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Abstract

Transient numerical simulations were carried out by placing dimples at the top, sides and bottoms of the tail car streamline area of a high-speed maglev train. The results of an improved delayed detached eddy simulation turbulence model using three-dimensional compressible Navier-Stokes and shear-stress transport K-Omega double equations were compared to the results of a wind tunnel test to verify the numerical simulation accuracy, within 5% of the ground truth, which is an acceptable precision range. The results show that dimples arranged on the streamline area atop the train tail car affected the locations at which the airflow at the top and bottom of the train met and weakened the strength of the wake. The aerodynamic drag and lift coefficient decreased by 3.40% and 4.27%, respectively. When the dimples were arranged on the streamline area at the sides or bottoms of the train tail car, they had little effect on the top of the tail car, so they did not destroy the balance of the airflow at the top and bottom. They also had little influence on the development of wake topology. Therefore, the aerodynamic drag and lift of the train changed little.

1. Introduction

It is known that with an increase in train speed, aerodynamic drag also increases. When the train speed reaches 250−300 km/h, the aerodynamic drag can account for 75%−80% of the total drag [1]. For high-speed maglev trains, which reach speeds up to 600 km/h, the aerodynamic problems caused by high-speed operation are more severe and the drag further increases [2]. Presently, research on train-drag reduction has focused on changing the aerodynamic shape of the train, such as increasing its streamline length [3−5] and optimizing its streamline shape [6,7]. Notably, research on streamline length seems to have reached its limit, as exemplified by China's high-speed railway, which has a maximum streamline length of 12 m, and Japan's new generation of Shinkansen high-speed test car, ALFA-X, has a maximum streamline length of 22 m [8]. Therefore, other methods must be adopted to achieve drag reduction, such as flow control.

In this regard, flow control is a method of changing the flow field to its required structure using passive or active control technology [9]. The passive control technology means changing the control mode of the flow environment through a predetermined control device, while the active control technology means controlling the flow environment by directly applying an appropriate disturbance to the flow field of the object [10]. The non-smooth structure based on bionics is one of the main drag-reduction methods in passive flow control. As early as the 1980s, scholars demonstrated the drag reduction ability of non-smooth structures with various shapes (e.g. fan, blade and dimple) [11]. Subsequently, scholars found that the drag reduction effect of non-smooth dimples was more obvious [12−14]. Therefore, in recent years, scholars have paid more attention to non-smooth dimples [15−17]. Some scholars have applied bionic non-smooth surfaces to the field of transportation. Song et al. [18] revealed that properly designed non-smooth surfaces arranged on the engine cover lid and vehicle body cap could effectively reduce the aerodynamic drag of the vehicle. Wang et al. [9] studied the influence of non-smooth dimples, which were arranged on the rear inclined plane of a vehicle, on aerodynamic drag, showing that the dimples reduced the wake length and turbulent energy loss. Furthermore, the aerodynamic drag coefficient was reduced by 5.2%. Wang et al. [19] studied dimples, arranged on the streamline area of the train tail car, located on the top and sides to study the influence of the dimple position on the aerodynamic performance of the CRH380A high-speed train, showing that dimples placed on the top or sides of the train tail car effectively delayed flow separation, inhibited the formation of wake vortices and reduced aerodynamic drag. The dimples placed on the sides of the train had the best drag reduction effect, reaching 1.63%.

The differences between high-speed maglev trains and wheel-rail trains are mainly reflected in three aspects: no wheel-rail contact, no bogie structure and different head shapes [20,21]. The special track form of the high-speed maglev train is responsible for the flow field with a relatively small air gap between the train body and the track, and the ground effect is more significant than that of the high-speed train. When the train speed reaches 600 km/h or above, the aerodynamic lift increases rapidly and even approaches the weight of the train itself under extreme conditions [22]. An excessive aerodynamic lift will easily cause a failure of the train suspension system, resulting in collisions between bottom equipment and track beam, thus affecting the safe operation of the high-speed maglev train [23]. Owing to its special track form, the drag-reduction mechanism of a bionic non-smooth structure may be different from that of wheel-rail trains and automobiles. Presently, there is no systematic study on the drag-reduction effect of adding dimples to high-speed maglev trains. To do so, the dimple drag-reduction method needs to be considered.

In this study, an improved delayed detached eddy simulation (IDDES) model with good simulation flow-field results around the train was used to numerically simulate a high-speed maglev train with dimples arranged on the streamline area of the train tail car. The influence of the non-smooth bionic dimples on the pressure distribution, surrounding flow structure, wake-vortex structure development and slipstream distribution of high-speed maglev trains were obtained. The drag reduction mechanism of the dimples was revealed, and the influence of dimple position on the drag reduction effect of high-speed maglev train was clarified.

2. Numerical methods

2.1. Geometry model

The model used in this study was a 1:10 scale TR-08 high-speed maglev train consisting of a head and a tail car, and running on the Shanghai Maglev demonstration line. At full scale, both vehicles are 27.2 m long. In total, the actual train is 54.4 m (long) × 3.7 m (wide) × 4.2 m (high). Unlike traditional high-speed train tracks, maglev tracks remain 2.35 m above the ground and have no catenary atop. Taking the height of the train model, H, as the characteristic unit, the geometric model parameters of the train are shown in Fig. 1.

Geometric model of maglev train: (a) 3D view; (b) front view
Fig. 1.

Geometric model of maglev train: (a) 3D view; (b) front view

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According to the research results of Wang et al. [19], dimples arranged on a streamline area of the train tail car can effectively reduce aerodynamic drag, delay flow separation and inhibit wake vorticity. Thus, dimples were arranged on the train tail car in this paper. To analyse the influence of different dimple positions on aerodynamic performance, the dimples were arranged on the streamline area, which has the greatest influence on the aerodynamic performance of high-speed maglev train, at the top, sides, and bottoms of the train tail car, respectively. The length of the dimple area was half that of the streamline area (see Fig. 2 and Table 1).

Dimple position
Fig. 2.

Dimple position

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Table 1.
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Dimple position

PositionCase
No dimplePrototype
Region ATop
Region BSides
Region CBottoms
PositionCase
No dimplePrototype
Region ATop
Region BSides
Region CBottoms
Table 1.
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Dimple position

PositionCase
No dimplePrototype
Region ATop
Region BSides
Region CBottoms
PositionCase
No dimplePrototype
Region ATop
Region BSides
Region CBottoms

There are few studies on drag reduction by adding dimples on the streamline area of the maglev train. Therefore, the optimal dimple parameters cannot be directly determined through the existing literature. In future research, we will optimize the shape, size and arrangement of dimples to achieve a better drag-reduction effect of maglev vehicles. By referring to relevant literature on the drag reduction of dimples, Choi et al. [24] confirmed that the drag-reduction effect could be achieved when the dimple radius was 5−10 mm. Huang et al. [25] found that the drag-reduction effect could still be achieved when the dimple spacing was significantly different from the dimple radius. Considering that the shape of maglev vehicles must be aesthetic, the dimples should not be too large or too dense. Therefore, the radius, R, of dimples in this study is 7.5 mm, the transverse spacing X and the longitudinal spacing Y of dimples are both 100 mm. Abbas et al. [26] studied the dimple depth on golf balls and found that the drag-reduction effect was better when the dimple depth was 0.68R−0.86R. Therefore, the dimple depth, D, adopted here was 5.625 mm. Taking the height of the train model, H, as the characteristic unit; the dimple radius, R, was 1.79×10−3H; the dimple depth, D, was 1.34×10−3H; the transverse spacing, X, was 2.38×10−2H and the longitudinal spacing, Y, was 2.38×10−2H, respectively, as shown in Fig. 3.

Key dimple parameters: (a) top view; (b) dimple distribution; (c) cutaway view
Fig. 3.

Key dimple parameters: (a) top view; (b) dimple distribution; (c) cutaway view

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2.2. Calculation domain and boundary conditions

The top and front views of the calculation domain are shown in Figs. 4(a) and (b), respectively. Based on the recommendations of CEN European Standard [27], the distance between the entrance of the calculation domain and the nose of the train should be greater than 8H. Simultaneously, considering the backflow phenomenon of the numerical solution, the distance between the entrance of the calculation domain and the nose of the train was set to 10H; the distance from the train tail car to the pressure outlet was 35H, and the width and height of the calculation domain were 20H and 10H, respectively.

Train calculation domain and boundary conditions: (a) top view; (b) front view
Fig. 4.

Train calculation domain and boundary conditions: (a) top view; (b) front view

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The inlet condition was set as the velocity inlet and the incoming airflow velocity U∞ was set to 600 km/h (166.7 m/s). The exit boundary of the calculation domain was set as the pressure outlet, the sides and top of the calculation domain were set as the slip wall, and the bottom boundary was the moving non-slip wall that moves relative to the train at the speed U∞.

2.3. Numerical method

All calculations in this study were carried out using STAR-CCM+13.02. Owing to the Mach number Ma = U∞/c, where the incoming airflow velocity U∞ = 166.7 m/s, and c is the local velocity, which is equal to 340 m/s, thus Ma = 0.49>0.3. The simulation in this study considered compressible fluid, and a three-dimensional compressible finite-volume solver based on the SST K-omega model, which is an IDDES separation eddy simulation method, was used. This method provides sufficient and reasonable flow-field information for analysis without significantly affecting calculation efficiency [28]. Owing to its excellent performance and applicability, the SST K-omega model has been widely used to study train aerodynamics [29−31]. For more information, see the work of Shur et al. [32].

Hybrid second-order upwind and bounded-central differencing was used for the convection term, and a second-order implicit scheme was used to discretize the time. The discrete time step was determined to be 0.08Tref (where Tref = H/U∞). By comparing the average values of the short average period at different time, the flow field is considered to reach the asymptotic statistical state when no significant difference is found, and the statistical results of the transient state are collected. The sampling rate for the unstable statistics was 400Tref (1 s), which approximately equates to the flow through the entire domain seven times.

2.4. Mesh strategy

The meshing module of the STAR-CCM+ software was used to mesh the training model and the calculation domain. To better simulate and capture the boundary-layer flow near the wall, a prismatic layer mesh was used to divide the near-wall region, and the computation domain was meshed using layer-by-layer encryption. The direction away from the train transitioned from a relatively smooth to a low-mesh resolution. An automatic encryption method was used to mesh the train surface. In addition, to accurately capture the vortex structure of the high-speed maglev train, a mesh length of 0.019H is used for encryption in the wake region to meet the requirements of IDDES solver to capture the details of the turbulent structure.

To accurately capture the flow near the wall of the train and the velocity gradient in the boundary layer, a prism layer was arranged around the train surface according to the predicted y+ value of the formula, ensuring that the y+ value on the prism layer of the first layer was approximately one.

Eqs. (1) and (2) are used to define the y+.
(1)
(2)
  where, |$\bar{u}$| is the time-average velocity of the fluid, |${u_\gamma }$| is the friction velocity of the wall, |${\tau _\omega }$| is the shear stress of the wall, and |$\Delta y$| is the thickness of the first layer of the mesh. The surfaces of the track and ground were laid out with relatively rough prismatic layers. An automatic encryption method was adopted for the mesh division of dimples, as shown in Fig. 5.
Mesh diagram: (a) side view; (b) front view
Fig. 5.

Mesh diagram: (a) side view; (b) front view

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2.5. Data processing

For the convenience of comparative analysis, dimensionless drag, lift and pressure coefficients are used for definition and analysis, as shown in Eqs. (3), (4) and (5).
(3)
(4)
(5 )
 where, Cx, Cz and Cp are drag, lift-force and pressure coefficients, respectively. Fd and Fl are the drag and lift, respectively. P is the local mean static pressure. P0 is the reference pressure, which is equal to 0 Pa. The air density, ρ, is considered to be 1.18 415 kg/m3. The incoming flow velocity, U∞, is 166.7 m/s. The reference area, S, is 0.1 184 m2.
In this study, UTF, VTF and WTF are the streamwise, spanwise and vertical components of the velocity based on the train-fixed reference system, respectively, obtained directly from the simulation. To make it easy for readers to understand, these velocity components are transformed into ground-fixed reference system. The streamwise, spanwise and vertical components of the dimensionless velocities (U, V and W) based on the ground-fixed reference system are defined in Eqs. (6), (7) and (8).
(6)
(7)
(8)
 
To better analyse the variation of the flow field around the train, the streamwise and spanwise component of the velocity are synthesized, namely, the slipstream velocity (UV), and UW, VW can be obtained by a similar method, as shown in Eqs. (9), (10) and (11).
(9)
(10)
(11)
 
At present, some researchers have used the Q-criterion to study the tendency of vortex structure development and separation along high-speed trains [5,33−35]. The iso-surface of the second invariant of the velocity gradient tensor Q is defined in Eq. (12) [34]:
(12)
where, u, v and w are the velocities in x, y and z directions monitored by the ground-fixed reference system, respectively.

2.6. Mesh independence verification

Considering the influence of the mesh size on the calculation results, the mesh independence was verified. Three mesh schemes were used to compare and verify the condition of the dimple arrangement atop the streamline area. The medium mesh encrypts all the meshes compared to the coarse mesh, whereas the fine mesh encrypts the mesh again based on the medium mesh. The specific values are listed in Table 2.

Table 2.
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Three mesh partitioning parameters

MeshDimple regionTrain surface around dimpleOther place of train surfaceTotal number of elements (106)
Coarse1.48×10−4H–2.98×10−4H2.98×10−4H–9.52×10−3H9.52×10−3H–1.90×10−2H28
Medium3.72×10−5H–1.49×10−4H1.49×10−4H–4.76×10−3H4.76×10−3H–9.52×10−3H43
Fine1.86×10−5H–7.44×10−5H7.44×10−5H–2.38×10−3H2.38×10−3H–4.76×10−3H59
MeshDimple regionTrain surface around dimpleOther place of train surfaceTotal number of elements (106)
Coarse1.48×10−4H–2.98×10−4H2.98×10−4H–9.52×10−3H9.52×10−3H–1.90×10−2H28
Medium3.72×10−5H–1.49×10−4H1.49×10−4H–4.76×10−3H4.76×10−3H–9.52×10−3H43
Fine1.86×10−5H–7.44×10−5H7.44×10−5H–2.38×10−3H2.38×10−3H–4.76×10−3H59
Table 2.
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Three mesh partitioning parameters

MeshDimple regionTrain surface around dimpleOther place of train surfaceTotal number of elements (106)
Coarse1.48×10−4H–2.98×10−4H2.98×10−4H–9.52×10−3H9.52×10−3H–1.90×10−2H28
Medium3.72×10−5H–1.49×10−4H1.49×10−4H–4.76×10−3H4.76×10−3H–9.52×10−3H43
Fine1.86×10−5H–7.44×10−5H7.44×10−5H–2.38×10−3H2.38×10−3H–4.76×10−3H59
MeshDimple regionTrain surface around dimpleOther place of train surfaceTotal number of elements (106)
Coarse1.48×10−4H–2.98×10−4H2.98×10−4H–9.52×10−3H9.52×10−3H–1.90×10−2H28
Medium3.72×10−5H–1.49×10−4H1.49×10−4H–4.76×10−3H4.76×10−3H–9.52×10−3H43
Fine1.86×10−5H–7.44×10−5H7.44×10−5H–2.38×10−3H2.38×10−3H–4.76×10−3H59

Figure 6 shows the train force coefficients under three mesh partitioning conditions. When three effective digits are reserved, the lift and drag coefficients under the conditions of medium and fine mesh are the same. Compared with the other two conditions, the coarse mesh differs in the drag coefficient of the train head and tail cars and the lift force of the train tail car, but the lift force of the train head car is the same.

Comparison of the maglev train force coefficient for different mesh types
Fig. 6.

Comparison of the maglev train force coefficient for different mesh types

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Therefore, it can be concluded that the train simulation results obtained using the medium mesh configuration are almost the same as those of the fine mesh configuration. To reduce calculation and time costs, the medium mesh configuration is used to simulate the following conditions.

2.7. Wind-tunnel test verification

In this study, data from a wind-tunnel test were used to verify the accuracy of the numerical simulation. The test was carried out in the wind tunnel high-speed test section of the National Engineering Laboratory of High-speed Railway Construction Technology at Central South University. The size of the wind tunnel test section is 15 m (long) × 3 m (wide) × 3 m (high), and the track length is 5 m. Considering the size of the wind tunnel and the measurement of aerodynamic performance of a high-speed maglev train, the scale of train to model is 1:16. The test model is shown in Fig. 7. The wind-tunnel test data were taken from Tan et al. [36]. The results of the numerical simulation and wind-tunnel test are shown in Table 3. The aerodynamic drag and lift coefficients of the head and tail cars obtained from the numerical simulation and wind tunnel test were very similar, and the difference in aerodynamic coefficients was within 5%. Therefore, it can be concluded that the simulation of the turbulence around the train was in an acceptable precision by using the numerical simulation. The parameters of the numerical simulation are reliable for the following analysis.

Experimental train model
Fig. 7.

Experimental train model

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Table 3.
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Comparison of aerodynamic coefficients between wind-tunnel test and numerical simulation of maglev train

ResultCxCz
HeadTailHeadTail
Wind-tunnel test0.1080.158−0.0250.132
Numerical simulation0.1110.164−0.0260.135
Difference2.78%3.80%−4.00%2.27%
ResultCxCz
HeadTailHeadTail
Wind-tunnel test0.1080.158−0.0250.132
Numerical simulation0.1110.164−0.0260.135
Difference2.78%3.80%−4.00%2.27%
Table 3.
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Comparison of aerodynamic coefficients between wind-tunnel test and numerical simulation of maglev train

ResultCxCz
HeadTailHeadTail
Wind-tunnel test0.1080.158−0.0250.132
Numerical simulation0.1110.164−0.0260.135
Difference2.78%3.80%−4.00%2.27%
ResultCxCz
HeadTailHeadTail
Wind-tunnel test0.1080.158−0.0250.132
Numerical simulation0.1110.164−0.0260.135
Difference2.78%3.80%−4.00%2.27%

3. Results and analysis

3.1. Flow-structure analysis

To study the influence of the non-smooth dimpled surface on the surrounding flow field, the velocity of the longitudinal section of the case top and the velocity of the prototype on this area were analysed and the normalized velocity in the UW direction was used for staining. As shown in Fig. 8, a high-speed vortex structure was generated inside the dimple at the case top. As a result, the flow along the flow direction of the near-wall surface in the surrounding area of the case top was disturbed, and the velocity attenuation perpendicular to the wall was slower than that of the prototype vehicle. The combination position of the airflow at the top and bottom of the train was affected, and the position and influence range of the maximum velocity near the nose of the tail car were changed.

Comparison of time-averaged UW magnitude on longitudinal central plane of the train
Fig. 8.

Comparison of time-averaged UW magnitude on longitudinal central plane of the train

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The influence of the dimple arrangement on the airflow around the high-speed maglev train was mainly located at the nose area of the train tail car, as shown in Fig. 8.

Therefore, the cloud map of the time-averaged velocity at the longitudinal section of the nose of the train tail car was selected for analysis, and the normalized velocity in the direction of UW was used for staining, as shown in Fig. 9. The position and internal size of the flowing vortices (vt0 and vb0) generated by the prototype train and the train with dimples arranged on the sides (vt2 and vb2) or bottoms (vt3 and vb3) of the train tail car were the same.

Time-averaged 7velocity cloud map of longitudinal section of train tail car nose
Fig. 9.

Time-averaged 7velocity cloud map of longitudinal section of train tail car nose

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The airflow atop and at the bottom of the train converged in the area below the bottom plate of the train tail car, forming two vortices in opposite directions. For the case top, because the dimples affected the airflow atop the train, the airflow atop and at the bottom of the train converged above the bottom plate of the train tail car (vt1 and vb1).

The airflow at the bottom of the train influences the formation and development of wake vortices, whereas it has a significant influence on the lift force of the train. Therefore, the flow at the bottom of the train was analysed and the time-averaged velocity curve at the bottom on the longitudinal central plane of the train (y = 0 plane) along the flow direction was obtained, as shown in Fig. 10. The position of H = 0 represents the nose of the train head car, and H = 12.95 represents the nose of the train tail car.

Time-averaged velocity curve at the bottom of train on the y = 0 plane along the flow direction
Fig. 10.

Time-averaged velocity curve at the bottom of train on the y = 0 plane along the flow direction

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The change law of the prototype train was the same as that of the train with dimples arranged on the sides or bottoms of the train tail car. This indicates that the location of dimples at the sides or bottom does not affect the airflow at the bottom of the tail car. The velocity at the bottom increases gradually along the running direction of the train, increases suddenly on the streamline area and begins to decrease at the nose of the train tail car.

As for the case top, the airflow at the bottom of the head car and the front part of the tail car did not change compared with the case prototype. However, the velocity of the streamline area at the tail car started to differ in two ways. First, the velocity of the airflow decreased compared with other cases. Second, the velocity of the airflow did not fall at the nose of the tail car, indicating that the drop point was not at the bottom area of the train.

The wake of the train refers to the chaotic eddy flow formed behind the train caused by the separation of the flow in the streamline-changing region of the moving train by the thin boundary layer on the train surface. Fig. 11 shows the top view of the transient flow topology structure at the tail of the train. There is no significant difference in the flow law between the cases of prototype and the side or bottom. There are vortices generated by the flow on both sides of the train, which develop backward and close to the track. They produce a large number of small vortex structures during development. Vortices generated by the airflow around the middle of the train develop upward and sideways at first, and then gradually descend and tighten, producing a large number of small vortex structures.

Top view of instantaneous iso-surface plot of Q criterion (Q = 10 000 s−2) colored by time-averaged slipstream
Fig. 11.

Top view of instantaneous iso-surface plot of Q criterion (Q = 10 000 s−2) colored by time-averaged slipstream

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The development law on the wake structure of the case top is the same as other cases. The difference lies in the fact that the vortices generated by the flow around the middle of the train have small amplitudes in the descending and tightening process, and it does not generate a large number of small vortex structures.

To show the changes in wake development, cross sections at 0, H and 3H from the nose of the train tail car under different cases were used for comparative analysis. Figure 12 shows the time-averaged velocity convolution cloud map of the cross-section at the tail car nose, and the normalized velocity in the VW direction was used for staining. Apart from the dimples being arranged on the top of the train, the conditions of the other positions are similar to those of the prototype in the vortex formation position and velocity of the cross-section at the train tail car nose. As for the case top, although the formation positions of the upper and lower main vortices (v11 and v12) are the same as those of the prototype train (v01 and v02), the small vortices formed outside of the track (v03) disappear. The velocity and action area inside the upper main vortices (v11) also reduced significantly compared with those of the prototype train (v01).

Time-averaged velocity convolution cloud map of the cross-section at the train tail car nose
Fig. 12.

Time-averaged velocity convolution cloud map of the cross-section at the train tail car nose

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Figure 13 shows the time-averaged velocity convolution cloud map of the cross-section at H distance from the train tail car nose. In the case prototype, the main vortices above the track (v01) move to the outer and upper parts of the track, and then split into two pairs of vortices (v011 and v012). The cases side and bottom have similar vortices position as the case prototype, but the flow velocity inside the vortices was larger. Small vortices formed outside of the track (v03, v23 and v33) were gradually dispersed.

Time-averaged velocity convolution cloud map of the cross-section at H distance from the train tail car nose
Fig. 13.

Time-averaged velocity convolution cloud map of the cross-section at H distance from the train tail car nose

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As for the case top, the small vortices formed outside of the track was still not observed. The development of the vortices on the lower part of the track (v12) was the same as that of the case prototype (v02). Compared with the prototype train, the velocity and action area of the upper vortices (v111 and v112) were reduced, and the development ranges of the upper and both sides were smaller than those of the other cases.

Figure 14 shows the time-averaged velocity convolution cloud map of the cross-section at 3H distance from the train tail car nose. The vortices above the track in prototype (v011 and v012), top (v111 and v112), side (v211 and v212) and bottom (v311 and v312) cases were formed, one (v012, v112, v212 and v312) developed upward and split into two vortices, the large (v0122, v1122, v2122 and v3122) and the small (v0121, v1121, v2121 and v3121). The other vortices (v011, v111, v211 and v311) developed downward to a position parallel to the track. Further, small vortices formed outside of the track (v03, v23 and v33) were completely dissipated.

Time-averaged velocity convolution cloud map of the cross-section at 3H distance from the train tail car nose
Fig. 14.

Time-averaged velocity convolution cloud map of the cross-section at 3H distance from the train tail car nose

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The development law of vortex in the bottom and prototype cases were the same. However, the internal velocity of vortices on the top of the track (v3122) in the case bottom was larger than that of the case prototype (v0122), and the upward development of the vortices above the track was smaller for the case side (v2121 and v2122) compared with the case prototype. For the case top, although the development of the vortices under the track (v12) was the same as that of the case prototype (v02), the development of the vortices above the track (v1121 and v1122) and its internal velocity were significantly different from that of the case prototype (v0121 and v0122).

3.2. Time-averaged pressure analysis

Owing to the existence of dimples, the surface pressure distribution of the high-speed maglev train changed during its operation. Figure 15 shows the time-averaged pressure coefficients of the train tail car surface. Compared with the case prototype, the pressure distribution changed the most in the case top, whereas the pressure distribution changes were not obvious in the cases of side and bottom. The change in the case top was mainly reflected in the area near the nose of the tail car. On the upper surface of the tail car, the negative pressure concentration area on both sides of the nose disappeared, whereas the positive pressure area around the middle of the nose increased and the pressure coefficient was also larger than that of the case prototype. Along the area under the train, the negative pressure area on both sides of the nose almost disappeared, whereas the positive pressure area around the middle of the nose decreased significantly, and its pressure coefficient was also much lower than that of the prototype train.

Time-average pressure coefficient of train tail car surface: (a) top view; (b) bottom view; (c) side view
Fig. 15.

Time-average pressure coefficient of train tail car surface: (a) top view; (b) bottom view; (c) side view

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From Fig. 15, the pressure distribution law around dimples in different cases were the same, but those in different pressure zones were different.

Compared with smooth surface, the pressure coefficient of the dimple in negative pressure area changed significantly. A large negative pressure area was generated at the first inner edge of the dimple along the flow direction, a very narrow positive pressure area was generated at the second inner edge, and a narrow negative pressure area was generated at the second outer edge of the dimple.

The negative pressure coefficient of the dimple in the low-pressure area increased slightly, compared with smooth surface. A narrow positive pressure area was generated at the second inner edge of the dimple along the flow direction, and a narrow negative pressure increasing area was generated at the second outer edge of the dimple along the flow direction. The change in pressure inside the dimple in the low-pressure area was smaller than that of the negative pressure area.

3.3. Slipstream analysis

A slipstream is produced by the high-speed train airflow movement, air pressure and flow rate of the rapid changes in ambient air disturbance. For passengers and workers on the platform, the slipstream is characterized by changing gusts that pose a safety hazard. Furthermore, it can pick up debris, creating a projectile threat.

Therefore, this study analyses the time-averaged slipstream and the maximum statistical slipstream in the longitudinal section at a position of 3.0 m (0.71H) distance from the full-size train centre. Thus, the influence law of the dimple position on the slipstream can be explored.

Figure 16 shows the time-averaged slipstream in the longitudinal section at a position of 0.71H distance from the train centre. The distribution of the slipstream in the cases of side and bottom are the same as that of the case prototype. The value of the slipstream began to increase at a position of 5H distance from the tail car nose, and reached its peak around 10H distance. Then, it gradually decreased. However, the size of the slipstream on the peak area was different. The side and bottom cases were obviously larger than those of the prototype. Regarding the case top, the distribution position and value of the time-averaged slipstream were obviously different from those of the prototype. The peak area started at a position of 2H distance from the tail car nose and ended at 4H distance. The value of the slipstream in the peak area was also much larger than that of the prototype.

Time-averaged slipstream cloud map
Fig. 16.

Time-averaged slipstream cloud map

Open in new tabDownload slide

Figure 17 shows the maximum statistical slipstream in the longitudinal section at a position of 0.71H distance from the train centre. The distribution position of maximum slipstream in the cases of side and bottom were almost the same as that of the prototype. The maximum statistical slipstream had peak areas at 7H and 15H distances from the train tail car nose. Regarding the case top, the peak areas were distributed at positions 2H and 15H distances from the train tail car nose, and the values of the slipstream in the peak areas were much smaller than that of the prototype.

Maximum statistical slipstream cloud map
Fig. 17.

Maximum statistical slipstream cloud map

Open in new tabDownload slide

Table 4 shows the maximum value of the time-averaged slipstream and maximum statistical slipstream in the longitudinal section at a distance 0.71H from the train centre. By comparison, the maximum time-averaged slipstream of the case top was larger than that of the prototype. However, the maximum value of the statistical slipstream was smaller. This is caused by the smaller fluctuation of the wake velocity in the case top.

Table 4.
Open in new tab

Maximum value of time-averaged slipstream and maximum statistics slipstream

CasePrototypeTopSideBottom
Maximum value of time-averaged slipstream0.1410.1690.1420.140
Maximum value of maximum statistics slipstream0.2490.1770.2340.316
CasePrototypeTopSideBottom
Maximum value of time-averaged slipstream0.1410.1690.1420.140
Maximum value of maximum statistics slipstream0.2490.1770.2340.316
Table 4.
Open in new tab

Maximum value of time-averaged slipstream and maximum statistics slipstream

CasePrototypeTopSideBottom
Maximum value of time-averaged slipstream0.1410.1690.1420.140
Maximum value of maximum statistics slipstream0.2490.1770.2340.316
CasePrototypeTopSideBottom
Maximum value of time-averaged slipstream0.1410.1690.1420.140
Maximum value of maximum statistics slipstream0.2490.1770.2340.316

The maximum value of the time-averaged slipstream and maximum statistical slipstream in the case side were not significantly different from those of the prototype, indicating that the dimples arranged on the sides had little effect on the slipstream. The maximum time-averaged slipstream in the case bottom was not much different from that of the prototype. However, the maximum value of the maximum statistical slipstream was larger than that of the prototype, indicating that the dimples arranged on the bottom greatly affected the wake velocity fluctuation.

3.4. Aerodynamic force analysis

The aerodynamic drag coefficients of the head and tail cars under different dimple positions were analysed, and the specific data are shown in Table 5. Regardless of the dimple location, the aerodynamic drag coefficient of the train tail car is affected, while that of the head car is not. Additionally, only the case top reduced drag. In terms of total drag coefficient, compared with the prototype, the aerodynamic drag coefficient of the entire train reduced by 3.40% with the case top.

Table 5.
Open in new tab

Aerodynamic drag coefficient

CasePrototypeTopSideBottom
Drag coefficient of the train head car0.0960.0960.0960.096
Drag coefficient of the train tail car0.1390.1310.1390.139
Drag coefficient of the whole train0.2350.2270.2350.235
Drag coefficient reduction rate of the whole train—3.40%00
CasePrototypeTopSideBottom
Drag coefficient of the train head car0.0960.0960.0960.096
Drag coefficient of the train tail car0.1390.1310.1390.139
Drag coefficient of the whole train0.2350.2270.2350.235
Drag coefficient reduction rate of the whole train—3.40%00
Table 5.
Open in new tab

Aerodynamic drag coefficient

CasePrototypeTopSideBottom
Drag coefficient of the train head car0.0960.0960.0960.096
Drag coefficient of the train tail car0.1390.1310.1390.139
Drag coefficient of the whole train0.2350.2270.2350.235
Drag coefficient reduction rate of the whole train—3.40%00
CasePrototypeTopSideBottom
Drag coefficient of the train head car0.0960.0960.0960.096
Drag coefficient of the train tail car0.1390.1310.1390.139
Drag coefficient of the whole train0.2350.2270.2350.235
Drag coefficient reduction rate of the whole train—3.40%00

Because the dimple mainly affects the aerodynamic drag coefficient of the train tail car, it has little effect on the drag coefficient of the head car. Therefore, to study the influence of dimples on the pressure drag coefficient and viscous drag coefficient of the tail car, the composition of the aerodynamic drag coefficient of the train tail car was analysed.

It can be seen from Table 6 that the case top significantly reduced the pressure drag coefficient of the train compared with the prototype, although it had no effect on the viscous drag coefficient. This was caused by the placement of dimples at the top of the streamline area, which can change the combination position of the top and bottom flows of the train. It changes the wake vortex loss position around the middle of the train, weakening the strength of the wake at the same time, reducing the area of the negative pressure zone, while increasing the area of the positive pressure zone at the top of the train tail car. Therefore, the case top can only reduce the pressure drag coefficient of the train tail car; it has no effect on the viscous drag coefficient.

Table 6.
Open in new tab

Pressure and viscous drag coefficient of the train tail car

CasePrototypeTopSideBottom
Pressure drag coefficient0.0550.0470.0550.055
Viscous drag coefficient0.0840.0840.0840.084
CasePrototypeTopSideBottom
Pressure drag coefficient0.0550.0470.0550.055
Viscous drag coefficient0.0840.0840.0840.084
Table 6.
Open in new tab

Pressure and viscous drag coefficient of the train tail car

CasePrototypeTopSideBottom
Pressure drag coefficient0.0550.0470.0550.055
Viscous drag coefficient0.0840.0840.0840.084
CasePrototypeTopSideBottom
Pressure drag coefficient0.0550.0470.0550.055
Viscous drag coefficient0.0840.0840.0840.084

The cases of side and bottom had no drag-reduction effect because they had little influence on the airflow atop the train, and did not break the balance between the airflow at the top and bottom. Thus, the shedding position and intensity of the wake generated by the flow around the middle of the train barely changed. Therefore, they had little influence on the drag coefficient of high-speed maglev trains.

After analysing the aerodynamic lift coefficient of the head and tail cars, as shown in Table 7, the aerodynamic lift coefficient of the entire train in the top case was reduced by 4.76% compared with the prototype, whereas the side and bottom cases had little influence on the aerodynamic lift coefficient of the train. Moreover, the dimple position had little effect on the aerodynamic lift coefficient of the train head car, but mainly affects the aerodynamic lift coefficient of the train tail car.

Table 7.
Open in new tab

Aerodynamic lift coefficient

CasePrototypeTopSideBottom
Lift coefficient of the train head car0.470.4690.4690.47
Lift coefficient of the train tail car0.4910.4510.4880.489
Lift coefficient of the whole train0.9610.920.9570.959
Lift coefficient reduction rate of the whole train—4.27%0.42%0.21%
CasePrototypeTopSideBottom
Lift coefficient of the train head car0.470.4690.4690.47
Lift coefficient of the train tail car0.4910.4510.4880.489
Lift coefficient of the whole train0.9610.920.9570.959
Lift coefficient reduction rate of the whole train—4.27%0.42%0.21%
Table 7.
Open in new tab

Aerodynamic lift coefficient

CasePrototypeTopSideBottom
Lift coefficient of the train head car0.470.4690.4690.47
Lift coefficient of the train tail car0.4910.4510.4880.489
Lift coefficient of the whole train0.9610.920.9570.959
Lift coefficient reduction rate of the whole train—4.27%0.42%0.21%
CasePrototypeTopSideBottom
Lift coefficient of the train head car0.470.4690.4690.47
Lift coefficient of the train tail car0.4910.4510.4880.489
Lift coefficient of the whole train0.9610.920.9570.959
Lift coefficient reduction rate of the whole train—4.27%0.42%0.21%

This was caused by the arrangement of the dimple at the top, which led to the upward movement of the shedding position of the wake generated by the airflow around the middle. As a result, the area of the negative pressure zone on the upper surface of the train tail car reduced, whereas the size of positive pressure zone increased, and the velocity under the train tail car bottom plate decreased. The area of the positive pressure zone under the bottom plate of the train tail car decreased, and the pressure coefficient decreased. Therefore, the pressure difference between the bottom and top of the train tail car decreased, which led to a decrease in the aerodynamic lift coefficient of the train. However, the dimples arranged on the sides or bottoms of the train tail car had little influence on the pressure on the top and bottom of the train tail car. Hence, it has little influence on the aerodynamic lift coefficient of the high-speed maglev train.

4. Conclusions

In this paper, the IDDES numerical simulation method was used to carry out a transient numerical simulation of a high-speed maglev train with dimples arranged on different positions in the streamline area, and the influence of dimple position on aerodynamic performance of the train was analysed. The following conclusions were drawn.

  1. When the dimples are arranged on the top of the train tail car streamline area, the vortex structure generated during the development of the wake is significantly reduced. The size of the vortex acting area and the velocity inside the vortex are also much smaller than those of the prototype train. When the dimples are arranged on the sides or bottoms of the train tail car streamline area, the formation position and velocity of the wake slightly differ from those of the prototype train.

  2. If the dimples are arranged on the top of the train tail car streamline, the pressure coefficient of the positive pressure zone on the upper surface of the train tail car will increase; the negative pressure zone on both sides of the nose will disappear; and the pressure coefficient of the positive pressure zone at the bottom of the train tail car will decrease. The sides and bottoms dimples had little effect on the pressure coefficient of the train tail car.

  3. Compared with the case prototype, the case top can reduce the aerodynamic drag coefficient of the entire train by 3.40%, and the main effect is the pressure drag coefficient of the train tail car. The side and bottom cases have little effect on the drag reduction of high-speed maglev trains. For the aerodynamic lift coefficient, the case top can reduce the aerodynamic lift coefficient of the entire train by 4.27%, whereas the side and bottom ones have little effect.

Author statement

I would like to declare on behalf of my co-authors that the work described was original research that has not been published previously, and not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.

ACKNOWLEDGEMENTS

This work was supported by the National Numerical Wind Tunnel Project (Grant No. 2018-ZT1A02), the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2021zzts0682) and the Fundamental Research Funds for the Central Universities of Central South University (Grant No. 2019zzts266).

Conflict of interest

No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication.

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© The Author(s) 2021. Published by Oxford University Press on behalf of Central South University Press.
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