Unsteady slipstream of a train passing through a high

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Unsteady slipstream of a train passing through a high

2024-07-12 09:46| 来源: 网络整理| 查看: 265

Abstract

The cave is of great importance for the storage of equipment and to avoid having workers in the tunnel, but it changes the tunnel section, leads to a change of slipstream and affects the safety of trains and workers. The Re-normalization group (RNG) k-ε turbulence method is used to investigate the slipstream induced by a single train passing through a double-track tunnel at 350 km/h. The slipstream in a tunnel with and without a cave is compared. The slipstream components in three directions are reported comprehensively. The results show that the existence of a cave changes the slipstream at the tail of the train. At measurement points before and after the train passes the cave, the intensity of the slipstream at the tail is mitigated; as the train passes the cave, the tail slipstream is enhanced to a certain extent. With increasing lateral distance, the peak value of the slipstream with a cave decreases faster than that without a cave. These findings suggest that the presence of a cave mitigates the slipstream intensity, but special attention should be paid to the design of ancillary facilities, especially their relative location.

1. Introduction

When a high-speed train is running, the air gradually separates around the train body. The corresponding gust load by this air movement presents a potential safety hazard to workers, platform passengers and the infrastructure alongside the track [1, 2]. Open air and tunnels are two typical train operating conditions. So far, extensive studies have been carried out on open slipstreams [3–10]. However, the existing research suggests that the transient slipstream in the tunnel is even more serious [11]. It is necessary and practical to study the slipstream characteristics of trains in tunnels and the corresponding optimization measures [12].

In practical applications, when the tunnel length exceeds 500 m, many recessed caves are set up in the tunnel to store communication equipment, relay stations, transformers, lighting tools, maintenance tools and other emergency equipment. Because many tunnel lines have been built in China with additional lines being planned, there will be more and more tunnels with caves. The existence of the cave changes the structure of the tunnel wall, but the effect it has on the slipstream and how it changes the slipstream in the tunnel are unclear.

Scholars have carried out research on the slipstream in a tunnel. When a train enters a tunnel, a high-pressure area forms in front of the train head, pushing the air forward; in contrast, when the tail enters the tunnel, it forms a low-pressure area and draws air into the tunnel. However, due to the semi-closed nature of the tunnel, the air in the front that is pushed to the side cannot be released from the slipstream as quickly as that in open air, and thus can flow only along the train body towards the front or tail. This phenomenon is known as the piston effect [13]. Based on a computational fluid dynamics (CFD) simulation, and by establishing a theoretical model of piston wind, Liu et al. [14] reported the influences of five factors on the slipstream and found that the blocking ratio had the greatest influence on the piston air volume. Other scholars have also analysed the impacts of different factors on the slipstream in a tunnel, including the length of the train head [15] and the overall length of the train [16]. Fu et al. [17] analysed the development of the slipstream in the tunnel and the influences of different factors on the slipstream through a numerical simulation, and provided a reference for evaluating the transient gust load on workers alongside the rail and on-side facilities in the tunnel. The coupling effect of the airflow caused by the piston effect and tunnel wall, tunnel lining, safety door and other facilities greatly influences the security of train, tunnel and its ancillary facilities. Accordingly, Heine et al. [18] explored the influences of the shape and size of a hole in the middle of a double-tube tunnel on the pressure wave and the load of the safety door. Wang et al. [19] researched the effect of the tunnel lining on the aerodynamic load in the tunnel, showing that a change in tunnel wall structure will lead to a change in the aerodynamic effect in the tunnel. At present, extensive studies have been conducted to investigate the effects associated with slipstreams in the case of a smooth tunnel wall. Hence, this research is aimed mainly at the influence of a cave on the transient slipstream, which has a greater practical reference value for the stress conditions of the auxiliary facilities in a tunnel.

Double-track tunnels are widely common because they enable the two-way operation of high-speed railways and provide many economic benefits, and it is most typical for a single train to pass through a double-track tunnel [20]. This research analysed the slipstream of a single train travelling at 350 km/h through a double-track tunnel with a cave and compared the resulting slipstream with the slipstream in a tunnel without a cave. The corresponding Reynolds number is Re = 2.9e7. The three-dimensional compressible and unsteady Reynolds-averaged Navier-Stokes (RANS) method was used to study the flow field in the tunnel, and the sliding mesh technique combining the two equations of the k-ε turbulence model from commercial STAR-CCM CFD software was used for the numerical simulation. The speed distribution of trains passing through tunnels with caves and smooth tunnels were compared, as were the outcomes. The research content of this paper is expected to provide data support for the planning and placement of ancillary facilities in tunnels.

2. Methodology 2.1 Geometry

Two tunnel models are adopted, one with a cave and the other without a cave. The calculation model used for the tunnel with a cave is explained here. As shown in Fig. 1, the model of a domestic high-speed train (HST) is utilized herein. This full-scale model consists of eight railroad cars. The shapes of the first and tail cars are the same; the first car and tail car are 27.5 m, the six middle cars are 25 m, the overall width of the train is 3.36 m and the height of the train is 4.05 m. The model preserves the general shape characteristics of an HST, including the bogie, windshield, etc.. As shown in Fig. 2, the width of the cave is 4.0 m, the height is 2.8 m and the top surface is composed of a circular arc with a radius of 2.5 m; these dimensions reflect the standard cross-sectional shape of a cave in an HST tunnel. As shown in Fig. 3, the tunnel model has a cross-sectional area of 100 m2. The train was raised 0.2 m to simulate the track height. There is a distance of 5 m between the centerlines of the two tracks. The train is simulated as running towards the positive X-axis direction.

Fig. 1.

High-speed train model: (a) streamlined area of the train; (b) under-body configuration; (c) the front view of the train; (d) the side view of the train.

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Fig. 2.

Cave configuration: (a) dimensions; (b) the cave configuration in the tunnel.

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Fig. 3.

Tunnel configuration.

Open in new tabDownload slideThe tunnel length is the critical tunnel length. When this is the case, trains pass through the tunnel exactly at the negative pressure extreme value of the pressure wave [15, 20, 21]. The slipstream is caused by the existence of pressure difference. In the critical tunnel length, the pressure fluctuation is relatively violent and complex, so the critical tunnel length is selected. The critical tunnel length is calculated by the following formula: $$ \begin{equation*} {L_{tu,crit}} = \frac{{{L_{tr}}}}{4}\ \frac{c}{{{v_{tr}}}}\left( {1 + \frac{c}{{{v_{tr}}}}} \right) \end{equation*} $$(1)where Ltu,crit is the critical tunnel length, Ltr is the length of the train, c is the propagation speed of sound (340 m/s) and vtr is the velocity of the train(350 km/h). Based on Equation (1), the tunnel length is 806 m. 2.2 Computational domain and boundary conditions

As shown in Fig. 4(a), the domain is divided into the tunnel domain and the outer domain. The outer domain is composed of two identical cuboids with a length of 400 m, width of 80 m and height of 40 m. The train position is visualized in Fig. 4(a). The whole calculation region is divided into two zones: Zone A is the sliding region and Zone B is the static region. Zone A is a slender rectangular slider containing the train used in the calculation, while Zone B contains the outer area and part of the tunnel domain. To ensure the stability of the train when it abruptly enters the tunnel from the outer area, the train is initially placed 50 m from the tunnel entrance. To analyse the influence of the cave on the slipstream in the tunnel, the cave is placed at the midpoint of the tunnel, i.e. at x = 403 m. The cave is connected with the tunnel wall, and the cave is interconnected with the tunnel. The boundary condition at the end of the cave is the wall. A diagram of the boundary conditions is shown in Fig. 4(b). The relative motion between the tunnel and the train is realized by the sliding grid technique, which is one of the most convenient and effective methods for simulating the relative motions of trains and tunnels [22, 23].

Fig. 4.

Numerical calculation model and boundary conditions: (a) schematic of the computational domain and location of the cave; (b) boundary conditions.

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The moving boundary of Zone A is used to simulate the motion of the train. The surfaces of the train cars, ground and tunnel and the fronts of the outer domain are defined as stationary wall boundaries. The end surfaces of the sliding region are located 1400 m beyond the end of the stationary region; this guarantees that the end of the sliding region will not enter the stationary region after the train exits the tunnel.

2.3 Mesh scheme

The train calculation model retains most of the general shape characteristics of an HST, including the bogie and windshield. The grid of the sliding region is discretized by an unstructured grid near the train body. In contrast, the stationary area, sliding area and the sliding area far from the train body, including the cave, adopt a structural grid because of its relatively regular geometric boundaries. The meshing scheme used in the sliding area and the stationary area shown in Fig. 5 is relatively mature, similar to the division in the literature [24, 25]. Coarse grids, medium grids and fine grids are established separately. The total number of coarse grids is 19 million, the total number of medium grids is 26 million and the total number of fine grids is 38 million, where the grid sizes near the train bogie are 0.010 m, 0.008 m and 0.005 m, respectively. Different from the references, which all employ smooth tunnel walls, the tunnel in this paper includes a cave. Due to this change in the tunnel wall structure, a more precise mesh division is implemented for the cave, as shown in Fig. 6.

Fig. 5.

Grid strategy: (a) surface mesh at the tunnel portal; (b) surface mesh of the train body.

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Fig. 6.

Surface mesh for the cave: (a) internal surface; (b) outside surface.

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The reason why the three-dimensional compressible k-ε turbulence model is used to solve the flow in the tunnel is that the compressibility of air cannot be ignored considering the confined space in the tunnel. It has been widely used in the study of tunnel train aerodynamics [26–28]. The governing equations are the continuity equation, Navier-Stokes equation and energy equation. A relevant introduction to the governing equations can be found in Ref. [22].

The finite volume method (FVM) is used to solve the above governing equations, and the semi-implicit method for pressure linked-equations consistent (SIMPLE) algorithm is applied to handle the pressure-velocity coupling equation. The second-order upwind scheme is utilized to discretize the convection-diffusion terms. The transient term is addressed by using the second-order implicit scheme for the unsteady simulation. The train enters the tunnel at 0.51 s and exits the tunnel at 10.0 s, and the time step is set as 0.0021 s. The total calculation time is 12.0 s, and the number of iterations for each time step is 30.

2.5 Layout of monitoring points

A total of 33 measurement points are deployed along the tunnel to monitor the slipstream of the train in the tunnel. To explore the impact of the slipstream on the workers in the tunnel, the average height of a person is set as 1.7 m, and the height of the escape passage is 0.3 m, so the height of z = 2.0 m is employed as the focus of the discussion, as shown in Fig. 7. Ten monitoring points with a spacing of 0.5 m are deployed in the vertical direction on the left side. On the right side of the tunnel, the same 10 monitoring points are located above the centreline of the unoccupied track. In the lateral plane, only five monitoring points are located on the left side, because of the narrow clearance between the tunnel wall and the train. In contrast, on the right side of the tunnel, because the space is relatively open, a total of 12 monitoring points, with an interval of 0.5 m, are deployed starting from the centreline of the tunnel.

Fig. 7.

Arrangement of the monitoring points: (a) arrangement along the tunnel length; (b) arrangement on the cross section of the tunnel.

Open in new tabDownload slide 2.6 Data processing Data are processed using dimensionless coefficients. This data processing method is consistent with the literature [20]. The longitudinal, horizontal and vertical components of the dimensionless slipstream velocity are defined as u/V, v/V and w/V, where V is the velocity of the train. The dimensionless composite slipstream velocity is denoted by VR, which is defined as follows by combining the above three velocity components: $$ \begin{equation*} {V_R} = \frac{{\sqrt {{u^2} + {v^2} + {w^2}} }}{V} \end{equation*} $$(2) 3. Validation 3.1 Mesh density

In order to verify that the grid setting of this paper is more than reasonable, a grid independence study was conducted. Three different scales of meshes, namely, a coarse mesh, medium mesh and fine mesh, were generated with approximately 19 million, 26 million and 38 million cells, respectively. With a change in the mesh scale, the time step in the solution process was also changed. The time step of the coarse mesh was 0.0031 s, that of the medium mesh was 0.0021 s and that of the fine mesh was 0.0010 s. The detailed parameters of these three different meshes are shown in Table 1. The fixed point at x = 300 m on the left was selected for comparison, as presented in Fig. 8: the longitudinal slipstream velocity component and the pressure of this point. The calculation results of the medium mesh are basically consistent with those of the fine mesh. Hence, to conserve computational resources, the medium mesh scheme is selected for grid division.

Fig. 8.

Comparisons of the slipstream velocity and pressure variations at the fixed point (x = 300 m) among the different meshes: (a) longitudinal slipstream velocity component; (b) pressure coefficient.

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Parameters used in the three meshing schemes.

The density of mesh . Smallest mesh size/m . Grid spacing in the x direction . Total number of cells . Bogie . Train surface . Tunnel surface . Coarse mesh0.0100.0150.30.519 millionMedium mesh0.0080.0100.20.526 millionFine mesh0.0050.0080.10.538 million The density of mesh . Smallest mesh size/m . Grid spacing in the x direction . Total number of cells . Bogie . Train surface . Tunnel surface . Coarse mesh0.0100.0150.30.519 millionMedium mesh0.0080.0100.20.526 millionFine mesh0.0050.0080.10.538 millionTable 1. Open in new tab

Parameters used in the three meshing schemes.

To ensure the validity of the proposed numerical algorithm, we employed the same working conditions for the numerical calculation as moving model experiment conducted by Fu [29] in 2017, and compared the numerical calculation results with the data from the moving model experiment. It should be noted that the model used in the experiment was a three-train model, so the numerical simulation was also conducted with a three-train model.

The experiment was carried out on the moving model rig developed and built by Central South University. The variation in the longitudinal slipstream velocity caused by the train passing through the tunnel was recorded. A 1:20 scale model was adopted for the experiment, as shown in Fig. 9. The train model was generated with a length of 3.9 m, a height of 0.185 m and a width of 0.169 m. The tunnel model with a length of 15 m, a headroom cross-sectional area of 0.25 m2 and a line spacing of 0.25 m was used to simulate an actual double-track tunnel with a cross-sectional area of 100 m2 and a length of 300 m.

Fig. 9.

Moving model test: (a) tunnel model; (b) train model.

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The measurement points were arranged at the tunnel entrance cross-section, while the measurement points for the slipstream velocity and pressure coefficient were deployed on the cross-section 1.35 m from the tunnel entrance. The measurement point of the slipstream velocity was 32 cm from the tunnel entrance and 10 cm above the ground. The measurement point of the pressure coefficient was 32 cm from the tunnel centreline and 20 cm above the ground.

Fig. 10 compares the numerical simulation curves of the slipstream velocity and pressure variations with the results of the moving model experiment, the curves of which were obtained by averaging the test results from three experiments. The simulation results show that the evolutionary processes of the simulated slipstream velocity and pressure coefficient are basically consistent with those recorded during the moving model test. Therefore, the proposed algorithm was deemed effective, and its calculation results can be considered reliable.

Fig. 10.

Comparisons of the slipstream velocity and pressure variations from the experiment and the simulation: (a) slipstream velocity 32 cm from the tunnel entrance; (b) pressure 32 cm from the tunnel entrance.

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Fig. 11.

Comparison of the results of tunnel wall wind pressure variation from the dynamic model test and numerical simulation.

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The tunnel wall in the above moving model test is a smooth wall. Considering that the change of the tunnel wall structure may have an impact on the flow field structure in the tunnel, the accuracy of the numerical method calculation should be verified under the condition with the change of the tunnel wall condition. Wang et al. [19] analysed the influence of tunnel lining on pressure fluctuations in the tunnel, so we established the same numerical simulation model of the tunnel with lining to monitor pressure waves near the tunnel wall. In this numerical simulation, the train passes through a 350 m long tunnel at a speed of 250 km/h, and the measuring point is located 49 m away from the tunnel entrance.

Table 2 and Fig. 11 are the comparison of numerical simulation results and 1:20 moving model test [19]. It can be seen that the pressure time-history curve waveform near the tunnel wall is in good agreement with the moving model test results. The maximum difference between the results of numerical calculation and moving model test is less than 3%. Since train wind is actually caused by changing pressure, the train wind velocity data is also reliable in the case of favourable pressure data. Therefore, the numerical calculation method in this study can accurately simulate the flow field structure in the tunnel when the tunnel wall condition changes.

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Comparison of peak wind pressure near the tunnel wall.

Type . Positive peak/Pa . Negative peak/Pa . Peak-to-peak/Pa . Moving model test1598.79−1381.082979.87Numerical simulation1551.84−1353.642905.48Error rate2.94%1.99%2.50% Type . Positive peak/Pa . Negative peak/Pa . Peak-to-peak/Pa . Moving model test1598.79−1381.082979.87Numerical simulation1551.84−1353.642905.48Error rate2.94%1.99%2.50%Table 2. Open in new tab

Comparison of peak wind pressure near the tunnel wall.

Aerodynamics is essentially a transient process, and thus the data from the measurement points at the same position in different time periods will vary considerably. In order to study the formation mechanism and evolution law of slipstream, the measurement points in the tunnel with a cave are analysed in this section. As the essence of slipstream is caused by the existence of pressure difference, when analysing slipstream, considering the full development of slipstream and the complexity of pressure wave system in a tunnel, the speed components of slipstream at position x = 656 m in all three directions are selected for analysis.The coordinates of one measurement point are x = 656 m, y = 5.5 m and z = 2.0 m, and the y-axis and z-axis coordinates of the following unmarked measurement points are the same as this measurement point.

Fig. 12 shows the time histories of the longitudinal (u/V), transverse (v/V) and vertical (w/V) slipstream components. The times when the first car and the tail car arrive at the measurement point are t = N and t = T, respectively. As shown in Fig. 11, before the train arrives at the measurement point, the velocities of the transverse and vertical components are stable at 0. When the train arrives at the measurement point at time N, both the transverse and the vertical slipstream velocity components generate positive fluctuations. After the first car passes, the slipstream velocity fluctuates near 0. With the passing of the tail car, the transverse slipstream component produces negative fluctuations, but the vertical slipstream component produces positive fluctuations due to the influence of the tail car. At t = T, when the tail car passes through the measurement point, the lateral and vertical components of the slipstream velocity decrease rapidly and stabilize at 0 after a period of fluctuation. These results demonstrate that the slipstream velocity in the tunnel is dominated by the longitudinal component, while the influences of the transverse and vertical velocity components on the resultant velocity are not obvious. The findings of previous studies conducted via model tests or numerical simulations seem to confirm this argument [30]. Therefore, the following analysis focuses mainly on the longitudinal slipstream velocity component.

Fig. 12.

Evolution of the three slipstream velocity components at x = 656 m.

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The time history of the longitudinal slipstream velocity can be divided into three stages with different characteristics according to the train arrival and departure times at the monitoring point. The train enters the tunnel at t = En. Due to the piston effect, the longitudinal slipstream velocity in the tunnel increases rapidly, approximately 0.5 s after the train enters the tunnel, and then fluctuates, but the slipstream velocity is always positive. When the train passes the measurement point, the slipstream velocity in the annular space increases first and then decreases rapidly, changes direction and finally reaches a negative peak. As the train passes, the longitudinal velocity decreases and the sign changes. In the wake area, the slipstream velocity reaches its peak when the tail car passes the measurement point. When the train passes through the measuring point at a high speed, the air velocity at the rear is far less than the speed of the train, so a partial vacuum area will be generated at the position where the train passes through, resulting in pressure difference. Therefore, when the train passes through the measuring point, the slipstream speed of the train will change significantly. After the train passes, the velocity of the slipstream at the measurement point decreases gradually, and then the train exits the tunnel.

The longitudinal slipstream velocity at x = 656 m experiences two stages of increase and two stages of decrease before the train reaches the measurement point. The piston effect is not responsible for this phenomenon. By observing the waveform of the slipstream at the measurement point and the time history of the wave, as shown in Fig. 13, it is not difficult to connect the slipstream in the tunnel with the compression wave and expansion wave when the train enters the tunnel. Fig. 13 shows the time histories of the slipstream velocity components at x = 656 m and their relation to the Mach wave. The pink line represents the path of the train head, while the yellow line represents the path of the train tail. The blue line represents the pressure wave generated by the first car, the red line represents the pressure wave generated by the tail car, the solid line represents the compression wave and the dashed line represents the expansion wave. The compression wave generated when the train enters the tunnel reaches the measurement point at t1 = 2.44 s, which is when the slipstream velocity increases for the first time. The second increase in the slipstream velocity occurs at t2 = 3.33 s, which is due to the reflection of the compression wave from the tunnel exit and its transformation into an expansion wave. The expansion wave generated when the tail car enters the tunnel reaches the measurement point at t3 = 4.55 s, which is when the slipstream velocity decreases for the first time. At t4 = 5.43 s, the expansion wave passes through the reflection of the tunnel outlet and transforms into a compression wave to reach the measurement point, causing the slipstream velocity at the measurement point to decrease for the second time.

Fig. 13.

Evolution of the airflow slipstream component u at x = 656 m: (a) propagation of compression and expansion waves; (b) time history of pressure variation.

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Then, both the train and the reflected compression wave arrive at the measurement point at nearly the same time; as a result, the slipstream velocity increases slightly and then drops rapidly. When the expansion wave reflected from the tunnel outlet reaches the measurement point at t6 = 8.07 s, the slipstream velocity increases. At t7 = 9.29 s, the tail end and the expansion wave generated by the tail end reach the measurement point; therefore, the slipstream velocity first increases and then obviously decreases, which is influenced by the superposition of the passage of the tail end and the expansion wave. Classification analysis reveals that when the compression wave propagates in the same direction as the train or when the expansion wave propagates in the opposite direction of the train, the slipstream velocity increases at the measurement points in the tunnel. When the compression wave propagates in the direction opposite to the train or when the expansion wave propagates in the same direction as the train, the slipstream velocity decreases at the measurement points in the tunnel. These outcomes are consistent with the relevant research [31, 32].

4.2 Influence of the cave on the slipstream

Scholars have found that changing the cross-sectional area of a tunnel changes the surrounding aerodynamics [26]. With the existence of a cave, the cross-sectional area of the tunnel changes at the location of the cave. Thus, to explore the influence of such a cave on the slipstream in the tunnel and the extent of its influence, this section comparatively analyses the slipstreams in the tunnel models with and without a cave. Fig. 14 shows the variations in the peak of the longitudinal slipstream velocity component along the tunnel direction under the two different tunnel wall conditions. The slipstream before reaching the cave area exhibits a relief effect. The location of the maximum mitigation effect is 300 m, and the mitigation effect reaches 26.7%. At the location of the cave, the slipstream peak is generated, and the enhancement effect reaches 17.6%. Subsequently, the peak of the slipstream in the latter half of the tunnel displays a mitigation effect, and the mitigation effect reaches 19.2% at x = 656 m. For the slipstream as a whole, the existence of a cave relieves the slipstream in the tunnel, although the relief effect at the entrance of the tunnel is small. This is mainly due to the higher complexity of changes in the flow at the tunnel entrance and tunnel exit; because these areas are directly connected with the outer area, the more comprehensive factors suffer from the flow being more complex.

Fig. 14.

Distribution of the slipstream peak along the tunnel.

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To analyse the effect of the specific position of the cave, Fig. 15 (a) shows the peak distribution of the slipstream near the cave location, and Fig. 15 (b) shows the time history curve of the slipstream velocity on a cross-section through the centre of the cave. In front of the cave, the peak value of the slipstream still shows the mitigation effect. Given a smooth tunnel wall, the peak slipstream velocity at the midpoint of the tunnel decreases gradually as the position of the measurement point moves forward. However, when there is a cave at the midpoint of the tunnel, the peak slipstream velocity increases at the location of the cave. The time history curve demonstrates that the influence of the cave on the slipstream in the tunnel is concentrated mainly in the wake area after the train passes. This is due to the asymmetry of the double-track tunnel when a single train passes through it. As the cross-sectional area of the cave increases, the air flow on the left is squeezed into the cave, resulting in more air behind the core of the wake offset to the side of the tunnel with the cave. Hence the position of the slipstream peak velocity in the longitudinal centre of the cave. Fig. 16 shows the slipstream profile when the rear of the train passes the cave, which confirms this hypothesis.

Fig. 15.

Slipstream velocity near the cave: (a) distribution of the peak; (b) comparison of the slipstream at x = 403 m.

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Fig. 16.

Velocity magnitude contours at t = 6.8 s.

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Because x = 300 m and x = 656 m are the positions where the slipstream velocities are optimally relieved in the first and second halves of the tunnel, respectively, the reasons for their influences are different. Fig. 17 shows the time history curves of the slipstream velocity in the case of a smooth tunnel and a tunnel with a cave. At x = 300 m, the area affected by the cave is the same as that at x = 403 m, which is the near-wake area after the train passes. However, at x = 300 m, there is a mitigation effect. This near-wake flow mitigation effect is mainly due to the slipstream flowing into the cave forming a vortex when the train passes by because of the obvious pressure difference between the interior and exterior of the cave. A slipstream flows into the tunnel with a certain angle in the direction opposite to that of the train, weakening the flow separation around the train surface. Therefore, the annular area contains more slipstream, which does not follow the train forward but remains at the tail of the train. As more of the slipstream stays at the tail of the train, the suction effect caused by the train passing through the tunnel is weakened. Therefore, the slipstream velocity peak at the measurement point in the first half of the tunnel shows a mitigation effect. This can be verified by Fig. 18.

Fig. 17.

Comparison of the slipstream velocities at (a) x = 300 m and (b) x = 656 m.

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Fig. 18.

Slipstream velocity profile in the wake region at t = 5.525 s.

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In contrast, at x = 656 m, after the train passes the cave, the influence of the cave is alleviated in the near-wake area. This is because when the train wake passes the cave, part of the high-speed wake near the tail is squeezed into the cave due to the asymmetry of the slipstream in the tunnel. Therefore, at the measurement point after passing the tunnel, the wake intensity generated by the train is reduced.

The velocity profile indicates that the slipstream velocity on the right side of the tunnel is relatively small, and the influence of the cave on the slipstream is relatively small. Fig. 19 plots the slipstream time history on the side of the track opposite the cave, indicating that the influence of the cave on the slipstream on this side of the tunnel exists in the near-wake area. However, a comparison of the peak values suggests that, different from the slipstream on the occupied track, on which the peak slipstream velocity occurs after the tail car passes, the peak value of the slipstream on the unoccupied track occurs before the train arrives. Nevertheless, the difference between the tunnels with and without a cave is relatively small, while the peak slipstream value on the train-occupied track is approximately six times that on the unoccupied track.

Fig. 19.

Comparison of the slipstream velocities on the side of the tunnel opposite the train.

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As many scholars have pointed out, the maximum intensity of the open-air slipstream is strongly related to the distance from the vehicle body [33]. According to the analysis of section 4.2, it can be known that the slipstream has been significantly enhanced at the location of the cave, and understanding the velocity flow field and velocity distribution near the cave is conducive to improving the safety of personnel and equipment at the location of the cave. Figs. 20 (a) and (b) show the slipstream time history curves at the cave location on the occupied and unoccupied tracks, respectively, and Figs. 20 (c) and (d) show the corresponding slipstream peak curves on the occupied and unoccupied tracks. With increasing transverse distance, the peak of the slipstream velocity decreases gradually. According to the rate of change in the slipstream peak value on the occupied track, the lateral distance can be roughly divided into a rapid descent region and a stable region. By comparing the slipstream peak in the presence of a cave with that in the case of a smooth tunnel wall, the limiting effect of the tunnel wall with a cave decreases due to the increase in tunnel cross-section area, so the slipstream peak on the train-occupied track decreases faster, while the peak velocity on the unoccupied track is almost unaffected by the presence of a cave.

Fig. 20.

Lateral distribution of the slipstream peak: (a) slipstream evolution on the occupied track; (b) slipstream evolution on the unoccupied track; (c) distribution of peaks on the occupied track; (d) distributions of peaks on the unoccupied track.

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The lateral distance on the unoccupied track can also be divided into a rapid descent region and a stable region based on the rate of change in the slipstream peak. This is because when at distances less than 2.5 m from the centreline of the tunnel, the slipstream peak appears at the train arrival time. However, before the passage of the train, the slipstream in the tunnel has a strong one-dimensional effect, so the slipstream peak on the unoccupied track remains basically the same.

Fig. 21 shows cross-sections of the velocity through the midpoint of the tunnel when the tail of the train passes through the cave. The slipstream is clearly inclined towards the cave; in addition, the wake height is raised, and due to the existence of the cave, the limiting effect of the tunnel wall is reduced, causing the transverse distribution of the slipstream at the tunnel position to be gentler. After the train passes, compared with when the train is passing by, the change in the slipstream peak shows the opposite trend. This is due to the asymmetry of the tunnel: there is a velocity pressure difference on the left and right sides. This phenomenon can be verified by the slipstream velocity profile in the train wake area shown in Fig. 22.

Fig. 21.

Comparison of velocity profiles at t = 6.8 s: (a) with cave; (b) without cave.

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Fig. 22.

Slipstream velocity profile in the wake region at t = 7.65 s.

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The vertical height in the tunnel is another important factor affecting the slipstream peak, as shown in Fig. 21, which indicates that the vertical distribution of the slipstream peak also changes due to the existence of the cave. Figs. 23 (a) and (b) show the variation curve of the longitudinal slipstream velocity peak with different vertical heights at the cave location of the occupied and unoccupied tracks, respectively. In general, the vertical and horizontal distributions of the longitudinal slipstream velocity component at different locations are the same, gradually decreasing with increasing distance. However, unlike that on the occupied track, the slipstream peak on the unoccupied track is reached before the train arrives. This is because the unoccupied track is far from the train body and is less affected by the wake of the train. Fig. 24 shows that with increasing vertical height, the rate of decrease in the slipstream peak velocity gradually slows. The slipstream velocities near the front of the vehicle, bogie and other equipment are maximal. In the middle area, the slipstream peak decreases quickly with increasing vertical height. In the upper area (near or above the top of the train), due to the large amount of open space at the top of the tunnel, the rate of decrease in the slipstream peak velocity is slow and is less affected by the movement of the train. According to the rate of change in the slipstream peak velocity, the vertical height can be roughly divided into a high-speed region, a rapid descent region and a slow descent region. The peak value of the slipstream velocity with a cave is larger than that without a cave in the range of 0-2.8 m, which is caused by the reduction in the limiting effect of the tunnel wall in the range of 0-2.8 m and the offset of high-speed slip flow in the wake area. The cave has little effect on the slipstream peak in the range from z = 2.8 m to z = 4.5 m, because the limiting effect of the tunnel wall is not reduced in this area. It should be noted that the sensitivity of the slipstream peak to the vertical height is greater than that to the transverse distance, which is very different from the characteristics in open air [34], where the sensitivity of the slipstream peak to the vertical height is much weaker than that to the transverse distance. This is because in the transverse direction, the tunnel wall has great limitation, while in the vertical direction, due to the greater amount of free space at the top of the tunnel, the air flow can ventilate.

Fig. 23.

Vertical distribution of the slipstream: (a) slipstream evolution on the occupied track; (b) slipstream evolution on the unoccupied track.

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Fig. 24.

Distribution of the peak value of slipstream velocity u with the vertical distance.

Open in new tabDownload slide 5. Conclusions

The unsteady RANS method is used to study the slipstream induced by a single train passing through a double-track tunnel. The numerical calculation method is validated by a previous moving model test, and good consistency is obtained. The results are summarized as follows:

1). The pressure wave in the tunnel has a certain impact on the air flow. When the propagation direction of the compression wave is the same as the train or when the propagation direction of the expansion wave is opposite the train, the slipstream velocity increases. In contrast, when the propagation direction of the compression wave is opposite the movement of the train or when the propagation direction of the expansion wave is the same as the train, the slipstream velocity decreases.

2). The influence of the cave on the slipstream in the tunnel can be divided into three sections: in front of the cave, the position of the cave and beyond the cave. In front of and beyond the cave, the influence of the cave on the slipstream is mitigated, but at the position of the cave, the slipstream velocity increases. The position in front of the cave at which this effect is optimally mitigated is 300 m from the tunnel entrance. Moreover, the existence of the cave weakens the flow separation around the train. In contrast, at the position of the cave, the tail flow direction at the core of the train tail deviates from the side of the cave, and the slipstream peak surges with a maximum enhancement effect of 17.6%. Then, beyond the cave, the effect is again mitigated. Because some of the high-speed wake in the near-wake area is squeezed into the cave due to the asymmetry of the slipstream in the tunnel, the wake intensity generated by the train passing by the measurement point beyond the cave is reduced.

3). With increasing lateral distance, the peak value of the slipstream velocity decreases gradually. According to the rate of change in the slipstream peak, the lateral distance on the occupied track can be roughly divided into a rapid descent region and a stable region. The slipstream peak value with a cave decreases faster than that with a smooth tunnel wall. Like the behaviour with the transverse distance, the slipstream peak value gradually decreases with increasing vertical height. According to the rate of change in the slipstream peak velocity, the vertical height can be roughly divided into a high-speed region, rapid descent region and slow descent region. Due to the offset of the high speed slipstream in the wake area, the slipstream of the train with a cave is relatively large near the ground. It should be noted that the sensitivity of the slipstream peak to the vertical height is greater than that to the transverse distance.

Credit authorship contribution statement

Xiaohui Xiong: Investigation, Writing – original draft, Writing – review & editing, Formal analysis. Rilong Cong: Investigation, Formal analysis, Writing – review & editing. Xiaobai Li: Writing – review & editing. Yutang Geng: Formal analysis, Writing – review & editing. Mingzan Tang: Investigation. Shujun Zhou: Investigation. Yanling Na: Formal analysis. Chongxu Jiang: Formal analysis.

ACKNOWLEDGEMENTS

The authors acknowledge computing resources provided by the High-Speed Train Research Center of Central South University, China. This work was supported by the National Key Research and Development Program of China (Grant No. 2020YFA0710903-01), and the Graduate Student Independent Innovation Project of Hunan Province (Grant No. CX20200196).

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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© The Author(s) 2022. Published by Oxford University Press on behalf of Central South University Press.This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact [email protected]

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