https://orcid.org/0009-0008-9703-2178
Abstract
When two trains going through a tunnel pass each other, the difference of the surrounding space between a train's both sides rises, which induces abrupt aerodynamic force variations on the trains, resulting in the phenomenon of sudden swaying. This study employs the unsteady Reynolds-averaged Navier-Stokes (URANS) method of numerical simulation to analyse the effects of two terrain conditions, that is, a tunnel with and without asymmetric mountain structures at its portals, on the aerodynamic characteristics of two trains during their intersections. The results indicate that during two trains’ intersections at tunnel portals, the rear car suffers the highest risk of swaying. The presence of asymmetric mountain structures at tunnel portals reduces the risk of swaying the train adjacent to the mountains but increases the risk for trains farther away from the mountains. When trains intersect at the exit (for the train adjacent to the mountain) of the tunnel, the presence of mountain structures at the portal reduces the peak-to-peak lateral force values by 12.7% for the front car of the train adjacent to the mountain and increases by 16.5% for the rear car of the train away from the mountain. The impact of the mountain structures on the peak-to-peak values of a train's lateral force is minimal when two trains intersect at the midpoint of the tunnel. Therefore, it is suggested to consider the placement of symmetrical buffer structures or the modification of existing mountain structures at appropriate locations near tunnel portals to mitigate the abrupt lateral force variations experienced by passing trains.
Highlights
Aerodynamic characteristics during train intersection in tunnels are investigated using numerical simulation
The impact of mountain structures at tunnel portals on train aerodynamics is thoroughly analysed
Trains meeting at tunnel portals exhibit a higher risk of swaying, particularly for the rear cars
Asymmetric mountain structures mitigate swaying risks for trains close to the mountains but amplify risks for those farther away
1. Introduction
When a train passes through a tunnel, the sudden alteration in airflow space results in transient aerodynamic effects as the train compresses the air within the tunnel. This phenomenon significantly impacts the pressure inside the tunnel and the aerodynamic loads acting on the train [1–3].
Scholars have conducted comprehensive research on the effects of the train-tunnel phenomenon on pressure variations within tunnels. The characteristics of pressure fluctuations inside tunnels are influenced by factors such as train operating speed [4], train composition [5], tunnel length [6] and tunnel portal shape [7]. The compression of air by the train entering a tunnel creates pressure waves within the tunnel, and the resultant micro-pressure waves generated by their propagation and superposition adversely affect the surrounding environment of tunnel portals [8–10]. Long-term pressure cycling on tunnel surfaces can lead to fatigue damage such as cracking and spalling of the lining [11–13]. Sudden fluctuations in internal pressure caused by the pressure difference between the inside and outside of the train result in passenger discomfort, posing health risks [14, 15].
The abrupt change in aerodynamic loads induced by pressure variations within tunnels can lead to lateral oscillations of the train body, thereby impacting both operational safety and passenger comfort. Suzuki and Sakuma [16] observed through field experiments that pressure fluctuations on either side of the train triggered aerodynamic forces, converting energy into vibrations as the train passed through the tunnel, and in single-track tunnels pressure fluctuations on opposite sides of the train occur in opposite phases. Rabani and Faghih [17] found that as trains enter double-track tunnels, asymmetrical spatial positioning subjects them to lateral forces directed towards adjacent tunnel walls, resulting in lateral oscillations. Chen et al. [18] conducted a comparative analysis of aerodynamic forces on the different cars when a train enters and exits single-track versus double-track tunnels. It was found that compared to other cars, the rear car experiences significant aerodynamic effects when entering and exiting tunnels, with greater aerodynamic forces observed when the lead car exits the tunnel compared to entering it. Moreover, aerodynamic forces acting on the lead car in single-track tunnels are generally lower than those in double-track tunnels, except for yaw moments. When a train enters a tunnel, aerodynamic forces on the rear carriage are lower in single-track tunnels than in double-track tunnels, while upon exiting, except for yawing moments, aerodynamic forces on the rear carriage are greater in single-track tunnels. Given the adverse effects of lateral oscillations on operational safety and passenger comfort, it is imperative to study the mechanisms and influencing factors of lateral oscillations when trains enter and exit tunnels. Akai et al. [19] attributed the lateral oscillations during a train entering a tunnel to changes in aerodynamic forces resulting from airflow separation and vortex shedding along the train surface. Some scholars have also tried new methods in flow field visualization [20, 21].
In practical applications, tunnel entrances in mountainous regions are often characterized by non-ideal terrain conditions. Hence, some studies have considered the influence of tunnel portal topography and surrounding terrain. Zhang et al. [22] analysed the process of trains entering tunnels when the tunnel portal is situated in a cutting or on an embankment. It was observed that the influence range of the cutting-tunnel transition segment on the surrounding wind speed is greater than that of the embankment-tunnel transition segment. The lateral force coefficient of trains increases and then decreases as they pass through the embankment-tunnel transition segment, whereas it increases initially and stabilizes when passing through the cutting-tunnel transition segment. Yang et al. [23] compared the aerodynamic effects of trains during transitions between tunnel-bridge and bridge-tunnel segments, highlighting a higher safety risk when trains pass through tunnel-bridge transition segments. Deng et al. [24] simulated the process of trains passing continuous tunnel-bridge-tunnel transition segments, identifying changes in aerodynamic forces on the lead and rear carriages as the primary factors influencing operational safety. However, studies concerning common mountainous terrain features at tunnel portals (Fig. 1) have not been adequately addressed, and the abrupt changes in train aerodynamics are closely related to the asymmetric flow field structure at tunnel portals. Therefore, it is essential to investigate the impact of asymmetric mountainous terrain structures at tunnel portals on train aerodynamics.
Asymmetric mountainous structures (a) and (b) at tunnel portal.
Compared to the situation of a single train passing through a tunnel, two trains intersecting within the tunnel make airflow dynamics considerably more intricate, and pressure variations more pronounced [25, 26]. Scholars have conducted extensive research on the aerodynamic effects of trains passing each other inside tunnels using methods such as full-scale experiments and numerical simulations. Liu et al. [27] analysed the impact of two trains passing inside tunnels on tunnel wall pressures through full-scale experiments and found that it significantly influenced the peak pressures and the locations of their maxima, with the maximum pressure peaks occurring at the midpoint when the two trains meet at the midpoint of the tunnel. Somaschini et al. [28] conducted a series of full-scale experiments on trains intersecting each other within tunnels, providing a basis for setting standards for parameters such as sensor positioning, train speed and boundary conditions of relevant numerical simulations. Li et al. [29] employed the three-dimensional unsteady Reynolds-averaged Navier-Stokes (URANS) method to numerically simulate the aerodynamic effects of high-speed trains intersecting within tunnels, revealing that different intersection positions and tunnel lining structures had relatively minor effects on aerodynamic drag and lateral forces, whereas train speed had a significant impact on both. Chu et al. [25] conducted numerical simulations on trains’ intersection under different tunnel lengths, blockage ratios, train speeds and passing positions, indicating that when trains meet at the midpoint of the tunnel, the pressure coefficient and drag coefficient reach their maximum values, with these coefficients increasing with train speed and blockage ratio, and the maximum lateral force coefficient occurs when the two trains are aligned side by side. The presence of asymmetric mountainous terrain at tunnel portals results in significant differences in the flow field around each of the intersecting trains, which may have a considerable impact on the aerodynamic loads; therefore, safety risks of the operating trains and the most adverse positions of their intersection in the tunnel are still unclear, posing new challenges to the daily operational safety of trains and thus serving as the motivation for this study.
This study, based on the sliding mesh technique, employs the three-dimensional compressible URANS method and an implementable k-ε turbulence model for numerical simulations. It examines the influence of two different terrain conditions at tunnel entrances and exits—namely, the absence of mountainous terrain and the presence of asymmetric mountainous terrain—on the aerodynamic loads during train intersections. Both scenarios of intersection at the midpoint and at the tunnel portal of double-track tunnels are considered. By comparing the temporal variations of train aerodynamic loads, surface pressures on the train and characteristics of the nearby flow field, the study elucidates the reasons behind the changes in aerodynamic loads induced by asymmetric mountainous structures at tunnel portals. This research aims to provide theoretical guidance for preventing lateral oscillations of trains and for designing tunnel portal structures.
2. Methodology
2.1. Computational models
As illustrated in Fig. 2, the train model utilized in this study is a type of power-distributed high-speed train. This type of train is mostly operated on railroad lines with many tunnels such as canyons and hilly areas in southwest China and in Xinjiang, China. Geometric modelling is based on the actual structure and dimensions of the train. The train consists of the first car (power car), followed by seven intermediate cars and the ninth car (control car). The train model is of full-scale size at a width of W = 3.10 m, with the power car and control car heights being H1 = 4.03 m and H9 = 4.43 m, respectively. The height of the intermediate cars matches that of the control car. Taking into account additional structures such as air-conditioning units, the overall height of the train, denoted as H, is 4.70 m. The total length of the train is Ltr = 234.7 m, with a maximum cross-sectional area of Atr = 11.765 m2. Given the complexity of the complete train structure and to balance simulation efficiency and accuracy, the model replicates the fundamental structure of the train body and bogies while certain simplifications and omissions are made regarding the bogie structure and other minor auxiliary facilities.
Train model (unit: m).
As depicted in Fig. 3, the tunnels utilized in this study are double-track tunnels with a cross-sectional area of 63 m², which is a common size for conventional railway tunnels. The cross-section dimensions are from the Code for the Design of Railway Tunnels, China (TB10003-2016). The blockage ratio during the passage of two trains through the tunnel is 37.4%. The clearance between the train and the ground is set to 0.2 m, and the spacing between the centrelines of the double-track rails is 4 m.
Cross-section of the double-track tunnel with an area of 63 m² (unit: cm).
2.2. Computational domain and boundary conditions
In this study, the computational domain and boundary conditions for the intersection of two trains are depicted in Fig. 4. The computational domain consists of an internal domain representing the tunnel and two external domains representing the tunnel entrances. The tunnel length is set to 1000 m, and the external domains are modelled as two identical half-cylinders with a diameter of 120 m and a length of 500 m each, as shown in Fig. 4(a). The trains are positioned sufficiently far from the boundaries of the computational domain to ensure that the simulation of the flow field is not influenced by boundary effects, thus replicating the motion of the trains in the atmosphere. The external half-cylinder domain is vertically truncated to simulate the presence of asymmetric mountainous terrain at the tunnel entrances, as illustrated in Fig. 4(b). The positioning of the intersecting trains relative to the mountainous terrain at the tunnel entrances is depicted in Fig. 5, with asymmetric mountainous terrain present on the side of Train A at both ends of the tunnel entrances. Trains are running on the left side of the track in their respective directions of travel.
Geometric dimensions of computational domain: (a) tunnel entrance without mountainous terrain; (b) tunnel entrance with asymmetric mountainous structure.
Relative positions of tunnel portal mountain boundary and intersecting trains.
The well-recognized sliding mesh technique was used for numerical computations of train intersections [29, 30]. The configuration of the sliding zones and boundary conditions is depicted in Fig. 6. The coordinate system's origin, denoted as O, is positioned at the ground level near the centreline of the tunnel entrance closest to Train A. The X-axis is aligned along the longitudinal direction, the Y-axis along the lateral direction and the Z-axis along the vertical direction. The initial position of the nose of the train is 50 m from the tunnel portal, a distance that avoids air disturbances caused by the start of the train interfering with the pressure changes as the train enters the tunnel. The surfaces of the trains, the internal surfaces of the tunnel, the ground and the vertical boundaries at the tunnel entrances are designated as non-slip walls. The other boundaries of the external domain of the tunnel are defined as pressure outlets, representing the far-field boundaries. Train A and Train B move with respect to Zones 1 and 2, respectively, with the front and rear boundaries of the sliding blocks set as stagnation inlets, and the other boundaries set as interfaces.
Configuration of sliding mesh and interfaces.
2.3. Meshing scheme
The computational domain is meshed using the trimmed cell, as illustrated in Fig. 7. For the external domain of the semi-cylindrical tunnel, a polygonal directional grid is employed [31, 32]. The basic grid size in the sliding zone and its vicinity is set to 0.2 m, while the minimum grid size on the train surface is 0.1 m. Grid refinement is applied near the bogies, leading car and trailing car to ensure the accuracy of flow field simulations in these regions, as they are subject to more intense disturbances. The total number of grid cells is 36.28 million when there is no mountainous terrain at the tunnel portal, and 34.05 million when there is mountainous terrain, exceeding the grid density reported in relevant Refs. [26, 33, 34].
Schematic of grid strategy: (a) surface mesh at the tunnel portal; (b) surface mesh on the train; (c) mesh at cross-section Y = −2 m.
2.4. Solver description
To accurately capture the compressible effects of the train on the air inside the tunnel, the three-dimensional compressible URANS method is employed. The URANS model is a sophisticated CFD approach designed to simulate turbulent flows with time-dependent characteristics. It extends the traditional Reynolds-Averaged Navier-Stokes (RANS) framework, which averages the Navier-Stokes equations to account for turbulence effects, by incorporating unsteady terms to capture transient phenomena. URANS employs turbulence models, such as k−ε or k−ω, to derive additional equations for the turbulent kinetic energy and its dissipation. Unlike steady RANS models that assume time-invariance, URANS allows for the simulation of unsteady flows. This is crucial for accurately predicting phenomena like vortex shedding, flow separation and transient responses in systems subjected to varying conditions. The implementation of URANS requires sophisticated numerical methods to solve the coupled partial differential equations over time. Techniques such as time-stepping algorithms and adaptive mesh refinement are often employed to enhance accuracy and efficiency [35, 36]. In summary, the URANS model offers a balanced approach to turbulence simulation, allowing for the capture of essential unsteady effects while maintaining manageable computational demands.
García et al. [38] compared the predictive capabilities of three methods—large eddy simulation (LES), improved delayed detached eddy simulation (IDDES) and URANS—on the flow field around trains. It was concluded that LES provided the most accurate prediction of coherent near-wall wake structures, while IDDES and URANS were suitable for the mean field of the studied fluid [36]. Given that this study focuses not on the fine structure of vortices but on the overall flow characteristics, URANS is chosen as it ensures computational accuracy within an acceptable range while significantly reducing computational costs [37, 38]. The realizable k−ɛ two-equation turbulence model is employed for numerical solution [39, 40]. The physical time step is set to Δt = 0.0045 s, consistent with settings in the Refs. [26, 33], to ensure that the sliding zone moves 0.2 m within each time step, which aligns with the basic grid size, thus enhancing the accuracy of data exchange at the interface. The total physical duration is 31.5 s, with a total of 7000 iterations and a maximum internal iteration count of 5.
3. Validation
3.1. Mesh sensitivity
In Fig. 8, the computed results obtained from three sets of grid strategies (Table 1) are compared. A measurement point is selected at the midpoint of the surface of the second car during two trains’ intersection at the midpoint of the tunnel. Compared to the maximum pressure peak value obtained from the fine grid, the results from the coarse grid and medium grid differ by 12.3% and 0.9%, respectively. Considering the conservation of computational resources and enhancement of computational efficiency, the medium grid, which has relatively lower grid density but higher predictive accuracy, is chosen for the numerical simulations in this study.
Pressure at surface measurement points of the train under three grid strategies.
Parameter settings in grid strategies.
| Grid strategy | Smallest grid size (m) | Total number of cells | |
|---|---|---|---|
| Train surface | Tunnel surface | ||
| Coarse | 0.24 | 0.80 | 18,457,650 |
| Medium | 0.20 | 0.60 | 36,280,917 |
| Fine | 0.12 | 0.40 | 70,835,958 |
| Grid strategy | Smallest grid size (m) | Total number of cells | |
|---|---|---|---|
| Train surface | Tunnel surface | ||
| Coarse | 0.24 | 0.80 | 18,457,650 |
| Medium | 0.20 | 0.60 | 36,280,917 |
| Fine | 0.12 | 0.40 | 70,835,958 |
Parameter settings in grid strategies.
| Grid strategy | Smallest grid size (m) | Total number of cells | |
|---|---|---|---|
| Train surface | Tunnel surface | ||
| Coarse | 0.24 | 0.80 | 18,457,650 |
| Medium | 0.20 | 0.60 | 36,280,917 |
| Fine | 0.12 | 0.40 | 70,835,958 |
| Grid strategy | Smallest grid size (m) | Total number of cells | |
|---|---|---|---|
| Train surface | Tunnel surface | ||
| Coarse | 0.24 | 0.80 | 18,457,650 |
| Medium | 0.20 | 0.60 | 36,280,917 |
| Fine | 0.12 | 0.40 | 70,835,958 |
3.2. Numerical verification
To validate the effectiveness of the numerical simulation methods employed in this study, the numerical simulation results are compared with the results of the full-scale experiment. The selected full-scale experiment involves data collected from a certain model of high-speed train passing through the Meilongling Tunnel on the Wuhan-Guangzhou High-Speed Railway, China. The tunnel is 1188 m long, and the speeds of the train entering and exiting the tunnel are 294 km/h and 275 km/h, respectively [34]. The numerical simulation method proposed in this study is used to replicate this full-scale experiment scenario. Fig. 9 illustrates the comparison between the full-scale experiment and the numerical simulation results. The pressure data is obtained from the midpoint measurement point on the side of the seventh car. Compared to the full-scale experiment, the peak-to-peak pressure difference in the numerical simulation is 2.7% (the peak-to-peak value (PPV) here refers to the difference between the maximum peak value and the minimum peak value in the process of continuous change of pressure or aerodynamic force, and the definition in the later text is consistent with here). This suggests that the numerical simulation method adopted in this study is effective in reproducing real scenarios.
Comparison of full-scale experiment and numerical simulation pressure results (midpoint measurement point on the side of the seventh car).
4. Results and analysis
4.1. Impact of different intersection positions on train aerodynamics
Considering that the changes in the spatial surroundings of the trains during their intersections inside the tunnel compared to those at the tunnel entrance, and the relative positions of the train to the single-side mountainous structure, are different when the former enters and exits the tunnel, a comparison of the aerodynamic loads on the train at different intersection positions was conducted. The PPV of lateral force for the cars of Trains A and B are shown in Figs. 10(a) and (b), respectively. ‘M’ indicates an intersection at the midpoint of the tunnel. The tunnel ‘entrance’ and ‘exit’ are defined as where Train A enters and exits the tunnel, and ‘Train A’ refers to the one closer to the mountainous structure. ‘EN’ and ‘EX’ represent intersections occurring at the tunnel entrance and exit, respectively. ‘0’ indicates no single-side vertical mountainous structure at the tunnel entrance or exit, while ‘1’ indicates the presence of such a structure. The PPV of lateral force refers to the difference between the maximum positive and negative peaks of the train during intersection.
PPV of lateral force of the trains under different intersection scenarios: (a) Train A; (b) Train B.
For intersections at the tunnel entrance, the maximum PPVs of lateral force for each car occur at Car 1 or Car 9 (as indicated by the dashed lines in Fig. 10). Comparing the maximum values observed in each condition, it is found that in the ‘EN’ scenario, an asymmetric mountainous structure at the tunnel entrance reduces the PPV of lateral force for Car 9 of Train A (Car A9) by 12.2%, while increasing it for Car 1 of Train B (Car B1) by 7.5%. In the ‘EX’ scenario, the presence of the asymmetric mountainous structure reduces the PPV of lateral force for Car 1 of Train A (Car A1) by 12.7%, while increasing it for Car 9 of Train B (Car B9) by 16.5%.
As shown in Fig. 10, when the intersection occurs at the midpoint of the tunnel (denoted as ‘M’), the overall PPV of lateral force of the intersecting trains is relatively smaller compared to intersections at other positions. Additionally, regardless of whether there are mountains at the tunnel portal, the trend of PPV of lateral force variation for each car of the intersecting trains remains consistent. This observation suggests that the presence or absence of mountains at the tunnel entrance has minimal impact on the lateral forces experienced by intersecting trains inside the tunnel.
Fig. 11 illustrates the temporal variation of pressure differences between measurement points on opposite sides of different cars of Train A when the intersection occurs at the tunnel midpoint. The influence of the presence or absence of asymmetric mountainous structures at the tunnel portals on the peak pressure difference is not significant. However, when Car A1 enters and exits the tunnel, the mountainous structure at the tunnel portal suppresses the generation of peak pressure differences. This indicates that the presence of asymmetric mountainous structures at the tunnel entrance causes changes in air volume around the train, which affect the pressure experienced by a single train passing through the tunnel portal. Nevertheless, compared to the abrupt pressure changes during intersections, the pressure variations during this process are relatively minor.
Pressure difference variation between measurement points on opposite sides of Train A during intersection at the tunnel midpoint
As shown in Fig. 12, under both scenarios of intersection at the midpoint and the portal of the tunnel, the cross-sectional pressure contour maps taken at locations where the pressure difference between the two sides of the train is significant reveal notable differences. Comparing the trains intersecting inside the tunnel with those at the tunnel portal, it can be observed that during intersection inside the tunnel, airflow diffusion is constrained due to spatial limitations, and the movement of the trains induces rapid airflow within the narrow area, creating negative pressure zones around the trains. When the two trains intersect at the midpoint of the tunnel, the relative pressure difference on both sides of the train bodies of Train A and Train B (Fig. 12(a)) is smaller than when intersecting at the tunnel portal (Fig. 12(b)). This difference in pressure leads to variations in the PPV of lateral force between the two scenarios. Furthermore, due to the influence of the tunnel length, the impact of mountainous structures at the tunnel portal on the development of the airflow around the trains inside the tunnel is minimal. Therefore, to investigate the effect of asymmetric mountainous structures at the tunnel portal on the aerodynamic loads of intersecting trains, this study focuses on analysing scenarios involving intersection at the tunnel portal.
Comparison of pressure distribution around the trains between intersection at the tunnel midpoint and the tunnel portal: (a) Intersection at the tunnel portal; (b) Intersection at the tunnel midpoint.
Fig. 13 illustrates the temporal variations of pressure differentials at measurement points on both sides of the trains for the EN and EX scenarios. Under the EN scenario, as shown in Fig. 13(a), each car of Train A exhibits a sudden transition from positive to negative pressure differentials upon intersection. Furthermore, from Cars A1 to A9, the magnitude of the pressure differential peaks increases successively. Conversely, in Fig. 13(b), the pattern of pressure differential changes for measurement points on Train B is precisely opposite. Upon the encounter of the trains, a transition from negative to positive pressure differentials occurs, with the maximum peak observed at Car B1. For the EX scenario, a similar but reversed pattern is observed. The peaks of pressure differential transitions are maximal at Car A1 (Fig. 13(c)) and Car B9 (Fig. 13(d)), aligning with the cars identified with the highest PPV of lateral force in Fig. 10. Moreover, the comparison between the curves with and without tunnel entrance mountainous structures in Fig. 13 reveals that the influence of the mountainous structure at the tunnel entrance on the forces acting on the trains is difficult to discern in the pressure differentials between pairs of measurement points. To obtain deeper understandings of the mechanisms underlying the impact of mountainous structures at the tunnel entrance on the aerodynamic loads of intersecting trains, subsequent sections will further analyse the effect of surface pressure distribution on lateral forces.
Variation of pressure differentials at measurement points on both sides of the train's carriages during tunnel portal intersections: (a) Train A in EN scenario; (b) Train B in EN scenario; (c) Train A in EX scenario; (d) Train B in EX scenario.
4.2. Impact of asymmetric mountainous structures at tunnel portals on aerodynamics
To uncover the reasons behind the influence of asymmetric mountainous structures at tunnel portals on the aerodynamics of trains, an analysis was conducted on the variations in lateral forces of trains during intersections when Train A enters or exits the tunnel (EN and EX scenarios).
4.2.1. Changes in the time course of the aerodynamic load of the trains
Figs. 14(a) and (b) respectively depict the trace of train intersections and the time history curves of lateral forces at the maximum PPV for the EN and EX scenarios. HA, HA', TA and TA' represent the path of Car A1 nose, Car A1 rear end, Car A9 front end and Car A9 nose, respectively, while HB, HB', TB and TB' represent the path of Car B1 nose, Car B1 rear end, Car B9 front end and Car B9 car nose, respectively. In the plot, the time points of peak occurrence correspond to the positions of the encountering trains, as shown in Table 2.
Train intersection trajectories and lateral force time histories: (a) intersection of Train A entering the tunnel (EN); (b) intersection of A train exiting the tunnel (EX).
Symbol definitions and corresponding time points.
| Symbol | Position of trains | Time point (s) |
|---|---|---|
| T1 | The two trains’ front noses meet. | 23.63 |
| T2 | The nose of Car B1 meets the front end of Car A9. | 25.95 |
| T3 | The nose of Car B1 meets the nose of Car A9. | 26.27 |
| Symbol | Position of trains | Time point (s) |
|---|---|---|
| T1 | The two trains’ front noses meet. | 23.63 |
| T2 | The nose of Car B1 meets the front end of Car A9. | 25.95 |
| T3 | The nose of Car B1 meets the nose of Car A9. | 26.27 |
Symbol definitions and corresponding time points.
| Symbol | Position of trains | Time point (s) |
|---|---|---|
| T1 | The two trains’ front noses meet. | 23.63 |
| T2 | The nose of Car B1 meets the front end of Car A9. | 25.95 |
| T3 | The nose of Car B1 meets the nose of Car A9. | 26.27 |
| Symbol | Position of trains | Time point (s) |
|---|---|---|
| T1 | The two trains’ front noses meet. | 23.63 |
| T2 | The nose of Car B1 meets the front end of Car A9. | 25.95 |
| T3 | The nose of Car B1 meets the nose of Car A9. | 26.27 |
In the EN scenario, for Train B, the maximum PPV of lateral force occurs in Car B1 (as shown in Fig. 10(a)). Fig. 14(a) displays that this occurrence is due to the negative peak at T1 and the positive peak at T3. As depicted in Figs. 15(a) and (b), at T1, the two trains meet at the tunnel entrance. As Train A enters the tunnel, it compresses the air inside, generating positive pressure (Len Region) acting on the side of Car B1, which has not yet exited the tunnel, resulting in a negative lateral force peak value. Furthermore, the comparison of pressure distributions on different cross-sections reveals that the lateral force on the train primarily depends on the surrounding pressure near the transition between the near-nose streamlined section and the roof section (near the x = +6 m cross-section). However, whether there is an asymmetric mountainous structure at the tunnel entrance only causes a difference of 0.7% in the absolute value of the peak, indicating that the influence of the mountainous structure outside the tunnel entrance on this variation process inside the tunnel is very weak. Comparing Figs. 15(a) and (b), the presence of the mountainous structure at the tunnel entrance increases the positive pressure in the Len Region while decreasing the absolute value of the negative pressure in the Ren Region, resulting in little change in the relative pressure difference between the two sides of the train. The variation in the PPV of lateral force of Car B1 due to the influence of the asymmetric mountainous structure at the tunnel entrance is mainly reflected in the change in the positive peak value at T3, which increases by 21.3%. For Train A, the PPV of the lateral force in Car A1 (as shown in Fig. 10(a)) is shown in Fig. 14(a) to be due to the continuous variation process from time T2 to T3, representing the complete passage of the nose of Car B1 over Car A9. The asymmetric mountainous structure at the tunnel entrance reduces the positive peak value at T2 by 9.0% and decreases the absolute value of the negative peak value at time T3 by 14.3%.
Comparison of pressure distributions across the cross-sections of the train inside the tunnel at T1: (a) EN-0; (b) EN-1; (c) EX-0; (d) EX-1.
In the EX scenario, the maximum PPV of lateral force of Car A1 is attributed to the positive peak at T1 and the negative peak at T3. The presence of the asymmetric mountain structure at the tunnel exit reduces the positive peak at T1 by 11.7% and decreases the absolute value of the negative peak at T3 by 2.4%. The variation in the lateral force PPV of Car A1 during the encounter is primarily influenced by the conditions at T1, contrary to the results obtained for Car B1 in the EN scenario. This indicates a more pronounced effect of the asymmetric mountain structure at the tunnel portal on the lateral force PPV of the tunnel interior trains near the mountain side. This is attributed to a more significant decrease in the absolute value of negative pressure inside the Rex Region compared to the Ren Region, as evident in Figs. 15(b) and (d), stemming from the restrictive effect of the mountain on the airflow ahead of the tunnel interior trains near the mountainside. The maximum PPV of the lateral force of Car B9 arises from the continuous variations between times T2 and T3, as depicted in Fig. 14(b). At T2, a negative peak occurs, and the asymmetric mountain structure increases its absolute value by 15.7%. At T3, a positive peak occurs, and the asymmetric mountain structure increases its magnitude by 16.9%. Consequently, the asymmetric mountain structure significantly increases the risk of swaying for Car B9 during the intersection.
4.2.2. Evolution of the flow field around the trains
The continuous variation in lateral force from time T2 to T3 is the direct cause of swaying and affects operational safety. The presence of the mountain structure at the tunnel portal increases the risk of swaying for the trailing car away from the mountain side while potentially alleviating the swaying for the trailing car near the mountain side. To analyse the underlying reasons behind this variation, we selected time T3, which corresponds to the moment with the maximum absolute peak value, and analysed the evolution of the flow field around the encountering trains during this period.
Fig. 16 illustrates the pressure evolution on the Z = 1.3 m plane (height of the train nose) and the surface of the train from t = T3−0.08 s to t = T3+0.08 s in the EN-1 scenario, with colours representing the pressure scalar values. It elucidates the cause of the sudden change in lateral force at time T3: a pronounced negative pressure zone (Pen Region and Pex Region) forms between the encountering trains at T3. This region is located near the transition between the streamline and the roof of the train nose. When the streamline portions of the trains meet, there is a sudden change in the airflow space between the trains, leading to the emergence of negative pressure in the Pen Region and Pex Region (at t = T3−0.04 s). After the separation of the streamline portions, the airflow becomes relatively stable, and the negative pressure zones disappear (at t = T3+0.08 s). The pressure changes on the surfaces of the two encountering trains and their surroundings mainly occur at the respective transitions between the train's streamline portion and the roof, corresponding to the SA and SB sections. Fig. 17 presents the pressure distribution around the train cross-sections in the EN-1 scenario.
Top-down view of the pressure contour plot on the Z = 1.3 m plane and the train surface (EN-1).
Cross-sectional pressure contour plot (EN-1): (a) Section SA; (b) Section SB.
As shown in Fig. 17, for section SA, at t = T3−0.08 s, there is positive pressure on the right side of Car A9. This is due to the strong positive pressure formed by the forward movement of Train B, compressing the air in the −X direction, which was also the cause of the positive peak in the lateral force of Car A9 at T2. By t = T3−0.04 s, negative pressure has already appeared between the meeting trains, reaching its maximum at T3, as shown in the Pen Region. The significant negative pressure values are concentrated between the side walls of the meeting trains, with lower negative pressure values in the roof and bogie areas due to the expansion of airflow space. This negative pressure in the area creates a noticeable pressure difference between the two sides of the train body, resulting in lateral forces acting along the −Y direction on Car A9 and along the +Y direction on Car B1.
Fig. 18 illustrates the pressure variation process from t = T3−0.08 s to t = T3+0.08 s in the EX-1 scenario, with similar mechanisms to those in the EN-1 scenario (Fig. 16). Fig. 19 presents the pressure contour plot around the train cross-section in the EX-1 scenario. For section SA, at T3, a strong negative pressure appears in the Pex Region, creating a noticeable pressure difference between the two sides of the train body, resulting in lateral forces acting along the −Y direction on Car A1 and along the +Y direction on Car B9. For section SB, at t = T3−0.08 s, positive pressure appears on the left side of Car B9 due to the compression of air by the forward movement of Car A1 in the −X direction, which was also the cause of the positive peak in the lateral force of Car A1 at T2.
Top-down view of the pressure contours on the Z = 1.3 m plane and the train surface (EX-1).
Cross-sectional pressure contour plot (EX-1): (a) Section SA; (b) Section SB.
4.2.3. Mechanism of the effect of the mountain at the tunnel portal on the aerodynamic load of the trains
To investigate the influence of the asymmetric mountainous structure at the tunnel portal on the peak values of the lateral force acting on the meeting trains at T3, Fig. 20 compares the pressure and velocity vector fields around the trains at this moment at the SA (SB) cross-sections. In the figure, vector arrows represent the direction and magnitude of the synthesized airflow velocity in the Y and Z directions at corresponding positions, while the background colour represents the pressure contour map.
Comparison of velocity vectors at section SA (t = T3): (a) EN-0; (b) EN-1; (c) EX-0; (d) EX-1
As shown in Fig. 20(a), when there is no mountainous structure at the tunnel portal, the velocity vectors on the left side wall of Car A9 are mostly orientated along the −Y direction. However, with the presence of an asymmetric mountainous structure at the tunnel portal, as depicted in Fig. 20(b), the velocity vectors on the left side wall of Car A9 tend to change towards the +Z direction, with a decrease in magnitude along the YZ plane. The restriction imposed by the mountainous structure accelerates the longitudinal flow velocity between the mountain wall and the train, resulting in a decrease in the corresponding flow field pressure. Similarly, as shown in Fig. 20(c), when there is no mountainous structure at the tunnel entrance, the velocity vectors on the left side wall of Car A1 are mostly orientated along the +Y direction. However, with the presence of an asymmetric mountainous structure at the tunnel portal, as shown in Fig. 20(d), similar to Fig. 20(b), the acceleration effect of the fluid in the narrow space leads to a decrease in the flow field pressure.
Fig. 21 depicts the distribution of surface pressure along the left-side, top and right-side profiles of the train body at section SA (SB) at T3. It illustrates the influence of asymmetric mountainous structures at the tunnel portal on the pressure at various locations on the train's surface. To quantitatively describe the difference in pressure distribution, the difference in average pressure coefficient (|$\overline {\Delta {C_P}} $|) is defined as:
where θ represents the angular coordinate corresponding to the position on the train surface (as illustrated in Fig. 21), and CP1 and CP0 respectively denote the dimensionless pressure coefficients under the conditions of presence and absence of asymmetrical mountain structures at the tunnel portal. The dimensionless pressure coefficient CP is defined as follows:
where P is the surface pressure on the train; P0 is the reference pressure (taken as 0 here); ρ is the air density (taken as 1.225 kg/m³); and v is the train velocity (taken as 44.44 m/s).
Surface pressure distribution along cross-section SA of the intersecting trains: (a) Car A9 in EN; (b) Car B1 in EN; (c) Car A1 in EX; (d) Car B9 in EX.
For the EN scenario, in Fig. 21(a), the presence of asymmetrical mountain structures increases the negative pressure along the surface contour lines of Car A9. The |$\overline {\Delta {C_P}} $| on the left and right side walls of the car body are −0.051 and −0.028, respectively. The increase in pressure on the left side wall is greater than that on the right side, leading to an increment in lateral force along the +Y direction. Consequently, the absolute value of the negative peak lateral force of Car A9 decreases due to the presence of asymmetrical mountain structures. In Fig. 21(b), for Car B1, compared to the absence of mountain structures at the tunnel portal, the presence of such structures results in an increase in negative pressure along the surface contour lines of the car body. |$\overline {\Delta {C_P}} $| on the left- and right-side walls of the car body are −0.021 and −0.007, respectively, with an overall increment notably smaller than that for Car A9. This suggests that the influence of mountain structures on surface pressure is more significant for trains on the side closer to the mountain. The increase in pressure on the left side wall of Train B's 1st car is also greater than that on the right side, resulting in an increment in lateral force along the +Y direction. Consequently, the absolute value of the positive peak lateral force of Car B1 increases due to the presence of mountain structures.
For the EX scenario, as shown in Fig. 21(c), since Car A1 is a locomotive with a flat roof, the lateral force on the car body depends on the pressure distribution on both sides. The |$\overline {\Delta {C_P}} $| on the left and right side walls of the car body are −0.147 and −0.092, respectively. The increase in pressure on the left side wall is greater than that on the right side, resulting in an increment in lateral force along the +Y direction. Consequently, the absolute value of the negative peak lateral force of Car A1 decreases due to the presence of mountain structures. In Fig. 21(d), compared to the absence of mountain structures at the tunnel portal, the presence of such structures results in |$\overline {\Delta {C_P}} $| on the left- and right-side walls of Car B9 of −0.046 and 0.005, respectively, with an overall change significantly smaller than that for Car A1. This suggests that the influence of mountain structures on surface pressure is more significant for trains on the side closer to the mountain. The increase in pressure on the left-side wall of Car B9 is also greater than that on the right side, and similarly, the presence of mountain structures results in an increase in the absolute value of the positive peak lateral force of Car B9.
To further analyse the differences in pressure and flow fields around the trains with and without the presence of mountain structures at the tunnel portal, Figs. 22 and 23 respectively depict the velocity streamlines at three horizontal planes (Z = 1.3 m, Z = 2.5 m and Z = 3.7 m) at T3 for the EN and EX scenarios. The colour map represents the magnitude of the flow velocity.
Velocity streamlines at horizontal planes at T3 (EN).
Velocity streamlines at horizontal planes at T3 (EX).
In the EN scenario, as shown in Fig. 22, without mountain structures, the movement of Train A induces air near the train's surface to flow along the direction of the train's motion due to air viscosity. Meanwhile, air on the left side of Train A, away from the body sidewall, remains relatively stationary. The difference in air velocities between these two locations results in the formation of a counterclockwise rotating vortex, denoted as V1, on the left side of Train A. The airflow fills the space left behind by the train's passage, resulting in higher airflow velocity at the rear of the train. This velocity difference causes V1 to separate into a smaller vortex, V2, with the same rotation direction but a smaller scale. V1 is observed near the front end of Car A9, while V2 is found near the streamline and roof transition of Car A9, specifically around the SA section. Across different horizontal planes, the core of V1 shifts closer to the front end of the train and the left sidewall of Car A9 with increasing height. Similarly, the core of V2 moves closer to the left sidewall of the train with increasing height, but the scale of the vortex decreases, likely due to the restraint by the wake vortex flow of the train, leading to a decrease in pressure on the left surface of the train with increasing height, as observed in the SA section. However, when the left side of Train A is obstructed by an asymmetrical mountain structure, the restricted space between Train A and the mountain surface prevents the formation of vortices similar to those observed without the mountain structure. Consequently, without the retarding effect of the vortices, the airflow near the left side of Car A9 flows rapidly, resulting in significantly higher airflow velocity near the sidewall compared to the case without the mountain structure. This explanation rationalizes the phenomena observed in Figs. 20(a) and 21(a). At the Z = 3.7 m section, smaller vortices are formed between Car A9 and the mountain surface due to the proximity of this height section to the open area above the train's top, where the airflow forms a vortex similar to V2 influenced by the flow field at the rear of the train. However, these vortices have a limited impact on the main airflow characteristics between Train A and the mountain. The presence of an asymmetrical mountain structure at the tunnel entrance also causes the centreline of Train A's wake to shift closer to the mountain surface across different horizontal planes. These factors induce accelerated airflow on the left side of Car A9, leading to an overall decrease in pressure in that area and an increase in lateral force in the +Y direction. The presence or absence of a mountain structure at the tunnel entrance has little effect on the airflow on the right side of Train B, indicating that the dominant factor affecting the lateral force peak of Train B1 is the flow field between the two trains, consistent with the results obtained in Figs. 20(b) and 21(b).
In the EX scenario, as shown in Fig. 23, two vortices (V1 and V2) are generated on the right side of Car B9, following the same principle as the vortex formation on the left side of Car A9 in the EN scenario. When there is no asymmetrical mountain structure at the tunnel portal, the airflow near the left side of car A flows along with the movement of the train due to viscous effects. However, the pressure exerted by the front of car A on the air ahead causes the air to spread sideways, resulting in predominantly lateral airflow near the left side of Car A and the absence of vortices similar to those on the right side of Train B. Therefore, the correlation between the pressure on the left side of Train A and the height at the SA cross-section is not significant (Fig. 21(c)). In the presence of an asymmetrical mountain at the tunnel portal, the portion of air displaced by the advancing front of Train A enters the narrow space between Train A and the mountain wall, hindering the flow of air in that area. Consequently, the airflow velocity in that region is reduced, resulting in minimal differences compared to the scenario without the mountain. Therefore, the difference in the lateral force PPV for car A1 is also insignificant, consistent with the observation in Fig. 14(b).
Based on the analyses above, it is evident that the asymmetrical mountain at the tunnel portal has a significant impact on the variation of lateral forces experienced by trains during the intersecting process, thereby affecting the swaying phenomenon of trains. Considering different passing positions, the influence of the mountainous asymmetry at tunnel portals on the train is minimal when the intersection occurs at the midpoint of the tunnel. However, when the intersection occurs at the tunnel portal, the relative motion of the two trains and the air volume of the tunnel portal jointly affect the aerodynamic loads of the trains during their intersecting process, resulting in significant differences with and without the asymmetrical mountain structure. Particularly, there is a certain inhibitory effect on the sudden change in lateral forces for trains close to the mountain wall. Therefore, based on the findings of this study, it may be worth considering the modification of mountain structures at tunnel portals or the addition of buffer-like structures to mitigate the adverse effects of train swaying during train intersections in similar scenarios.
5. Conclusions
This study employs the URANS method to investigate the effect of asymmetrical mountain structures at tunnel portals on the aerodynamic loads of intersecting trains. Various passing positions are selected for comparison, and the influence of tunnel portal mountain structures on the peak lateral forces is analysed. The following conclusions are drawn:
1) When trains meet at the midpoint of a tunnel, the peak lateral forces of each carriage are generally smaller compared to when they meet at the tunnel portal. The influence of mountain structures at the tunnel portal on the peak lateral forces is minimal in such cases. For the meeting at the tunnel portal, the maximum peak lateral force of each carriage typically occurs at either the leading or the tail car. In the case of EN (encounter when Train A enters the tunnel), the presence of tunnel portal mountain structures leads to a 12.2% decrease in the peak lateral force of the 9th car of Train A and a 7.5% increase in the peak lateral force of the 1st carriage of Train B. In the case of EX (encounter when Train A exits the tunnel), the tunnel portal mountain structures cause a 12.7% decrease in the peak lateral force of Car A1 and a 16.5% increase in the peak lateral force of Car B9.
2) When the noses of the leading cars of both trains meet at the tunnel portal (t = T1), the lateral force on the leading car inside the tunnel reaches its peak. When the mountain presents at same side to the train at the tunnel portal, the absolute peak value of the lateral force significantly reduces by −11.7%. However, when the mountain is on the other side, its impact on the lateral force of the train is minimal (0.7%).
3) During the process when the nose of Car B1 completely passes over Car A9 (t = T2 − T3), significant changes occur in the lateral forces between the two trains, making the trailing car of the passing trains most susceptible to swaying. In the EN scenario, the presence of a mountain structure at the tunnel portal reduces the peak positive lateral force of Car A9 by 9.0% and decreases the absolute value of the peak negative force by 14.3%. Conversely, in the EX scenario, the mountain structure at the tunnel portal increases the absolute value of the peak negative lateral force of Car B9 by 15.7% and raises the peak positive force by 16.9%. At the tunnel portal encounter, the asymmetric mountain structure reduces the risk of swaying for the trailing car near the mountain but increases it for the trailing car away from the mountain.
4) When the two intersecting trains are exactly aligned laterally (t = T3), the absolute peak value of lateral force occurs during the continuous variation of lateral forces. At this moment, the pressure changes at the transition section between the head's streamline portion and the train body of the passing trains are the main factors contributing to the peak lateral force. In the EN scenario, the average pressure coefficient differences (|$\overline {\Delta {C_P}} $|) between the left and right sidewalls at the transition section between the streamline segment and the body of Car A9 are −0.051 and −0.028, respectively, while for Car B1 they are −0.021 and −0.007, respectively. In the EX scenario, |$\overline {\Delta {C_P}} $| at the transition section between the streamline segment and the body of Car A1 are −0.147 and −0.092, respectively, while for Car B9, they are −0.046 and 0.005, respectively.
5) The research conclusions above can provide guidance for preventing the lateral swaying of trains at tunnel portals. Asymmetrical flow field structures are the primary cause of sudden lateral force variations in intersecting trains. Subsequent studies could explore how to set up corresponding symmetrical buffer structures on the opposite side of the single-sided geological structure at tunnel portals or to modify the geological structure itself to alter the asymmetrical flow field characteristics. This approach aims to reduce the sudden lateral force variations experienced by intersecting trains when passing through tunnel portals, thus enhancing passenger comfort and operational safety.
Acknowledgements
This work was carried out in part using computing resources at the High Performance Computing Center of Central South University.
Funding
This work was supported by the Science and Technology Research and Development Program of China Railway (Grant No. N2023J016), the Science and Technology Innovation Program of Hunan Province, China (Grant No. 2022RC3040), the Natural Science Foundation of Hunan Province, China (Grant No. 2022JJ30727) and the Major Project of China Railway Design Corporation (Project No. 2022A02480004).
Conflict of interest statement
None declared.
