Numerical Comparison in Aerodynamic Drag and Noise of High-Speed Pantographs with or without Platform Sinking

Abstract

Flat roofs and platform sinking are two common installation configurations for high-speed pantographs. The cavity formed by the platform sinking is a potential source of aerodynamic drag and noise. In this paper, the shape of the rectangular cavity is optimized, and the aerodynamic performance of the high-speed pantograph with or without platform sinking is compared and discussed based on the optimized cavity results. The flow field and sound propagation are predicted by the improved delayed detached eddy simulation (IDDES) method and the FW-H equation. The results show that the rectangular cavity produces the largest aerodynamic drag and radiation noise. The upstream, downstream, and bottom surfaces of the cavity can be optimized by rounded and sloped edges to reduce aerodynamic drag and noise. The unstable shear flow and recirculation zone formed by flow separation and reattachment can be reduced by modifying the upstream and downstream surfaces of the cavity. In addition, the vortex in front of the downstream surface of the cavity can be reduced or even eliminated by modifying the bottom surface. When the upstream and downstream surfaces of the cavity are rounded and the bottom surface is sloped (R/H = 0.8), the aerodynamic performance of the cavity is better. Compared with the pantograph installed on the flat roof, the aerodynamic drag and noise of the pantograph with platform sinking are significantly reduced due to the shielding of the lower structure by the cavity, and the total drag and noise are reduced by 5.22% and 1.45 dBA, respectively.

1. Introduction

The increase in train speed leads to a sharp increase in the contribution of aerodynamic noise to the total noise and causes noise pollution in the surrounding environment [1,2]. High-speed trains are composed of components with different noise radiation characteristics. Reducing the aerodynamic noise generated by each component has become the main research content [3,4]. The pantograph is also considered to be one of the main contributors to train noise. However, the special installation position of the pantograph limits the effect of some conventional noise shielding methods.

The research on pantograph aerodynamic noise focuses on sound source identification and noise control. Tan et al. [5] investigated the composition of pantograph noise and pointed out that up to 90% of the radiated noise comes from the base, balance arm, insulators, and upper and lower arms. The aerodynamic noise generated by each component of the pantograph can be used to predict the far-field noise of the whole pantograph [6], and the prediction results are in good agreement with the wind tunnel test results. Liu et al. [7] considered the characteristics of the pantograph composed of slender rods and predicted the radiation noise of the train pantograph through the aerodynamic noise results of a single cylindrical rod. The method is verified by numerical simulation and line experiment. Li et al. [8] analyzed and discussed the sound pressure effect of the aerodynamic noise generated by the pantograph on the train surface through numerical simulation. The noise generated by the pantograph installed on the flat roof will significantly affect the train body surface near the pantograph. The farther away from the pantograph, the smaller the sound pressure level. In addition, the author also points out that flow can facilitate sound propagation upstream. Wang et al. [9] carried out bionic optimization of the pantograph strips. By reducing the flow separation and recirculation zone on the surface of the strips, the surface fluctuation pressure is reduced, resulting in drag and noise reduction of the pantograph.

Pantograph installation platform sinking can significantly reduce the aerodynamic drag of the widely used pantograph. However, studies have shown that the noise level of the cavity formed by the platform sinking is similar to that of the pantograph [10]. Noger [11] evaluated the effect of pantograph recess on the flow field and noise through wind tunnel tests. It is pointed out that the pantograph recess is similar to the cavity, and the downstream area of the cavity is the main source of noise. The interaction between the cavity flow and the pantograph structure will increase the upstream turbulence intensity and decrease the downstream turbulence intensity. Kim et al. [12] numerically simulated the aerodynamic noise of a pantograph with and without a cavity. The airflow separates from the leading edge of the cavity and interacts with the pantograph to generate a large fluctuating pressure on the structural surface. The flow field velocity distribution around the pantograph with a cavity is smaller and the radiation noise is lower. Plumble et al. [13] studied the flow-induced vibration of an open cavity by wind tunnel test. The turbulent shear layer provides a noise source for the self-excited oscillation of the cavity. The excitation source is broadband noise, and some frequency components are amplified into tonal noise under certain conditions.

Based on previous studies, the noise reduction of pantograph recess has not been considered in depth. Therefore, this paper optimizes the shape of the installation platform to achieve aerodynamic drag and noise reduction. The flow separation of unstable airflow generated on the upstream and downstream surfaces of the cavity is the main source of noise. Therefore, the upstream, downstream, and bottom surfaces of the cavity are rounded and chamfered to systematically study the aerodynamic performance of different shape cavities. In addition, the aerodynamic drag and noise differences between the pantograph installed on the flat roof and the platform sinking are compared and discussed.

2. Numerical Method

A method combining Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) is widely used in the aerodynamic calculation of high-speed trains [14,15]. It can obtain high-precision flow field results and meet the computational efficiency requirements, which is called the detached eddy simulation (DES) method. It can consider some basic flow fields details, such as flow separation and vortex shedding. In practical applications, the improved delayed detached eddy simulation (IDDES) method has become the preferred numerical simulation method because it avoids the problems of logarithmic layer mismatch and grid-induced separation in the standard DES method [16]. The Ffowcs Williams Hawkings (FW-H) equation can be used to predict sound propagation. Some detailed information can be obtained in the literature [17,18].

In this paper, the IDDES hybrid model and FW-H equation are used to solve the unsteady flow field and sound field step by step. The convection term, momentum term, and time term of the governing equation are solved by the second-order discrete scheme. The turbulence effect can be defined by setting turbulence intensity and characteristic scale at the inlet and outlet boundaries of the computational domain. The simulation time steps of the unsteady flow field and the sound source are both 5 × 10⁻⁵ s, with 5000 and 3000 iterations, respectively, and the total simulation time is 0.4 s.

3. Aerodynamic Drag and Noise of Cavities with Different Shapes

In the following, the effects of different modification methods of the cavity edges on its aerodynamic drag and noise are studied.

3.1. Numerical Information

As shown in Figure 1, the recess formed by the sinking of the installation platform of the pantograph can be represented by a simplified rectangular cavity. The cavity length L = 2.8 m, width W = 2.2 m, and depth D = 0.38 m. The shape modification of the cavity edge adopts sloped and rounded. The sloping angle θ is defined in the range of 0~75°, and the rounded edge size R/D is limited to 0~1.

The computational domain for numerical simulation is similar to a hexahedral box, as shown in Figure 2. At the upstream boundary of 35D from the cavity, the far-field boundary condition with a Mach number of 0.327 is applied. The downstream boundary of 50D from the cavity is set as the pressure outlet. The symmetric boundary and the slip wall boundary are defined at the top and ground surfaces of the computational domain. The boundary conditions of the two sides are periodic boundaries, and the properties of the cavity surface are non-slip walls.

Different mesh sizes are set to discretize the computational domain around the cavity. A total of three sets of grids are used for numerical calculation, and the results are shown in

Table 1. Grid independence test of cavity.

Mesh	Base Size/m	Grid Number/Million	Cd	Difference
Fine	0.020	20.21	0.223	--
Medium	0.050	16.49	0.222	−0.45%
Coarse	0.080	13.68	0.219	1.35%

. In predicting the aerodynamic drag coefficient (C_d) of the cavity, the three sets of grids give approximate results. However, the difference between fine grids and medium grids is less than 1%. Considering the calculation accuracy and efficiency [19,20], the number of medium grids has verified the independence of grids. The setting of the grid discrete size of the subsequent model can refer to the medium grid.

The mesh results are shown in Figure 3. Based on the minimum requirements of the selected turbulence model for the grid [21,22], a boundary layer grid is generated on the surface of the cavity, and the dimensionless value y+ of the wall distance is adjusted to be less than 1. In addition, the meshes around the cavity are encrypted to improve the mesh quality. For the flow simulation of all modified cavities, the same meshing strategy is used.

3.2. Flow Field

Figure 4 and Figure 5 show the streamlined distribution around the modified cavity. It can be seen that a large recirculation zone is formed inside the rectangular cavity, which is caused by the backflow generated by the airflow separating from the cavity edge and then hitting the downstream surface and flowing to the bottom. When the cavity edges are sloped or rounded, the position where the upstream airflow produces flow separation changes, and the speed of the high-speed airflow decreases, which leads to a decrease in the recirculation zone. With the increase of θ, the flow separation weakens or even disappears, which is beneficial to the drag reduction of the cavity itself, but the shielding effect on the object located in the center of the cavity decreases, which is not conducive to the overall drag reduction. With the increase of R/D, the position point of the airflow impacting the bottom of the cavity moves upstream. When R/D is about 0.8, the recirculation zone is the smallest. However, when the round continues to increase, another recirculation zone will appear. Flow separation and reattachment also occur at the rear edge of the cavity, resulting in a recirculation zone, as shown in Figure 6 and Figure 7. The recirculation zone at the trailing edge of the cavity can be weakened or eliminated by sloped or rounded edges, which also avoids potential aerodynamic noise sources.

Figure 8 and Figure 9 show the turbulent kinetic energy (k) distribution around the modified cavity. Flow separation occurs when the incoming flow passes through the upstream surface of the cavity, resulting in the formation of unstable shear layer airflow. The highly unstable airflow will act on the bottom of the cavity and the downstream surface, thereby forming a highly unstable fluid flow region. It is worth noting that the aerodynamic radiation noise comes from these key locations in the highly turbulent kinetic energy region. Optimizing the shape of the cavity edge to be sloped or rounded can significantly attenuate the turbulence intensity around the cavity. With the increase of sloping angle (θ) and rounded (R/D), the high turbulent kinetic energy region formed by the collision of the airflow upstream of the cavity with the downstream surface can be reduced.

3.3. Aerodynamic Drag and Noise

Figure 10 shows the results of the aerodynamic drag coefficient (C_d) of the modified cavity, and the corresponding values are listed in

Table 2. The aerodynamic drag of the optimized cavity.

θ (°)	Cd	Difference (%)	R/D	Cd	Difference (%)
0	0.222	—	0	0.222	—
15	0.234	5.266	0.2	0.179	−19.482
30	0.238	7.295	0.4	0.157	−29.347
45	0.217	−2.367	0.6	0.152	−31.445
60	0.171	−22.939	0.8	0.144	−35.171
75	0.124	−44.334	1.0	0.149	−32.840

. The windward cross-sectional area of the cavity is selected as the reference area. With the increase of the sloping angle, the C_d of the cavity increases first and then decreases. When the sloping angle is greater than 30°, the cavity achieves drag reduction. When the sloping angle is 75°, the aerodynamic drag of the cavity is reduced by 44.3%. For all cavities with rounded edges, the aerodynamic drag of the modified cavity is smaller than that of the rectangular cavity. The aerodynamic drag of the modified cavity corresponding to R/D = 0.8 is reduced by 35.18%. The roundness of the cavity with rounded edges is not the greater, the smaller the resistance. When the roundness of the cavity edges is large enough (R/D > 0.8), new recirculation zones form within the cavity, creating additional drag sources and leading to further increases in aerodynamic drag. Therefore, in the rounded edge cases, an appropriate roundness is necessary to achieve lower aerodynamic drag of the cavity.

The flow recirculation zone formed by separating the airflow from the leading or trailing edge of the cavity is one of the main sources of aerodynamic drag. Another main source of aerodynamic drag is the high positive pressure region formed by the impact of high-speed airflow on the downstream surface of the cavity. When the sloping angle of the cavity edge is small, the recirculation region in the cavity changes little, but the high positive pressure region formed on the downstream surface increases, which will lead to the increase of the aerodynamic drag of the cavity. As the sloping angle of the cavity edge increases, the recirculation region significantly decreases, and the decrease in the velocity of shearing airflow also reduces the impact of the airflow on the downstream surface of the cavity, thereby reducing the positive pressure on the trailing edge of the cavity, resulting in a reduction in aerodynamic drag. For all cavities with rounded edges, similar physical mechanisms are involved. The difference is that the pressure change on the downstream surface of the cavity with a small, rounded edge is also small. However, the rounded edges can significantly improve the airflow separation at the leading edge of the cavity, reducing the separation zone and causing a decrease in aerodynamic drag. Overall, the aerodynamic drag is smaller when the cavity has a larger slopped edge or a rounded edge with appropriate roundness. However, the cavity with a too-large, sloped edge will expose the bottom structure of the pantograph to high-speed airflow, which is not conducive to the aerodynamic drag reduction of the pantograph. Therefore, the rounded edge (R/D = 0.8) can be selected for cavity optimization.

An acoustic receiver 25 m away from the cavity and located on the side is used to evaluate the cavity noise. The results of the overall sound pressure level (OASPL) are listed in

Table 3. OASPL at the side receiver positions.

θ (°)	OASPL	Difference (dB)	R/D	OASPL	Difference (dB)
0	81.25	—	0	81.25	—
15	80.13	−1.12	0.2	76.43	−4.82
30	78.78	−2.47	0.4	74.28	−6.97
45	75.83	−5.42	0.6	72.23	−9.02
60	74.35	−6.9	0.8	71.12	−10.13
75	73.21	−8.04	1.0	71.71	−9.54

. Compared with the unmodified rectangular cavity, the two modification methods of the cavity achieve different degrees of noise reduction. The noise is reduced by 8.04 dB when the sloping angle of the cavity is 75°. Meanwhile, for the cavity with R/D = 0.8 rounded edges, the noise is reduced by 10.13 dB.

3.4. Results of Optimized Cavities

According to the previous results, the cavity with a rounded edge has better aerodynamic performance than the sloped edge. Therefore, the cavity edges are optimized by rounded. In addition, the bottom surface of the cavity can also be further optimized with rounded and sloped edges. The geometric model is shown in Figure 11, and R/H is selected as 1/4, 2/3, 1/1, 3/2, and 4/1.

The results of the C_d of the cavity are shown in

Table 4. The aerodynamic drag coefficient of the cavity with different bottom surfaces.

R/H	Unmodified	Rounded Edge	Difference (%)	Sloped Edge	Difference (%)
1/4	0.179	0.169	−5.29	0.168	−6.33
2/3	0.157	0.155	−1.37	0.153	−2.41
1/1	0.154	0.152	−1.16	0.151	−2.13
3/2	0.152	0.151	−1.02	0.150	−1.79
4/1	0.144	0.143	−0.69	0.142	−1.39

. At the same R/H, the C_d of the cavity can be further reduced by optimizing the bottom surface of the cavity to rounded or sloped edges, and the effect of the sloped edges is better. When the roundness of the cavity edge is small (R/H = 0.25), the rounded and sloped bottom surfaces can reduce drag by 5.29% and 6.33%, respectively. With the increase of R/H, the aerodynamic drag coefficient of the cavity gradually decreases, and the influence of the modification of the bottom surface on the aerodynamic drag coefficient of the cavity also decreases.

Figure 12 shows the streamline distribution around the cavity with R/H = 4. The optimization of the bottom surface of the cavity to sloped or rounded edges can suppress the generation of vortices downstream of the cavity to a certain extent, thereby achieving drag reduction. Both optimization methods do not significantly reduce the recirculation zone behind the upstream surface of the cavity, so the drag reduction effect is limited. Compared with the original rectangular cavity, the aerodynamic drag of the final optimized cavity model is reduced by 36.04%.

4. Results of Pantographs with or without Platform Sinking

Finally, the aerodynamic performance of the pantograph with or without platform sinking is compared and discussed.

4.1. Numerical Geometry and Information of Pantograph

The pantograph model used for simulation calculation is shown in Figure 13. The pantograph mainly comprises four parts: panhead, frame system, base, and insulators. The top of the train is the actual installation position of the pantograph. As shown in Figure 14, the train body is approximated to shorten the calculation time. The three-dimensional size of the pantograph is L = 2.20 m, W = 1.95 m, H = 2.12 m. The size of the computational domain is 40 L × 16 W × 8 H. The bottom boundary condition of the computational domain is a slip wall, while the surface of the pantograph and the train body is a non-slip wall. At the top and both sides of the boundary, symmetry boundaries are used. The inlet and outlet boundary settings of the computational domain are consistent with Section 3.1.

Two refinement boxes are used around the pantograph to generate a higher-resolution mesh. A total of 18 layers of boundary layer meshes are applied around the pantograph surface. The distance from the first layer grid to the wall and the grid growth rate largely determine the quality of the boundary layer grid. The initial grid height of 0.005 mm and the growth rate of 1.1 are set to make the dimensionless y+ value of the wall distance less than 1 to meet the needs of the turbulence model. The mesh results are shown in Figure 15.

4.2. Aerodynamic Results

Figure 16 shows the flow field around the pantograph with or without the platform sinking. The difference in pressure between the windward surface and the leeward surface of the pantograph causes aerodynamic drag. The platform’s sinking causes a significant change in the bottom flow field of the pantograph. Compared with the installation platform without sinking, the positive pressure amplitude of the windward surface of the base and insulator is significantly reduced. In addition, the downstream surface of the cavity is impacted by high-speed airflow to form local high pressure, which is one of the main sources of additional cavity resistance. The lower structure of the pantograph is shielded by the upstream surface of the cavity, and the strength of the airflow acting on the structure will be weakened, which reduces the aerodynamic drag. The flow of the airflow inside the optimized cavity is smooth, and there is no obvious large-scale vortex and recirculation zone. Compared with the improvement of the aerodynamic performance of the pantograph, the cavity flow-induced effect will become less important.

Figure 17 shows the distribution of turbulent kinetic energy around the pantograph with and without the platform sinking. Turbulent kinetic energy can effectively evaluate the intensity of highly unstable airflow around the pantograph, which is related to the generation of aerodynamic noise in the pantograph area. For the pantograph without platform sinking, the area with larger turbulent kinetic energy is concentrated around the bottom structure of the pantograph. After the platform sinks, the turbulent kinetic energy in the cavity decreases. The trailing edge of the optimized cavity reduces the flow separation. It improves the stability of the airflow, resulting in a decrease in the downstream high turbulent kinetic energy region, which indicates that the aerodynamic performance of the optimized cavity is better.

The far-field receiver for evaluating aerodynamic radiated noise is 25 m away from the pantograph. As shown in Figure 18, a total of 19 acoustic receivers are arranged at an interval of 5 m from the ground 3.5 m. Figure 19 shows the far-field noise of the pantograph. Compared with the pantograph sinking without the platform, the pantograph cavity can significantly reduce the radiation noise of the pantograph. However, this does not change the sound propagation characteristics of the pantograph in the far field. The maximum reduction of the acoustic receiver is 1.99 dBA, and the average sound pressure level of all acoustic receivers is reduced by 1.31 dBA.

The aerodynamic and acoustic results of the high-speed pantograph with or without platform sinking are shown in

Table 5. Comparison of Aerodynamic Drag and Noise.

Parts	Aerodynamic Drag (N)		Far-Field Noise (dBA)
	Original	Optimized	Original	Optimized
Cavity	—	754.2	—	79.77
Panhead	911.2	916.9	86.48	84.74
Upper frame system	356.6	347.1	83.65	82.73
Lower frame system	253.7	204.8	79.24	77.66
Base	1144.4	634.2	84.97	82.15
Insulators	546.6	187.5	78.22	71.14
Pantograph	3212.5	2290.5	90.57	88.58
Total (Pantograph + cavity)	3212.5	3044.7	90.57	89.11

. The main sources of aerodynamic drag and noise of the pantograph without platform sinking are the panhead, base, and insulators. The aerodynamic drag of the base and insulators accounts for more than 50%, and the noise radiation energy accounts for 33.4%. After the installation platform sinks, the aerodynamic drag of the base and insulators decreases by 44.6% and 65.7%, respectively, the aerodynamic drag of the pantograph decreases by 28.7%, and the total drag (pantograph and cavity) decreases by 5.22%. In addition, the noise generated by each component of the pantograph is reduced. The noise of the pantograph at the y₈ receiver is reduced by 1.99 dBA, and the total noise is reduced by 1.45 dBA.

5. Conclusions

In this paper, the influence of platform sinking shape on aerodynamic drag and noise of high-speed pantograph is studied by numerical simulation. The flow and acoustic fields are predicted by the IDDES method and the FW-H equation. The difference of aerodynamic performance of pantograph with or without platform sinking is compared and discussed. The conclusions are as follows:

(1) The highly unstable shear layer airflow is separated from the upstream surface of the cavity and hits the bottom and downstream surface of the cavity, forming a recirculation zone. The key position of aerodynamic noise generation is downstream of the cavity with a highly turbulent kinetic energy region. In addition, the cavity has a larger downstream windward surface, which will form a local high-pressure zone and generate additional cavity resistance. The flow separation of the cavity with rounded or sloped edges is weakened and the recirculation area is reduced.

(2) With the increase of the sloping angle of the cavity edges, the aerodynamic drag of the cavity gradually decreases. Too-large, sloping angles will significantly reduce the shielding effect of the cavity, which is not conducive to the drag reduction of the whole system. With the increase of the roundness of the cavity edges, the aerodynamic drag of the cavity reaches the minimum when R/D is about 0.8. Continuing to increase the roundness will lead to a recirculation zone. Compared with the unmodified rectangular cavity, the sloped and rounded cavities reduce the noise by 8.04 dB and 10.13 dB, respectively.

(3) The bottom structure of the pantograph without platform sinking is exposed to high-speed airflow, resulting in excessive aerodynamic drag. However, the cavity formed by the sinking of the installation platform reduces the velocity of the airflow, weakens the airflow impact on the bottom structure of the pantograph, and reduces the turbulent energy around the pantograph. The optimized cavity structure reduces the aerodynamic drag and noise of the pantograph by 28.7% and 1.99 dBA, respectively. However, the cavity must also be considered as an additional aerodynamic drag and noise source. Overall, the total drag and radiated noise of the entire pantograph system are reduced by 5.22% and 1.45 dBA, respectively.