J. Cent. South Univ. (2018) 25: 2831-2840

DOI: https://doi.org/10.1007/s11771-018-3956-8

Influence of enlarged section parameters on pressure transients of high-speed train passing through a tunnel

WANG Tian-tian(王田天)¹, LEE Chun-hian(李椿萱)¹, YANG Ming-zhi(杨明智)²

1. National Laboratory for Computational Fluid Dynamics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China;

2. Key Laboratory of Traffic Safety on Track of Ministry of Education, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: The influence of enlarged section parameters on pressure transients of high-speed train passing through a tunnel was investigated by numerical simulation. The calculation results obtained by the structured and unstructured grid and the experimental results of smooth wall tunnel were verified. Numerical simulation studies were conducted on three tunnel enlarged section parameters, the enlarged section distribution along circumferential direction, the enlarged section area and the enlarged section distribution along tunnel length direction. The calculation results show that the influence of the different enlarged section distributions along tunnel circumferential direction on pressure transients in the tunnel is basically consistent. There is an optimal enlarged section area for the minimum value of the pressure variation amplitude and the average pressure variation in the tunnel. The law of the pressure variation amplitude and the average pressure variation of the enlarged section distribution along tunnel length direction are obtained.

Key words: high-speed train; enlarged section parameters; tunnel; pressure transients

Cite this article as: WANG Tian-tian, LEE Chun-hian, YANG Ming-zhi. Influence of enlarged section parameters on pressure transients of high-speed train passing through a tunnel [J]. Journal of Central South University, 2018, 25(11): 2831–2840. DOI: https://doi.org/10.1007/s11771-018-3956-8.

1 Introduction

With the increase of train running speed, the pressure transients of high-speed train passing through a tunnel will increase sharply, which will lead to more intense alternating tunnel wall pressure load [1]. It will increase the fatigue damage to the tunnel wall. The most basic remedy to the problem is to slow down the pressure transients in the tunnel.

The study of the flow field around train is the basis for studying the pressure transients of high-speed train passing through a tunnel. KIM et al [2], FU et al [3], TIAN et al [4] and MEHRDAD et al [5] experimentally and numerically studied the slipstream development and the flow structure of airflow around train. LIU et al [6] studied the transient loads and their influence on the dynamic responses of trains in a tunnel. The influence of tunnel parameters on the pressure transients in tunnel is obvious. ZHOU [7], LIU et al [8], DANIEL et al [9] and ZHOU et al [10] numerically studied pressure transients in high-speed trains passing through tunnels of different tunnel parameters. In order to reduce the pressure transients, YANG et al [11] and ZHANG et al [12] studied oblique tunnel portal effect on pressure transients of high-speed train passing through a tunnel. LI et al [13, 14] studied the effect of auxiliary structures, such as cross passage and shaft, on pressure transients in a tunnel.

However, the influence of the change of tunnel wall shape on the pressure transients of high-speed train passing through a tunnel is rarely studied. PESAVA et al [15] and HOWE et al [16] studied the effect of baffle plates on the propagation of compression waves through a tunnel. LUO et al [17] studied the influence of overall enlarged sections on pressure waves in high-speed metro tunnels. In fact, because the tunnel is relatively sealed, the pressure transients in tunnel are very sensitive to the change of tunnel wall shape when high-speed train passes through the tunnel at high speed. In this work, the influence of enlarged section parameters on pressure transients of high-speed train passing through a tunnel is adopted for studying the effect of the change of tunnel wall shape on pressure transients. The results are the basis for research on engineering reducing the pressure transients of high-speed train passing through a tunnel.

2 Calculation model and method

A certain type of three-car marshalling train was adopted for calculation, with 79.77 m length. Schematic diagram is shown in Figure 1.

The 70 m² standard tunnel was adopted for calculation, with 350 m length. Tunnel cross- section dimensional drawing is shown in Figure 2.

Figure 1 High-speed train model

Figure 2 Tunnel cross-section dimensional drawing (unit: m)

In this work, three tunnel enlarged section parameters were studied, namely, the enlarged section distribution along circumferential direction, the enlarged section area and the enlarged section distribution along tunnel length direction.

A total of 4 groups of the enlarged section distributions along circumferential direction were selected in this work. The enlarged section in each distribution was 2.2 m in width, 1 m in height and 5 m in length along tunnel length direction. The enlarged section distributions and dimensions are shown in Figure 3.

Figure 3 Enlarged section distribution along circumferential direction (unit: m)

In the distribution ①, an enlarged section was added at the top of the tunnel. In the distributions ②–④, an enlarged section was added in the symmetrical position of the left and right sides of the tunnel. The positions of the enlarged section in the distributions ②–④ were 7.54 m, 5.77 m and 2.68 m to the tunnel bottom, respectively. According to the experimental and calculation results of the smooth wall tunnel, the location of 70–100 m away from the tunnel entrance is an important position for the pressure transients in the whole tunnel. As a result, the enlarged section was added at this location. The front end of the enlarged section in each distribution was 70 m, 80 m and 90 m away from the tunnel entrance, respectively. Therefore, a total of 12 enlarged section distributions along circumferential direction were set.

A total of 4 groups of the enlarged section areas were selected in this work. The enlarged section in each distribution was magnified by a certain proportion of the smooth wall tunnel cross-section, as shown in Figure 4. The area was 81.36 m², 93.48 m², 106.38 m² and 120.05 m², respectively. The enlarged section in each distribution was 5 m in length along tunnel length direction. For the mentioned reason, the front end of the enlarged section in each distribution was 70, 80 and 90 m away from the tunnel entrance, respectively. A total of 12 enlarged section areas were set.

Figure 4 Enlarged section area

According to the calculation results of different groups of the enlarged section areas, the 93.48 m² enlarged section was selected to study the influence of the enlarged section distribution along tunnel length direction on pressure transients in the tunnel. The front end of the enlarged section was 60, 70, 80, 90, 100, 110, 120, 130, 140 and 150 m away from the tunnel entrance, respectively. The enlarged section in each distribution was 5 m in length along tunnel length direction.

For each enlarged section distribution, the train passed through the tunnel at 250, 300 and 350 km/h. Therefore, 36, 36 and 30 calculation examples for the enlarged section distribution along circumferential direction, the enlarged section area and the enlarged section distribution along tunnel length direction were studied.

In this work, the 3D unsteady compressible Reynolds-averaged Navier-Stokes equation (RANS) was adopted for calculation. The Standard k–ε model was chosen to solve the turbulence flow in tunnel. The computational domain was discretized using the finite volume method (FVM). The moving mesh method was applied to solving the pressure–velocity field.

Two kinds of grids are built for numerical simulation: structured and unstructured grid. The structured grid is built by software Pointwise and the unstructured grid is built by software Gambit. For structured grid, as the bogies are too complex, the grid in this space is unstructured. In other parts, including the space around train body, the structured grid is adopted and the boundary layer of train body surface is set. The first boundary layer grid is 1 mm and the total grid number is 5×10⁷. For unstructured grid, the first grid around train body surface is 1 mm and the total grid number is 4.1×10⁷.

3 Calculation model and method

The experiments of the smooth wall tunnel were carried out at the Central South University’s Moving Model Experiment Platform in China. A detailed description of the experiment platform is available in Refs. [18, 19]. The experiment platform has obtained CMA (China Metrology Accreditation) qualification in China (Certificate number 2014002479K). The experimental results are verified by using the structured grid and the unstructured grid.

Figure 5 shows comparison of pressure transients curve of the smooth wall tunnel between experimental results and simulation results of structured/unstructured grid at 99 m away from the tunnel entrance. The moment of the train head entering the tunnel is fixed as the time origin. The moment of the train tail exiting the tunnel is the last measuring time.

As can be seen from the figure, the experimental and calculation results of pressure waveform are basically consistent. For each speed, the calculation results of the initial compression wave (the first positive pressure wave) waveform are identical to the measured results. After the initial expansion wave (the first negative pressure wave), the pressure peak values of the experimental and calculation results are basically the same. The pressure waveforms of the experiment have a certain delay relative to the calculation. This is because the experiment uses the ejection mode to launch the moving model to ensure it to reach the target speed at the tunnel entrance. The moving model is affected by resistance in the tunnel movement and has a certain speed reduction (about 5 km/h reduction at the tunnel exit). Therefore, the pressure waveform is delayed to a certain extent in the later part of the time.

Figure 5 Comparison of pressure transients curve between experimental and simulation results at 99 m:

For 350 km/h, there is a little difference between calculation and experimental results of the waveform around the initial expansion wave peak. This is because the sampling frequency of the tunnel wall pressure sensor in the experiment is 1 kHz. For a very short period of time, the change of pressure back and forth will not be measured.

Table 1 shows the ratio of experimental and simulation results of peak–peak value of the smooth wall tunnel. The peak–peak value is the difference between the peak value of the initial compression wave and the initial expansion wave. The P_s, P_u and P_e in the table represent the peak–peak value of the structured grid calculation results, the unstructured grid calculation results and the experimental results, respectively.

Table 1 Ratio of experimental and simulation results of peak–peak value of the smooth wall tunnel

As can be seen from the table, the difference between the structured grid calculation results and the experimental results of the peak–peak value is within 5%. The maximum numerical error of the unstructured grid is over 9%. The calculation results of the structured grid are closer to the experimental results compared with the unstructured grid. Therefore, the structured grid is selected for the tunnel enlarged section parameter calculation examples.

4 Results and discussion

Table 2 shows the initial compression wave amplitude, the initial expansion wave amplitude, the pressure variation amplitude and the corresponding locations along tunnel length direction of the smooth wall tunnel. The initial compression wave amplitude is the maximum pressure of the initial compression wave. The initial expansion wave amplitude is the minimum pressure of the initial expansion wave. As the speed varies, the initial compression wave amplitude, the initial expansion wave amplitude and the corresponding locations along tunnel length direction will change. The initial compression wave amplitude and the initial expansion wave amplitude are the maximum and the minimum pressure values in the tunnel without considering the reflection pressure waves at the tunnel exit. The pressure variation amplitude is the maximum pressure difference of any position in the tunnel (the maximum peak–peak value of any position in the tunnel). The pressure variation amplitude represents the maximum pressure difference in the tunnel.

Table 2 Pressure amplitudes and corresponding locations along tunnel length direction of smooth wall tunnel

The S-grid and U-grid in the table represent the calculation results of the structured grid and the unstructured grid, respectively. P_c0, P_e0 and P_max0 represent the initial compression wave amplitude, the initial expansion wave amplitude and the pressure variation amplitude, respectively. L_c0, L_e0 and L_max0 represent the corresponding locations along tunnel length direction. In the calculation, 350 measurement points (1 m apart) are distributed along tunnel length direction. The maximum pressure difference of all measurement points is identified as the pressure variation amplitude. The location of the measurement point is identified as the location of the pressure variation amplitude. The initial compression wave amplitude, the initial expansion wave amplitude and the corresponding locations along tunnel length direction are obtained in the same way.

As can be seen from the table, the location of the initial compression wave amplitude is 83–91 m away from the tunnel entrance. The location of the initial expansion wave amplitude is 110–143 m away from the tunnel entrance. And with the increase of the speed, the locations of the initial compression wave amplitude and the initial expansion wave amplitude extend into the tunnel along tunnel length direction. The location of the pressure variation amplitude basically coincides with the location of the initial expansion wave amplitude. For different speeds, the range of the initial compression amplitude location is not big, so the location in the range is chosen to study the influence of the enlarged section distribution along circumferential direction and the enlarged section area on pressure transients in the tunnel. The locations in section 2 are 70, 80 and 90 m away from the tunnel entrance.

4.1 Enlarged section distribution along circumferential direction

Table 3 shows the pressure variation amplitude and the average pressure variation change rate of the enlarged section distributions along circumferential direction. The average value of the peak–peak value of all 350 measurement points is defined as the average pressure variation. ①–④ in the table represent the enlarged section distributions in Figure 3. P_max0 and P_ave0 represent the pressure variation amplitude and the average pressure variation of the smooth wall tunnel, respectively. ΔP_max and ΔP_ave represent the difference of the pressure variation amplitude and the average pressure variation between the smooth wall tunnel and the tunnel with added enlarged section, respectively. When the ΔP_max and ΔP_ave are positive, the pressure variation amplitude and the average pressure variation of the tunnel with added enlarged section are smaller than that of the smooth wall tunnel.

For the distributions ②–④, the pressure variation amplitude and the average pressure variation change rate are basically the same and the difference between each other is no more than 0.1‰. For the distribution ①, the change rate law of the pressure variation amplitude and the average pressure variation are the same as the distributions ②–④. As two enlarged sections added in the distributions ②–④ and one enlarged section added in the distribution ①, the pressure variation amplitude and the average pressure variation change rate of the distribution ① are smaller than that of the distributions ②–④. And the two times the pressure variation amplitude and the average pressure variation change rate of the distribution ① are larger than that of the distributions ②–④. The influence of the different enlarged section distributions along tunnel circumferential direction on pressure transients in the tunnel is basically consistent. Therefore, the influence of the enlarged section distribution along circumferential direction is not considered when the influence of the enlarged section area and the enlarged section distribution along tunnel length direction are studied. The enlarged sections of the two enlarged section parameters studies were magnified by a certain proportion of the smooth wall tunnel cross-section.

Table 3 Pressure variation amplitude and average pressure variation change rate of enlarged section distributions along circumferential direction

4.2 Enlarged section area

Figure 6 shows the law of the pressure variation amplitude change rate of the enlarged sections 70, 80 and 90 m away from the tunnel entrance with area change rate. The area change rate in the figure represents the change ratio of the enlarged section area and the smooth wall tunnel cross-section area.

Except for the 250 km/h curve in Figure 6(c), the pressure variation amplitude in each example decreases first and then increases with the increase of the enlarged section area. For each speed and enlarged section distribution along tunnel length direction, there is an optimal enlarged section area for the minimum value of the pressure variation amplitude in the tunnel. When the pressure variation amplitude reaches the minimum, the corresponding enlarged section area will decrease with the increase of speed. For each enlarged section area and enlarged section distribution along tunnel length direction, the decrease ratio of the pressure variation amplitude basically decreases with the increase of speed.

For the 250 km/h curve in Figure 6(c), all the enlarged section areas increase the pressure variation amplitude. As can be seen from Table 2, the location of the initial expansion wave amplitude at 250 km/h is 83 m away from the tunnel entrance. The enlarged section added 90 m away from the tunnel entrance is 7 m behind the location along tunnel length direction. The distance is far away. For the remaining 35 calculation examples, the enlarged section is before or near the location along tunnel length direction. Therefore, the result of the enlarged section added 90 m away from the tunnel entrance at 250 km/h is not the same as other calculation examples.

Figure 7 shows the law of the average pressure variation change rate of the enlarged section 70, 80 and 90 m away from the tunnel entrance with area change rate.

As can be seen from the figure, the average pressure variation in each example decreases first and then increases with the increase of the enlarged section area. For each speed and enlarged section distribution along tunnel length direction, there is an optimal enlarged section area for the minimum value of the average pressure variation in the tunnel. Especially for the enlarged section added 80 m away from the tunnel entrance, the average pressure variation at each speed is most obvious. The maximum decrease is nearly 3%, and the corresponding total volume change (the increase ratio of the volume of the tunnel with added enlarged section and the volume of the smooth wall tunnel) is about 7‰. Except for the 250km/h curve in Figure 7(c), for each enlarged section area and enlarged section distribution along tunnel length direction, the decrease ratio of the average pressure variation basically decreases with the increase of speed.

Figure 6 Law of pressure variation amplitude change rate with area change rate:

The data curve in Figures 6 and 7 are fitted. It is found that the fitting curve of the three-order polynomial formula is very consistent with the data curve. Limited to the manuscript space, the three-order polynomial formula of each data curve is not given in this paper.

Figure 7 Law of average pressure variation change rate with area change rate:

Table 4 shows the fitting measured coefficient (determination coefficient) for each three-order polynomial formula fitting curve. The R²_max and R²_ave in the table represent the determination coefficient of the fitting curve for the law of the pressure variation amplitude and the average pressure variation change rate with area change rate, respectively. It can be seen from the table, the determination coefficient of each fitting curve is larger than 0.993. That is to say, the pressure variation amplitude and the average pressure variation are changed following the three-order polynomial formula with the increase of the enlarged section area.

Table 4 Determination coefficient of three-order polynomial formula fitting curve

4.3 Enlarged section distribution along tunnel length direction

According to the calculation results in Section 4.2, the pressure variation amplitude and the average pressure variation of the 93.48 m² enlarged section at each speed are changed obviously. Therefore, the 93.48 m² enlarged section is selected for studying the influence of the enlarged section distribution along tunnel length direction on pressure transients in the tunnel.

Figure 8 shows the law of the pressure variation amplitude change rate with the 93.48 m² enlarged section distribution along tunnel length direction. The enlarged section location in the figure represents the distance between the front end of the enlarged section and the tunnel entrance.

For 250 km/h, the pressure variation amplitude of the tunnel with added enlarged section 60–80 m away from the tunnel entrance is smaller than that of the smooth wall tunnel. The pressure variation amplitude of the tunnel with added enlarged section 90–110 m away from the tunnel entrance is larger than that of the smooth wall tunnel. The ratio increases with the increase of the distance from the tunnel entrance and reaches the maximum at 110 m. The pressure variation amplitude of the tunnel with added enlarged section 120–150 m (except 140 m) away from the tunnel entrance is larger than that of the smooth wall tunnel. The pressure variation amplitude in the calculation examples of 300 km/h and 350 km/h has a similar law. In the calculation examples of 300 km/h and 350 km/h, the pressure variation amplitude begins to increase from the decrease with added enlarged section 100 m and 110 m away from the tunnel entrance, respectively. The pressure variation amplitude of the tunnel with added enlarged section reaches the maximum at 120 m and 130 m, respectively.

Figure 8 Law of pressure variation amplitude change rate with enlarged section distribution along tunnel length direction

For 250 km/h, compared with the locations of the initial compression wave amplitude and the initial expansion wave amplitude, when the enlarged section is before or near the location of the initial compression wave amplitude along tunnel length direction, the pressure variation amplitude of the tunnel with added enlarged section is smaller than that of the smooth wall tunnel. When the enlarged section is after the location, the pressure variation amplitude is larger. When the enlarged section is located at the near area before the location of the initial expansion wave amplitude, the pressure variation amplitude of the tunnel with added enlarged section reaches the maximum. The pressure variation amplitude in the calculation examples of 300 km/h and 350 km/h has a similar law.

Figure 9 shows the law of the average pressure variation change rate with the 93.48 m² enlarged section distribution along tunnel length direction.

For 250 km/h, the average pressure variation of the tunnel with added enlarged section 60–80 m away from the tunnel entrance is smaller than that of the smooth wall tunnel and reaches minimum at 80 m. The average pressure variation of the tunnel with added enlarged section 90–120 m away from the tunnel entrance is larger than that of the smooth wall tunnel and reaches the maximum at 100 m. The pressure variation amplitude of the tunnel with added enlarged section 130–150 m away from the tunnel entrance is smaller than that of the smooth wall tunnel. The average pressure variation in the calculation examples of 300 km/h and 350 km/h has a similar law. The reason can also be explained by the locations of the initial compression wave amplitude, the initial expansion wave amplitude and the enlarged section. The overall law of the average pressure variation is the same as the pressure variation amplitude. The difference is that when the enlarged section is located after the location of the initial expansion wave amplitude, the pressure variation amplitude of the tunnel with added enlarged section is larger than that of the smooth wall tunnel, while the average pressure variation of the tunnel with added enlarged section is smaller than that of the smooth wall tunnel.

Figure 9 Law of average pressure variation change rate with enlarged section distribution along tunnel length direction

5 Conclusions

1) The calculation results of the structured grid are closer to the experimental results compared with the unstructured grid.

2) The initial compression wave amplitude, the initial expansion wave amplitude, the pressure variation amplitude and the corresponding locations along tunnel length direction of the smooth wall tunnel are obtained.

3) The influence of the different enlarged section distributions along tunnel circumferential direction on pressure transients in the tunnel is basically consistent.

4) The pressure variation amplitude and the average pressure variation are changed following the three-order polynomial formula with the increase of the enlarged section area.

5) There is an optimal enlarged section area for the minimum value of the pressure variation amplitude and the average pressure variation in the tunnel.

6) The law of the pressure variation amplitude and the average pressure variation of the enlarged section distribution along tunnel length direction are obtained.

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(Edited by YANG Hua)

中文导读

局部扩大段参数对高速列车过隧道引起的压力波动的影响规律

摘要：数值模拟研究了局部扩大段参数对高速列车过隧道引起的压力波动的影响规律。对比验证了光滑壁面隧道的实验数据和由结构及非结构网格计算获得的数值模拟结果。对三个局部扩大段参数进行了数值模拟研究：局部扩大段沿隧道周向分布、局部扩大段截面积和局部扩大段沿隧道长度方向分布。数值模拟结果表明：局部扩大段沿各隧道周向位置分布的压力波动基本相同。存在一个最佳的局部扩大段截面积使得压力变化幅值和平均压力差值为最小值。获得了压力变化幅值和平均压力差值随局部扩大段沿隧道长度方向分布的变化规律。

关键词：高速列车；局部扩大段参数；隧道；压力波动

Foundation item: Project(2016YFB1200602-11) supported by National Key R & D Plan of China

Received date: 2018-01-01; Accepted date: 2018-10-10

Corresponding author: WANG Tian-tian, PhD; Tel: +86-13401157826; E-mail: wangtt1107@126.com; ORCID: 0000-0003-0137-7881