Field Test and Numerical Investigation of Tunnel Aerodynamic Effect Induced by High-Speed Trains Running at Higher Speeds

Featured Application

Outcomes of the present research will directly assist the practical design of the high-speed railway tunnel regarding the maximum affordable pressure load of tunnel lining and internal facilities.

Abstract

After decades of research in the field of high-speed railway technique, technology of running high-speed trains at the velocity level of 350 km/h gradually become mature. It is of great importance to capture the variation regular of aerodynamic parameters in the situation that the high-speed train runs at a higher speed level. The present paper is motivated by this knowledge gap, both field tests and numerical simulations were conducted to help illustrate the basic characteristic of transient pressure loads, micro-pressure wave, as well as the wave propagation inside the tunnel regrading train’s passage and intersection. Results present the major findings as: (1) Transient pressure loads acting at tunnel surface and train body unevenly distributes along the longitudinal, transverse, and vertical directions. Pressure peak along the longitudinal direction occurs nearly at tunnel center and fast decreases from the radiated center to the remote positions. (2) Variation of pressure peak near the tunnel portal in the situation of train’s passage and intersection is limited while its value becomes doubled at the intersection location. Field measurements suggest the maximum pressure load acting at tunnel sidewall at $x_{tin}$ = 200 m and tunnel center being 4.29 and 5.63 kPa, respectively; (3) The maximum value of micro-pressure wave (namely MPW) detected in the field test is approximately 36.73 Pa. Amplitude of MPW at tunnel portal is inversely proportional to its attenuated distance. Through data fitting, an empirical prediction model was established. Outcomes of this paper is anticipated to improve the understanding of tunnel aerodynamic effect regarding higher speed level and its associated problems. Besides, findings of this paper are useful for the future tunnel design.

1. Introduction

The rapid growth of tunnel mileage throughout the world greatly boosts the technical development of high-speed railway industry. Targeted operating speed of the railway high-speed train is constantly lifted up since the Shinkansen was put into operation in Japan in 1964. So far, high-speed train (HST) running at 350 km/h speed level in China railways has been achieved in many lines, e.g., the Beijing-Shanghai line and the Nanchang-Ganzhou line. With extensive efforts being paid in the last few decades, a further step regarding the acceleration of high-speed train velocity exceeding 400 km/h has been scheduled in many countries.

Tunnel aerodynamic effect is one of the most important issues as it may lead to serious discomfort, noise and safety related problem. Extensive efforts have been paid in the last few decades, wherein the research interest can be roughly classified into two aspects, i.e., (1) the micro-pressure wave (MPW) emitted at the tunnel portal; and (2) the transient pressure load (TPL) acting at tunnel lining, internal facilities, and train body.

Ozawa et al. [1,2] are among the first few investigating tunnel aerodynamic effect by utilizing both theoretical and experimental methods. Their research interest inclined to the reduction of MPW which was firstly observed at Sanyo Shinkansen laid between Osaka and Fukuoka. A fruitful study focusing on the tunnel aerodynamic effect was then carried out by Raghunathan et al. [3]. Investigation was made to explore the aerodynamic force and the shape design of train body, the transmission of pressure waves inside tunnel, and the impulsive wave discharged from tunnel exits, as well as its accompanied aero-acoustic problems. Research of their study related to MPW illustrated (1) the basic varying trend and the strength of MPW versus tunnel length and train speed; and (2) the control methodologies by promoting the design of train body, hoods and branches at tunnel exits or interior. However, findings of their research are bounded by the research background where values of train speed in data analysis are mostly around 200 km/h. Through theoretical analysis and scaled model tests, Howe et al. [4,5,6,7] systematically discussed the optimization of vented hoods by designing three type of tunnel hoods. Alleviation of aerodynamic effect was evaluated through plotting the peak pressure and pressure gradient versus train speed. Good agreement was achieved between the predicted the pressure waveform by theoretical models and measurements from scaled model experiments considering different tunnel hoods.

Despite of studies based on theoretical concern, engineering oriented researches are conducted by many scholars, wherein parametric optimization of the tunnel and train structure is highlighted. By comparing field and scaled model measurements with numerical simulation data, Baron et al. [8] analyzed both the transient pressure and micro-pressure regarding different blockage ratio, train nose, and train speed (220~380 km/h). Variation of the amplitude of MPW regarding the aforementioned parameters was primarily addressed. Through data analysis from simulation and model-scale experiment, Liu et al. [9] studied the alleviation effect of MPW by using tunnel hoods that prevalently adopted in actual railway lines, such as the enlarged-transect windowless hood, gradient hood, linear horn hood, etc. Results imply that reduction rate within 20~50% is feasible for the most tunnel hoods by optimizing their design parameters. The most favorable condition appears at the linear horn hood (reduction rate $=$ 71.6%) with the extended hood length $L_{eh}$ being three times the equivalent diameter of the tunnel. Recently, Kim et al. [10,11] proposed a newly designed tunnel hood with multiple air-slits at both sides. Measurements presented by the 1/64.2 scaled tests show that for the train speed at 250 km/h, the maximum reduction rate of pressure gradient and MPW approaches 56.3% and 78.3%, respectively. For the purpose of decreasing MPW, installing transverse branches [12,13], optimizing the opening area [14,15], cutting angles of tunnel hood [16], and hood length [17] are also proved to be effective.

Research with respect to the pressure spread and waveform of the pressure waves inside tunnel predominately focus on two aspects, i.e., the prediction of compression waves and the reduction method. Field tests from three Shinkansen tunnels were earlier carried out by Mashimo et al. [18], according to which the pressure history at different longitudinal locations and the pressure gradients in slab and ballast track tunnels were compared. Measurements denote that the strength of compression waves exponentially attenuate with the spreading distance in ballast track tunnels while the compress wave is likely to be steepened in the slab track tunnel. Through theoretical and experimental means, William-Louis [19] and Ricco [20] respectively investigated the influence of tunnel length, intersection of trains, train length, and nose shape designs. Aerodynamic effect caused by the intersection of HSTs was then studied by Chen et al. [21] and Lu et al. [22], respectively addressing the influence of train nose length and tunnel cross-section area. In addition to the research focusing on the pressure wave calculation, damage evaluation of tunnel linings subjected to the pressure load induced by tunnel aerodynamic effect was studied by Chen et al. [23] and Du et al. [24].

Without doubt, tunnel aerodynamic effect has been investigated by many scholars in the past few decades by conducting full-scale test, moving model test, and numerical simulation. There is still a shortage regarding field measurements. Research in this field is restricted due to following shortcomings: (1) speed level of previous field test is relatively low (approximately 300 km/h). For example, test speed in the Terranuova Le Ville tunnel at Italian high-speed line by Reiterer et al. [25], Shinkansen tests by Fukuda et al. [26] in Japan, is relatively low. (2) testing scenarios are limited as geometry/dimension of the moving rig is predetermined; (3) most studies were conducted by simulation means while measurements from field test are still insufficient. Motivated by such gaps, the present study combined field test with numerical means. Crucial parameters, namely the transient pressure load (tunnel surface and train body) and amplitude of micro-pressure wave are both investigated. Train speed in the field test is very representative as they are regularly operated speed in Chinese high-speed railways. Higher velocities, ranged within 400~495 km/h, is simulated through numerical means which has been validated by field measurements. Correspondingly, tunnel aerodynamic effect was investigated with a wide range of train speed (250~495 km/h) being considered. Besides, test condition contains both train’s passage and intersection, providing reliable results for various scenarios. Outcomes of the present study are expected to help improve the understanding of tunnel aerodynamic effect caused by HSTs and the pressure spreading characteristics inside and outside the tunnel.

2. Full-Scale Tests

2.1. Test Condition

The test tunnel is 628 m in length (including the 16 m long hood at tunnel exit), with the clearance of cross-section area being 100 ${\mathrm{m}}^2$ referring to the general design of double-track tunnel constructed in China high-speed railways. Slab track using CRTS-Ⅲ is mounted throughout the whole tunnel, with the distance between two parallel tracks being 5.0 m. As shown in Figure 1, a hat oblique hood is constructed at the tunnel entrance while the tunnel exit is designed with a straight-cut opening without buffer. No additional holes are applied at either tunnel roof or sidewall as the steepened effect of compression wave is usually limited in the short tunnel. The test train holds 8 carriages, and is 209 m long, 3.36 m wide, 4.05 m tall. The streamline length of train head is about 12.0 m and the maximum cross-section area of train body is 11.95 ${\mathrm{m}}^2$, giving the blockage ratio being around 0.12. A wide range of the train speed varying from 250 km/h to 350 km/h is applied in the field test to obtain the basic character of pressure waves.

2.2. Measurements

The measuring system contains GPS devices, pressure sensors, shield signal wires, multi-channel amplifiers and A/D converters. Before the test, the local time recorded by the IMC data acquisition is standardized by the GPS devices. Pressure sensors produced by Endevoco and Head-Artemis are utilized (see in Figure 2) to detect TPL acting at tunnel surface and MPW emitted at tunnel portal, with measuring range respectively being −8.0~8.0 kPa and −500.0~500.0 Pa. Along the longitudinal direction, two set measuring points are respectively mounted at $x_{tin}$ = 200 m away from the tunnel entrance and tunnel center ($x_{tin}$ = 314 m). Besides, each set holds two measuring points respectively installed at $z_{tin}$ = 1.2 m and 2.0 m. Outside the tunnel, two pressure sensors are mounted at the distance of 20 m and 50 m away from the tunnel exit. Measured values will be captured by the IMC data acquisition system at the collecting frequency being 1000 Hz for TPL and 500 Hz for MPW. Each test was repeated at least twice to ensure the reliability of the measurements. As shown in Figure 3, pressure history for a given location shows very good agreement, indicating the test data being reliable.

3. Numerical Simulation

3.1. Methodology

Test condition where high-speed train travels the tunnel at a higher speed and intersects within the tunnel is realized through numerical means by STAR CCM+ whose reliability in simulating tunnel aerodynamic effect related problems has been widely proved in previous studies [27,28,29]. In the simulation, gas is assumed to be compressible. Finite volume method is applied in the pressure-based solver when solving the Shear-Stress Transport (SST) model adopted in $\kappa -\omega$ turbulence model. The SST $\kappa -\omega$ turbulence model is established by combing the standard $\kappa -\omega$ and $\kappa -\epsilon$ models through a hybrid function. It is thus accuracy of the solution near the wall region where Reynolds number is relatively low and the core region within the turbulence are both inherited from $\kappa -\omega$ and $\kappa -\epsilon$ models by the SST model.

The pressure and velocity couplings are processed by semi-implicit method for the pressure-linked equations (SIMPLE) algorithm. Second-order upwind schemes are used to discretize the convective terms of the momentum. A second-order implicit scheme is employed for the time integrals. The physical time step is set as $∆t$ = 0.0025 s with the maximum inner iterations being 20 for each time step. Calculation will move to the next time step until either the iterations were done or the residual of turbulent equations have reached 10⁻⁵. The above settings result in the exact value of $y^{+}$ near the wall and train bodies respectively being 0.44 and 0.35.

3.2. Computation Domain and Boundaries

3.2.1. Geometries

So far, dynamic and sliding mesh [30] methods are the two most frequently used techniques in tunnel aerodynamic effect related research where the relative motion between HST and internal tunnel space is solved. The present investigation was conducted relying on the sliding mesh due to its accurate resolution and relatively low cost in the computation resource compared to the dynamic mesh. The overall computation domain is divided into two individual parts, namely the static zone and moving region as shown in Figure 4.

The static zone is 1628 m in length, 100 m wide and 50 m tall, containing both the external flow field and internal test tunnel area. As shown in Figure 4a, the static zone denotes the computation domain within and outside the tunnel except the region within the yellow dotted lines. For any situation, HST starts running through the tunnel entrance portal is named as Train A while the other one corresponds to Train B. Without doubt, the body of Train A and B, as well as their surrounding area are classified into the moving regions as exhibited in Figure 4b. The 800 m long extra moving region, is constructed outside the external flow field to ensure the moving region being located within the static zones in the whole simulation period [31]. In addition, interface is applied to achieve the exchange of solution data from static and moving zones. An overview of the computation domain constructed in simulation can be found in Figure 4c.

The test tunnel and HSTs built-up in the computation domain is the 1:1 reproduction of those applied in the field tests. Simplification is considered to the physical model construction of HST to avoid unnecessary time cost as the research interest of this paper is tunnel aerodynamic effect instead of the pressure loads at vehicle components. Thus, lightings, handles, and bogies are ignored, and carriages are merged.

3.2.2. Meshes and Boundaries

Meshes was dealt by the Trimmed Mesher embedded in the software. Taking account of both calculation accuracy and computational resources cost, local meshes at some special regions, like the tunnel hood, train nose, and train tail, are refined (as shown in Figure 5). Grid size is defined with four levels, i.e., 0.5 m, 1.0 m, 2.0 m, and 4.0 m, giving to the total number of cells being 4,072,472 and 5,541,780 for the scenarios that passage of a single train and intersection of two trains, respectively. To improve the solution of flow field at boundary layer and give the consideration to $k-\omega$ model which belongs to the low-Reynold model requiring $y^{+}\le 1$, eight hexagonal prism layer meshes with growing ratio being 1.2 are applied to the train body where the first layer height at train body is 1.5 × 10⁻⁶ m. Similarly, six layer meshes with growing ratio being 1.5 are utilized at tunnel surface where the first layer height is 2.0 × 10⁻⁵ m. The above settings result in the exact value of $y^{+}$ near the wall and train bodies respectively being 0.44 and 0.35.

Surfaces of tunnel linings, floor, and train body are defined as non-slip wall boundaries. Pressure outlets are applied to tunnel portals, surfaces of external flow domain (except the floor). Nearby the wall boundaries, solution of turbulence is very sensitive to the settings. To simulate the realistic situation, roughness of tunnel sidewalls and floor are respectively 2.0 mm and 5.0 mm. Besides, roughness is set as 1.0 mm for all the train surfaces so that friction at train body can be deemed to be evenly distributed. For the simulated scenario of single train’s passage, HST is initially placed 200 m away from the tunnel entrance portal to ensure the external flow field being not disturbed as much as possible. By changing the initial location of Train B, the crossing-point of train’s intersection is predefined to be tunnel center only.

3.2.3. Measurements and Scheme

Within the computation domain, a total number of 89 measuring points are mounted in three sets, namely Set A, Set B, and Set C. Set A and B are respectively equipped at tunnel sidewall and train surface to record TPL acting on the tunnel lining and train body. Measuring points in Set C are installed outside the tunnel entrance to detect the micro-pressure. As shown in Figure 6, Set A is divided into elven sub-sets with each one holding seven measuring points at the same transverse cross-section with different positions, namely PA*-1 to PA*-7. More concretely, PA*-4 locates at tunnel ceiling along tunnel centerline while PA*-1 to PA*-2 and PA*-5 to PA*-7 are respectively mounted at the height of 1.20 m, 2.0 m, and 5.0 m. Symbol ‘*’ marked in Figure 6a denotes the cross-section number, corresponding to the longitudinal location of each cross-section introduced as below. Along the longitudinal direction, measuring points are placed at $x_{tin}$ = 10 m, 20 m, 50 m, 100 m, 200 m, 300 m, 400 m, 500 m, 552 m, 592 m, and 602 m. Four measuring points in Set B are respectively placed at train nose, train tail, and two quadratic points at sidewall. Outside the tunnel entrance, micro-pressures at $x_{tin}$ = 10 m, 20 m, 30 m, 50 m, 75 m, and 100 m along the tunnel centerline and sideway are measured by Set C.

As shown in

Table 1. Simulation plans.

Test No.	Train A/km·h−1	Train B/km·h−1	Test Scenario
1	350	/	Single train
2	385	/
3	390	/
4	400	/
5	420	/
6	440	/
7	460	/
8	480	/
9	490	/
10	495	/
11	400	400	Intersection
12	450	450
13	495	495
14	495	450
15	495	400
16	450	400

, the present paper conducts 16 numerical simulations with three issues being addressed. Test 1–10 corresponds to the test condition where high-speed train travels through the tunnel. Simulation results from these tests will assist the illustration of flow field and pressure transmission. Higher velocities are designed in Test 5–10 as 450 km/h is likely to be the targeted operating velocity in the high-speed railways in the near future. A 10% surplus addition to the operation speed shall be considered, allowing the upper velocity limit of the simulated train speed being 495 km/h. The intersection of two HSTs are highlighted in Test 11–16 by letting HST running at different velocity levels, i.e., 400 km/h (low speed), 450 km/h (normal speed), and 495 km/h (high speed). Besides, intersection happens in the situation that velocity of Train A being equivalent or different from Train B are both considered to cover the real scenarios that are likely to appear in real tunnels.

Before the scheduled tests being lunched, validation was first carried out to ensure the accuracy of simulation results. As seen in Figure 7, validation was carried out from two aspects, i.e., mesh sensitivity analysis and comparison with field test data. Simulated data calculated from three meshes with total grid number being 3,209,670 (Grid-1), 4,072,472 (Grid-2), and 4,805,237 (Grid-3) are plotted in Figure 7a. The plotted curves show very good agreement with the maximum pressure difference is only 2.53%, implying that resolution of the present mesh grid is reasonable. Besides, as shown in Figure 7b, history of the MPW obtained from Test 3 in Table 1 and the field test shows good agreement. The maximum pressure difference of MPW caused by HST is only about 3.50 Pa at 50 m away from the tunnel portal. Small fluctuation of pressure wave in the simulated curve is still observed within $t=$ 0.60~1.20 s. However, this is reasonable as (1) the external domain was confined space while the full-scale filed test was conducted in the open space, and (2) train speed in field tests usually fluctuates very often due to many uncertain factors, i.e., tunnel slope and local landform. Overall, the present settings are reasonable to be used for the further simulation.

4. Results and Discussion

4.1. Aerodynamic Pressure Caused by the Single Train

Figure 8 plots the spread of pressure wave inside the test tunnel and the evolution of pressure load recorded by the measuring point at sidewall surface ($x_{tin}$ = 200 m, $v_{tr}=$ 369 km/h). Assisted by the pressure spreading lines in Figure 8, typical pressure increase or pressure drop can be well illustrated. The first pressure peak appears at $t=a$, corresponding to the moment when the pressure wave approaches the measuring point. The subsequent pressure increase respectively occurs at $t=e$, g, and h are all caused by reflected compression pressure waves. Similarly, pressure drops emerged at $t=f$ is induced by the expansion wave. When the expansion pressure wave approaches the measuring point at $t=c$, the pressure evolution curve shows a shortly increase instead of decreasing due to the expansion wave effect. However, this is rational to occur in the full-scale test as it is technically hard to maintain the train velocity being unchanged. Such velocity fluctuation is likely to result in the dislocation of time point corresponding to the wave diagram. Besides, pressure drop and increase appearing at $t=b$ and d are respectively resulted by the passage of train head and train tail [32].

In the following, dimensionless pressure $p^{\mathrm{*}}$ and velocity $v_{tr}^{\mathrm{*}}$ will be used for the further discussion associated with the aerodynamic pressure and the relationship between pressure and train velocity. The normalized pressure $p^{\mathrm{*}}$ is the ratio of measured pressure $p$ to the pressure amplitude of the first compression wave for reference [33], i.e.,

$$p^{\mathrm{*}}=p/J_1$$

(1)

with

$$J_1=\frac{{\rho }_0{\left(v_s{M}_{tr}\right)}^2{\varphi }_{tr}\left(1+{\varphi }_{tr}\right)}{\left(1-{M_{tr}}^2\right)}$$

(2)

with Mach number of HST being generated as

$$M_{tr}=\frac{v_{tr}}{v_s}$$

(3)

blockage ratio ${\varphi }_{tr}$ being calculated as

$${\varphi }_{tr}=\frac{A_{tr}}{A_{tu}}$$

(4)

where ${\rho }_0$ is the ambient air density, $v_s$ indicates the velocity of sound, $A_{tr}$ and $A_{tu}$ respectively denotes the area of HST and tunnel. To be clarified, as displayed in Figure 8, pressure peak periodically repeats due to the reflection of pressure waves. The maximum value of TPL and MPW is likely to occur at the later peaks due to the pressure superposition. To simplify the calculation, values of $p$ in Equation (1) represents the first pressure peak are utilized for the data analysis in the present study. In the similar way, dimensionless velocity of HST $v_{tr}^{\mathrm{*}}$ is calculated as

$$v_{tr}^{\mathrm{*}}=v_{tr}/\sqrt{g{R}_{tu}}$$

(5)

with

$$R_{tu}=\frac{4A_{tu}}{S_{tu}}$$

(6)

where $R_{tu}$ represents equivalent tunnel diameter, $S_{tu}$ is the perimeter of tunnel, and $g$ is gravity.

Histories of the initial pressure waves derived from field tests, considering different train speeds at $x_{tin}$ = 200 m and tunnel center $x_{tin}$ = 314 m are exhibited in Figure 9. Similar varying trend can be found in the plotted lines. As the train speed increases from 250 km/h to 376 km/h, the maximum value of TPL at tunnel surface gradually increases. Peak values of the transient pressure, namely $P_{tr-max}$, at $x_{tin}$ = 200 m and $x_{tin}$ = 314 m (tunnel center), are 1.72 kPa and 1.37 kPa, respectively. Such pressure difference indicates that aerodynamic pressure acting at tunnel lining is unevenly distributed along the longitudinal direction. To be noticed, for a certain varying range of train speed, i.e., 328 km/h to 376 km/h exhibited in Figure 9, the increase of the peak pressure $P_{tr-max}$ at $x_{tin}$ = 314 m is generally higher than the value recorded at $x_{tin}$ = 200 m while the pressure trough $P_{tr-min}$ shows opposite varying trend. This is due to the non-uniform distribution of pressure wave induced by the wave superposition during its reciprocation within the tunnel, which will be discussed later.

By utilizing the numerical method, spread of pressure waves can be well illustrated. The plotted curves drawn in Figure 10 are pressure histories from different velocities recorded at 20 m and 100 m away from tunnel portals. Pressure curves show different varying tendencies when the measuring position changes. For the pressure waves recorded nearby the tunnel portals, i.e., $x_{tin}$ = 20 m and 602 m, even though the peak value of $P_{tw}^{\mathrm{*}}$ presents significant difference, both these two curves show a sharp pressure jump (see the dotted lines in Figure 10) where the pressure peak occurs. On the contrary, pressure variation at $x_{tin}$ = 100 m and 500 m are more moderate within its peak region. The total increase of pressure at $x_{tin}$= 100 m is decomposed into two parts (marked as $∆P_1$ and $∆P_2$), wherein the time cost to approach its maximum value is much longer. Pressure variation at $x_{tin}$ = 500 m also behave similarly with what observed at $x_{tin}$ = 100 m, indicating the transient pressure loads acting at the tunnel sidewall being influenced by the longitudinal locations.

Investigation associated with the pressure distribution has been addressed by some previous studies wherein different opinions are observed. Based on the research addressing the wave spread of compressed gas conducted by Bannister et al. [34], an earlier study from Mashimo et al. [35] through field measurements and CFD simulation declare that the compression wave exponentially attenuates with the distance $x_{tin}$ inside both the slab track and ballast track tunnels, i.e.,

$$\frac{∆P_{x_{tin}}}{∆P_{x_0}}=exp(-\kappa \frac{x_{tin}-x_0}{D_{tu}})$$

where $x_0$ represents the reference point at tunnel entrance, $∆P_{x_{tin}}$ and $∆P_{x_0}$ are respectively the pressure rises at $x_{tin}$ and $x_0$, $\kappa$ is the attenuation factor determined by experiments, $D_t$ is the equivalent diameter of the tunnel. According to the field measurements from Shinkansen tunnels, values of $\kappa$ for the tunnel utilizing slab and ballast track are adopted as 4.5 $\times$ 10⁻⁴ and 6.5 $\times$ 10⁻⁴ for the condition that the train speed reaches 215 km/h. The later researches conducted by Chen et al. [21] and Liu et al. [36] declare different findings. In their research, filed measurements derived from Xiyema Tunnel located at Chinese Beijing-Shanghai line indicate that the pressure amplitude recorded at sidewall surface first increases and then decrease as the longitudinal distance $x_{tin}$ increases from 20 m to 680 m. Both the growing and decreasing lines show linear-like tendency instead of the exponential trend.

Further investigation is thus conducted by plotting the maximum pressure load $P_{tr-max}^{\mathrm{*}}$ derived from different transverse and longitudinal locations in Figure 11 as below. Dimensionless tunnel length $L_{tu}^{\mathrm{*}}$, generated as $L_{tu}^{\mathrm{*}}=\frac{x_{tin}-x_0}{L_{tu}}$, is obtained to represent the relative position of measuring points. At the speed of 385 km/h and 495 km/h, values of $P_{tr-max}^{\mathrm{*}}$ obtained from the given cross-section, i.e., PA*-1 to PA*-7, first increases and then decreases as the longitudinal distance $x_{tin}$ increases. The peak value of $P_{tr-max}^{\mathrm{*}}$ appears at roughly the middle of the tunnel, i.e., $L_{tu}^{\mathrm{*}}=$ 0.5, which is consistent with Chen’s research [21], and is also consistent with results from the present field measurements (pressure variation in the tunnel center is higher than those detected at remoted locations). Besides, it is very interesting to find out that values of $P_{tr}^{\mathrm{*}}$ (1) coming from sidewall at right hand (PA*-1 to PA*-3) are generally higher than that of the ceiling point PA*-4 and the measuring points from sidewall at left hand (PA*-5 to PA*-7); (2) decreases as the measuring height increases when the dimensionless tunnel length $L_{tu}^{\mathrm{*}}<$ 0.5; (3) is not sensitive to the change of measuring height once value of $L_{tu}^{\mathrm{*}}$ is beyond 0.5. This is reasonable as pressure spreads radiantly within the tunnel so that sidewall closer to HST suffers higher pressure load. Due to the pressure reflection and superimposed effect, variation of pressure amplitude is likely to be non-monotonic in the tunnel.

Illustration by utilizing the pressure contour is then given in Figure 12 to help support the above discussion. For the typical train velocity used in Figure 12 for data analysis ($v_{tr}=$ 385 km/h, 390 km/h, 400 km/h, and 460 km/h), pressure contour of the transverse cross-section at $x_{tin}$ = 120 m provides a good example of the uneven distribution of pressure waves. Correspond to the data shown in Figure 11, pressures in the contour are also normalized as $P_{tr}^{\mathrm{*}}$. To be clarified, pressure contours regarding different train velocities are measured at different time so that the maximum and minimum value of the color bar are different in the sub-figures. Due to the velocity difference, it is technically hard to capture the pressure contours at the same time. However, this will not challenge the readability of Figure 12 as the overall pressure distribution is not significantly affected by such time delays.

Despite of the peak pressure, the peak-to-peak pressure, representing the maximum transient pressure variation, is attached with a lot of concern when conducting engineering-oriented safety evaluations associated with tunnel linings and internal facilities. Thus, the maximum, minimum, and peak-to-peak values of pressures at $x_{tin}$ = 200 m and $x_{tin}$ = 314 m in the field tests are then plotted in Figure 13. For a given location, $x_{tin}$= 200 m for example, measurements from Figure 13a denote a linear-like tendency for the maximum, minimum, and peak-to-peak values of pressure. In general, the absolute value of $P_{tr-max}$, $P_{tr-min}$, and $∆P_{transient}$ increases with train speed. The maximum pressure difference $∆P_{transient}$ occurs when the train speed is about 370 km/h, where $∆P_{transient}$ at $x_{tin}$ = 200 m and $x_{tin}$ = 314 m respectively equals to 4.29 and 5.63 kPa. Different from $P_{tr-max}$, $∆P_{transient}$ at $x_{tin}$ = 314 m is approximately 1.34 kPa higher than the value measured at $x_{tin}$ = 200 m. Such pressure difference is consistent with the simulation results from Figure 11 and are also observed in some other studies. Measurements from field tests carried out by Liu et al. [32] show that the pressure peak roughly occurs at tunnel center at the speed of 330 km/h. Research of Liu et al. [36] obtained similar conclusion, i.e., field measurements from China Beijing-Shanghai line indicate the peak pressure appears at tunnel center when train’s velocity is about 300 km/h.

Figure 14 presents pressure histories of MPW at $x_{tu-out}=$ 20 m regarding different train velocities ranged within 305 km/h to 495 km/h. The plotted data in Figure 14a,b, field measurements and simulated values, both declare that both the maximum value of measured $P_{micro-20}$ and normalized $P_{micro-20}^{\mathrm{*}}$ increase with train velocity. Analysis associated with the attenuation of micro-pressure wave is also conducted by revealing the relationship between dimensionless MPW $P_{micro}^{\mathrm{*}}$ and attenuated distance $L_{tu-out}^{\mathrm{*}}$ (generated as $L_{tu-out}^{\mathrm{*}}=\frac{x_{tu-out}}{D_{tu}}$). In the previous studies [3,10], amplitude of MPW emitted from tunnel portal was found to be inversely proportional to the attenuated distance $x_{tu-out}$, i.e., $P_{micro}\propto \frac{1}{x_{tu-out}}$. Data process in the present paper utilizes the maximum value of MPW derived from monitoring points along the tunnel centerline. The dotted line drawn in Figure 15a shows good agreement between the simulated data and the empirically fitting line. To be noticed, for a certain value of $L_{tu-out}^{\mathrm{*}}$, discrepancy still exists as train velocity $v_{tr}$ changes, even though such difference gradually become insignificant as $L_{tu-out}^{\mathrm{*}}$ increases. Coefficient $C_p$ is thus introduced to characterize the influence caused by train velocity $v_{tr}$, i.e.,

$$P_{micro}^{\mathrm{*}}=C_p·L_{tu-out}^{\mathrm{*}}$$

(7)

where $C_p$ is a function of train velocity $v_{tr}$. As displayed in Figure 15b, through simple data fitting using dimensionless quantity, coefficient $C_p$ is then determined as

$$C_p=0.0084·v_{tr}^{\mathrm{*}}$$

(8)

Combine Equations (7) and (8), we have

$$P_{micro}^{\mathrm{*}}=0.0084·\frac{v_{tr}^{\mathrm{*}}}{L_{tu-out}^{\mathrm{*}}}$$

(9)

By using the empirical model obtained above, amplitude of MPW emitted from tunnel portal becomes predictable. To be noted, Equation (9) is limited by the current scenarios where the tunnel structure, i.e., tunnel length and hoods, are pre-designed and train velocity varies within 350~495 km/h only. Further investigation focusing on the other influencing factors, such as the tunnel length and local landform, have already been lunched by the authors, which will be discussed in our future work.

4.2. Aerodynamic Pressure Regrading Train-Intersection

Discussion in this section will highlight the aerodynamic effect caused by the intersection of HSTs. TPLs acting at tunnel sidewall and train surface are both addressed with research interest inclined to the pressure difference caused by the intersection at different velocity levels.

Firstly, Figure 16 displays the wave propagation and pressure history measured at the head and tail of Train A in Test 13. Pressure counterbalance, superposition, as well as its coupling effect performing as TPLs are revealed. Further investigation associated with the pressure waveform considering the intersection effect is illustrated by Figure 17. After the entry of two high-speed trains running through tunnel portals from each side, the initial pressure waves appear at $t=a$ s exhibited in Figure 16a,c lead to the (1) pressure increase $∆P_{h-1}$ due to the compression wave produced at train head and (2) pressure drop $∆P_{t-1}$ attributed to the expansion wave generated at train tail. Detailed change of pressure waveform can be observed in in Figure 17. The second pressure increase appeared at train head and tail, marked as $∆P_{h-2}$, is clearly explained by the diagram of wave propagation shown in Figure 16b. The reason behind is due to the compression wave caused by the entry of Train B at $t=b$ s marked in both Figure 16a,c. Continuous pressure decreases in Figure 16a appeared between $t=c~f$ s shown in both Figure 16a,c are respectively resulted by the head-to-head intersection, expansion wave for train head, and head-to-tail intersection for train tail. Increase of the pressure measured after $t=c~f$ s is due to the reflected compression wave, which will not be further discussed.

Figure 18 lists the pressure contours recorded at different time in Test 11 where train’s intersection is conducted at the speed of 400 km/h. As shown in Figure 18a–c, pressure in the overall flow field shows growing trend from the portal side to the tunnel center with all the values being positive before the intersection. As the decease of train’s head-to-head distance, area within the high pressure marked within the dotted lines is reduced. After the shortly head-to-head intersection at $t=$ 4.475 s, as shown in Figure 18d, a fast pressure decrease in the whole flow field is observed. Afterwards, area of the negative pressure field expands as time goes, resulting the pressure field within the intersected area (marked in Figure 18e within dotted lines) being entirely negative.

TPL acting at train body is plotted in Figure 19 considering intersection carried out by both equivalent and unequal train speed (Test 12 and 14 for example). The pressure waveform drawn in Figure 19 show very limited difference in such two conditions. Besides, for a given location at train surface, the pressure load measured at the intersection side agrees well with what obtained from the non-intersection side. Pressure difference exists only when the measuring position moves along the longitudinal direction, which matches well with what observed in the pressure contours exhibited in Figure 18.

In the similar way referring to Figure 11, Figure 20 reveals the pressure changes measured at different positions regarding train’s intersection with both equivalent and unequal train speed (Test 13 and 15 for example). In general, results from both Test 13 and 15 denote values of $P_{tw-max}^{\mathrm{*}}$ first increase and then decrease with $L_{tu}^{\mathrm{*}}$. The turning point, as well as the maximum value of $P_{tw-max}^{\mathrm{*}}$ occurs at tunnel center. However, different varying trend can still be observed compared with what seen in Figure 11. Firstly, increase of $P_{tw-max}^{\mathrm{*}}$ seems to be not significant when $L_{tu}^{\mathrm{*}}$ increases from 0 to 0.3. Rather, $P_{tw-max}^{\mathrm{*}}$ within 0 $<L_{tu}^{\mathrm{*}}<$ 0.3 maintains relatively equivalent level with those plotted in Figure 11, i.e., 0.8~1.6. Secondly, for a given location (see the dotted line marked in Figure 20a), values of $P_{tw-max}^{\mathrm{*}}$ change with measuring locations. When the two HSTs meet at the same velocity, $P_{tw-max}^{\mathrm{*}}$ measured with $L_{tu}^{\mathrm{*}}<$ 0.5 decreases as the measuring height increases, or the transverse location varies from the non-intersection side to the intersection side, i.e., $P_{A-1}^{\mathrm{*}}$ to $P_{A-7}^{\mathrm{*}}$. On the contrary, $P_{tw-max}^{\mathrm{*}}$ obtained from $L_{tu}^{\mathrm{*}}>$ 0.5 show opposite varying trend. When the two HSTs intersect at different velocities, $P_{tw-max}^{\mathrm{*}}$ within $L_{tu}^{\mathrm{*}}<$ 0.5 show almost the same tendency with what observed in Figure 20a. Different varying trend appears at $L_{tu}^{\mathrm{*}}=$ 0.63, where $P_{tw-max}^{\mathrm{*}}$ is not sensitive to the measuring location.

5. Conclusions

Tunnel aerodynamic effect, accompanied with environmental noise, facility safety, as well as human health problems, challenges the operation safety of high-speed railways. As the targeted velocity of HSTs is likely to approach 450 km/h in the near-future, investigation in this filed indicates urgent practical need. The present paper conducted a set of field tests and numerical simulations regarding train’s passage and intersection with train’s velocity ranged within 350~495 km/h. Numerical results were first validated by field measurements, indicating the discrepancy being less than 10%. Research concludes the following findings:

(1)

TPL acting at tunnel surface and the train body presents unevenly distribution trend as the longitudinal distance to tunnel entrance increases. Pressures measured near tunnel center is generally higher than that those detected near tunnel portal. The pressure peak measured at tunnel surface first increases and then decreases with the maximum value appearing at the intersection position (tunnel center in the current research). Besides, for a given location, TPL nearby the train side increases with the measuring height and show slight difference on the other side.

(2)

Amplitude of micro-pressure wave increases with train’s velocity. The maximum value of MPW detected in the field test is approximately 37.63 Pa. Meanwhile, amplitude of MPW is inversely proportional to the attenuated distance, i.e., $P_{micro}\propto \frac{1}{x_{tu-out}}$. Through data fitting, empirical model was established to predict the longitudinal attenuation of amplitude of MPW.

(3)

Pressure rapidly increases before the heat-to-head intersection and then fast decreases due to the tail-to-tail intersection. In the situation of train’s intersection, variation of the pressure peak near the tunnel portals is insignificant though train’s velocity changes. On the contrary, pressure peaks measured at the intersection position are doubled. The peak pressure load appears at the train head while carriages of the train body will be within the negative region after the head-to-head intersection. For the given location, values of pressure peak obtained from both the intersection side and non-intersection side presents limited variation while values change when the longitudinal location varies.