Aerodynamic impact of train-induced wind on a moving motor-van

Abstract

The newly-built single-level rail-cum-road bridge brings the issue of the aerodynamic impact of train-induced wind on road automobiles. This research introduced a validated computational fluid dynamics (CFD) model regarding this concern. Such an aerodynamic impact mechanism was explored; a relationship between the transverse distance between train and motor-van (hereinfafter referred to as van) and the aerodynamic effects on the van was explored to help the optimization of bridge decks, and the relationship between the automobile speed and aerodynamic variations of a van was fitted to help traffic control. The fitting results are accurate enough for further research. It is noted that the relative speed of the two automobiles is not the only factor that influences the aerodynamic variations of the van, even at a confirmed relative velocity, the aerodynamic variations of the van vary a lot as the velocity proportion changes, and the most unfavorable case shows an increase of over 40% on the aerodynamic variations compared to the standard case. The decay of the aerodynamic effects shows that not all the velocity terms would enhance the aerodynamic variations; the coupled velocity term constrains the variation amplitude of moments and decreases the total amplitude by 20%–40%.

Graphical abstract

Keywords

rail-cum-road bridge / aerodynamic impact / train-induced wind / CFD / aerodynamic force / quantitative analysis / fitting

1 Introduction

The increasing traffic and diverse demands of highway and railway transportation have promoted the development of rail-cum-road bridges [1,2]. The newly-built rail-cum-road bridges in recent years, such as the Tongling Yangtze River bridge, the Pingtan strait bridge and the Changtai Yangtze River bridge, have shown great practicability and economic benefit. In contrast with traditional long-span bridges [3], greater variety of layout of the bridge deck is inevitable with rail-cum-road bridges. Among them, the single-level arrangement, which accommodates highway and railway on the same level, is a new format in practical engineering.

Compared with the two-level arrangement, the single-level arrangement is superior in transverse stiffness, bearing capacity, maintenance, appearance, etc. [4]. Nevertheless, when the highway and railway are on the same level, there is a new issue of aerodynamic interference between road automobiles and high-speed trains. According to relevant reports (Huang et al. [5]; Xiong et al. [6]; Zhang et al. [7]), this sudden change of wind environment may create potential for accidentsautomobile. Therefore, a large space between the railway and highway is usually introduced. As shown in Fig.1, the Yibin Lingang Yangtze River bridge employs four train tracks in the middle, three car lanes on both sides with sidewalks and bicycle lanes on the cantilevers. The total width is 63.9 m and the transverse distance between the centerline of the closest highway and railway is 8.75 m.

Based mainly on field measurement, experiments and CFD, researches have shown that rain-induced wind has an influence on nearby buildings and auxiliary facilities. Zhou et al. [8] experimentally researched the transient pressure on a station platform when a high-speed train passed by. The results showed that the pressure pulse on the platform screen doors is the combination of the train head and tail pressure pulses and their pressure waves. Based on field measurement and CFD software, Yang et al. [9] explored the train-induced aerodynamic effect on an overhead bridge. The research pointed out that turbulent flow between the train and the overhead structure should be taken into consideration in the structural design of the structure. Yao et al. [10] explored the aerodynamic effect from train-induced wind and crosswind on a truss girder; it is noted that the truss segment also suffers sudden changes of aerodynamic loads from a moving train, and the aerodynamic variation of truss segment is directly proportional to the square of train speed. Using field measurement, Xiong et al. [6] investigated the pressure variation on noise barriers due to train-induced wind. They conducted parameterized researches on the influence of train speed, running lines and locations of measurement points. Similarly based on field measurements, Zou et al. [11] studied the effect of train-induced wind on a wind barrier. Through multi-resolution analysis, their study revealed that the frequency of pulse excitation of train-induced wind loads may overlap with the natural frequency of barriers and may lead to fatigue failure due to the repeated passage of high-speed trains. Through field measurement, Tokunaga et al. [12] researched the dynamic response of tall noise barriers under train wind pressure. The resonance effect between the pulse excitation of the train wind and the natural frequency of the noise barrier as well as the tail-pulses overlap effect were concluded to be the main explanation of the dynamic responses of the noise barriers.

Moreover, researches on the aerodynamic interference of two traveling trains has indicated that there is a potential for traveling accidents due to the strong transient aerodynamic load, which could result in window breakage, sideward shaking, trackside worker injuries, and facility fatigue. Chen and Wu [13] researched the aerodynamic characteristics of two trains meeting in the open air based on finite volume method and moving grid technologies. The study showed that the damage of the lateral window glass derives from suction, or negative pressure, and the aerodynamic interference between two moving trains would generate a large and sudden change of aerodynamic force. Through CFD technology, Huang et al. [5] quantitatively analyzed the pressure distribution derived from a maglev train and explored the slipstream velocity. They researched the pressure attenuation with the distance from the center of a rail, through which the safe distance is calculated. Li et al. [14] researched the aerodynamic effects induced by two trains passing each other in a tunnel. Their work indicated that the piston effect was more pronounced when space is constrained by another train for the crossing-trains case, and the maximum inner pressure is thus 34% larger than that of the single-train case. Sun et al. [15] compared the two scenarios of trains passing by each other. The research showed that the variation of drag and lateral force is significantly affected by the pressure distribution on the streamline of the leading and trailing automobiles of the opposite train, and meeting in a tunnel would generate a much larger variation of aerodynamic forces.

Preceding literatures have evaluated the significant influence of train-induced wind. To reduce the impact of train-induced wind, a sing-level rail-cum-road bridge usually introduces a conservative distance between the highway and railway, which, however, increases the width of the bridge deck and limits the practicability of such bridges. Reducing the width of this kind of bridge relies on research on the aerodynamic interference between railway and highway. There are at least three significant aspects worth further attention:

1) exploring the impact mechanism of train-induced wind on road automobiles could help engineers to better understand the influence of train-induced wind on the aerodynamic variations of road automobiles;

2) reducing the transverse distance between highway and railway is of great economic benefit, but it must guarantee the traveling safety of road automobiles;

3) exploring the influence of automobile speed on the aerodynamic impact could help better understand the superposition effect of automobile-wind, which is also the basis for traffic control.

To achieve the above purposes, this paper explored the aerodynamic variation of a moving van under the train-induced wind through CFD technology. The influence mechanism is explained through the flow field visualization technology and the van’s aerodynamic forces. The quantitative relationship between the aerodynamic forces and transverse distance of automobiles and the quantitative relationship between the aerodynamic forces and the automobile speed are examined and tested using proposed fitting models.

Section 2 below describes the details of the numerical model introduced in this paper; Section 3 gives the validation on the numerical model; Section 4 offers an explanation on the impact mechanism and discusses the influence of transverse distance; Section 5 discusses the influence of automobile speed on the aerodynamic variations; Section 6 offers conclusions.

2 Numerical model

2.1 Geometric model and calculation domain

The CRH3 locomotive, widely employed in the rail-transport system of China [16], is introduced in the present research. To comprehensively explore the influence of the nose, the tail and the middle part of the train [17-19], three carriages, namely, the head carriage, the middle carriage and the tail carriage constitute the entire train model. The length of the head carriage and tail carriage is 24.6 m and the length of the middle carriage is 24.8 m. The height and width of the typical train section are 3.48 and 3.28 m, respectively. The key aerodynamic feature of the CRH3 model is kept while the substructure of the CRH3 model is simplified to improve the mesh quality and calculation efficiency. Fig.2 shows the head carriage, the scale ratio is 1:1.

Road automobiles with high-sides suffer from rollover and sideslip more easily than other automobiles under crosswind conditions [20]; the high-sides feature can also provide a clearer vision on the variation of the pressure distribution. Therefore, a van is selected as the research object. The length, height and width of the van are 7.7, 3.4 and 2.2 m respectively. The geometric features of the bottom structure are kept to some extent. Fig.2 demonstrates the van model, showing the force definition.

As demonstrated in Fig.1, the single-level rail-cum-road bridge requires a wide bridge deck to accommodate highways, railways and varieties of auxiliary facilities on the same level. When there is no wind, the traveling environment on a wide deck is similar to that on flat ground. Moreover, the area where aerodynamic impact occurs most strongly is close to the centerline of the bridge;the influence on the flanges of the bridge is limited. In addition, introducing an actual single-level rail-cum-road bridge would bring extra computational expenses without much improvement results. Therefore, the aerodynamic impact on flat ground is discussed. Moreover, this paper aims to discuss the pure relationship between aerodynamic variation of the van and the transverse distance as well as the automobile speed, the bridge deck system is omitted.

The calculation domain depicted in Fig.2 is determined by the blocking ratio requirement and the traveling distance. The width is 130 m and the height is 120 m, the blocking ratio is less than 5%. The total length is 444 m and there is 316.1 m between automobiles to ensure that the flow field is stable before the interference.

2.2 Achievement of dynamic mesh and mesh strategy

The achievement of dynamic mesh is determined prior to the mesh generation. The dynamic mesh module in Fluent provides several ways on the motion of rigid body. Considering the mesh update efficiency and the engineering feature, the layering technology combined with sliding mesh is adopted. To meet the requirement of the selected dynamic mesh method, the calculation domain is divided into a static zone and two moving zones (shown in Fig.2). The CRH3 and the van possess individual moving zone, both are 4.4 m in width and 4.7 m in height. Interfaces are applied on the mutual faces of the static zone and moving zone and on the mutual faces of the moving zones. Huang et al. [5] used the same dynamic mesh technique for exploring the aerodynamic interference between two maglev trains. This method turns out to be capable of capturing the main flow structures around high-speed trains.

With the layering method, all the meshes in the moving zone move forward during the motion, the meshes near the ends of the moving zone get compressed and merged or get stretched and split according to the merge factor and split factor, which are 0.4 and 0.2, respectively, based on the trial cases. The data exchange on the interface of sliding mesh is shown in Fig.3. Zone 1 and Zone 2 represent two zones in the processing of data exchange; B-D-F-H and A-C-E-G-I represent the mutual boundary. Before each time step, a combined face a-b-c-d-e-f-g-h-i is generated. To acquire the information of unit 3 in Zone 1, information on nodes d, e and f is needed, which are provided by unit 6, unit 8 and unit 10 in Zone 2. Similarly, to acquire the information of unit 6 in Zone 2, unit 1 and unit 3 in Zone 1 would provide the basic information of node c, d and e [8].

The structural hexahedral unit has the advantage of improving the mesh quality and calculation accuracy [22], thus the static zone and the moving zone of the train employ the structural hexahedral unit. Nevertheless, the structural hexahedral unit cannot be directly introduced into the moving zone of the van because of the van’s complex configuration. Besides, the non-structural meshes have compatibility issues with the layering update. To solve this, a hybrid mesh strategy is applied to this zone. A non-structural tetrahedral unit and a prism unit are applied in a prearranged box, and the structural hexahedral unit is introduced in the rest space of the moving zone. To fulfill smooth data transportation between the structural zone and non-structural zone, a conformal operation is executed. The meshes of the train are shown in Fig.4(b), the meshes of the van are shown in Fig.4(c).

The first layer around walls greatly influences the flow feature near the walls, and it is usually judged by the value of y+. After the trial cases, the thickness of the first layer of the train is set as 3 mm with an expansion ratio of 1.1. It contains eight layers of wall-boundary meshes and produces a value of y+ from 70 to 210.

The van contains 8 layers of wall-boundary mesh, the thickness of the first layer is 5 mm with the same expansion ratio of 1.1 and it creates a value of y+ from 60 to 170. There are 4.87 million units in the static zone and 4.11 million units in the train’s moving zone. There are 1.44 million tetrahedral units and 0.64 million hexahedral units in the van’s moving zone.

2.3 Turbulent model and solution parameter

In the simulation, the air is considered incompressible since the train speed is around 300 km/h and the discussed van speed is less than 100 km/h, the Mach number Ma < 0.3 accordingly.

Turbulent models could reflect the regularity of flows close to walls. Among them, the Scale-Resolving Simulation (SRS) models are superior because it could solve a portion of the turbulence for a portion of the flow domain. The most widely known one is Large-Eddy Simulation (LES). Nevertheless, the application of LES requires a large number of meshes close to walls and the computation cost is high (Baker [20]). In contrast, Reynolds Averaged Navier-Stokes (RANS) turbulent models offer the most economic approach for computing complex turbulent industrial flows (Fluent Users’ Guide). Typical examples are k–ω models, which simplifies the problem by two additional transport equations and introduces an eddy-viscosity term to compute the Reynolds Stresses. In the k–ω turbulent model, the additional equations are shown as:

(1)\frac{\mathrm{\partial }\rho k}{\mathrm{\partial }t}+\frac{\mathrm{\partial }\rho u_{j}k}{\mathrm{\partial }{x}_j}={\tilde{P}}_{\text{k}} -{\tilde{D}}_{\text{k}}+\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_j}\left[\left(\mu +{\sigma }_{\text{k}}{u}_{\text{t}}\right)\frac{\mathrm{\partial }k}{\mathrm{\partial }{x}_j}\right],

(2)\begin{array}{rl}\frac{\mathrm{\partial }\rho \omega }{\mathrm{\partial }t}+\frac{\mathrm{\partial }\rho u_j\omega }{\mathrm{\partial }{x}_j}=& \alpha \frac{\omega }{k}{\tilde{P}}_{\text{k}}-{\tilde{D}}_{\text{ω}}+\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_j}\left[\left(\mu +{\sigma }_{\text{ω}}{u}_{\text{t}}\right)\frac{\mathrm{\partial }\omega }{\mathrm{\partial }{x}_j}\right]\\ & +2\left(1-F_1\right)\rho {\sigma }_{\text{ω2}}\frac{1}{\omega }\frac{\mathrm{\partial }k}{\mathrm{\partial }{x}_j}\frac{\mathrm{\partial }\omega }{\mathrm{\partial }{x}_j},\end{array}

where t, \rho and u_j are the time, the air density and the flow velocity components in the x_j direction, respectively. F_1, {\tilde{P}}_{\text{k}} and {\tilde{D}}_{\text{ω}} are the blending function, the production term and the destruction term for the turbulence kinetic energy equation, respectively.

The present study adopts the Shear Stress Transport k–ω (SST k–ω) model [21]) as the turbulent model. The SST k–ω model is capable of simulating the flow field with large and adverse separation, and the decrease in the simulation accuracy is slight [18].

In terms of the solution parameters, the semi-implicit method for the pressure-linked equations (SIMPLE) algorithm is applied to the solution of the pressure and velocity coupling equation. The second-order upwind format is employed on the discretization of the momentum continuity, the turbulent kinetic energy and the dissipation rate. According to the verification cases, the solution time step is set as 0.005 s, the maximum iteration number in each time step is 30.

3 Numerical model verification

3.1 Grid independence

To guarantee that consistent results are obtained, including the set of meshes in Subsection 2.2, three sets of meshes are compared to validate the grid independence. The American Society of Mechanical Engineers (ASME) has recommended a refinement ratio (r) higher than 1.3 [22] when adjusting the mesh density. However, when it comes to the aerodynamic issues of traveling automobiles, it would be not very appropriate and necessary because it would double the number of grids when refining the meshes. However, as the flow field variation is centralized near the moving automobiles, the doubled meshes provide limited help for enhancing the simulation accuracy, which might be the reason why researchers in this field haven’t followed this principle [13,14,18].

To introduce the basic idea of the grid independence verification into the present study, the refinement ratio was applied on the “reference size”, which indicates the maximum cell size near the automobiles. When refining the meshes, the finer set has a reference size that is half of the coarser set. The adjusted refinement ratio, defined as the one third power of the quotient of the reference sizes, is 1.26 accordingly. Moreover, to perform a smooth transition between the moving zones and static zone, the minimum size of meshes in the static zone is equal to the maximum size in the moving zones, and the meshes in the static zone have an expansion ratio of 1.1. The reference sizes of the “Coarse Mesh”, the “Medium Mesh” and the “Fine mesh” are 0.24, 0.12, and 0.06 m, respectively, and the corresponding total number of meshes is 8.74 million, 11.06 million, and 14.84 million.

To give a concise explanation, the maximum drag force and lift force of the van when meeting a moving train are extracted for comparison. The speed of the van is set at 80 km/h and the speed of the train is considered to be 250 km/h. The results of the three sets of meshes are shown in Tab.1. It can be seen that from the “coarse mesh” to the “medium mesh”, an obvious drop occurs in both drag force and lift force, while there is a very slight drop from the “medium grid” to the “fine grid”. In conclusion, the results of the “medium mesh” are good enough.

3.2 Validation on the aerodynamic load of the train-induced wind

The research of Xiang et al. [23] provides the basic idea of mesh generation strategy for the CRH3 model, which has provided results nicely consistent with the wind tunnel tests. To further validate the aerodynamic load derived from the train-induced wind on the van, a moving model test was conducted.

The test system refers to the moving device of Xiang et al. [24,25]. The dynamic system is composed of a servomotor and a linear module (including a synchronous belt, a guideway and a sliding plate). Automobiles are installed on the sliding plate, which is connected with the synchronous belt and driven by the servomotor. The moving model test introduced a scale of 1:20, the geometric features of automobile models in the moving model test and numerical simulation are the same, while the length of CRH3 is set to 1.75 m (35 m in prototype) due to the limited length of the guideway.

Because the test system cannot achieve the motion of the van and train simultaneously, the case when the van is static and the train moves toward the van at the speed of 7 m/s is compared. The transverse distance between the centerline of the van and train is 22 cm (4.4 m in prototype). The test system and automobile models are shown in Fig.5.

The drag force acting on the van is obtained and transformed into aerodynamic coefficient C_d by Eq. (3).

(3)C_{\text{d}} ={\displaystyle \frac{F_{\text{S}}}{{\displaystyle \frac{1}{2}}\rho V_{\text{t}}^{2}HL}},

where ρ is the air density, L and H are the length and the height of the van, respectively. V_t is the speed of the train. The comparison between test and simulation of C_d during aerodynamic impact of the train-induced wind is illustrated in Fig.6 [26].

Fig.6 shows that the variation trend of C_d is parallel in the moving model test and numerical model. Both of the variation curves possess two peak values and two valley values, and the locations of the peak/valley values show a good match. Fig.6 also shows that, unlike in previous researches [8,26], another peak value denoted by “M” occurs between V1 and V2, which is due to the short length of the train model. The major difference is at the curve of M-V2-P2, which may derive from the vibration of the test system as well as the velocity difference between the test and numerical simulation. The quantitative difference about the peak/valley values is given in Tab.2.

Tab.2 indicates that the numerical model is capable of simulating the aerodynamic load derived from the train-induced wind. The peak/valley values of the numerical match well with the ones of the moving model test. The largest absolute errors are 6.82% in P2 while the others are within 5%, thus the simulation error is in a reasonable range.

4 Impact mechanism and influence of transverse distance

The single-level rail-cum-road bridge usually introduces a wide deck in consideration of the various transportation ways [4]. As depicted in Fig.1, there is about 8.75 m between the closest track line and road lane. The optimization of the transverse distance between the railway and highway can further enhance the practicability of this new format of bridge deck, and the optimization relies on the aerodynamic interference between the railway and highway. Thus, to figure out how the effect of the train-induced wind on the van attenuates with the transverse distance, relevant cases are conducted.

The case details are listed in Tab.3. As the transverse distance applied in the Yibin Lingang Yangtze River bridge is 8.75 m, the largest transverse distance is set as 9 m. The smallest distance is 4.4 m, which is a common distance used in two adjacent railways and thus is considered as the extreme minimum distance that could be reached, and the distance step is 0.5 m. All the cases have the same initial location and the same automobile velocity.

4.1 Impact mechanism

4.1.1 Pressure distribution on the van

To understand the impact process as it affects the van, the pressure distribution on the van body under the train-induced wind of Case 1 is extracted here for a preliminary discussion. Sun et al. [15] found that the pressure variation due to the head of the train and the tail of the train are similar in variation amplitude but reversed in time sequence. To make a brief demonstration, only the process when the van travels near the head of the head carriage is discussed here. During the process, the prescribed x (shown in Fig.7, x = x₁– x₂), defined as the distance between the nose of the train and the front of the van along the traveling direction, is utilized to show the relative location of the automobiles.

The pressure distribution on the van during the aforementioned process is shown in Fig.8. The flank of the van shown in the figure is the side closer to the train. Through examining Fig.8, some typical processes are observed.

When the van is traveling alone, the pressure distribution is characterized by a positive pressure zone on the front face and negative pressure zones near the van head (seen in the 1st picture). Yao et al. [10] and Yang et al. [9] discovered that moving trains would bring alternative positive and negative pressure on the structures nearby, and create a fierce transformation of push and suction both at the time when the train approaches and when it leaves. A parallel phenomenon appears on the flank of the van, the major variation could be summarized as the following 4 processes.

Process 1: From the 2nd picture to the 6th picture, a moving positive high-pressure zone is located on the flank of the van, and the initial positive pressure on the front face experiences a rise and a fall.

Process 2: From the 5th picture to the 7th picture. When the positive high-pressure zone moves across the center of gravity, a negative pressure zone located on the flank side and moves with the positive one. The pressure on the front face turns negative.

Process 3: From the 7th picture to the 8th picture. The positive pressure zone is out of the van’s body in behind. The negative pressure zone moves along the flank and gets superposed with the original pressure distribution of the sole-traveling state.

Process 4: In the 8th picture. The van runs near the middle carriage, and the high-pressure zones move out of the van body. The influence from the head of the train fades away, the pressure distribution during this period is similar to the one of sole-traveling state, but the pressure is slightly lower.

Moreover, the following three points are worth paying attention to.

Point 1: By comparing the 4th picture with the 7th picture, it can be seen that the center of the positive pressure zone is closer to the ground while the center of the negative pressure zone is closer to the center of gravity in height direction.

Point 2: Comparing the 4th picture with the 7th pictureleads to the identification that the area of the negative pressure zone is a bit larger than the positive one.

Point 3: According to the 5th picture and the 6th picture, there are moments when the positive pressure zone and the negative pressure zone act on the flank, and the superposition effect is time-dependent.

The preceding processes and points will be introduced into the explanation of the variation trend of the aerodynamic forces in the following section.

4.1.2 Variations of aerodynamic forces

The 5-component aerodynamic forces during the whole process are illustrated in Fig.9. To be concise, only the results of Cases 2, 4, 6, 8, and 10 are depicted. Moreover, the peak values and valley values are numbered for all the aerodynamic forces, and vertical red dotted lines are added on the peak values and valley values of d = 5 m to observe their shift with the time in different cases.

The discussion on the feature of variation the aerodynamic effects is conducted before the discussion of the influence of the transverse distance. It is noted that the variation of all the aerodynamic effects could be divided into three stages, namely the “M” (stands for “meet”) stage, the “L” (stands for “leave”) stage and the stable “P” (stands for “Plateau”) stage. Major fluctuation exists in the “M” stage and “L” stage, while the “P” stage provides a stable transition. These three stages are consistent with the times when the van travels near the nose, the middle and the tail of the train. In addition, for case 1, it is noted that the C_d of the first peak P1 is 0.049, which has a percentage error of 7.5% with the moving automobile test and shows good consistency.

As can be seen in Fig.9(a) and 9(c), variation trends of F_S, F_L, and M_R are similar during the interaction, the significant change in the “M” and “L” stage is characterized by a fierce transformation from one peak/valley value to another, thus, two peak values P1 and P2 as well as two valley values V1 and V2 are produced. These features could be explained by the adjacent moving high-pressure zones shown in Fig.8. Furthermore, in each of ‘M’ and ‘L’ stages, the first peak/valley value is larger than the second one. Taking F_S as an example, the F_S of the van before the interaction is defined as “N”. In the “M” stage, the difference value of N-P1 is larger than the one of N-V1, in the “L” stage, the difference value of N-V2 is larger than the one of N-P2. As can be inferred from Fig.8, P1 happens at the time when the whole positive pressure zone acts on the flank of the van, and the V1 occurs when the positive pressure zone left the van body and the whole negative zone acts on the van’s flank. Theoretically speaking, the negative pressure zone has not affected P1, and V1 has not been influenced by the positive pressure zone either. The larger value of the first peak/valley implies a larger product of pressure and area. As described in Points 2 of Fig.8, the positive pressure zone is more centralized, so the pressure value is higher in the positive pressure zone. Another phenomenon that is noteworthy lies in the comparison of F_S and M_R. It is observed that the difference value between P1 and V1 in F_S is small while that in M_R is large. This phenomenon could be explained by Point 1 of Fig.8. As the positive pressure zone is closer to the ground and further away from the center of gravity of the van, it produces a larger arm of force, and the difference between the peak/valley values in M_R is hence further enlarged.

M_Y (seen in Fig.9(d)) and M_P (seen in Fig.9(e)) as contrast, possess at least three peak/valley values in “M” and “L”. The multiple peak/valley values are the results of the superposition of the high-pressure zones. Taking the “M” stage of M_Y as an example, the first peak value P1 results from the push of the positive pressure zone mentioned above. Itoccurs at the time when the positive pressure zone moves completely onto the van body. Then, as the positive pressure zone moves behind, it gets closer to the center of gravity of the van, and brings a smaller arm of force, then the positive yawing moment starts to decrease. After that, the following negative pressure zone acts on the van body; the superposition of the two high-pressure zones generates suction on the van’s head and push on the van’s tail, and creates a negative valley V1 whose absolute value is larger than that of P1. Finally, the positive pressure zone moves out of the van body, and then the negative pressure zone moves across the center of gravity and brings another positive peak P3.

4.2 Influence of transverse distance on the curve characteristics

As for the influence of the transverse distance, Fig.9(a) and 9(b) suggest that the influence of transverse distance on F_S and F_L is similar. The peak and valley values caused by the train-induced wind decrease as the transverse distance increases. The magnitude of variation is more obvious when transverse distance increases from 5 to 6 m, which may relate to the pressure distribution around moving trains. Huang et al. [5] found that the closer to the surface of the train body, the larger the pressure gradient is, so the variation magnitude of F_S and F_L is larger. It can also be noted that the increasing transverse distance also weakens the fluctuation of F_L in the “P” stage, which implies the vertical flow due to the moving train has also been weakened as the transverse distance increases. It is noteworthy that hysteresis effects are observed on the second peak/valley value in the “M” stage and in the “L” stage. As the transverse distance increases, it delays the time of the second peak/valley value. This can be explained by reference to Fig.10, which shows the pressure distribution and the streamline around the sole-traveling CHR3 (for which the selected plane is 1.5 m above the ground). As Fig.10 demonstrates, the positive and negative high-pressure zones around the train are radial, and a fierce transition exists between them. The increasing transverse distance not only increases the corresponding length and the area of the high-pressure zones but also enlarges the transition area between them. Hence it delays the time when the second pressure zone acts on the van and the time when the second peak/valley value appears.

Fig.9(d) shows a similar phenomenon in M_Y. As the transverse distance increases, the first peak/valley value happens earlier and the third one happens later, while there is no time shift for the second one. This phenomenon has a close relationship to the area of the high-pressure zones. Taking the P1 as an example, it derives from the positive pressure zone of the head of the train. In condition of a small transverse distance, P1 occurs when the whole positive pressure zone acts on the van’s flank. As the transverse distance increases, the area of the pressure zone is larger. When the whole positive pressure zone acts on the van’s flank, parts of it are not on the same side of the center of gravity. This generates a negative yawing moment, so the time of P1 is advanced. As the transverse distance increases, the variation magnitude decreases too, and different transverse distance has little influence on the variation trend of M_Y.

In terms of the M_R (seen in Fig.9(c)), it is noted that in the “M” and “L” stages, the transverse distance has a larger influence on the second peak/valley value compared to the first one. A larger transverse distance decreases the magnitude and delays the time of its appearance, it also smooths the variation and even eliminates a local fluctuation near V1 and P2. The smoothing effect is more distinct in M_P (see Fig.9(e)), where the number of peak/valley values decreases with the increase of the transverse distance.

4.3 Quantitative influence of transverse distance and fitting model

An in-depth discussion of quantitative information, the variation amplitude of all the aerodynamic forces under different transverse distances is provided in this subsection. For F_S, M_R, F_L, and M_Y, the value of P1 is selected; for M_P, the value of P is selected. Through subtracting the aerodynamic forces of the sole-traveling state, the variation amplitudes of the aerodynamic forces are obtained.

The formula of EN 2013 (CEN European Standard, 2013) and the formula proposed by Baker et al. [27] reflect the basic relationship between the pressure variation caused by train-induced wind and the distance. Xiang [28] also proposed a formula concerning the relationship between the distance and the pressure coefficient on a wind barrier under the train-induced wind by comparing the regularity of the attenuation of the pressure waves. The above three formulas are introduced to fit the numerical points. Since the fitting formulas are targeted at the pressure coefficient, only the structure of the formulas is applied. In the process of data fitting, the fitting formula fails to converge when leaves all the parameters to be unknown. Therefore, parts of the initial values of the original formula remain. The adjusted formulas are shown in Eqs. (4)–(6):

(4)\text{BasedonEN}2013:F_i(d) =\frac{a_0}{{(d+0.25)}^2}+a_1,

(5)\text{BasedonBaker:}{F}_i(d)=\frac{a_0}{{(d+1.75)}^2},

(6)\text{BasedonXiang}:F_i(d) =\frac{a_0}{{\left({\displaystyle \frac{d}{1.75}}\right)}^2+a_1},

where F_i(d) (i = 1, 2, 3, 4, 5) represents the relationship between the transverse distance d and the variation amplitude of transverse force, lift force, rolling moment, yawing moment and pitching moment, respectively. a₀ and a₁ are the parameters to be determined. The variation amplitudes of all the aerodynamic forces in Cases 1–10 as well as the fitting curves are shown in Fig.11.

Fig.11 shows that compared with the adjusted formula based on Baker et al. [27], the adjusted formula based on EN 2013 (CEN European Standard, 2013) and the one based on Xiang [28] can better represent the relationship between the variation amplitude of aerodynamic forces and the transverse distance. The adjusted formulas of EN 2013 (CEN European Standard, 2013) and Xiang [28] provide accurate results for all the aerodynamic forces. However, the fitting accuracy of the fitting model based on Baker et al. [27] is poor. The fitting parameters and the adjusted coefficients of determination are listed in Tab.4.

As can be seen in Tab.4, the adjusted formula based on EN 2013 (CEN European Standard, 2013) gets the highest fitting accuracy; the values of R_{\text{adjust}}^2 are above 0.99. The results of the formula based on Xiang [28] are slightly poorer; the values of R_{\text{adjust}}^2 are above 0.98. The results of the formula based on Baker et al. [27] are the poorest; the minimum R_{\text{adjust}}^2 is 0.7925 in the fitting of M_P.

It can be noted that when d is large enough, there should be no influence derived from the moving train, and then the bias a₁ in Eq. (4) is supposed to be zero. However, all the aerodynamic forces get a negative bias with a small absolute value, which is similar to the initial state of the EN 2013 (CEN European Standard, 2013). This implies that the adjusted formulas are only suitable for a specific range. Nevertheless, the actual single-level rail-cum-road bridge is restrained by the limited width of the bridge deck, so there isn’t a large transverse distance between the railway and highway, and the researched distance can cover the common range. Thus, the proposed formula based on EN 2013 (CEN European Standard, 2013) can be adopted into relevant researches. In contrast, Eqs. (5) and (6) can meet the aforementioned basic idea. Since the fitting accuracy is also enough for Eq. (6), it can be introduced into a larger range of transverse distance.

5 Influence of automobile speed

The relative speed of the two automobiles is considered as the main factor that influences the variation amplitude of aerodynamic forces. The increase in relative speed will enhance the variation of aerodynamic force and automobile response [15]. Future research could help provide suggestions on traffic control.

5.1 Influence of train speed and fitting model

Compared with the speed of road automobiles, the train’s speed is much higher. Therefore, the speed of the train can be taken to be the major factor influencing aerodynamic impact. To quantize the influence of the train speed and propose a fitting model, cases listed in Tab.5 are calculated and discussed.

According to the results of the above cases, the variation curves of the aerodynamic forces are similar under different train speeds. For brevity, discussion of the variation trend is omitted. To provide comprehensive research on the relationship among the peak/valley values, three prescribed values, namely, A₁, A₂, A₃ are extracted. The definitions are given in Tab.6, and corresponding symbols are listed in Fig.9.

Previous researches [12,8] considered that the maximum pressure value the train-induced wind applies to structures is proportional to the square of the train speed. Based on this idea, Eq. (7) is proposed to fit the numerical results.

(7)A=a{V}_{\text{c}}^2+b{V}_{\text{t}}^2+c{V}_{\text{c}} V_{\text{t}} ,

where a, b, c are the fitting parameters, V_c and V_t are the speed of the van and the speed of the train, respectively. The fitting results are shown in Fig.12.

As can be seen in Fig.12, A₁, A₂, A₃ increase when the train speeds up, but the magnitudeare different. The proposed formula is capable of reflecting the relationship between the train speed and aerodynamic variations. There is a small difference between the numerical points and fitting curves for F_S, F_L, M_R, and M_Y, while a relatively larger difference is observed in A₂ of M_P. Relevant fitting parameters and the adjusted coefficient of determination are listed in Tab.7.

Tab.7 shows that the values of R_{\text{adjust}}^2 are generally beyond 0.98, which proves the good performance of Eq.(8). The worst value of R_{\text{adjust}}^2 is 0.8404, which is at A₂ of M_P. In addition, Fig.9(e) illustrates that the value of A₂ is small in contrast with A₁, and the curve after V2 shows a great sign of fluctuation. Therefore, it is not unreasonable to deduce that the value of V2 is significantly influenced by the airflow at the bottom of the van since the substructure is complicated in the geometric model. This could explain the poor performance of fitting of A₂ of M_P. Nevertheless, as the sum of A₁ and A₂, A₃ shows good consistency with the simulation values, the performance of Eq. (8) is acceptable.

It can also be also noted that most of the fitting parameters have positive values, which implies the enhancement of a larger automobile speed. However, there are three exceptions worth further discussion:

Exception 1: For F_S, the value of a in A₁ and the value of c in A₂ are negative, which indicate the suppression of the van speed term and the coupled velocity term; however, the value of a is small compared to that of c. Increase of van speed still enhances the value of A₁.

Exception 2: the value of a in F_L is negative, which implies the protection of the van-induced wind on the lift force variation. Moreover, the absolute value of a is smaller than that of c. As the speed of the train is larger than the speed of the van, the variation amplitude still increases as the van speeds up.

Exception 3: the values of c are all negative in M_R, M_Y and M_P, and the absolute values are comparatively large compared to the other parameters. It can be concluded that the coupled velocity term has greatly suppressed all the moment forces.

Another phenomenon that is worth mentioning is that in A₃ of all the moments, the value of a is generally larger than the value of b, which implies that when the variation of automobile speed is confirmed, the change in the van speed would influence the aerodynamic forces more significantly.

5.2 Decay of aerodynamic variations

A further discussion is provided in this section on each velocity term of the variation amplitude A₃. The van speed term, the train speed term and the coupled velocity term are extracted for comparison. To make the sum of the above three terms equal to 1 and reflect the negative effect on the aerodynamic variation simultaneously, the calculation of the proportion is adjusted. The proportion of each term in the variation amplitude is calculated by Eq. (8). The proportion for each term is listed in Tab.8.

(8)\begin{array}{rl}\epsilon =& \frac{a{V}_{\text{c}}^2}{\left|a{V}_{\text{c}}^2\right|+\left|b{V}_{\text{t}}^2\right|+\left|c{V}_{\text{c}}{V}_{\text{t}}\right|},\frac{b{V}_{\text{t}}^2}{\left|a{V}_{\text{c}}^2\right|+\left|b{V}_{\text{t}}^2\right|+\left|c{V}_{\text{c}}{V}_{\text{t}}\right|},\\ & \frac{c{V}_{\text{c}}{V}_{\text{t}}}{\left|a{V}_{\text{c}}^2\right|+\left|b{V}_{\text{t}}^2\right|+\left|c{V}_{\text{c}}{V}_{\text{t}}\right|}.\end{array}

Tab.8 suggests that the rise in train speed increases the proportional contribution of the train speed term. It also decreases the proportional contribution of the coupled velocity term and the van speed term. For F_S, the train speed term takes 80%–90% of the variation amplitude, while the van speed term and the coupled velocity term equally share the remaining 10% to 20%. For F_L, the suppression of the van speed term is about 10%–20%, and the train speed term and the coupled speed term are almost equal in the researched velocity range. The components of M_R and M_P are parallel; the proportion of the van speed term is about 20%–30%, the proportion of the train speed term is about 30%–40% and that of the coupled velocity term is about –40%. In terms of M_Y, the train speed term is the dominant factor, which takes 60%–70% of the variation amplitude, while the proportion of the van speed term and coupled velocity term is close, the coupled velocity term takes –20% of the variation amplitude.

5.3 Influence of velocity proportion

The speeds of the car and the train vary greatly, and their geometrical shapes are different. Hence, even at the same relative speed, the different velocity proportion may bring obvious changes.The influence of automobile speed proportion on aerodynamics remains to be studied. Future research will be helpful to further understand the impact mechanism and help to determine the most unfavorable conditions.

The case details are listed in Tab.9, with the relative velocity set as 330 km/h. The percentage of the train speed is calculated by Eq. (9), the symbols refer to those in Eq. (7):

(9)\xi =\frac{V_{\text{t}}}{V_{\text{c}}+V_{\text{t}}}.

The time-history of the aerodynamic forces under different conditions is shown in Fig.13. The abscissa x refers to the definition in Fig.7.

Fig.13 shows that on one hand, as the train speed increases, the variation amplitude of aerodynamic forces denoted by increases. On the other hand, as the van speed decreases, it gets a more stable “P” stage while the van travels near the middle carriage. Fig.13(a), Fig.13(c), and Fig.13(d) illustrate that the influence on the first peak/valley value in the “M” stage and “L” stage is small; the major difference one is the second one. Moreover, the different velocity components do not affect the variation trend and the time when peak/valley occurs except for M_R. For M_R, the increase in the train speed gradually removes the local plateau of x = –10 m to x = 10 m, and produces P1 and V1 with close absolute values.

To quantize the influence of the train speed proportional contribution, ΔF is selected for a quantitative comparison; ΔF is transformed into amplitude coefficient by Eq. (10).

(10)C_{\text{F}}=\frac{\text{Δ}{F}_i}{\text{Δ}{F}_{\text{C}80}},

where \text{Δ}F (i = 1, 2, 3, 4, 5) is the variation amplitude in different cases, \mathrm{\Delta }{F}_{\text{C}80} is the maximum variation amplitude of Case 2. The values of C_F in the above four cases are listed in Tab.10.

Tab.10 indicates that compared with Case 2, when the train speed increases or decreases by 20 km/h, the percentage variations of C_F of F_S, F_L and M_Y are about 10%. When the speed of the train decreases, it does not affect M_R and M_P greatly, but a 20 km/h rise in the train speed increases the C_F of M_R and M_P by 6% and 23%, respectively. The most unfavorable case is Case 4 when the van is static. Compared to Case 2, the C_F of F_S, which controls the sideslip, and the C_F of M_R, which controls the rollover, have increased about 40%, the C_F of M_Y, which controls the lateral deviation, has increased 64%. In addition, the C_F of F_L and the C_F of M_P have increased 23% and 67%, respectively, which indicates a more uneven distribution of load between the front axes and the behind one, and this further threatens traveling security.

5.4 Further verification on the fitting model

To verify the possibility of the further application of the proposed fitting model, the proposed fitting model is introduced in the predictions of the cases in Subsection 5.3. The cases could represent typical cases in different combinations of van speed and train speed. Relevant fitting errors defined by Eq. (11) are listed in Tab.11.

(11)error =\frac{A_{\text{fitting}}-A_{\text{simu}}}{A_{\text{simu}}}\times 100\text{\%} ,

where A_fitting and A_simu are the fitting results and the simulation results, respectively.

Tab.11 shows that as long as the van is moving, the fitting model gives accurate predictions on the largest variation amplitude A₃. The fitting results are generally larger than the numerical results and the percentage errors are within 5% in F_S, F_L, M_R and M_Y. For M_P, however, the values are significantly influenced by the complex substructure of the van, which might produce an unconsidered nonlinear relationship, so the predictions are poorer than for other aerodynamic forces. However, the fitting accuracy is still acceptable as the maximum error is under 10%. In terms of A₁ and A₂, the fitting results are generally larger and are with reasonable difference in the first three cases. The fitting error of A₂ in M_P is the largest due to the relatively small value of N-V2.

For the static case, the fitting results are significantly larger than the simulation ones. It is believed that the airflow near the moving van possibly changed the interaction mechanism between the van and the train, which explains the poor performance in predicting the case when the van is still. The van-induced wind is deduced as an enhancement of the aerodynamic variation in the fitting model, so when the van is static, the fitting model overestimates the aerodynamic force variation of the van.

6 Conclusions

Based on a verified numerical model, this paper has researched the influence of the train-induced wind on a moving van. The impact mechanism is discussed based on the visualization techniques of computational fluid dynamics. The relationship between the transverse distance and aerodynamic variations is fitted to help to optimize the distance between railway and highway, and the relationship between the automobile speed and aerodynamic variation is fitted to help traffic control. The main conclusions are summarized as follows.

1) The adjacent high-pressure zones near the train head and train tail cause the major variation of aerodynamic forces of the van, and the middle carriage provides a stable plateau. The superposition of the high-pressure zones reverses the direction of F_S, F_L and M_R twice during the aerodynamic impact from the head and from the tail of the train, while it brings 3 inverses on the variation of M_Y and continuous fluctuation in M_P.

2) Different transverse distance changes the variation amplitude of all aerodynamic forces and the variation trend of M_R and M_P. The two proposed fitting models show good performance in the fitting of the relationship between the transverse distance and the aerodynamic variation of van. One of them is better in accuracy in the discussed range, the other could be used in a larger range of transverse distance.

3) For the fitting between the automobile speed and aerodynamic variations. The proposed fitting model gives slightly conservative predictions on the variation amplitude of all the aerodynamic forces in the dynamic cases. The van-induced wind is deduced to be an enhancement to the variation amplitude.

4) The train speed term takes more than 50% in the variation amplitude of F_S and M_Y, the proportion of the coupled velocity term is close to the one of the train speed term in F_L, M_R and M_P, and the van speed term takes no more than 20% in all the aerodynamic forces. Moreover, the coupled velocity term shows a suppression effect on the M_R, M_Y and M_P, the relevant proportion is about –20% to –40%.

The present study focuses on the aerodynamic variations acting on the road automobile. Itt would be more valuable if relevant calculations about the automobile response are added, which is more intuitive. Moreover, the wind environment on an actual rail-cum-road bridge could be further considered to explore the non-linear superposition effect of crosswind and train-induced wind, which will be explored in our future work.

References

[1] Pu Q, Liu J, Gou H, Bao Y, Xie H. Finite element analysis of long-span rail-cum-road cable-stayed bridge subjected to ship collision. Advances in Structural Engineering, 2019, 22(11): 2530–2542

[2] Shao C. Shanghai Yangtze River Bridge—the longest road-cum-rail bridge in China. Structural Engineering International, 2010, 20(3): 291–295

[3] Shao F, Chen Z, Ge H. Parametric analysis of the dynamic characteristics of a long-span three-tower self-anchored suspension bridge with a composite girder. Advances in Bridge Engineering, 2020, 1(1): 1–17

[4] Wang Y, Saul R. Wide cable-supported bridges for rail-cum-road traffic. Structural Engineering International, 2020, 30(4): 551–559

[5] Huang S, Li Z, Yang M. Aerodynamics of high-speed maglev trains passing each other in open air. Journal of Wind Engineering and Industrial Aerodynamics, 2019, 188: 151–160

[6] Xiong X, Li A, Liang X, Zhang J. Field study on high-speed train induced fluctuating pressure on a bridge noise barrier. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 177: 157–166

[7] Zhang T, Xia H, Guo W W. Analysis on running safety of train on the bridge considering sudden change of wind load caused by wind barriers. Frontiers of Structural and Civil Engineering, 2018, 12(4): 558–567

[8] Zhou D, Tian H Q, Zhang J, Yang M Z. Pressure transients induced by a high-speed train passing through a station. Journal of Wind Engineering and Industrial Aerodynamics, 2014, 135: 1–9

[9] Yang N, Zheng X K, Zhang J, Law S S, Yang Q S. Experimental and numerical studies on aerodynamic loads on an overhead bridge due to passage of high-speed train. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 140: 19–33

[10] Yao Z, Zhang N, Chen X, Zhang C, Xia H, Li X. The effect of moving train on the aerodynamic performances of train-bridge system with a crosswind. Engineering Applications of Computational Fluid Mechanics, 2020, 14(1): 222–235

[11] Zou Y, Fu Z, He X, Cai C, Zhou J, Zhou S. Wind load characteristics of wind barriers induced by high-speed trains based on field measurements. Applied Sciences (Basel, Switzerland), 2019, 9(22): 4865

[12] Tokunaga M, Sogabe M, Santo T, Ono K. Dynamic response evaluation of tall noise barrier on high speed railway structures. Journal of Sound and Vibration, 2016, 366: 293–308

[13] Chen Y G, Wu Q. Study on unsteady aerodynamic characteristics of two trains passing by each other in the open air. Journal of Vibroengineering, 2018, 20(2): 1161–1178

[14] Li W, Liu T, Chen Z, Guo Z, Huo X. Comparative study on the unsteady slipstream induced by a single train and two trains passing each other in a tunnel. Journal of Wind Engineering and Industrial Aerodynamics, 2020, 198: 104095

[15] Sun Z, Zhang Y, Guo D, Yang G, Liu Y. Research on running stability of CRH3 high speed trains passing by each other. Engineering Applications of Computational Fluid Mechanics, 2014, 8(1): 140–157

[16] Tokunaga M, Sogabe M, Santo T, Ono K. Dynamic response evaluation of tall noise barrier on high speed railway structures. Journal of Sound and Vibration, 2016, 366: 293–308

[17] Bocciolone M, Cheli F, Corradi R, Muggiasca S, Tomasini G. Crosswind action on rail vehicles: Wind tunnel experimental analyses. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96(5): 584–610

[18] Liu T, Chen Z, Zhou X, Zhang J. A CFD analysis of the aerodynamics of a highspeed train passing through a windbreak transition under crosswind. Engineering Applications of Computational Fluid Mechanics, 2018, 12(1): 137–151

[19] Niu J, Zhou D, Wang Y. Numerical comparison of aerodynamic performance of stationary and moving trains with or without windbreak wall under crosswind. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 182: 1–15

[20] Baker C J. High sided articulated road vehicles in strong cross winds. Journal of Wind Engineering and Industrial Aerodynamics, 1988, 31(1): 67–85

[21] Menter F R, Kuntz M, Langtry R. Ten years of industrial experience with the SST turbulence model turbulence heat and mass transfer. Turbulence, Heat and Mass Transfer, 2003, 4(1): 625–632

[22] Lee M, Park G, Park C, Kim C. Improvement of grid independence test for computational fluid dynamics model of building based on grid resolution. Advances in Civil Engineering, 2020, 1–11

[23] Xiang H, Li Y, Wang B, Liao H. Numerical simulation of the protective effect of railway wind barriers under crosswinds. International Journal of Rail Transportation, 2015, 3(3): 151–163

[24] Xiang H, Li Y, Chen S, Hou G. Wind loads of moving vehicle on bridge with solid wind barrier. Engineering Structures, 2018, 156: 188–196

[25] Xiang H, Li Y, Chen S, Li C. A wind tunnel test method on aerodynamic characteristics of moving vehicle s under crosswinds. Journal of Wind Engineering and Industrial Aerodynamics, 2017, 163: 15–23

[26] He J, Xiang H, Ren W, Li Y. Numerical simulation on aerodynamic characteristics of moving van under the train-induced wind. Wind and Structures, 2021, 33(1): 41–54

[27] Baker C, Jordan S, Gilbert T, Quinn A, Sterling M, Johnson T, Lane J. Transient aerodynamic pressures and forces on trackside and overhead structures due to passing trains. Part 1: Model-scale experiments. Proceedings of the Institution of Mechanical Engineers. Part F, Journal of Rail and Rapid Transit, 2014, 228(1): 37–56

[28] XiangH. Protection effect of wind barrier on high speed railway and its wind loads. Dissertation for the Doctoral Degree. Chengdu: Southwest Jiaotong University, 2013 (in Chinese)

RIGHTS & PERMISSIONS

Higher Education Press