the three cases. The ordinate set of S8 is used for the discretization of DOM to ensure the balance between accuracy and computing time. This is 80 ordinates computed as ( 2) Sk k k = + . equations to cover all solid angles.

Numerical method
The simulations that are presented in this article were made using a segregated where P is the pressure, R is the gas constant, and T is the temperature.

Validation of the CFD method (Stationary fire in tunnel)
The static fire in the tunnel has been widely studied and there are a series of detailed experimental and numerical simulation data. In this section, the published temperature distribution in the tunnel is used to verify the calculation model, to accurately simulate the smoke transport process. It is verified that the model tunnel is a typical highway tunnel, the fire size is 150 10 5 m mm ××and the fire source is located in the center of the width of the tunnel, the distance from the left opening is 50m, the initial ambient temperature is 20 C  , and the temperature measuring position is shown in Fig. 5. The ratio of characteristic fire diameter to grid size * Dx δ is recommended in the range of 4-16, which has been widely used to evaluate grid resolution. * D is expressed as: The IDDES model can better capture the dynamic characteristics of smoke transport, so this paper uses IDDES model for the simulation of moving train on fire.

Validation of the CFD method (Grid independence)
Grid refinement can affect the CFD prediction. In this paper, three different meshes of coarse mesh, medium mesh and fine mesh are studied to eliminate the influence of grid size and distribution. The three grids adopt the same scale partition strategies, using the same thickness and layer number of surface layer to maintain the same Y+ and only changing the distribution of train and tunnel surface. The three types of grids are about 17.6million, 27 million and 38.7 million respectively. Fig. 8 (a) shows that the longitude temperature distribution 0.2 m beneath the top tunnel surface under 70kPa ambient pressure at 240 s and Fig. 8 (b) is its local magnification. It can be seen from Fig. 8 that the temperature curves of the three mesh densities do not differ much, and the variation laws are basically the same. The maximum temperature under coarse mesh is slightly larger than that of middle meshes and fine meshes. In this paper, medium grid is used for numerical simulation. delayed. Fig. 10 shows the velocity variation at the tunnel roof over time at 808 , 4.75 x mz m = = for three different ambient pressure. According to the velocity curve of this point, the specific time when the smoke begins to flow back is inferred, that is, when the velocity is zero, representing the flowing back of the smoke. As is shown in Fig.10, the time for the smoke under 50kPa, 75kPa and 100kPa to spread to the tail of the car is 125s, 164s and 203s, respectively. Therefore, when a fire breaks out in a subway train at lower ambient atmospheric pressure, mechanical ventilation should be turned on earlier so that the smoke can always spread downstream.
The temperature change with time around the train in 0 y = section under different ambient pressures is shown in Fig. 11 Zhang et al., 2018a), and the position of the maximum is also changing. The difference between 50kpa and 75kpa is greater than that between 75kpa and 100kpa, indicating that the influence of ambient pressure on smoke diffusion decreases with the increase of pressure. Table 2 presents a summary of the smoke front at different time under different ambient pressure. The smoke is found to move farther over time before the mechanical ventilation is turned on. The larger the ambient pressure is, the shorter the distance over which smoke travels becomes.
The same pattern is observed at other moments, but there are some variations in the size of the difference.

Influence of tunnel inclination angle
The smoke movement and temperature distribution of static fire sources in horizontal and inclined tunnels have been widely studied. However, the smoke movement and temperature distribution under the combined effect of piston wind caused by train movement and the stack effect induced by inclined tunnel have not been seen yet. According to previous research, the due to the influence of thermal buoyancy near the fire source, the fluctuation of the smoke is consistent with that in Fig. 11, until the time is 240s (specific time is 205s in Fig.10), the smoke begins to flow back, and the wind speed in the upstream annular space becomes negative again.
According to the previous study on the static fire source of inclined tunnel and comparative analysis of Fig. 15-17, the longitudinal velocity caused by stack effect is from the downstream to upstream when the tunnel inclination angle is negative (Fig. 16) which will counteract the piston wind caused by train movement and cause the smoke to return to the upstream in advance.
When the tunnel inclination is positive, the situation is just the opposite. the longitudinal velocity caused by the stack effect is from upstream to downstream (Fig. 17), which strengthens the piston wind and the smoke never flows back towards the upstream within the simulation time of this paper. Fig. 18 shows the velocity variation at the tunnel roof over time at 808 , 4.75 x mz m = = for three different tunnel inclination angles. As is shown in Fig.18, the time for the smoke under =0 and-1.5 α  to spread to the upstream is 123s and 203s respectively, the smoke under +1.5  never flows back towards the upstream. Therefore, when a fire breaks out in a subway train at negative tunnel inclination angle, mechanical ventilation should be turned on earlier so that the smoke can always spread downstream.  can be seen intuitively that the positive inclination angle of the tunnel can effectively prevent the smoke countercurrent, the temperature and smoke concentration near the fire source are also lower, mainly due to the larger longitudinal velocity, which strengthens the mixing of smoke and fresh air and improves the entrainment effect efficiency. Table 3 summarizes the specific positions of the smoke front upstream and downstream of the fire source at different tunnel inclination angles with time. It can be seen from the table that when the time is less than 90s, the upstream smoke front is basically the same, and there is only a difference in the downstream, which is the joint action of piston wind and thermal buoyancy.

Conclusions
The IDDES turbulence model based on k sst ω − RANS combined with the overset grid technology is used to simulate the subway train movement and the detailed flow field. The distribution characteristics of velocity field, temperature field and smoke concentration field are studied in detail. The effects of ambient pressure and tunnel inclination angle on the smoke transport of moving train in a subway tunnel were investigated in this paper. The results can be summarized as follows:  For the certain HRR, the soot density of smoke and temperature increases with reduced ambient pressure, because the decrease of pressure leads to the decrease of air density, which leads to the weakening of air entrainment. The difference between 50kpa and 75kpa is greater than that between 75kpa and 100kpa, indicating that the influence of ambient pressure on smoke diffusion decreases with the increase of ambient pressure. When a fire breaks out in a subway train at lower ambient atmospheric pressure, the smoke flows back early due to the too low atmospheric pressure, so that mechanical ventilation should be turned on as early as possible so that the smoke can always spread downstream.
 The longitudinal velocity caused by stack effect is from the downstream to upstream when the tunnel inclination angle is negative which will counteract the piston wind caused by train movement and cause the smoke to return to the upstream in advance. When the tunnel inclination is positive, the longitudinal velocity caused by the stack effect is from upstream to downstream, which strengthens the piston wind.
 Within 90s, the temperature and soot density of smoke distribution is dominated by the piston wind, after 90s, the longitudinal airflow induced by the stack effect plays a leading role, resulting in a wider distribution of high temperature and a larger maximum temperature for the negative inclination angle of the tunnel.
As the fire source location and heat release rate are fixed in this paper, and no ventilation settings are adopted, it is hoped that the effects of fire source location, heat release rate and ventilation on smoke transport in tunnels with different ambient pressures and inclined angles can be studied in the future.