Influence of wind barrier on the transient aerodynamic performance of high-speed trains under crosswinds at tunnel–bridge sections

Porous wind barriers (PWBs) are gradually applied to tunnel–bridge–tunnel infrastructures (TBTIs) along high-speed railway lines. Due to the remarkable aerodynamic effect of high-speed trains (HSTs), the windproof performance of a PWB at tunnel–bridge section (TBS) is particularly critical when a HST passes through the TBTI under crosswind. And it seems to be easily ignored by researchers. This study aims to determine the influence mechanism of the PWB in the TBS. A CFD dynamic model of air–train–PWB was built based on porous media theory, and its reliability is verified by model and field tests. The main results are as follows: the corresponding variation amplitudes of the train’s aerodynamic load coefficients are reduced by 36–95% when a PWB is set in the TBS; adopting the same design parameters along the full-length PWB on the TBTI is unreasonable; the PWB height and porosity in the TBS must be increased and reduced more than 33%, respectively, to achieve equivalent windproof performance. The conclusions in this paper can provide a preliminary idea for the optimization design of the PWB on the TBTI.


Introduction
In mountainous areas, tunnel-bridge section (TBS) has become the most common infrastructure scenario for high-speed railway (HSR) lines crossing canyons Olmos & Astiz, 2018). For example, in the Lanzhou-Chongqing Railway Line, bridges and tunnels account for 70-80% of the total line length Liu et al., 2019). When the air from the open area flows into the canyon where two mountains face each other, this air will accelerate through the canyon and form the canyon wind (Li et al., 2017;Yu et al., 2019). Therefore, high-speed trains (HSTs) often encounter strong crosswind when they run to the tunnel-bridge-tunnel infrastructure (TBTI). Chen et al. (2019) used driving simulators and observed that the running stability of a box truck is considerably worse when it runs to a TBS under crosswind, even if its running speed is far lower than that of an HST. Deng et al. (2019), ,  also found that the train body experiences a strong aerodynamic impact when an HST drives into (or out of) a tunnel under crosswind. This situation seriously threatens the safety of train running. Porous wind barriers (PWBs) are gradually applied to bridges in this area to improve the running CONTACT E. Deng denge12@csu.edu.cn safety of the HST and the structure stability of the bridge ( Figure 1). Many researchers have conducted a series of research on the aerodynamic effect of PWBs in the bridge section (BS) in recent years. However, they mainly focused on the steady or quasi-steady-state process when a vehicle runs completely into the PWB section of a bridge and did not involve the transformation of infrastructure scenarios during the running process. For example, Avila-Sanchez et al. (2016) used the particle image velocimetry method to observe the effect of a solid wind barrier on the transverse streamline characteristics around the bridge. Xiang et al. (2018) studied the effect of the height of a solid windbreak on the aerodynamic loads of a cuboid vehicle moving on a bridge through an indoor test and discussed the difference in the results of static and dynamic models. The relative motion between the train and windbreak will intensify the aerodynamic effect of the train, and the aerodynamic loads acting on the train will decrease with increasing barrier height. Kozmar et al. (2012Kozmar et al. ( , 2014 studied the effect of the porosity and height of a PWB on the flow field characteristics of trains running on a bridge through an indoor test. A set of optimal parameters of the PWB, namely, porosity of 30% and height of 5 m, was obtained. Chen et al. (2015) studied the influence of PWBs with different pore types on the running safety of road vehicles running on a bridge by establishing a large-scale wind tunnel test model. He, Fang, et al. (2019) studied the influence of a louver-type PWB on the aerodynamic characteristics of a vehicle-bridge based on a wind tunnel experiment and optimized its parameters.
The windproof performance of a PWB in a TBS is particularly critical when an HST runs in this section under the condition of crosswind. The simulation of a PWB is the key link. A PWB (especially the louver type) is simulated by scale model test due to the heavy workload of establishing its 3D numerical model (Xiang et al., 2018). For example, Telenta et al. (2014) and He et al. (2016) and studied the aerodynamic performance of an adjustable louver PWB through a wind tunnel test. However, the relative motion between train and PWB is difficult to realize in an indoor test, especially for the study of the transient flow field in the HST running process. The numerical simulation method is used in the study of solid windbreak. Liu et al. (2018), Niu, Zhou, andLiang, (2018) and Niu, Zhou, and Wang (2018), for example, studied the influence of windbreaks on the aerodynamic performance of HSTs running on embankment (or flat ground) based on the shear-stress transport (SST) k-ω turbulence model. Although a few researchers (Bendjebbas et al., 2018;He, Zhou, et al., 2019;Telenta et al., 2014) have used numerical methods to simulate the complex PWBs, they are limited to the 2D characteristics of the flow field. For the traditional vertical PWB (e.g. porous or fencetype) that is widely used in a TBS, porosity and height are the main factors affecting its windproof performance (He, Zhou et al., 2019;Kozmar et al., 2014). The effect of the pore form on the train's aerodynamic characteristics is limited if the porosity and height are the same (Xiang et al., 2013). Therefore, a porous medium model is an economical, efficient and satisfying choice for simulating a PWB approximately aiming at the transient aerodynamic effects of trains in the TBS.
Based on a typical TBTI along a HSR in China, this study completes the following works. Firstly, A CFD dynamic model of air-train-PWB was built based on the porous media theory, and its reliability is verified by model and field tests. Secondly, the transient aerodynamic load coefficients and the change in carriagerunning postures in the critical process are the objects, and the differences in aerodynamic performance when a train runs on this infrastructure under crosswind with or without PWBs are compared. Thirdly, aiming at the process in the TBS (i.e. the process of the HST passing from the tunnel to the bridge or vice versa), the influence mechanism of the existence of a PWB on the transient aerodynamic effect is determined from the viewpoint of the field of flow. Fourthly, the influences of the porosity (α) and height (H) of the PWB on the transient aerodynamic performance of the HST are discussed. The conclusions in this paper can provide a preliminary idea for the optimization design of the PWB on the TBTI.

Turbulence model
The estimated maximum Mach number (Ma) is less than 0.3, and the corresponding Reynolds number (Re) is greater than 1×10 6 in accordance with the background of this study. The air flow involved is incompressible and highly turbulent. The Detached eddy simulation (DES) method is the current mainstream for solving the flow field with higher Re. (Chen et al., 2016;Guo et al., 2020;Li et al., 2020). Based on the SST κ-ω turbulent model, delayed DES method (DDES) was applied in the present paper because it can further prevent the separation of premature flow based on DES (Niu, Zhou, & Wang, 2018). The SST k-ω turbulence model (Niu, Zhou, & Liang, 2018;Ramezanizadeh et al., 2019) was used to simulate the region near the train surface, as shown below: where ρ is the density of the air flow; u represents the velocity of the flow; Ω is the vorticity; y represents the distance from the wall; ν t represents the eddy viscosity; μ t represents the viscosity of turbulence; k represents the turbulence kinetic energy; δ is the Kronecker delta; and F 2 are the blending functions; the subscripts i and j represent the directions; a 1 , σ k , σ ω , β, β * , ω and γ are the empirical parameters.

Porous media model
This study only focuses on the flow field characteristics of the leeward side after the air flows through the PWB. The flow state of the airflow inside the PWB can be ignored. Thus, the porous medium model is used to simulate the PWB. The specific implementation method is typically used to add a source term representing the momentum consumption to the fluid momentum equation (Rosenfeld et al., 2010) as follows: where u represents the velocity vector of the air; x represents the scale vector; the subscript i, j = 1, 2, 3 represent three directions; p represents the aerodynamic pressure; v represents the kinematic viscosity of the air; v represents the density of the air; and S i represents the additional source terms. The additional source terms can be written as follows: where μ represents the dynamic viscosity of the air; k ij represents the seepage coefficient; D ij represents the viscous resistance coefficient; and C ij represents the inertial resistance coefficient. The additional source terms consist of viscous and inertial loss terms. For the perforated plate, when the incoming flow from a single direction is vertical through it, the internal air cannot flow along the plane direction. In other words, the flow velocities in the two directions perpendicular to the incoming flow direction in Equation (11) are zero. Therefore, on the premise that the incoming flow direction is fixed, this paper only simplifies the momentum additional source terms in the incoming flow direction. Furthermore, due to the very large seepage coefficient in the thickness direction (estimated to be about 10 7 -10 8 m/s) in the perforated plate, the viscous resistance coefficient is almost zero, and only the inertial loss term is retained. Equation (11) can be rewritten as follows: where the inertial resistance coefficient C 2 in the incoming flow direction is closely related to the α of the PWB, which can be calculated in accordance with the test method in Figure 2. The formula is as follows: Various researchers have presented different inertial resistance coefficient models through experiments. Three models (Yeh et al., 2010), i.e. Reynolds, Hoerner and Bailey, are commonly used and are respectively represented by the following Equations (14)-(16). According to Deng et al. (2021), the Reynolds model is applied in this paper to simulate porous media.

Dimensionless aerodynamic forces and moments
A scheme for calculating aerodynamic forces and moments has been proposed and verified in . The corresponding dimensionless calculation formula is shown below. The definition of each symbol is given in Deng et al. (2021).

Geometry and boundary conditions
The CRH3 train commonly used in China's HSRs is adopted as the train model in the present study. The geometric model of the real HST is simplified to a certain  from Tunnel 1 inlet. The train running speed (V t ) is set to 250 km/h. The atmospheric field at both ends of Tunnel 1 is a semi-infinite space simulated by a semicylinder. The outside of Tunnel 1 inlet is flat ground, and the corresponding atmospheric field has a diameter of approximately 38 m and a length of 200 m. No crosswind occurs, and pressure-outlet boundary conditions are adopted. The atmospheric field in the BS is approximately 240 in diameter, and pressure-far-field boundary conditions are adopted. The crosswind velocity relative to the ground (V w ) is set to 25 m/s and is perpendicular to the bridge. The pressure-outlet boundary condition is also used at Tunnel 2 outlet. Nonslip wall boundary conditions are applied to the surface of the train and the bridge, the wall of tunnels and the ground.

Mesh strategy and solution scheme
The mesh model is shown in Figure 5. In the present paper, the porous medium zone (corresponding to PWB) is added on the basis of mesh model in . An 8-layers prism grid is generated on the PWB surface (Mou et al., 2017). The y + value is about 10. The model has approximately 32 million grid cells. Based on the ANSYS FLUENT, the discretised equations are solved by the semi-implicit approach (Yang et al., 2018). The size of time-step for calculation is fixed at 1×10 −4 s.

Verification of partition scheme independence
The purpose of this section is to choose a reasonable aerodynamic coefficient calculation scheme that can also balance the efficiency and accuracy of the calculation. Among them, the number of longitudinal sections is fixed at 20, and the number of circumferential faces is increased from 6 to 48. The corresponding results have been given in . The results show that the scheme with 24 circumferential calculation faces is appropriate.

Analysis of mesh sensitivity
In this section, the calculation results of 3 models with different mesh element numbers (16, 32 and 48 millions) are compared. The 3 models were established by reducing the longitudinal size of the grids, and other conditions (e.g. the height of the first boundary layer near the train) remained the same. Other parameters and processes are consistent with .  shows the comparison results. The results show that the quantity of mesh cells is reasonable at 32 million. Figure 7 shows the time-histories of the aerodynamic coefficients when a HST runs on the TBTI with or without PWB. The H and α of the PWB are 3.0 m and 30%, respectively. In the figure, 'OUT' means the time period when the HST leaves Tunnel 1 (t = 4.02-5.12 s); 'IN' means the time period when the HST enters Tunnel 2 (t = 6.33-7.43 s); the solid blue line indicates the case without PWB; and the solid red line indicates the case with PWB. Deng et al. (2019) showed that an obvious correlation exists between the fluctuation amplitude of the aerodynamic coefficient (C) and running safety. Table 1 shows the comparison of the peak C of three carriages in the two processes, with or without PWB. The schematic of the change behavior of the carriage's running posture in the 'OUT' and 'IN' processes is also given in Figure 7 to illustrate the fluctuation amplitude of aerodynamic coefficient vividly. Figure 7(a-e) shows the lateral movement, vertical movement, overturning movement on the cross-section, yawing movement on the horizontal plane, and the nodding movement on the verticalsection, respectively. Among them, Steps 1-4 are in strict chronological order, respectively. The distance between steps can qualitatively reflect the fluctuation amplitude of the corresponding aerodynamic load.

Aerodynamic coefficients
All the aerodynamic coefficients exhibit striking 'pulse' behavior in the 'OUT' and 'IN' processes under the condition without PWB. This phenomenon is similar to those reported in Yang et al. (2019), , Yang, Deng, Zhu, Lei, et al. (2020). The three carriages also show complex posture change behavior, which is composed of lateral movement, jump, overturn, deflection and nod, in the 'OUT' and 'IN' processes. The running safety and ride comfort in the 'OUT' and 'IN' processes are considerably poorer than those in other periods, when the HST driving on the TBTI in the absence of a PWB on the bridge.
The C in the 'OUT' and 'IN' processes decrease considerably under the condition with PWB. The head carriage is an example; the peak fluctuation amplitudes of C z , C y , C mx , C my and C mz decrease by 86%, 82%, 80%, 59% and 36%, respectively, in the 'OUT' and by 87%, 83%, 83%, 61% and 61%, respectively, in the 'IN'. The amplitude and step number of the running posture change behavior of each carriage are consequently reduced considerably. For example, for the lateral movement, the head carriage changes from the original 'right to left' behavior to single 'left' behavior in the 'IN' process ( Figure 7(a 1 )). For the jump behavior, the middle carriage changes from the original 'up to down' behavior to single 'down' behavior in the 'IN' process ( Figure 7(b 2 )). For the deflection behavior, the front of the head carriage changes from the original 'right to left' behavior to single 'left' behavior in the 'OUT' process ( Figure 7(d 1 )). For the nod behavior, the rear of the tail carriage changes from the original 'up to down to up' behavior to a single 'down' behavior in the 'OUT' process ( Figure 7(e 3 )).
The reduction rate of the side force fluctuation amplitude of each carriage is more prominent compared with the other four aerodynamic coefficients under the condition with PWB, whether in the 'OUT' process or the 'IN' process. For example, the respective reduction rates of the head, middle and tail carriages are 86%, 95% and 87%in the 'OUT' process and 87%, 95% and 89% in the 'IN' process. The reduction rate of pitching moment fluctuation amplitude of the three carriages is relatively small. The change in aerodynamic side force of the HST when running in the TBS is most sensitive to the existence of a PWB, whereas the sensitivity of pitching moment is relatively weak.
The C and the corresponding step number of the running posture change behavior of each carriage in the 'IN' process are greater than those in the 'OUT' process under the condition without PWB. For example, for the lateral movement, the head carriage presents 'right to left' behavior in the 'IN' process but only single 'right' behavior in the 'OUT' process ( Figure 7(a 1 )). For the deflection behavior, the front of the head carriage presents 'right to left to right' behavior in the 'IN' process but only 'right to left' behavior in the 'OUT' process ( Figure 7(d 1 )). The ratio IN/OUT is applied to reflect the difference in the value of C in the 'OUT' and 'IN' processes. The IN/OUT values are greater than 1 under the condition without PWB. It's worth noting that the IN/OUT value is 1 for the case with PWB.

Flow field during the 'OUT' process
The influence mechanism of the existence of PWB on the train's aerodynamic sudden change effect is revealed from the perspective of flow field, aiming at the 'OUT' process, in this section. The horizontal plane Y = 1.5 m is an example. Figure 8 shows the comparison of the flow field in the 'OUT' process with or without PWB. The H and α of the PWB are 3.0 m and 30%, respectively. Figure  9 shows the streamline and pressure on several typical sections at t = 4.58 s for additional flow field information. The legend of pressure nephogram in Figure 9(b) is consistent with that in Figure 8, Figure 9(c) is the pressure distribution on the contour line of Y = 1.5 m on the train surface. The following findings are obtained from Figures 8 and 9.
For the part of the train body within tunnel, the surrounding streamline and the pressure distribution on the train surface show similar characteristics, regardless of with or without the PWB. The airflow direction on two sides is opposite the train running direction and converges at the tail carriage tip. The pressures on two sides are roughly the same (negative), and the pressure value is basically the same. t = 4.58 s is used as an example. The pressure distribution on the train surface (S1 and S2 in Figure 9(b)) within the tunnel is even, and the pressure coefficient values are maintained between −0.1 and −0.2. The PWB on the bridge has a minimal effect on the flow field and pressure within Tunnel 1. For the part of the train body on the bridge, a large longitudinal horn-shaped vortex is generated on the leeward side by the combined action of the side flow and the train slip-stream under the condition without PWB (Figure 8(a 1 -g 1 )). The vortex zone corresponds to the negative pressure zone. t = 4.58 s is taken again as an example; the maximum negative pressure coefficient flat train surface is about −0.2 (Leeward side, Figure 9(c)). The positive pressure is uniformly distributed along the longitudinal direction on the windward side of the flat train surface under the front extrusion of the crosswind, and the corresponding value is approximately 0.1 (e.g. S4 and S5 in Figure 9(b)). This condition is the main reason for the considerable lateral movement and deflection behavior of the middle carriage in the 'OUT' process ( Figure 7(a 2 and d 2 )). A towering negative pressure zone exists at the junction of the windward surface and roof on the flat train body due to the rapid increase in the crosswind flow velocity when it bypasses the windward surface (S5 in Figure 9(b), the maximum negative pressure coefficient can reach approximately −0.5). It is also the main reason for the obvious jump, overturn and nod behavior of the middle carriage in the 'OUT' process ( Figure  7(b 2 , c 2 and e 2 )). The difference of the pressure between the leeward and windward sides is greatest at the head carriage tip. The peak positive and negative pressure coefficients are 0.4 and −0.7, respectively, as shown in Figure  9(c).
Under the condition with PWB, the area between the PWB and the train body is a negative-pressure zone ( Figure 8(a 2 -g 2 )). With t = 4.58 s as an example, the negative pressure is distributed on the flat train surface under the windproof effect of the PWB, even if some streamlines penetrate the PWBs on both sides and collect at the HST's leeward side to form a large vortex. The corresponding negative pressure coefficient values are maintained between −0.1 and −0.2, which are consistent with the values on the train surface within Tunnel 1 (S1-S5 in Figure 9(b)). The pressure difference at the head carriage tip is also considerably weakened, with the maximum positive and negative pressure coefficients falling to 0.2 and −0.3, respectively (Figure 9(c)). In other words, the difference in the longitudinal distribution of the pressure on the carriage surface is remarkably reduced. Therefore, the aerodynamic coefficient fluctuation amplitudes are greatly reduced in the 'OUT' process. The aerodynamic side force of each carriage is most sensitive to the influence of the existence of PWB, because the PWB weakens the kinetic energy of crosswind flow in the transverse direction. Figure 10 shows the comparison of the flow field in the 'IN' process with or without PWB. The remaining conditions remain the same as in the previous section. For detailed flow field information, Figure 11 shows the streamline and pressure on several typical sections at t = 6.87 s. The legend of pressure nephogram in Figure 11(b) is consistent with that in Figure 10. Figure  11(c) is the pressure distribution on the contour line of Y = 1.5 m on the train surface. The following findings are obtained from Figures 10 and 11.

Flow field during the 'IN' process
The PWB on the bridge has a minimal effect on the streamline and pressure on the train body within Tunnel 2. The streamline at the head carriage tip presents a source flow characteristic, regardless of with or without the PWB. The area near the head carriage tip is a strong positive pressure zone, because it is compressed; the air in front of the head carriage flows forward; the other part of the air flows out at Tunnel 2 inlet along the gap between the carriage and tunnel, forming a jet flow. The direction of the jet flow is approximately parallel to the longitudinal direction of the tunnel before it ejects the tunnel entrance ( Figure 10(a 1 -g 1 )). The pressure in the gap area between the train body and tunnel is evenly distributed along the longitudinal direction, and the pressure values on both sides are basically equal. t = 6.87 s is used as an example. The pressure on the two sides of the HST within Tunnel 2 is symmetrically distributed, with head carriage tip as the center (Figure 11(c)). The positive peak of the pressure coefficient (approximately 0.6) appears at the head carriage tip. The pressure on the flat train surface is evenly distributed, and the pressure coefficient values are kept near 0 (S4 and S5 in Figure 11(b)). For the part on the bridge without PWB, the transverse airflow circumvents the carriage top and creates longitudinal vortexes on the leeward side of the train. It appears as a horn under the combined effect of the train wind (Figure 10(a 1 )). The triangular negative pressure area corresponds to the longitudinal horn-shaped vortex area, and the negative pressure value also changes with the shape of the vortex. Under the suppression of jet flow, the horn-shaped vortex stops at the entrance of Tunnel 2 with the train entering. The direction of the jets near the entrance changed to some extent, and the residual longitudinal vortex attached to the train leeward surface expanded to a certain extent (Figure 10(b 1 -g 1 )). Consequently, the negative pressure acting on the train leeward surface is greater than the corresponding value in the 'OUT' process. Given t = 6.87 s, the negative pressure coefficient at the leeward side of S1 and S2 sections in Figure 11(b) is greater than that of S4 and S5 sections in Figure 9(b). The jet flow on the windward side dissipates at the inlet of Tunnel 2, because it combines with the crosswind to produce vertical vortex (Figure 10(b 1 -g 1 )). Therefore, the jet flow has little effect on the positive pressure on the windward side. The positive pressure coefficient on the flat HST surface outside the tunnel remains at approximately 0.1 (Figure 11(c)). The main reason for the fact that the train's aerodynamic coefficient fluctuation amplitudes in the 'IN' process are greater than those in the 'OUT' process under the condition without PWB may be that the residual longitudinal eddy expands radially under the longitudinal extrusion of the jet flow.
The squirt flow from Tunnel 2 entrance converges at the tail carriage tip under the condition with PWB ( Figure 10(c 2 -g 2 )). The interference of crosswind to the streamline structure between the two PWBs is considerably weakened. With t = 6.87 s as an example, the pressures on the two sides of the HST outside the tunnel remain symmetrical, and the pressure coefficient values on the flat train surface are maintained between 0 and −0.1 (S1-S3 in Figure 11(b)). Therefore, the train's aerodynamic coefficient fluctuation amplitudes are considerably reduced compared with the corresponding values under the condition without PWB in the 'IN' process.

Effect of height
This section discusses the effect of PWB height on the transient aerodynamic performance of the train. Figure 12 shows the variation of the aerodynamic coefficients (solid lines) as the train runs on the TBTI at different PWB heights (H = 2.5, 3.0, 3.5, 4.0 m; α = 30%). The corresponding values are based on the left ordinate.
A train is a vibrational system with multiple degrees of freedom. Transient aerodynamic loads will threaten the safety of the train during operation . The running safety of the HST was evaluated by the change rate of the aerodynamic coefficient ( C' (0.035s) , . The C' (0.035s) variations are presented as the dashed lines in Figure 12. Here 'OUT' and 'IN' are defined as in Figure 9, and 'BR' denotes the period of the HST running only on the bridge. To further reveal the influence law of the PWB height, Figure 13 shows the peak absolute values of C' (0.035s) , denoted as Max | C' (0.035s) |, during the 'OUT', 'BR', and 'IN' processes at different PWB heights. At different PWB heights, the time histories of the aerodynamic coefficients of each carriage were consistent during complete running in Tunnels 1 and 2, demonstrating the reliability of Figure 12. The PWB height affected the aerodynamic coefficient fluctuation law in all three processes. At a given PWB height, the C values were higher in the 'OUT' and 'IN' processes than in the 'BR' process. In the 'BR' process, the C z of the first car monotonously decreased with increasing PWB height ( Figure 12(a 1 )). The yawing and pitching moments of the head and middle carriages were less sensitive to PWB height in the 'BR' process than in the other processes because both indexes mainly reflect the difference in longitudinal pressure distribution on the carriage. In particular, their sensitivities decreased with decreasing longitudinal pressure difference (see the last paragraph in Section 5.2). In contrast, the yawing moment of the tail carriage was influenced by PWB height (Figure 12(d 3 )), possibly because the unsteady wake structure was susceptible to PWB height (Bell et al., 2016).
At the same PWB height, the C' (0.035s) values of each carriage presented towering peaks in the 'OUT' and 'IN' processes but relatively smooth fluctuations in the 'BR' process ( Figure 12). Accordingly, Max | C' (0.035s) | was considerably lower in the 'BR' process than in the 'OUT' and 'IN' processes ( Figure 13). The 'OUT' and 'IN' processes are the controlling links of the PWB design of TBTI.
In all three processes, Max | C' (0.035s) | trended downward with increasing PWB height. The occasional abnormal phenomenon in the middle (Figure 13(a 0 , c 2, and d 2 )) and tail ( Figure 13(b 3 )) carriages during the 'IN' process was possibly induced by the jet flow effect, which increases with PWB height. Max | C' (0.035s) | was less sensitive to PWB height in the 'BR' process than in the 'OUT' and 'IN' processes (as evidenced by the amplitude reduction of Max | C' (0.035s) | when H increased from 2.5-4.0 m). Taking the head carriage as an example; the sensitivities of Max | C z ' (0.035s) | and Max | C my ' (0.035s) | were 3.0 and 2.1 times higher, respectively, in the 'IN' process than in the 'BR' process ( Figure 13(a 1 and d 1 )); similarly, the sensitivities of Max | C y ' (0.035s) | and Max | C mz ' (0.035s) | were 2.0 and 3.8 times higher, respectively, in the 'OUT' process than in the 'BR' process ( Figure  13(b 1 and e 1 )).
Adopting the same design parameters along the fulllength PWB on the TBTI is clearly unreasonable. The PWB parameters in the BS (H = 3.0 m, α = 30%) are assumed to meet the windproof performance demands of that process. To achieve the equivalent windproof performance in the TBS, the PWB must be 4 m high (33% higher than its present height) ( Figure 13(a 1 , a 2 , b 1 , b 3 , c 1 , c 2 , d 3 , e 1 and e 2 )). Taking the head carriage as an example, the Max | C z ' (0.035s) | values at H = 3.0 m were 0.11 and 0.28 in the 'BR' and 'IN' processes, respectively. To reduce Max | C z ' (0.035s) | to the value nearest 0.11 (i.e. 0.14), H of the 'IN' process must be increased to 4 m ( Figure 13(a 1 )). Meanwhile, the Max | C mx ' (0.035s) | values at H = 3.0 m were 0.018 and 0.04 in the 'BR' and 'IN' processes, respectively, so H of the 'IN' process must reach 4 m to reduce Max | C mx ' (0.035s) | to the   (Figure 13(c 1 )). Finally, the Max | C mz ' (0.035s) | values at H = 3.0 m were 0.29 and 0.41 in the 'BR' and 'OUT' processes, respectively. To reduce the Max | C mz ' (0.035s) | to less than 0.29 (i.e. 0.22) in the 'OUT' process, H must again be increased to 4 m ( Figure  13(e 1 )).

Effect of porosity
To investigate the influence law of PWB porosity, Figure  14 shows the variations of the aerodynamic coefficients (solid lines) of the train running on TBT1 and their corresponding change rates (dashed lines) for different PWB porosities (α = 20%, 30%, 40%; H = 3.0 m), and Figure  15 shows the peak absolute C' (0.035s) values of each carriage in the 'OUT', 'BR', and 'IN' processes for each porosity. The findings obtained from these figures are described below.
The α of the PWB affected the aerodynamic coefficient fluctuation law in all three processes. In the 'BR' process, C z and C y and C mx monotonously increased with PWB porosity (Figure 14(a-c)). The yawing and pitching moments were minimally sensitive to PWB porosity in the three processes ( Figure 14(d and e)).

Optimization of PWB
Based on the analysis of the previous two subsections, the PWB on TBTI was preliminarily optimized (see  In general, the porosity and height of the PWB in the TBS must be reduced and increased by more than 33%, respectively.

Conclusions
This study compares the aerodynamic performance when a train runs on TBTI under crosswind with or without PWBs by building a CFD dynamic model of air-train-PWB. Aiming at the process in the TBS, the influence mechanism of the existence of PWB on the transient aerodynamic effect is revealed from the view point of the flow field. The influences of the height and porosity of the PWB on the transient aerodynamic performance of the HST are discussed. The main conclusions are as follows: (1) All the aerodynamic coefficients exhibit striking 'pulse' behavior in the process in the TBS under the condition without PWB. The corresponding pulse amplitudes will be reduced by 36-95%, once a PWB is installed. (2) The pulse amplitudes of the train's aerodynamic loads in the process from bridge to tunnel are 1.03-1.89 times compared with those in the process from tunnel to bridge under the condition without PWB, because the jet flow interferes with the residual longitudinal eddy. The pulse amplitudes in the two processes will be equal when the PWB is installed. (3) The aerodynamic side force of each carriage is most sensitive to the influence of the existence of PWB, because the PWB weakens the kinetic energy of crosswind flow in the transverse direction. (4) The TBS is the controlling link of PWB design for TBTI. The sensitivity of the peak values of the aerodynamic coefficient change rates to the influence of PWB height in the TBS are 2.0-3.8 times compared with those in the bridge section. (5) Adopting the same design parameters along the fulllength PWB on the TBTI is unreasonable, e.g. the porosity and the height of the PWB in the TBS need to be reduced and increased by more than 33%, respectively, to achieve equivalent windproof performance.
The results of this study are based on a specific case, and a set of universal design parameters of PWBs in the TBS cannot be obtained yet. Although a preliminary idea for the optimal design is proposed, numerous model and field tests are required to verify its validity. Furthermore, the parameters such as length (L in Figure 16) and the transition form from the bridge-tunnel section to the bridge section also need to be studied and determined. Next step, the authors will do further researches for this issue mentioned above.