Characteristics of Sudden Change in Aerodynamic Load of High-Speed Train Caused by Wind Barrier and Its Buffer Measure

Abstract

When high-speed trains (HSTs) rapidly enter or exit the wind barrier area of the bridge, the quick change in the operating environment can lead to sudden changes in train aerodynamic loads, resulting in the deterioration of their aerodynamic performance and adversely affecting safe and stable operation. In this paper, the effects of wind barrier porosity, crosswind speed, and train speed on the sudden change in the aerodynamic load of the HST induced by wind barriers are analyzed, and the reasons for the sudden change from a flow field perspective are given. Additionally, the influences of the buffer structure with three lengths of 45 m, 90 m, and 135 m on the sudden change in the aerodynamic load of HSTs are studied. The results show that the lower the porosity of the wind barrier, the higher the crosswind speed, and the lower the speed of trains entering and exiting the wind barrier area, resulting in a greater degree of sudden change in the aerodynamic load of the HST. The buffer structure measuring 90 m in length is considered the most suitable, as it can significantly alleviate the sudden change in the aerodynamic load and effectively enhance the safety of train operations.

1. Introduction

The modern railway infrastructure is continuously being improved, leading to a gradual increase in the construction of high-speed railway lines in regions prone to strong winds. However, when a high-speed train (HST) runs in crosswind environments, its aerodynamic performance deteriorates, potentially jeopardizing the safety of train operations. With the rapid advancements in science and technology, trains are becoming lighter and faster, which boosts operational efficiency but also exacerbates their susceptibility to crosswinds. The crosswind stability of a HST has thus become a significant area of focus and concern [1,2,3,4].

To ensure the smoothness of railway lines and conserve land resources, the construction of bridges plays a significant role in high-speed railways. When HSTs traverse these bridges, they encounter a more complex wind environment, resulting in an increased risk of accidents such as overturning or derailment [5,6,7]. One of the most effective measures to counter these risks is the installation of wind barriers on railway bridges. These wind barriers significantly improve the train operating environment, ensuring both safety and passenger comfort. Extensive research has been carried out on the wind-resistant performance of wind barriers [8,9,10,11]. According to these research findings, the external structure and inherent parameters of wind barriers (such as the height, porosity, and opening configurations) have been optimized, providing crucial theoretical support for the widespread application of wind barriers. However, there is a challenge when HSTs enter or exit the wind barrier areas on bridges under strong crosswinds and experience a rapid shift in their operating environment. The sudden transition in operating conditions leads to a sudden change in the aerodynamic load of the HST, thereby endangering its safe and steady operation.

Some scholars have begun to focus on the impact of the sudden change in the aerodynamic load when passing through wind barriers on the dynamic performance of HSTs. Zhang et al. [12] conducted theoretical calculations to analyze the fluctuations in aerodynamic loads when HSTs traverse wind barriers on bridges. They developed a coupled dynamic model and examined the impact of the sudden change in the aerodynamic load on the safety index of a HST. Yang et al. [13] conducted a comparative study to assess the aerodynamic characteristics of HSTs when passing through two different windproof facilities. Their findings indicated that during the moments of entering or exiting the windproof facility, there was a substantial increase in the fluctuation amplitude of the aerodynamic load of the HST, in contrast to other time intervals. Han et al. [14] conducted a study to examine the influence of sudden changes in the wind load induced by wind barriers on the dynamic response of HSTs using coupled numerical simulations. Their study revealed that wind barriers with lower porosity have a more substantial impact on the safety of HST operations. Liu et al. [15] conducted a CFD analysis and found that when the HST traverses the windbreak transition between a cutting and an embankment under crosswind conditions, there is a notable increase in pressure, force, and moment coefficients, resulting in reduced safety of train operations. These studies primarily focus on the impact of the sudden change in the aerodynamic load on dynamic responses and running safety of HSTs. However, there is a lack of research on the factors affecting the degree of the sudden change in the aerodynamic load of the HST caused by wind barriers. Furthermore, specific or effective mitigation measures to address this issue have not been provided.

This study utilizes the sliding mesh technique and the improved delayed detached-eddy simulation (IDDES) method to analyze the factors affecting the degree of the sudden change in the aerodynamic load when the HST passes through wind barrier areas in crosswind conditions and explains the reasons for the sudden change from the perspective of flow fields. Furthermore, three different lengths of buffer structures installed at the ends of the wind barriers are proposed, and their effectiveness in mitigating the sudden change is compared and analyzed.

2. Numerical Simulation

2.1. Geometric Model

In the present study, the HST model is the CRH3-type train, which includes three carriages: the head, middle, and tail cars, as depicted in Figure 1a. The head car measures 25.25 m in length, the middle car is 25.00 m long, and the tail car spans 25.25 m. The width and height of the train are 3.27 m and 3.89 m, respectively. The wind barrier is a commonly used curved fence-type wind barrier widely applied in engineering projects, as depicted in Figure 1b. It has a quarter-ellipse shape with horizontal and vertical dimensions of 0.9 m and 3.0 m, respectively.

The bridge model utilized is a streamlined flat box girder with dimensions of 530 m in length, 19.60 m in width, and 2.92 m in height. Figure 1c shows the specific dimensions of the system model. The curved wind barrier section has a length of 150 m, with a distance of 82.5 m from the nose tip of the head car. To effectively mitigate the influence of the bridge end on the initial flow field around the train, a distance of approximately 32 m is maintained between the nose of the tail car and the end of the bridge. Only the aerodynamic shapes of the HST and the bridge were considered, while other details, such as wheelsets, bogies, and pantographs, as well as the track and railings on the bridge deck, were neglected.

2.2. Turbulence Model

Detached-eddy simulation (DES) is a turbulence simulation method that combines the Reynolds-Averaged Navier–Stokes (RANS) and large-eddy simulation (LES) methods. The RANS model is employed to accurately predict turbulence near the wall and within the boundary layer, capturing the intricate details of the flow. In regions further away from the wall, the LES model is employed to solve these issues for larger-scale turbulent structures. Nevertheless, DES has certain weaknesses, such as a reduction in modeled stress and the occurrence of grid separation. To address these vulnerabilities, an improved and extended version of DES called delayed detached-eddy simulation (DDES) was developed. DDES introduces a delayed transition from RANS to LES, allowing the RANS model to be effective in regions far from the wall [16]. Building upon DDES, the IDDES method further enhances simulation accuracy by using RANS in regions with a lower turbulence intensity and LES in regions with a higher turbulence intensity and well-defined dissipation. By employing the IDDES method, a more precise representation of turbulent flow characteristics can be achieved while reducing the computational resources required.

Based on the shear stress transport $k-\omega$ (SST $k-\omega$) turbulence model, the IDDES method is employed to investigate the characteristics of the sudden change in aerodynamic load of a HST induced by bridge wind barriers in crosswind environments, as well as the mitigation effect of buffer structures on these sudden changes. The SST $k-\omega$ turbulence model is well-known for its accurate prediction of flow separation and is widely recognized as one of the most reliable turbulence models in engineering applications [17]. It is possible to estimate the length scale of IDDES by employing the following formula [18]:

$$l_{hyb}=f_{hyb}(1+f_e)l_{RANS}+(1-f_{hyb})l_{LES}$$

(1)

$$l_{RANS}={\displaystyle \frac{\sqrt{k}}{C_{\mu }\omega }},l_{LES}=C_{DES}\Delta$$

(2)

$$f_{hyb}=\max \left\{(1-f_{dt}),f_{step}\right\}$$

(3)

$$f_{dt}=1-\tanh [{(20r_{dt})}^3]$$

(4)

$$r_{dt}={\displaystyle \frac{{\nu }_t}{{\kappa }^2{d}_w^2\sqrt{0.5(S^2+{\Omega }^2)}}}$$

(5)

where $f_{hyb}$ is a mix function, $f_e$ is known as the elevation function and is designed to prevent the excessive reduction of RANS Reynolds stresses. The scales of the RANS and LES regions are represented by $l_{RANS}$ and $l_{LES}$, respectively. $k$ denotes the turbulent kinetic energy, $\Delta$ is the LES length scale, and $f_{step}$ is a function that provides a rapid switch from RANS to LES deep inside the boundary layer. $f_{dt}$ is the delay function of DDES, ${\nu }_t$ denotes the eddy viscosity, $\kappa$ symbolizes the von Karman constant, $d_w$ is the distance to the wall, and $S$ and $\Omega$ denote the normalized strain rate and rotation rate tensors in relation to the turbulence time scale, respectively.

2.3. Computational Domain

The sliding grid technique is adopted to simulate the passage of a HST through wind barrier areas on bridges, which is extensively employed in simulating HST aerodynamics [19,20,21]. Figure 2 shows the computational domain for fluid simulation. The overall computational domain is divided into a stationary domain and a moving domain. The stationary domain has dimensions of being 650 m long, 340 m wide, and 120 m high. The curved wind barrier is placed at the center of the bridge. There is a distance of 60 m between the ends of the bridge and the front and back walls of the stationary domain. The moving domain, which encompasses the HST, is a slender computational domain. It is essential for the moving domain to have sufficient length to ensure that the two end faces do not enter the stationary domain during movement.

In the stationary domain, the face ABCD is defined as a uniform velocity inlet. The faces ADHE, BCGF, and EFGH are designated as pressure outlets. The upper face CGHD is set as a symmetry boundary. On the other hand, the lower face ABFE, as well as the surfaces of the bridge and curved wind barrier, are defined as no-slip walls. In the moving domain, faces IJKL and MNOP are specified as pressure outlets, and the surfaces of the HST are set as no-slip walls. Furthermore, the contact faces between the stationary and moving domains are defined as interfaces to facilitate the exchange of flow information between them.

2.4. Mesh Strategy

The overall grid is divided into stationary and moving grids, as shown in Figure 3. The process of grid generation is carried out using the commercial software ANSYS ICEM 2020 R2 and FLUENT MESHING 2020 R2. A hybrid mesh approach is used to further divide the stationary domain into coarse, fine, and extra-fine regions. The coarse and fine regions further away from the system model have minimal impact on the simulation results. To optimize grid quality and reduce the number of grid cells in these regions, larger structured grids are used in ANSYS ICEM. However, the extra-fine region and moving domain include the wind barrier, bridge, and HST models, which have complex curved surfaces and complex structures. To accurately capture these intricate features, a highly adaptive poly-hexcore mesh was used to discretize these two regions in FLUENT MESHING.

The extra-fine region and moving domain are crucial for the simulation calculations, with grid densities approximately three times and five times higher than the fine region. To accurately capture the flow field information around the models, 15 boundary layers were applied to the surface of the curved wind barrier, bridge, and HST, as shown in Figure 3a. The grid height of the first layer is set to 2 mm for the wind barrier and train and 6 mm for the bridge. The growth factor is set to 1.1. The surfaces of the system models consist of structured polygonal grids. The surface mesh size of the HST is between approximately 20 and 35 mm, while the mesh size of the curved wind barriers is 30 mm, and the maximum surface mesh size of the bridge is 150 mm, as shown in Figure 3b,c.

Computational fluid dynamics calculations were performed using ANSYS FLUENT 2020 R2, which is based on the finite volume method in a high-performance computing center. The IDDES with the SST $k-\omega$ turbulence model is used for the transient solution; the transient formulation uses second-order implicit. The resolution of the pressure and velocity coupling equation utilized the semi-implicit method for the pressure-linked equations (SIMPLE) algorithm. The gradient of the resulting variable at the cell center was determined using the least squares cell-based method. The second-order upwind scheme was used to solve the $k$ and $\omega$ equations. A transient calculation model was adopted with a time step size of 0.001 s. To ensure accurate results, a total of 30 iterations were conducted for each time step. The convergence criteria were set with a residual tolerance of 10⁻⁵ for all physical quantities.

2.5. Data Processing

Figure 4 illustrates a schematic diagram representing the aerodynamic load experienced by a train under crosswind conditions. This study primarily focuses on the lateral force, lift, and rolling moment of the HST. In order to simplify the analysis of the train’s aerodynamic performance, it is common to normalize the aerodynamic load. The mathematical expressions for the aerodynamic load coefficients of the HST are presented below:

$$C_D={\displaystyle \frac{F_x}{0.5\rho V_a^{2}A}}$$

(6)

$$C_L={\displaystyle \frac{F_{\mathrm{y}}}{0.5\rho V_a^{2}A}}$$

(7)

$$C_M={\displaystyle \frac{M_Z}{0.5\rho V_a^{2}Ah}}$$

(8)

where $C_D$, $C_L$, and $C_M$ represent the coefficients for the lateral force, lift, and rolling moment, respectively. $F_x$, $F_y$, $M_Z$ represent the lateral force, lift force, and rolling moment, respectively. $\rho$ is air density of 1.225 kg/m³. The combined speed $V_a$ = $\sqrt{V_t^2+U_w^2}$, $V_t$ is the running speed of the HST, while $U_w$ represents the wind speed. The head car and the tail car each have a side area of 89.97 m², referred to as A, while the middle car has a side area of 95.42 m²; h denotes the characteristic height of the carriage, which is 3.82 m.

During the instantaneous moments as a HST enters or exits the wind barrier area in a crosswind environment, there is a drastic change in the aerodynamic load coefficients. Therefore, $\Delta C$ is introduced to represent the amplitude of changes in the aerodynamic load coefficients [22]

$$\Delta C=C_{\max }-C_{\min }$$

(9)

where $C_{\max }$ and $C_{\min }$ represent the maximum and minimum aerodynamic load coefficients, respectively.

Furthermore, $\Delta C^{\prime }$ is introduced to represent the rate of changes in the aerodynamic load coefficients for a HST within a time interval of 0.035 s. A time interval of 0.035 s is essential for assessing the safety of train operation [23].

$$\Delta C^{\prime }={\displaystyle \frac{\left|C_{t+0.035}-C_t\right|}{0.035}}$$

(10)

The degree of the sudden change in the aerodynamic load during the HST entering or exiting the bridge wind barrier area is evaluated in this study by using $\Delta C$ and $\Delta C_{\max }^{\prime }$.

3. Validation

3.1. Grid Independence

Grid independence analysis plays a crucial role in ensuring the accuracy and efficiency of numerical simulations. Figure 5a shows three different mesh models, namely coarse, medium, and fine, which were created by adjusting the mesh sizes of the train surface and the moving area. The total number of grid cells in the respective computing domains is 25.4 million, 34.3 million, and 44.7 million, respectively.

The process of a HST passing through the curved wind barrier area of a bridge with a speed of 83.33 m/s under a crosswind of 15 m/s was simulated using three different mesh models. Figure 5b shows a comparative analysis of the lateral force coefficient obtained from the simulations using the three mesh models. It can be seen that a significant error was observed when using the coarse mesh model, while the results obtained with the medium mesh model had smaller deviations compared to the fine mesh model. Therefore, to maintain a balance between computational accuracy and efficiency, the medium mesh model was selected for subsequent numerical calculations.

3.2. Numerical Model

3.2.1. Surface Pressure on the HST

Du et al. [24] carried out a 1:20 scaled model experiment of a moving train at the Key Laboratory of Railway Safety at Central South University to investigate the dynamic changes in pressure when a HST passes through noise barriers. The experimental setup by Du is illustrated in Figure 6a. An aerodynamic model with the same dimensions as described in Ref. [24] was constructed, as shown in Figure 6b. The numerical simulation results were compared with Du’s experimental results to validate the accuracy of the train surface pressure obtained in this study. The computational domain had dimensions of 12 m × 5 m × 60 m, with the HST and noise barrier models positioned at the center of the computational domain.

Figure 6c shows a comparison of the aerodynamic pressures at measurement point T2 on the train surface, obtained through numerical simulations and the experimental measurements by Du. The results indicate that, unlike the moving model experiment, the pressure curve obtained through numerical simulation exhibits smoother fluctuations. Moreover, there is a high degree of consistency between the two sets of results, which strongly validates the reliability of the surface pressure on the HST obtained by numerical simulation.

3.2.2. Aerodynamic Load Coefficients of the Train

Dorigatti et al. [25] have pointed out the significant consistency in the experimental results for the aerodynamic load coefficients between static and moving train models. In a separate study, Schober et al. [26] conducted experiments using static train models to measure the aerodynamic load coefficients of the ICE3 train under different conditions. Considering the similarity in external appearance between the CRH3 train and the ICE3 train, the numerical simulation results are compared with the experiment results conducted by Schober to confirm the accuracy of the aerodynamic load coefficients acquired through simulation in this study. Figure 7 shows a CRH3 train-ground model at a 1:15 scale consistent with Schober’s experiment. The computational domain has a dimension of 8 m in width, 5 m in depth, and 15 m in height, and the train model is positioned in the center. The airflow velocity in the simulation is 78 m/s, and various wind yaw angles (10°, 20°, 30°, 40°, 50°, and 60°) are considered to investigate their influence on the aerodynamic load coefficients of the tail car.

Figure 8 presents a comparison between the aerodynamic load coefficients of the train, obtained through numerical simulation, and the results from Schober’s experiments. The comparison shows that the variation trend of the aerodynamic load coefficients through numerical simulation aligns with the results obtained from the experiment, with an acceptable margin of error. This indicates that the aerodynamic load coefficients obtained through numerical simulation for the train in this study are accurate and reliable.

In conclusion, the accuracy of the method employed in this paper, along with the established CFD model, has been affirmed by comparing the surface aerodynamic pressure variations and aerodynamic load coefficients of the HST obtained through numerical calculations with the experimental results documented in the existing literature.

4. Results and Discussion

4.1. Influencing Factors of the Sudden Change in the Aerodynamic Load of the HST Induced by Wind Barriers

4.1.1. Porosities of Curved Wind Barriers

Figure 9 illustrates the variations in aerodynamic load coefficients when the HST traveling at 300 km/h passes through curved wind barriers with three different porosities (10%, 30%, and 50%) in a crosswind of 15 m/s.

Table 1. Amplitude of changes in aerodynamic load coefficients for the HST passes through curved wind barriers with different porosities.

Porosity	Carriage	$\mathbf{\Delta }\mathit{C}$
		Enter			Exit
		${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$
10%	Head	0.1067	0.0399	0.0235	0.1004	0.0430	0.0212
	Middle	0.0299	0.0546	0.0050	0.0277	0.0599	0.0049
	Tail	0.0315	0.0249	0.0066	0.0278	0.0279	0.0060
30%	Head	0.0824	0.0429	0.0117	0.0771	0.0396	0.0116
	Middle	0.0234	0.0566	0.0021	0.0233	0.0515	0.0021
	Tail	0.0211	0.0125	0.0042	0.0191	0.0113	0.0042
50%	Head	0.0552	0.0343	0.0081	0.0514	0.0291	0.0077
	Middle	0.0205	0.0290	0.0015	0.0182	0.0293	0.0014
	Tail	0.0126	0.0095	0.0040	0.0091	0.0030	0.0036

and

Table 2. Amplitude of the rate of changes in aerodynamic load coefficients for the HST passes through curved wind barriers with different porosities.

Porosity	Carriage	$\mathbf{\Delta }{\mathit{C}}_{\mathbf{max}}^{\prime }$
		Enter			Exit
		${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$
10%	Head	0.8269	0.2306	0.1369	0.6249	0.2029	0.11
	Middle	0.1494	0.1797	0.0201	0.1163	0.2514	0.0177
	Tail	0.2286	0.1046	0.0289	0.1727	0.1003	0.0351
30%	Head	0.5794	0.2220	0.0923	0.5269	0.1837	0.0797
	Middle	0.0829	0.1657	0.0106	0.0791	0.1871	0.0094
	Tail	0.1011	0.0857	0.0171	0.1146	0.0551	0.0183
50%	Head	0.3717	0.1651	0.058	0.342	0.1317	0.0546
	Middle	0.0654	0.1026	0.008	0.0617	0.0946	0.0063
	Tail	0.0540	0.0406	0.0146	0.0489	0.0271	0.012

present the amplitude of changes in the aerodynamic load coefficients and the amplitude of change rates of the aerodynamic load coefficients for the HST passes through curved wind barriers with different porosities. In these tables, “Enter” refers to the period from the nose tip of the head car entering until the nose tip of the tail car entering the wind barrier area, corresponding to the time interval of 0.990 s to 1.896 s. On the other hand, “Exit” represents the period from the nose tip of the head car exiting until the nose tip of the tail car exiting the wind barrier area, corresponding to the time interval of 2.790 s to 3.696 s.

Based on Figure 9 coupled with Table 1 and Table 2, it can be concluded that the aerodynamic load coefficients of each car of the train have a similar trend when entering and exiting the wind barrier area. These coefficients rapidly decrease upon entering the wind barrier area and sharply increase when exiting. The lower the porosity of the curved wind barriers, the greater the degree of the sudden change in the aerodynamic load of the HST. For example, when the head car of the HST enters a wind barrier with 50% porosity, the amplitude of the change in the lateral force coefficient is 0.0552, and the amplitude of the change rate is 0.3717. However, when the head car enters a wind barrier with a porosity of 10%, the corresponding values are 0.1067 and 0.8269, representing an increase of 93.30% and 122.46%, respectively. Compared with exiting the wind barrier area, the degree of the sudden change in the aerodynamic load of the HST entering the wind barrier area is greater. Furthermore, the head car exhibits the largest variations in aerodynamic load, while the tail car experiences the most intense fluctuations.

4.1.2. Crosswind Speed

Figure 10 depicts the change in aerodynamic load coefficients for the train passing through the wind barrier area with a 30% porosity under different crosswind speeds. The speed of the HST is 300 km/h.

Table 3. Amplitude of changes in aerodynamic load coefficients for the HST passes through the curved wind barrier at different crosswind speeds.

Crosswind Speed (m/s)	Carriage	$\mathbf{\Delta }\mathit{C}$
		Enter			Exit
		${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$
10	Head	0.0519	0.0155	0.0083	0.0492	0.0131	0.0079
	Middle	0.0097	0.0324	0.0006	0.0089	0.0302	0.0006
	Tail	0.0093	0.0238	0.0018	0.0116	0.0243	0.0019
15	Head	0.0824	0.0430	0.0117	0.0771	0.0396	0.0116
	Middle	0.0234	0.0566	0.0021	0.0233	0.0515	0.0021
	Tail	0.0211	0.0125	0.0042	0.0191	0.0113	0.0042
20	Head	0.1116	0.0857	0.0146	0.1056	0.0830	0.0145
	Middle	0.0458	0.0517	0.0067	0.0438	0.0523	0.0063
	Tail	0.0329	0.0195	0.0106	0.0264	0.0071	0.0107
25	Head	0.1467	0.1401	0.0184	0.1348	0.1398	0.0178
	Middle	0.0728	0.0362	0.0151	0.0696	0.0413	0.0150
	Tail	0.0425	0.0427	0.0128	0.0367	0.0242	0.0139

and

Table 4. Amplitude of the rate of changes in aerodynamic load coefficients for the HST passes through the curved wind barrier at different crosswind speeds.

Crosswind Speed (m/s)	Carriage	$\mathbf{\Delta }{\mathit{C}}_{\mathbf{max}}^{\prime }$
		Enter			Exit
		${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$
10	Head	0.3611	0.0860	0.0554	0.3349	0.0763	0.0480
	Middle	0.0449	0.0929	0.0034	0.0446	0.0829	0.0034
	Tail	0.0706	0.0800	0.0048	0.0709	0.0814	0.0083
15	Head	0.5794	0.2220	0.0923	0.5269	0.1837	0.0797
	Middle	0.0829	0.1657	0.0106	0.0791	0.1871	0.0094
	Tail	0.1011	0.0857	0.0171	0.1146	0.0551	0.0183
20	Head	0.7763	0.3989	0.1306	0.7617	0.3740	0.1120
	Middle	0.1746	0.1914	0.0269	0.1797	0.2446	0.0229
	Tail	0.1583	0.1463	0.0366	0.13	0.0691	0.0334
25	Head	0.9594	0.5969	0.1686	0.9428	0.5597	0.1449
	Middle	0.2831	0.1614	0.0529	0.2237	0.1871	0.0477
	Tail	0.2163	0.2114	0.0431	0.1723	0.1014	0.0511

present the amplitude of changes in the aerodynamic load coefficients and the amplitude of the rate of changes in the aerodynamic load coefficients during the process. According to Figure 10 and Table 3 and Table 4, it can be observed that the crosswind speed significantly influences the aerodynamic load coefficient of the HST when passing through the wind barrier area. As the crosswind speed increases, the aerodynamic load coefficients also increase. Moreover, the amplitude of the aerodynamic load coefficient variation becomes more pronounced when entering and exiting the wind barrier area. For example, at a wind speed of 10 m/s, the amplitude of the change in the lateral force coefficient and the amplitude of the rate of change in the lateral force coefficient of the head car are 0.0519 and 0.3611, respectively. However, when the wind speed escalates to 25 m/s, the corresponding indicators are 0.1467 and 0.9594, respectively, increasing by 182.66% and 164.33%. Therefore, it becomes evident that as the crosswind speeds rise, the degree of the sudden change in the aerodynamic load of the HST when entering and exiting the wind barrier area of a bridge is significantly intensified.

4.1.3. Running Speed of the HST

Figure 11 illustrates the changes in the aerodynamic load coefficients of a HST passing through a wind barrier with a porosity of 30% under a 15 m/s crosswind at different running speeds (200, 250, 300, and 350 km/h).

Table 5. Amplitude of changes in aerodynamic load coefficients for the HST passes through the curved wind barrier at different running speeds.

Running Speed (km/h)	Carriage	$\mathbf{\Delta }\mathit{C}$
		Enter			Exit
		${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$
200	Head	0.1320	0.1094	0.0168	0.1211	0.1090	0.0164
	Middle	0.0592	0.0420	0.0109	0.0551	0.0445	0.0104
	Tail	0.0477	0.0237	0.0123	0.0310	0.0122	0.0133
250	Head	0.1003	0.0714	0.0135	0.0947	0.0640	0.0137
	Middle	0.0371	0.0567	0.0045	0.0357	0.0556	0.0040
	Tail	0.0265	0.0136	0.0084	0.0240	0.0079	0.0087
300	Head	0.0824	0.0430	0.0117	0.0771	0.0396	0.0116
	Middle	0.0234	0.0566	0.0021	0.0233	0.0515	0.0021
	Tail	0.0211	0.0125	0.0042	0.0191	0.0113	0.0042
350	Head	0.0701	0.0306	0.0106	0.0647	0.0267	0.0100
	Middle	0.0164	0.0485	0.0011	0.0153	0.0441	0.0012
	Tail	0.0153	0.0211	0.0023	0.0174	0.0204	0.0026

and

Table 6. Amplitude of the rate of changes in aerodynamic load coefficients for the HST passes through the curved wind barrier at different running speeds.

Running Speed (km/h)	Carriage	$\mathbf{\Delta }{\mathit{C}}_{\mathbf{max}}^{\prime }$
		Enter			Exit
		${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$	${\mathit{C}}_{\mathit{D}}$	${\mathit{C}}_{\mathit{L}}$	${\mathit{C}}_{\mathit{M}}$
200	Head	0.6171	0.3506	0.1086	0.6631	0.3229	0.0966
	Middle	0.1606	0.1240	0.0277	0.1451	0.1271	0.0254
	Tail	0.1501	0.0926	0.0287	0.1341	0.0530	0.0323
250	Head	0.6013	0.2627	0.1003	0.5827	0.2583	0.0899
	Middle	0.1249	0.1667	0.0147	0.1178	0.2088	0.0133
	Tail	0.1057	0.0977	0.0249	0.0963	0.0874	0.0289
300	Head	0.5794	0.2220	0.0923	0.5269	0.1837	0.0797
	Middle	0.0829	0.1657	0.0106	0.0791	0.1871	0.0094
	Tail	0.1011	0.0857	0.0171	0.1146	0.0551	0.0183
350	Head	0.5577	0.1738	0.0850	0.4905	0.1470	0.0731
	Middle	0.0718	0.1573	0.0080	0.0724	0.1591	0.0073
	Tail	0.0942	0.1013	0.0111	0.1116	0.0750	0.0111

provide the amplitude of changes in the aerodynamic load coefficients and the amplitude of the rate of changes in the aerodynamic load coefficients for the HST passes through the wind barrier at different running speeds. According to Figure 11, combined with Table 5 and Table 6, it becomes apparent that as the speed of the HST increases, the aerodynamic load coefficients decrease. Additionally, the amplitude of changes in the aerodynamic load coefficients and the amplitude of the rate of changes in the aerodynamic load coefficients also decrease. For example, for the head car of the HST, when the train enters the wind barrier at a speed of 200 km/h, the amplitude of the change in the lift force coefficient and the amplitude of the rate of change in the lift force coefficient are 0.1094 and 0.3506, respectively. However, when the train enters the wind barrier at a speed of 350 km/h, the corresponding indicators of the head car are 0.0306 and 0.1738, respectively, decreasing by 72.03% and 50.43%. These results indicate that as the running speed increases, the degree of the sudden change in aerodynamic load during the HST entering or exiting the wind barrier area will be mitigated.

4.2. Flow Field Characteristics of HSTs Entering Curved Wind Barriers

Figure 12 illustrates a comparison of the lateral cross-sectional pressure distribution cloud maps at the center of the head car of a HST before entering a bridge wind barrier and after entering wind barriers with three different porosities (10%, 30%, and 50%). It is obvious that the train is directly exposed to airflow before entering the wind barrier, leading to positive pressure on the windward surface that reaches a maximum value exceeding 120 Pa. Simultaneously, due to airflow separation and acceleration, a high-pressure zone is formed above the train roof, generating a maximum negative pressure of more than −500 Pa. When the train enters the wind barrier area, the presence of the wind barrier significantly affects the surface pressure distribution. The positive pressure on the windward surface decreases while the negative pressure on the leeward surface increases. Furthermore, the negative pressure on both the train roof and bottom decreases. The degree of pressure variation on the train surface depends on the porosity of the curved wind barrier, with a smaller porosity resulting in a greater pressure variation. The process of a HST entering a wind barrier involves intense variations in aerodynamic pressure on the different surfaces of the train. This leads to a significant difference in pressure between the windward and leeward surfaces, as well as the top and bottom of the train, ultimately causing a sudden change in the aerodynamic load of the HST.

Figure 13 illustrates the velocity streamline diagram of the lateral cross-section of the HST as it enters wind barrier areas with different porosities. Plane 1, Plane 2, and Plane 3 represent the cross-sections at the center positions of the head, middle, and tail cars, respectively. The streamlines are represented by the dimensionless speed $U/U_w$, where $U$ is the airflow speed near the train and $U_w$ represents the crosswind speed. From Figure 13a, it can be observed that the incoming airflow undergoes separation and acceleration before entering the wind barriers near the leading edge of the bridge, resulting in a slightly higher wind speed around the windward surface of the train compared to the incoming airflow. The wind speed at the top of the train is significantly higher and exceeds twice the speed of the crosswind. In Plane 1, the airflow remains relatively stable, without any noticeable vortex structures. Conversely, in Plane 2 and Plane 3, medium-sized vortices form near the leeward surface of the train.

When the HST enters the wind barrier area, as shown in Figure 13b–d, the wind-blocking effect of the wind barriers significantly reduces the wind speed in the running area of the train, especially near the roof. Furthermore, the disturbance caused by the wind barrier on the flow field leads to the formation of multiple large-scale vortex structures on the windward and leeward surfaces of the train in Plane 1, Plane 2, and Plane 3. These vortex structures result in train vibrations and oscillations. The porosity of the curved wind barrier directly affects the decrease in wind speed, with lower porosity resulting in a more noticeable reduction. Moreover, a higher number of larger vortex structures appear on both sides of the train. When the train enters the wind barrier, there is a sharp decrease in wind speed in the operating area, as well as significant changes in the flow field around the HST. This leads to substantial pressure fluctuations on the train’s surface and is the fundamental reason for the sudden change in the aerodynamic load of the HST after entering the wind barrier.

4.3. Buffer Measure

4.3.1. Buffer Scheme

To tackle the challenges posed to the stability and safety of HSTs when passing through wind barrier areas in crosswinds, this section proposes a buffer structure installed at the end of the bridge wind barrier. The objective of the buffer structure is to provide a smooth transition for HSTs between the interior and exterior areas of the bridge wind barrier. The buffer structure consists of three sections of curved wind barriers with gradually varying porosities, as depicted in Figure 14a. The curved wind barrier on the bridge has a porosity of 30%. The three sections of the buffer structure are consistent with the curvature of the curved wind barrier and have porosities of 40%, 50%, and 60%, respectively.

Figure 14b illustrates a schematic diagram of buffer structures with three different lengths (45 m, 90 m, and 135 m). Taking the process of the HST entering the wind barrier area of the bridge as an example, there is a distance of 290 m between the nose tip of the head car and the bridge wind barrier. At a crosswind speed of 15 m/s, the HST travels through the buffer structure at a speed of 250 km/h until reaching the middle of the bridge wind barrier area, covering a running distance of approximately 415 m.

To examine the effects of buffer structures on the sudden change in aerodynamic load coefficients of the HST, two evaluation indices are introduced: the rate of reduction in the amplitude of changes in the aerodynamic load coefficients ($D$) and the rate of reduction in the amplitude of the rate of changes in the aerodynamic load coefficients ($D^{\prime }$).

$$D={\displaystyle \frac{\Delta C-\Delta C_S}{\Delta C}}\times 100\%$$

(11)

$$D\prime ={\displaystyle \frac{\Delta C_{\max }^{\prime }-\Delta C_S{\prime }_{\max }}{\Delta C_{\max }^{\prime }}}\times 100\%$$

(12)

where $\Delta C_S$ represents the amplitude of changes in the aerodynamic load coefficients and $\Delta C_S{\prime }_{\max }$ represents the amplitude of the rate of changes in the aerodynamic load coefficients within 0.035 s when the HST enters the wind barrier area after installation of buffer structures, respectively.

4.3.2. Influence of Buffer Structures on the Sudden Change in Aerodynamic Load of HST

Figure 15 illustrates the variation in the aerodynamic load coefficients as the HST enters the wind barrier area through buffer structures with different lengths.

Table 7. Decrease rate in the amplitude of changes in aerodynamic load coefficients of HST when installing a buffer structure of different lengths.

Aerodynamic Load Coefficient	Carriage	Without Buffer Structure $\mathbf{\Delta }\mathit{C}$	$\mathit{D}$
			45 m	90 m	135 m
$C_D$	Head	0.0944	6.93%	10.04%	10.83%
	Middle	0.0339	5.38%	8.01%	8.53%
	Tail	0.0273	18.08%	28.13%	29.04%
$C_L$	Head	0.0763	5.51%	7.92%	8.34%
	Middle	0.0563	1.71%	5.70%	6.17%
	Tail	0.0272	8.39%	10.85%	11.07%
$C_M$	Head	0.0134	10.68%	15.68%	16.13%
	Middle	0.0040	2.53%	5.81%	6.42%
	Tail	0.0089	1.24%	2.70%	3.17%

and

Table 8. Decrease rate in the amplitude of the rate of changes in aerodynamic load coefficients of HST when installing a buffer structure of different lengths.

Aerodynamic Load Coefficient	Carriage	Without Buffer Structure $\mathbf{\Delta }{\mathit{C}}_{\mathbf{max}}^{\prime }$	${\mathit{D}}^{\prime }$
			45 m	90 m	135 m
$C_D$	Head	0.6177	31.41%	55.59%	56.97%
	Middle	0.1394	40.77%	59.66%	60.94%
	Tail	0.1506	38.15%	54.18%	57.10%
$C_L$	Head	0.3386	39.14%	54.63%	55.56%
	Middle	0.1629	52.48%	66.30%	66.13%
	Tail	0.1094	8.27%	18.11%	15.88%
$C_M$	Head	0.0943	30.82%	49.55%	50.76%
	Middle	0.0151	21.07%	29.44%	31.48%
	Tail	0.0301	42.19%	57.81%	59.42%

present the decrease rate in the amplitude of changes in the aerodynamic load coefficients and the decrease rate in the amplitude of the rate of changes in the aerodynamic load coefficients, respectively. It can be concluded from Figure 15, as well as Table 7 and Table 8, that buffer structures effectively mitigate the abrupt change in the aerodynamic load of the HST, with effectiveness correlated with the length of buffer structures.

Compared to scenarios without a buffer structure, a buffer structure of 45 m leads to a 6.93% reduction in the amplitude of the change and a 31.41% reduction in the amplitude of the rate of change in the lateral force coefficient of the head car. When the length of the buffer structure is increased to 90 m, the amplitude of the change and the amplitude of the rate of the change in the lateral force coefficient of the head car decrease by 10.04% and 55.59%, respectively. However, when the length of the buffer structure is further increased to 135 m, the corresponding indicators decrease by 10.83% and 56.97%, respectively. These results indicate that a buffer structure with a length of 45 m has limited effectiveness in mitigating abrupt aerodynamic load changes. However, a buffer structure of a 90 m length exhibits substantial improvement in mitigating such an abrupt change. Beyond this length, the enhancement in the buffering effect becomes negligible. Therefore, a buffer structure measuring 90 m in length is considered the most suitable.

4.3.3. Effectiveness of the Buffer Structure

A dynamic model of the three-carriage CRH3 train was established in UNIVERSAL MECHANISM (UM). Each carriage consists of, from top to bottom, the car body, the secondary suspension, the frame, the primary suspension, the axle box, and the wheelset. The car body, bogie frame, axle box, and wheelset are assumed to be rigid, with no deformation of vehicle components. The car body, bogie, and wheelset are all considered to have 6 degrees of freedom, while the axle box is considered to have only 1 degree of freedom (pitch), totaling 50 degrees of freedom. Both the primary and secondary suspensions are modeled using spring-damping elements, with viscous elastic linear force-element simulations employed in UM. Additionally, with the CRTSII-type slab ballastless track and box girder as the research subjects, the finite element software ABAQUS is employed to construct a three-dimensional geometric model of the track–bridge system. Modal analysis and mass structure analysis are conducted to generate a flexible file that can be utilized by UM, which is subsequently imported into UM for further processing. The track–bridge model comprises the following components, listed from top to bottom: rail, fasteners, rail support groove, track slab, mortar layer, base slab, and flat box girder. The rails are modeled using CHN60 rail with Timoshenko beam elements. The fasteners are represented by three-dimensional spring-damper elements, while the track slab, mortar layer, and base slab are modeled using solid elements. The bridge is also represented with solid elements, taking into account the impact of the bridge shape on the aerodynamic loads from the train. Binding constraints are applied between the track slab and both wide and narrow cracks, between the track slab and the mortar layer, between the mortar layer and the base slab, and between the base slab and the bridge deck.

The vehicle multi-body dynamics model, flexible track, and bridge models established above are imported into the UM software and combined to form a dynamics model of the vehicle–track–bridge coupled system, as shown in Figure 16. The track irregularity spectrum is based on the Chinese high-speed railway slab track spectrum. The time-varying aerodynamic load of each carriage of the HST is recorded in a standardized format as .txt files, which are then imported into UM and applied to the center position of each car using T-force elements.

In this study, the wheel load reduction rate (WLRR) and derailment coefficient (DC) are adopted to assess the running safety of the train passing through the wind barrier area in crosswind conditions. The safety limits of WLRR and DC are 0.6 and 0.8, respectively [27].

Figure 17 shows the variations in the WLRR and the DC of the head car as the HST enters the wind barrier area with and without a buffer structure under a crosswind speed of 15 m/s. The running speed of the HST is 250 km/h. It can be observed from Figure 16 that the WLRR and the DC of the head car significantly increase when the train enters the wind barrier without the presence of a buffer structure, with maximum values of 0.4484 and 0.3643, respectively. However, with a buffer structure of 90 m in length, the maximum values of the WLRR and DC of the head car decrease to 0.3843 and 0.3457, respectively, representing reductions of 14.30% and 5.11%. This indicates that the buffer structure installed at the end of the wind barrier of the bridge significantly enhances the safety of the HST operations.

5. Conclusions

Based on the IDDES method and sliding grid technique, the effects of three factors— such as the porosity of the wind barrier, the crosswind speed, and the running speed of the HST—on the sudden change in the aerodynamic load of the HST induced by a wind barrier are analyzed, and the reasons for the sudden change from a flow field perspective are given. The influences of the buffer structure with the three different lengths of 45 m, 90 m, and 135 m on the sudden change in aerodynamic load of a HST are investigated. The main conclusions are as follows:

• The lower the porosity of the wind barrier, the higher the crosswind speed, and the lower the running speed of the HST, leading to a larger sudden change in the aerodynamic load of the HST. Comparatively, the degree of the sudden change in the aerodynamic load is greater for the HST entering the wind barrier area of the bridge than exiting.
• When a HST traverses the wind barrier area of a bridge, there are noticeable changes in the wind speed within the running area and the flow field around the HST. These changes lead to significant fluctuations in aerodynamic pressure on surfaces of the HST, leading to a drastic variation in the pressure difference between the windward and leeward surfaces, as well as between the top and bottom of the train. As a consequence, the HST experiences a sudden change in its aerodynamic load.
• A buffer structure measuring 45 m in length demonstrates limited effectiveness in reducing the sudden change. However, increasing the length of the buffer structure to 90 m significantly improves its ability to mitigate these fluctuations. This results in a 10.04% reduction in the amplitude of the change and a 55.59% reduction in the amplitude of the rate of change in the lateral force coefficient of the head car. On the other hand, a further increase in the length of the buffer structure to 135 m leads to a negligible enhancement in the buffering effect. Therefore, a 90 m buffer structure is considered the most suitable option.
• The installation of a 90 m buffer structure significantly enhances the safety of HST operations. It decreases the WLRR and DC of the head car by 14.30% and 5.11%, respectively.