Moving model experimental analysis of the slipstream produced by a simplistic square-back high-speed train

Abstract

High-speed trains (HSTs) are being buffeted by accelerating running speed, and with that comes the aerodynamic issues. The slipstream is related to the train aerodynamic characteristics and of importance to the safety of surrounding people and structures. In this study, the ensemble-averaged and instantaneous characteristics of the slipstream of a simplistic high-speed train model with a square-back were experimentally investigated using a novel moving model rig. The present investigation indicates that the double-line substructure causes obvious asymmetry in the slipstream even at locations apart from the bridge surface with a large distance. The square-back of the HST attenuates its slipstream significantly relative to that with a streamlined tail. Besides, the decaying rate of the slipstream is higher in the wake of a square-back HST. The presents results suggest that the trailing vortices downstream of the square-back HST are substantially suppressed.

Keywords

aerodynamics high-speed train slipstream bridge moving model test

Introduction

The propagation of train-induced airflow and its influence on surrounding infrastructures need systematical investigation with the spectacular expansion of the high-speed railway (HSR) network. As a vital component in the HSR network worldwide, the bridge has been widely used. For example, the Japanese HSR system has an average bridge ratio of 33.3–61.5% for various railway lines. This ratio in France HSR is reported as 1.3–32.2%. Particularly, it reaches 94.2% in the Guang-Zhu intercity railway in China (He et al., 2017).

The movement of surrounding air caused by a running train is called slipstream, which significantly affects efficiency and safety, e.g., the transient aerodynamic effects on surrounding structures (Soper et al., 2014). A strong slipstream threatens the environment and the safety of surrounding structures even causes injuries and deaths (Hardy, 2007). The slipstream is often divided into several regions from upstream of the train head to the wake downstream of its tail (Baker et al., 2001; Sterling et al., 2008), as shown in Figure 1. Due to the complexity of the flow around a train, research developments mainly rely on full-scale tests (Baker et al., 2013a, 2013b; Sterling et al., 2008), scaled model tests (Baker et al., 2001; Temple and Dalley, 2001), and computational fluid dynamic (CFD) simulations (Rocchi et al., 2018; Wang et al., 2018a; Wang et al., 2018b).

The full-scale field test is a reliable method for measuring the slipstream of high-speed trains, i.e., HSTs (TSI, 2008; CEN 2013). Baker et al. (2013a, 2013b) investigated the slipstream of different train types via full-scale field measurement. Their results showed that the slipstream caused by different trains (HST or freight train) could be significantly different and each gap between two carriages causes a peak in the slipstream. However, a full-scale field test intervenes too late in the development process of HST-related issues (Pii et al., 2014) and the field test is susceptible to environmental conditions, e.g., natural crosswinds.

The model test is an alternative experimental method to overcome the field test’s disadvantages, which can be classified into two main categories: wind tunnel test with a stationary model and moving model test. A number of investigations have been conducted to figure out the experimental techniques to reproduce the slipstream identical to that in a real case. Weise et al. (2006) performed a wind tunnel test to analyze the specific region of the slipstream and the near wake of an HST. Their flow visualization found two typical flow patterns, i.e., separation bubble and vortex shedding, occur in the near wake of the HST, depending on its geometry. Muld et al. (2012) identified the two typical dominant flow modes using the CFD technique, either a large separation bubble or two counter-rotating vortices extending far into the wake, for the trains with different tails geometry. Based on wind tunnel experiments with a stationary train model, Bell et al. (2014) found the substructure has significant effects on the near wake and slipstream. For the flat ground configuration, the trailing vortices of the train move outwards in a lateral direction more quickly, relative to those for the single-track ballast and rail configurations. Recently, the effects of ground configurations on the slipstream and near wake are widely concerned, especially the boundary layer developed on the bottom wall under the train model (Bell et al., 2014; 2017a; Nayeri, 2013; Xia et al., 2017a; Zhang et al., 2016). Zhang et al. (2016) suggested that a moving ground configuration can eliminate the effects of the boundary layer on the ground, which increases the velocity under the train relative to the stationary ground condition. Xia et al. (2017b) found that a moving ground configuration reduces the dominant frequency of vortex shedding in the near wake. Besides, the longitudinal vortices oscillate more significantly than those with a stationary ground configuration.

Although the geometry similarity was satisfied greatly in the above-mentioned wind tunnel experiments, the relative motion between the train and ground and the associated transient behaviors, i.e., the compression and expansion process of the air due to HST passing by, are not considered. The slipstream of an HST is more likely a transient and tension-compression alternating flow process (Lighthill, 1962). Baker et al. (2001) also pointed out that the slipstream has highly three-dimensional and unsteady properties in the full-scale tests.

Considering the effects of ground configuration, a scaled moving model test is recommended by CEN (2013) because this technique involves the relative motion between the train and ground, which makes it a suitable technique for assessing TSI-type slipstream risk at the design phase of HSTs (Bell et al., 2017a). Although the length to height ratio (L/H) and Reynolds number are generally smaller for moving model test than those in real cases, the reduced L/H has the potential to be offset by the reduced Reynolds number since the boundary layer thickness on the model surface is inversely proportional to Reynolds number (Bell et al., 2014).

Since the first high-speed (or bullet) train in Japan in the 1960s, at a speed of 210 km/h, the obvious advantages of a streamlined head of an HST have become evident. But for the same geometry of streamlined tail, the wake of a modern HSTis in general expected to be a complex, unsteady, three-dimensional structure consisting of shear layers, vortex shedding, separation and recirculation regions, and a pair of counter-rotating streamwise vortices (Bell et al., 2014; Morel, 1980; Muld et al., 2012; Weise et al., 2006). As reported in much previous research, a pair of strong helical vortices presences downstream an HST, extending to a considerable distance into its wake and significantly affecting the slipstream around the train. In particular, some evidence pointed to the problem of the high slipstream velocities in the wake caused by the streamwise vortex pair (Bell et al., 2014; Xia et al., 2017c). Thus, the question is whether it is necessary to have a streamlined tail of an HST and reduce the aerodynamic problem by optimizing shape needs to be carefully reconsidered.

The main objective of the present work is to explore the slipstream and near wake of an HST with a simplistic square back tail using a moving model rig. This study looks at the distribution of the slipstream around the train model, ensemble-averaged and instantaneous information of the gust. Results are compared with those reported in literatures for the HST with a streamlined tail to get a comprehensive understanding of the effects of tail geometry on its slipstream. Furthermore, the present work provides basic information about the airflow around the train, which is a prerequisite for understanding the aerodynamic mechanism of a running train on a bridge under crosswinds.

Experimental set-up

Moving model rig

The moving model experiment was performed in the National engineering laboratory for HSR construction at Central South University. The moving model test rig has a 34 m long double-line track across the low-speed test section of a closed-looped low-speed wind tunnel, as shown in Figure 2. The test section has a dimension of 12 m wide, 3.5 m height, and 18 m long. For the present experiments, the wind tunnel was not started. So, there was no crosswind during the experiment.

Figure 2 shows the schematic diagram of the moving model rig, which consists of acceleration, test, and deceleration sections. The acceleration and deceleration parts are located at both sides, and the available test section is 12 m long across the wind tunnel’s test section. A 1/16.8 scaled model of a Fuxing HST, an HST in operation throughout China, was used in the present experiment. Two pairs of photoelectric gates were installed at the test section entrance to determine the model speed. Another two were placed at the exit of the test section, as shown in Figure 2. The model train speed U_t was 32 m/s at the entrance. It reduced by about 0.4 m/s when the train model reached the exit of the test section. Considering the deceleration of the model was very limited, U_t was considered constant in the present experiment. Based on U_t and H, the corresponding Reynolds number Re was 4.91 × 10⁵.

As shown in Figure 2, the L/H of the train model was 7.12, which was smaller than a real train with multiple carriages. This reduced L/H may limit the development of the boundary layer along the train and the associated shear layer thickness in the wake. As pointed out by Bell et al. (2015), a small Reynolds number in the experiment can compensate for the effects of a reduced L/H. That is, the effects of the smaller L/H have the potential to be offset by the reduced Reynolds number of the scaled model compared to the full-scale case (Bell et al., 2014).

Slipstream measurements

Instantaneous velocities within the slipstream and near wake were measured using a Cobra Probe (Turbulent Flow Instrumentation), a four-pressure-hole probe with a high-frequency response capable of measuring velocities in three directions. The Cobra probe can measure velocities with an accuracy of 0.5 m/s within a ± 45° cone angle (Hooper and Musgrove, 1997).

To get a comprehensive understanding of the slipstream and near wake of the present tested model, velocities were measured at a set of monitoring points, as shown in Figure 3. Specifically, the two particular positions corresponding to the monitoring points at the track-side and on the platform (European Rail Agency, 2008; CEN, European Standard, 2013) were also included in the present experiment, as marked by the solid points in Figure 3. The x-axis was defined along the track, the y-axis was the lateral direction, and the z-axis was the vertical direction. X = 0 corresponds to the tip of the train nose. The measurement points are located at |Y|/W = 0.55, 0.65, 0.75, 0.85, 0.95 and Z/H = 0.17, 0.26, 0.35, 0.44, 0.53, respectively, where W is the width of the train model. The measurements were conducted at both sides of the train model, as shown in Figure 3, to reveal the effects of the asymmetric double-track bridge. The measurement plane was located at the center of the bridge model along the x-direction. For each point, the Cobra probe was synchronized with the photoelectric gates with a sampling frequency of 2000 Hz, thus the measured velocity could be coordinated with the location of the train model.

The Cobra probe points to the x-direction during the measurement. Thus, u, v, and w velocity components correspond to velocities in the x-, y-, and z-directions, respectively. Previous research disclosed that, except around the train nose and tail, the contributions from v and w to the total slipstream velocity is smaller than 2% and below the performing range of the Cobra probe, suggesting the slipstream is dominated largely by u. The present paper only used u to represent the slipstream, which follows the regulations of TSI (European Rail Agency, 2008) and EN (CEN European Standard, 2013). Considering the unstable characteristics of the slipstream, the measured time history of u at a specific position can vary significantly from each run (Baker et al., 2001; Bell et al., 2015). Following the TSI regulations, the measurement at each monitor point was repeated 20 times to ensure reliable ensemble-averaged results (Gil et al., 2010). Besides, for easy comparison, the spatial coordinates are converted into full-scale quantities. For example, L = 1.616 m of the model corresponds to 27.15 m for the full-scale train.

Results and discussions

Effects of train speed

Baker et al. (2001) and Gil et al. (2008) suggested that the slipstream of an HST with an identical streamlined head and tail is not sensitive to the train speed if it is normalized by U_t. To confirm this conclusion is still applicable for the present tested train model with a blunt tail, measurements are repeated at U_t = 8 m/s, 10 m/s, 15 m/s, 20 m/s, 25 m/s and 32 m/s, respectively. The corresponding Reynolds number ranges from 1.24 × 10⁵ to 4.91 × 10⁵.

Figure 4. shows the normalized ensemble-averaged slipstream velocity u/U_t at Y/W = −0.55 and Z/H = 0.79 for different U_t. The variation of u/Ut is similar for all U_t, with two peaks at the train nose and tail, respectively. Generally, the peak value of u/U_t at the train nose is almost identical for all U_t. For all plots the development of slipstream and magnitudes match closely for all train speeds, indicating a general linear relation between slipstream velocity magnitudes and train speed. Although the maximum value of the second peak is also similar, the u/U_t in the wake region near the train tail presences obvious random jittering. This observation may be ascribed to the highly unsteady and three-dimensional features of the wake.

Since the behavior of u/U_t is similar for all U_t (as shown in Figure 4), only the results obtained at U_t = 32 m/s are discussed in the following sections. The corresponding Re is 4.91 × 10⁵, which is higher than 2.5 × 10⁵ and fulfills the requirement of the CEN European Standard (2013).

Slipstream at different positions

For an HST running on symmetrical substructures, e.g., single-line ballast, the ensemble-averaged flow is largely symmetrical, despite some random minor differences (Muld et al., 2014; Wang et al., 2017). This section reveals the effects of the asymmetric double-track bridge on the slipstream by comparing the results at both sides of the train (see Figure 3).

Figure 5 compares the u/U_t measured at both sides of the train. For the locations very close to the train surface, as shown in Figure 5(a), the u/U_t at the inner position (Y/W = 0.55) presents more violent fluctuation than that at the outer position (Y/W = −0.55), especially near the tail of the model. Besides, the peak value of u/U_t at the inner position is slightly smaller. These differences can only be ascribed to the asymmetric substructures in the present experiments. In addition, the tracks and ballasts of the other line on the bridge have significant effects on the u/U_t measured close to the train. Once the train passes by, the u/U_t reduces to a very small value quickly, especially for the outer location, as shown in Figure 5(a). At further downstream of the train, the u/U_t presents some large-scale fluctuations, e.g., at about 27 m and 50 m downstream from the train nose, as shown in Figure 5(a), which may associate with the swing of the near wake.

Figure 5(b) and (c) present the u/U_t at lateral positions relatively apart from the train at Y/W = ±0.95. Regardless of Z/H, the maximum u/U_t at these positions is larger than near the train surface, as shown in Figure 5(a). This observation suggests that the strongest slipstream in the boundary layer region occurs not near the train surface but at a certain distance apart from the train body, where the flow has highly unsteady turbulent structures (Baker et al., 2001; Bell et al., 2015). Moreover, the difference in u/U_t between the inner and outer measurement locations is still less obvious at the height of Z/H = 0.44. Despite of the u/U_t at a smaller |Y/W| (Figure 5(a)), the u/U_t at a larger |Y/W| (Figure 5(b) and (c) decays more slowly in the train wake with increasing X. Besides, the slipstream in the far wake region presences an intermittent oscillation, where the trailing vortices dominate.

Generally, the strength and fluctuation of u/U_t at the outer positions (Y/W < 0) are smaller than those at the inner positions (Y/W > 0), suggesting the substructures on the bridge tend to suppress the slipstream velocity. Despite the difference mentioned above, considering the general similarity of u/U_t at both sides of the train, only the results at outer positions (Y/W < 0) will be discussed in the following sections.

Comparison of the slipstream for different train types

Figure 6 compares the u/U_t for different types of trains, including passenger trains ICE2, ICE3 (Baker et al., 2001; Bell et al., 2015), freight train Class 66 (Soper et al., 2014), and the present Fuxing HST. The results can be divided into two groups, i.e., HSTs with identical streamlined heads and tails and freight trains with bluff heads and tails. It is worth mentioning that the present tested HST model has a streamlined head and a blunt tail, as shown in Figure 3. The horizontal axis in Figure 6 is normalized using the model length for easy comparison. Particularly, X/L = 0 is the location of the train nose, while X/L = 1 indicates the location of its tail.

Figure 6(a) compares the ensemble-averaged u/U_t measured at Y = 3m and Z = 2.25 m for different trains. Several observations can be made: Firstly, the u/U_t of Class 66 (Soper et al., 2014) is much larger than that of the HSTs with streamlined heads, e.g., ICE2 (Baker et al., 2001) and present tested Fuxing. For example, the maximum u/U_t occurred near the train nose of Class 66 is almost doubled relative to the corresponding value of ICE2 and Fuxing. Secondly, once the train head passes by, the u/U_t drops quickly to a very small value for the trains with streamlined heads, e.g., ICE2 and Fuxing, as shown in Figure 6(a). However, the u/U_t of Class 66 is still far larger than the corresponding value of the streamlined HSTs. This observation may be ascribed to the fact that the surface of an HST is smoother relative to a freight train. Thirdly, for ICE2, u/U_t presents another peak when the train tail passes by, which is associated with the strong trailing vortices in its near wake. This peak in u/U_t disappears for the present tested Fuxing, suggesting the strength of trailing vortices may be suppressed for an HST with a streamlined head but a blunt tail. Finally, in the far wake region, u/U_t of the present measured Fuxing HST is significantly smaller than that of ICE2, which may suggest the trailing vortices decay more quickly for an HST with a blunt tail.

In order to confirm the above observations, Figure 6(b) shows the u/U_t measured at Y = 3 m and Z = 1.58 m, i.e., the platform monitoring position (European Rail Agency, 2008), for both ICE 3 (Bell et al., 2015) and the Fuxing. Similar to that shown in Figure 6(a), the peak of u/U_t occurs at the trail of ICE3 does not present for the present blunt tail train. Moreover, u/U_t in the far wake of the train is far smaller for the blunt tail train relative to that of the streamlined tail train.

As shown in Figure 6(a), the first peak of u/U_t depends on the geometry of the train head. The train with a streamlined head (ICE 2 and Fuxing) suppresses the u/U_t by about 1/2 relative to that for a train with a blunt head (Class 66). On the other hand, the second peak of u/U_t, which occurs near the train tail, depends on the geometry of the train tail (Figure 6(b)). As Bell et al. (2014, 2016) report on the wake structure of an HST, there is a pair of strong counter-rotating trailing vortices occurs in the wake of HST with a streamlined tail (Wang et al., 2017; Xia et al., 2017a), which associates with the largest slipstream velocity (second peak) of u/U_t near the train tail (Baker et al., 2013a; Bell et al., 2015). These trailing vortices are qualitatively similar to that downstream an Ahmed model (Bayraktar et al., 2001; Thacker et al., 2013; Tunay et al., 2014), which are sensitive to the slant angle α of the tail. For the Ahmed model with 12.5° < α < 30°, i.e., a streamline lined tail to some extent, the trailing vortices are much stronger than those with α > 30° (Strachan et al., 2007; Wang et al., 2016). This observation for the Ahmed model may be essentially consistent with that shown in Figure 6(b). That is, an HST with a blunt tail suppresses the trailing vortices and the associate u/U_t in its wake, compared with that for an HST with a streamlined tail. The existence of a streamwise vortex is the key to the largest slipstream velocity in the wake for the HSTs with streamlined tails, and no coherent streamwise vortices exist in the wake for the blunt tail (Bell et al., 2017b). These results are consistent with experimental and numerical work that established the sensitivity of the wake structure to the tail geometry, as well as the tendency of the wake to be dominated by trailing vortices or large-scale separation (Morel, 1980; Muld et al., 2013; Weise et al., 2006). In addition, the studies on-road vehicles may also provide some related evidence that the blunt tail can contribute to more rapid cross-annihilation and lead to less coherent wake vortices from the body (Avadiar et al., 2019; Mcarthur et al., 2016; Parkin et al., 2015).

Spatial distribution of slipstream velocity

Figure 7 shows the contours of ensemble-averaged u/U_t at different cross-sections along the train. Note that X = 0 m indicates the train nose, X = 8.4 m is the end of the nose, X = 13.57 is the middle of the train and X = 27.15 indicates the train tail.

Apparently, u/U_t presents its maximum at X = 0 and decays quickly with increasing X. Interestingly, there are two local peaks present at X = 0, one near the train nose and the other presences near the ground shown in Figure 7. The u/U_t at the peak near the train nose reaches 0.3, far larger than the corresponding value at other locations. The distribution of u/U_t at X = 8.4 m, i.e., the end of train nose, is completely different from that at X = 0. For example, the strong peak at the height of the train nose disappears completely at X = 8.4 m. This variation in u/U_t along X indicates the flow around the train nose is highly three-dimensional. u/U_t decays quickly with increasing X, and no pronounced peak occurs at X = 27.15 (at the tail of the train), except near the bridge surface.

On the other hand, velocities peaks seem sporadic in the measurement along the lateral axis on the train side. This could be closely pertinent to turbulence at which alternating vortices are shed from the train. The Turbulence intensity (Ti) of these locations will be analyzed in detail.

Evaluation of turbulence intensity

Turbulence intensity of the slipstream within the shear region around the train can be used as a measure for the gustiness of the flow which is defined as the ratio of the SD of velocity to its mean value (Davidson, 2004). Figure 8(a) and (b) illustrate the instantaneous slipstream at the Y = −0.55 W, Z = 0.17 H, and Y = −0.75 W, Z = 0.35 H for 25 individual runs. The red and blue lines are the ensemble mean values and Ti, respectively. Another way to evaluate slipstream velocity is the MOSMA technique in CEN (2013) and TSI (2008), which is defined as $u_{2 σ} = \bar{u} {+ 2 σ}_{u}$ , where $\bar{u}$ is the ensemble mean velocity and $σ_{u}$ is the SD of the 20 independent runs. As shown in Figure 8(a) and (b), the difference between the results of each individual run is significant, especially for those shown in Figure 8(a), which are measured near the train and track.

Ti is similar in Figure 8(a) and (b) before the arrival of the train nose, suggesting the low turbulence level in the upstream region (Baker et al., 2001). In the area around the train nose, relatively higher Ti occurs, with its peak value of 29% and 20%, respectively. This is expected because the wheelset and underbody components increase the surface roughness of the train, thus increasing Ti at a lower location (Figure 8(b)). As the flow moves backward along the train, Ti reduces gradually. It is remarkable that the Ti in Figure 8(a) experiences two local peaks caused by the front and rear wheels. This observation disappears in Figure 8(b).

Moreover, the present measured maximum Ti in the wake is around 10%, smaller than that reported by Hemida et al. (2013) of 13–16% in the near wake from a passenger train. Therefore, the higher Ti at a lower location could cause safety problems for workers on the bridge deck and impact the aerodynamic characteristic of the bridge. However, the smaller Ti in the blunt tail’s wake and the effect will diminish.

Generally, the present measured Ti is smaller than that in previous studies of both passenger trains and freight trains (Hemida et al., 2013; Sterling et al., 2008; Soper et al., 2014; Tian et al., 2015). In addition, a 1 s running average is applied to each instantaneous velocity, together with the resulting mean and $u_{2 σ}$ as regulated by the TSI and EN (ERA, 2008; CEN, 2013) for gust analysis, as shown in Figure 8(c). The running-averaged results show a similar pattern but also bear significant differences for each run. Particularly, there are wide differences in the position and value of the individual maxima. However, a higher Ti in the region near the train nose and a significantly lower Ti in the wake region for the present HST with a square back tail are still obvious. Therefore, the locations of the peak value for each run are not necessarily within the appropriate $\bar{u}$ and $u_{2 σ}$ peak. It highlights the equally important fact that the $\bar{u}$ Ti and $u_{2 σ}$ could not completely represent the feature of gust.

Decay of u/U_t in the wake region

As presented in previous sections, there is a clear decay of u/U_t in the wake region. Muld et al. (2012) mentioned that either a large separation bubble or a pair of counter-rotating vortices occurs in the wake depending on the geometry of the train tail. For streamlined HSTs, some full-scale measurement results found a peak of u/U_t occurs at approximately 7–15 H downstream from the tail (Baker et al., 2013a; Sterling et al., 2008). However, this peak disappears in the present measurement. A possible explanation for this difference is that the blunt tail of the present train suppresses the peak of u/U_t in the wake region. Moreover u/U_t decays more rapidly in the wake of the present blunt-tail HST relative to that reported in works of literature (Baker et al., 2001; Bell et al., 2015; Soper et al., 2014). The aerodynamic features of the train in the present work are hauled by a streamlined nose at the front and a blunt tail similar to a freight train or coach. Note that the velocity loses its intensity fairly rapidly, and it quickly to 1/3 in size and switched from high level to zero. In the far wake region, a steep decay is observed in velocity because the flow separation, which drove the velocity is no longer present and allows for efficient control of the bluff tail’s wake the negative effects of trailing edge separation can be avoided. From this, it can be inferred that in the far wake velocities should be significantly low so as not to pose a safety threat, such as affecting a person’s stability in the same way. Previous studies suggested the decay of u/U_t follows a power-law function u/U_t = a(X)ⁿ, where X is the longitudinal position, as Baker et al. (2013a) summarized. They found that the decay of u/U_t is similar in the far wake region for different types of passenger trains. A similar observation was also found by Soper et al. (2014) for freight trains. Baker et al. (2013a) suggested that n = −0.39 ∼ –0.57 for HSTs, n = −0.46 ∼ –0.67 for short passenger trains, and n = −0.5 for locomotive coach combinations. Following this idea, Soper et al. (2014) claimed that n = −0.85 in the far wake of a freight train. Figure 9 shows the decay of u/U_t in the far wake of the present train model. For the present blunt-tail train, n = −0.66, suggesting u/U_t decays more quickly at greater distance compared to that of a streamlined-tail HST.

Peak of near wake comparison

Ensemble average presents the ensemble-average feature of the slipstream, the maximum of average ensemble profile is an important index of slipstream for describing and measuring the differences in the feature of train induced airflow. As the train passes, and even for a time after it has passed, the peak of the slipstream depends mainly on the train speed; the distance of the object, or observer, from the train; ambient wind speed and direction, and shape and surface profile finish of the train (Pope, 2007).

In this section, data from previous studies are compared to other measurements taken in the open-field test site, but in a successive test campaign where the probe was placed at the Z = 0.17 H and 0.53 H Y = 0.95 W for the two heights as shown as the black solid points in Figure 3.

Since this is a radically different shape of the train’s tail in the real application and also to understand and analyze the difference better, comparison of the near wake peaks for the track-side and platform levels are within the range of slipstream magnitudes for the common high-speed train with the different methods noted by other researchers as provided in Table 1.

Table 1.

Compare near wake peak slipstream magnitudes to previous works.

No.	Reference	Method	Scale	Re	Train type	Original length (m)	Peak
No.	Reference	Method	Scale	Re	Train type	Original length (m)	Track-side	Platform
1	Baker et al. (2013a)	Field	1:1	1.7 x 10⁷	ICE3	200.3	0.23	—
2	Baker et al. (2001)	MMT	1:25	2.5 x 10⁵	ICE2	67.5	—	0.09
3	Sterling et al. (2008)	MMT	1:25	3.3 x 10⁵	ICE3	67.5	0.23	0.10
4	Sterling et al. (2008)	MMT	1:25	2.5 x 10⁵	ICE 4 car	100	—	0.25
5	Sterling et al. (2008)	MMT	1:25	2.5 x 10⁵	ICE2 4 car	99.6	0.23	0.10
6	Sterling et al. (2008)	Field	1:1	1.5 x 10⁷	ICE1 14 car	364	0.28	—
7	Sterling et al. (2008)	Field	1:1	1.5 x 10⁷	ICE2 8 car	206	0.18	—
8	Xia et al. (2017b)	CFD	1:8	1.65 x 10⁶	CRH3	76.536	0.25	0.15
9	Xia et al. (2017c)	CFD	1:8	1.65 x 10⁶	CRH3	76.536	0.21	0.14
10	Hemida et al. (2013)	CFD	1:20	3 x 10⁵	ICE2	125.63	0.31	0.19
11	Bell et al. (2014)	WT	1:25	6.0 x 10⁵	ICE3	50	0.23	0.15
12	Bell et al. (2015)	MMT	1:25	1.85 x 10⁵	ICE3	50	0.16	0.08
13	CSU-WT	MMT	1:16.8	4.91 × 10⁵	Fuxing Hao with a blunt tail	27.15	0.094	0.047

Full-scale results themselves are susceptible to significant differences in peak magnitudes between experiments (Sterling et al., 2008). The sensitivity of the train’s length on the results has also been widely concerned and verified (Baker et al., 2013a; Bell et al., 2015). A train drags a streamlined tail, the platform height having a lower magnitude peak than the track-side height is also consistent with full-scale (Baker, 2010; Baker et al., 2013a; Sterling et al., 2008). Likewise, in Table 1, for the same train, it is shown that the platform height has a lower magnitude peak than the track-side height in the full-scale test and MMT (Baker, 2010; Baker et al., 2013a; Sterling et al., 2008). Moreover, magnitudes of the slipstream peaks calculated with the static model in the wind tunnel and CFD simulation are greater than all others found in the literature at both measurement heights. This further illustrates that the moving train experimental results are a more realistic simulation method. From this perspective, it is also in line with the experimental outcomes in this investigation. In this study, the measured values at two typical present study positions are smaller than the common streamlined tail. Even more to the point, at these two locations, a dramatic difference in the peak value by comparing the same method and values are far less than a streamlined tail. Thus it can be seen that this exploration and pursuit are valuable attempts for the development of new HST models.

Conclusion

A moving model rig is used to study the slipstream velocity u/U_t around a 1:16.8 scale model HST with a simplistic squared back running on an asymmetric double-line bridge. The following conclusions can be drawn:

(1) The asymmetric substructure causes asymmetry in the slipstream, even at locations apart from the bridge surface with a large distance. At one side of the HST, there are two local peaks of u/U_t occur near the train head. One presents at the height of the train nose, the other near the bridge surface.

(2) The HST with a square back suppresses the trailing vortices and associated slipstream velocity significantly in the near wake relative to those of an HST with a streamlined tail. Besides, the decay ratio of u/U_t in the far wake region of the square-back HST also follows a power-law with increasing longitudinal distance. The index is −0.66, indicating a higher decay ratio for the square-back HST.

(3) The Ti Ti is relatively higher near the train nose and near the wheelset. It becomes significantly lower in the wake region. Thus, the lower Ti in the wake region reflects a reduction effect to the turbulence from the square-back HST.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research described in this paper was financially supported by the National Natural Science Foundations of China (Grant No. 51925808, U1934209) and the Tencent Foundation (Xplorer Prize 2021), and China Postdoctoral Science Foundation (Grant No. 2022TQ0376,2022M713516).

Data Availability

Some or all data, models, or code generated or used during the study are proprietary or confidential in nature and may only be provided with restrictions.

Ethical approval

Compliance with ethical standards

ORCID iDs

Simin Zou

Xuhui He

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Moving model experimental analysis of the slipstream produced by a simplistic square-back high-speed train

Abstract

Keywords

Introduction

Experimental set-up

Moving model rig

Slipstream measurements

Results and discussions

Effects of train speed

Slipstream at different positions

Comparison of the slipstream for different train types

Spatial distribution of slipstream velocity

Evaluation of turbulence intensity

Decay of u/Ut in the wake region

Peak of near wake comparison

Conclusion

Footnotes

Declaration of Conflicting Interests

Funding

Data Availability

Ethical approval

ORCID iDs

References

Decay of u/U_t in the wake region