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Rail. Eng. Science (2022) 30(1):117–128 https://doi.org/10.1007/s40534-021-00258-7 Numerical simulation and optimization of aerodynamic uplift force of a high-speed pantograph 1 1 1 1 1 • • • • Zhiyuan Dai Tian Li Ning Zhou Jiye Zhang Weihua Zhang Received: 29 April 2021 / Revised: 21 August 2021 / Accepted: 23 August 2021 / Published online: 6 October 2021 The Author(s) 2021 Abstract Aiming at the problem that aerodynamic uplift respectively, which are almost equal and both meet the forces of the pantograph running in the knuckle-down- requirements of the standard EN50367:2012. stream and knuckle-upstream conditions are inconsistent, and their magnitudes do not satisfy the corresponding Keywords High-speed pantograph Aerodynamic uplift standard, the aerodynamic uplift forces of pantographs with force Baffle Numerical simulation Multibody baffles are numerically investigated, and an optimization simulation method to determine the baffle angle is proposed. First, the error between the aerodynamic resistances of the pan- tograph obtained by numerical simulation and wind tunnel test is less than 5%, which indicates the accuracy of the numerical simulation method. Second, the original pan- 1 Introduction tograph and pantographs equipped with three different baffles are numerically simulated to obtain the aerody- The static and aerodynamic uplift forces are important namic forces and moments of the pantograph components. components of the pantograph–catenary contact force of a Three different angles for the baffles are -17,0 and 17. high-speed train, in addition to dynamic components Then the multibody simulation is used to calculate the caused by vibration [1, 2]. The static uplift force is pro- aerodynamic uplift force of the pantograph, and the opti- vided by the airbag, and the aerodynamic uplift force is the mal range for the baffle angle is determined. Results show force between the strip and the catenary under the action of that the lift force of the baffle increases with the increment aerodynamic forces and moments of the pantograph com- of the angle in the knuckle-downstream condition, whereas ponents. The pantograph–catenary contact force is an the lift force of the baffle decreases with the increment of important factor that affects the quality of current collec- the angle in the knuckle-upstream condition. According to tion. If the contact force is too large, it will increase the the results of the aerodynamic uplift force, the optimal wear of the strip and the contact wire. When the contact angle of the baffle is determined to be 4.75 when the force is too small, it will increase the resistance of current running speed is 350 km/h, and pantograph–catenary con- collection, and also produce arc [3]. Moreover, the con- tact forces are 128.89 N and 129.15 N under the knuckle- nection between the pantograph and the catenary will be downstream and knuckle-upstream operating conditions, broken when the contact force is zero, and arc discharge will occur, which will cause ablation of the catenary line and strip, and seriously affect the running safety of trains & Tian Li [4, 5]. litian2008@home.swjtu.edu.cn The effect of aerodynamics performance on the pan- Zhiyuan Dai tograph-catenary system was ignored when the train was daizhiyuan18@my.swjtu.edu.cn running at a low speed [6, 7]. However, the aerodynamic State Key Laboratory of Traction Power, Southwest Jiaotong effect cannot be ignored with the increment of the University, Chengdu 610031, China 123 118 Z. Dai et al. operating speed. When the running speed is not less than 2 Computational model 250 km/h, the aerodynamic resistance accounts for about 75%–80% of the total resistance [8–10], and the aerody- 2.1 Geometry and mathematical models namic resistance of the pantograph accounts for about 12% of the total aerodynamic resistance [11]. Moreover, aero- A type of pantograph used in China is adopted to build the dynamic forces have a significant effect on the contact models. The height of the pantograph is 1600 mm, and force [1, 12]. Therefore, it is necessary to study the effect there are no baffles installed on the panhead for the original of aerodynamics on the pantograph–catenary contact force. pantograph, as shown in Fig. 1a. The panhead in Fig. 1bis Song et al. [13] obtained the aerodynamic uplift force of equipped with baffles, whose angle can be adjusted to the pantograph at a running speed of 350 km/h using an optimize the aerodynamic uplift force of the pantograph. empirical formula by means of computational fluid The running speed of the high-speed train is lower than dynamics. Yang et al. [14, 15] obtained the aerodynamic 360 km/h in this study, and the fluid can be considered as uplift forces of pantographs under the conditions of con- the incompressible one [17]. Therefore, the incompressible sidering the drag and lift forces of the pantograph rods and Reynolds averaged Navier–Stokes (RANS) and k-x shear panhead. However, the effect of the moment of pantograph stress transport (SST) turbulence model are used to solve components on the aerodynamic uplift force was ignored. the governing equations [18, 19]. Li et al. [16] proposed a new method to calculate the The upper arm, lower arm, upper link and lower link of aerodynamic uplift force of a pantograph based on the the pantograph constitute a frame system, which has only statics analysis method. The variation of the uplift force one degree of freedom (DOF) of raising angle a [20]. The was consistent with the results of the wind tunnel test. panhead has 6 DOFs as it is supported on springs, of which However, the pantograph was simplified to a two-dimen- only the vertical displacement, roll and pitch angles are sional model, and the effect of moment was also ignored. considered since they affect the pantograph–catenary con- Based on the multibody simulation, a comprehensive tact force. dynamic model with aerodynamic forces and moments of each pantograph component is established, and a new 2.2 Computational domain and boundary method to calculate the aerodynamic uplift force of the conditions pantograph is proposed in this study. Meanwhile, the longitudinal asymmetry of the pan- The computational domain shown in Fig. 2 is established. tograph leads to differences in the aerodynamic uplift force A cuboid named T-body is set on the bottom of the domain under the knuckle-downstream and knuckle-upstream to simulate the high-speed train body, and the pantograph conditions. As a result, manual adjustment of the airbag or is placed on the top of the T-body. A curved roof surface of the control system can regulate the static uplift force when the T-body and geometric changes of the T-body near the the high-speed train is running in different directions, so as pantograph have little effect on the flow field above the to make the pantograph–catenary contact force meet the pantograph. On the contrary, it will increase the number of requirements. Therefore, the dependence on the airbag grids and reduce computational efficiency. Therefore, the system can be reduced by adjusting the aerodynamic uplift simplified train roof is used in numerical simulation. The forces under the knuckle-downstream and knuckle-up- origin of the coordinates is located on the base of the stream conditions to be close. It is of great significance to pantograph, as well as the longitudinal median plane of the alleviate the fatigue damage of the airbag system and the computational domain, as shown in Fig. 1a and Fig. 2. The possibility of pantograph–catenary accidents. In this study, length of the computational domain is 60 m, the height and the aerodynamic uplift force is optimized by means of width are 10 m and 20 m, respectively. The distances setting the baffle. The calculation method and the opti- between the pantograph and the inlet and outlet boundaries mization process of the aerodynamic uplift force of the of the domain are both 30 m. The selected computational pantograph proposed in this study are general, which can domain satisfies the standard EN 14,067–6:2010 [21]. The be applied to various types of pantographs, and can provide other sizes of the computational domain are shown in a reference for the design and optimization of high-speed Fig. 2. pantographs. The running speed of the high-speed pantograph is 300–350 km/h in operation; therefore, 350 km/h is selected in numerical simulation. When the pantograph is running in the knuckle downstream, the front side of the domain is set as the velocity inlet boundary, and the velocity is 97.22 m/s. Meanwhile, a pressure-outlet condition is prescribed at the Rail. Eng. Science (2022) 30(1):117–128 20 Numerical simulation and optimization of aerodynamic uplift force of a high-speed pantograph 119 (a) (b) Panhead Original panhead Upper link Upper arm Balance arm Optimized panhead Air bag Lower arm Lower link Baffles and its support Base Fig. 1 Models of the pantograph and panheads: a pantograph and b panhead experimental data to verify the accuracy of the numerical simulation. Sym Step 2 Obtain the aerodynamic uplift forces of the Outlet pantograph running in both the knuckle-downstream and knuckle-upstream conditions, and judge whether the aerodynamic uplift forces are consistent in two condi- tions and whether the magnitudes satisfy the standard EN50367:2012 [22]. If one of them is not satisfied, the pantograph should be optimized. Step 3 Obtain the aerodynamic uplift force of the pantograph with three different baffles. Three different angles for the baffles are -17,0 and 17. The limit is large enough to ensure that the optimal angle is included. Then, the optimal range of the baffle angle is determined according to the results of the aerodynamic uplift force. Fig. 2 Computational domain (unit: m) Step 4 Study the relationship between the aerodynamic lift force and the baffle angle by independently applying back side of the domain with a magnitude of 0. The setting the aerodynamic study of the baffle, and determine the of the knuckle-upstream condition is opposite to that of the possible angle using the aerodynamic uplift forces of the knuckle-downstream condition. Symmetry condition is pantograph with baffles. Establish the baffle models with used to model zero-shear slip walls in viscous flows; different angles around the possible angle, and obtain the therefore, the side and top boundaries are set as symmetry aerodynamic uplift forces of the pantograph. According condition. The top and sides of the T-body are set as no- to the results, judge whether the aerodynamic uplift slip wall, the ground is set as a slip wall, and the velocity is forces are consistent in the knuckle-downstream and 97.22 m/s. knuckle-upstream conditions, and whether the magni- tudes satisfy the standard. If one of them is not satisfied, continuously find a suitable angle according to the 3 Optimization process previous results. The above procedures are illustrated in Fig. 3. The flowchart for the numerical simulation and optimiza- tion of the aerodynamic uplift force of the pantograph can be described as follows. Step 1 Carry out the mesh sensitivity firstly, and then the numerical simulation results are compared with the Rail. Eng. Science (2022) 30(1):117–128 Strip-support Inlet Ground Roof T-body Sym 6.5 10 120 Z. Dai et al. differences in lift forces of the strip and panhead are both 4 Validation of numerical simulation less than 1 N, and all the relative errors of resistance 4.1 Mesh sensitivity between mesh 3 and mesh 4 are less than 1%. As shown in Fig. 5, the pressure distribution for 4 meshes is basically Three regions are set in the computational domain to refine the same from 1500 to 4000 mm. The pressure distribution obtained using mesh 3 and mesh 4 at a position closer to the mesh. The basic size of the mesh is H, and the sizes of H H H the strip is also basically the same, and the results of the three zones are ; ; , respectively. Meanwhile, 3 2 aerodynamic forces and pressure distribution in the flow 2 2 2 H H field show that the accuracy of mesh 3 and mesh 4 is the cell size of the pantograph surface is . There are 7 4 2 2 equivalent, mesh 3 will be used for numerical simulation in 18 boundary layers in total. The height of the first boundary subsequent work considering the calculation efficiency. layer is 0.01 mm, and the growth ratio is 1.2. The boundary layers ensure that the y ? of the pantograph is around 1. 4.2 Experimental validation The cells of the boundary layer and refined regions are shown in Fig. 4. In order to study the influence of the mesh A pantograph is meshed with the same size as Mesh 3, quantity on the numerical results, 4 basic sizes of 130, 140, which was tested in a wind tunnel at the China Aerody- 150 and 160 mm are chosen to generate 4 different meshes, namics Research and Development Center [23]. The speed which are named mesh 1, mesh 2, mesh 3 and mesh 4, range of the wind tunnel test is 300–500 km/h, and the respectively, and the number of cells are 20.53 million, aerodynamic drag coefficient C of the pantograph in this 25.20 million, 31.20 million and 36.6 million, respectively. speed range is obtained. The aerodynamic drag coefficient Four meshes are numerically simulated to obtain the C is defined as. aerodynamic forces of the strip, panhead and pantograph, as shown in Table 1. Figure 5 shows the pressure distri- C ¼ ; ð1Þ 0:5qv S bution along a line, which is 650–4000 mm behind the strip at a height of z = 1260 mm, and it is located on the section where F is the aerodynamic drag force, q is the density of of x =0. the airflow, v is the speed of the incoming flow, and S is the It can be seen from the aerodynamic forces that the windward area. In this paper, S is assumed to be 1 as the results obtained using mesh 3 and mesh 4 are close, the experimental pantograph of each condition is the same. Aerodynamic uplift force of the original pantograph Calculate the uplift force Establish multibody Calculate the uplift Do the No Yes Is the uplift force of the pantographs values meet the dynamics model of force of the original in two conditions equipped with baffles standard? the pantograph pantograph the same? Yes No No need to optimize Validation of simulation Calculate the baffle separately to study the Mesh sensitivity Wind tunnel test relationship between the lift force and the angle Optimization of aerodynamic uplift force Do the Determine the first angle, and Yes No Is the uplift force Adjust the angle values meet Start establish baffles with different in two conditions according to results the standard? angles around this angle the same? Yes No End Fig. 3 Optimization process Rail. Eng. Science (2022) 30(1):117–128 Numerical simulation and optimization of aerodynamic uplift force of a high-speed pantograph 121 Fig. 4 Computational meshes Table 1 Aerodynamic force of the pantograph and its components (N) Mesh Lift force of strip Lift force of panhead Drag force of strip Drag force of panhead Drag force of pantograph 1 -15.75 -10.06 576.10 721.79 2175.00 2 -16.47 -10.25 585.07 731.18 2290.49 3 -17.59 -10.82 594.51 744.12 2196.41 4 -17.76 -11.02 596.92 746.63 2200.05 400 results in order to verify the accuracy of the numerical simulation, as listed in Table 2. It can be seen from Table 2 that the aerodynamic drag coefficient of the pantograph obtained from numerical simulation is slightly less than that of the wind tunnel test in both knuckle-downstream and upstream condition; -400 Mesh 1 however, the errors are within 5%. Some small parts of the Mesh 2 pantograph, such as bolts, nuts and wires, were deleted Mesh 3 when meshing to improve the quality of the mesh. There- Mesh 4 -800 fore, the results of numerical simulation are slightly smaller. In summary, the numerical simulation in this study can accurately match the experimental results. The purpose -1200 of validations is to verify the reliability and accuracy of the 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 numerical simulation method. Although there is no y-coordinate (m) experimental data for aerodynamic lift force coefficient, Fig. 5 Pressure distribution in the flow field the coincidence of aerodynamic resistance coefficient can also demonstrate that the numerical simulation method can Numerical simulation is performed on the experimental reproduce the wind tunnel test well, so as to prove the pantograph, and the running speed of the pantograph is accuracy of the numerical simulation method. 97.22 m/s, which is 350 km/h. The aerodynamic drag coefficients of the experimental pantograph obtained using numerical simulation are compared with the experimental Rail. Eng. Science (2022) 30(1):117–128 Pressure (Pa) 122 Z. Dai et al. Table 2 Aerodynamic drag coefficient obtained using the numerical simulation and wind tunnel test Condition Wind tunnel test Numerical simulation Relative error Knuckle downstream 0.403 0.387 4.0% Knuckle upstream 0.390 0.372 4.6% obtained, as shown in Table 3. It is noted that the upper and 5 Results lower surfaces are the main parts that affect aerodynamic 5.1 Calculation method of aerodynamic uplift force lift forces, so these two parts are analyzed separately. In addition to the upper and lower surfaces, the baffle also has The 3D multibody simulation model of the pantograph is other surfaces such as its support. According to the requirements in the standard EN50367:2012, the pan- established using the software of SIMPACK, as shown in Fig. 6, and the system has only one DOF in the vertical tograph–catenary contact force should be in the range of 110–180 N when the operating speed is 350 km/h. The direction. The aerodynamic drag and lift forces, aerody- namic moments in three directions are applied to each static uplift force provided by the airbag is 80 N. It can be seen from Table 3 that the aerodynamic uplift forces of the components of the pantograph. The strip is fixed on the original pantograph in the knuckle-downstream and catenary, and the reaction force of the contact point in the knuckle-upstream conditions are -27.1 and 46.18 N, z direction is solved, which is the aerodynamic uplift force respectively. The pantograph–catenary contact force satis- of the pantograph. Upper arm, lower arm, balance arm, upper link, lower link and base are hinged to each other. fies the standard in the knuckle-downstream condition, while fails to satisfy the standard in the knuckle-upstream Panhead and balance arm are connected by a spring, which is located between the balance arm and the strip-support, condition. In addition, the difference in the aerodynamic uplift forces of the original pantograph in two operating and the stiffness in x, y and z directions are all 10 N/m. Numerical simulations of multibody and fluid dynamics condition is relatively large, about 73 N. Therefore, the original pantograph needs to be optimized. are performed on the original pantograph and the pan- tograph equipped with three different baffles. Three dif- The baffle is installed on the support of the strip, and its resistance and moments have no effect on the aerodynamic ferent angles for the baffles are -17,0 and 17, as shown uplift force, and the aerodynamic lift force of the baffle will in Fig. 7. The baffle angle of the pantograph currently in operation is mostly in the range of 10–15. Based on the completely be transformed into the aerodynamic uplift force of the pantograph. As shown in Table 3, the change in actual experience, this study takes the limit angle as 17, and the limit angle is large enough to ensure that the the aerodynamic uplift force of the pantograph with baffles is almost the same as the aerodynamic lift force of the optimal angle is included. The aerodynamic uplift force of the pantograph, the lift baffle, which indicate consistency of the results between the multibody and fluid dynamics. The -17 baffle pro- force of the upper and lower surfaces of baffles are vides a negative lift force in the knuckle-downstream condition, and a positive lift force in the knuckle-upstream condition, which intensifies the inconsistency of the aero- dynamic uplift force of the original pantograph in two operating conditions. The 0 baffle provide basically the same lift force in the knuckle-downstream and knuckle- upstream conditions, about 36 N. However, the inconsis- tency of aerodynamic uplift force is not improved. For the 17 baffle, it can provide a larger positive aerodynamic lift force in the knuckle-downstream condition, and a negative lift one in the knuckle-upstream condition, which leads to a greater uplift force in the knuckle-downstream condition. Therefore, the optimal angle of the baffle should be in the range of 0–17. Fig. 6 Multibody simulation model of pantograph Rail. Eng. Science (2022) 30(1):117–128 Numerical simulation and optimization of aerodynamic uplift force of a high-speed pantograph 123 (a) (b) -17° Knuckle-downstream condition 0° 17° Fig. 7 The baffle model: a baffle and its support; b baffles with different angles Table 3 Aerodynamic forces and uplift force of the pantograph Condition Baffle angle () Lift force of the upper Lift force of the lower Lift force of the baffle Aerodynamic surface of the baffle (N) surface of the baffle (N) and its support (N) uplift force (N) Knuckle downstream No baffle – – – -27.10 -17 12.92 -62.73 -17.91 -44.89 0 63.87 -23.28 37.63 10.56 17 121.15 59.88 160.77 132.50 Knuckle upstream No baffle – – – 46.18 -17 122.29 57.57 157.62 202.47 0 59.31 -26.08 36.16 81.47 17 15.41 -64.65 -20.74 26.15 5.2 Relationship between the aerodynamic lift force less than 12, whereas the decreasing trend of the lift force and baffle angle slows down when the angle is greater than 12. Figure 9a shows the lift force of the upper and lower In order to improve the optimization efficiency, the rela- surfaces of the baffle in the knuckle-downstream condition. tionship between the aerodynamic lift force and the baffle It can be seen that the lift forces of the upper and lower angle is studied by independently applying the aerody- surfaces increase with the angle. The lift force of the upper namic study of the baffle. The baffle models with 9 angles surface increases slowly when the angle is small, whereas of 0,2,4,6,8,10,12,14 and 17 are selected, as the lift force of the lower surface basically maintains the shown in Fig. 8a. same increasing trend. The model of the baffle in the numerical simulation is Figure 10 shows the pressure distribution around baffles shown in Fig. 7a, the overall height of the baffle is about with different angles in the knuckle-downstream condition. 0.2 m. Meanwhile, Fig. 8b shows the computational With the baffle angle increases, the negative pressure on domain for the isolated baffle, and the baffle is located at the upper surface and the positive pressure on the lower the center of the domain. The cell size of the baffle surface surface both increase gradually; therefore, the lift forces of and the size of the surrounding cell are completely con- the upper and lower surfaces increase. There is a vortex sistent with the main CFD model, as well as the boundary underneath the baffle when the angle is less than 8, and the conditions and solving algorithm. lower surface of the baffle presents negative pressure. As shown in Fig. 8c, the lift force of the baffle increases Therefore, the lower surface has a smaller lift force, and with the angle in the knuckle-downstream condition, and it even shows a negative lift force when the angle is less than basically increases linearly. In the knuckle-upstream con- 4. It can be seen from streamlines that the vortex gradually dition, the lift force of the baffle decreases as the angle moves toward the front end of the baffle as the angle increases. The decrease is almost linear when the angle is increases, the positive pressure at the rear end enlarges, and Rail. Eng. Science (2022) 30(1):117–128 4 124 Z. Dai et al. gradually enlarges, so as to the lift force of the upper (a) Knuckle-downstream surface increases. condition As shown in Fig. 9a, the lift forces of the upper and lower surfaces of the baffle both decrease in the knuckle- upstream condition. The lift forces of the upper surface decreases rapidly when the angle is less than 12. When the 0° angle is greater than 12, the decrease of the lift force of 8° the lower surface slows down, and then basically unchan- 17° ged. Therefore, the trend of the lift force reduction slows down when the angle is greater than 12 in the knuckle- upstream condition. Figure 11 shows the pressure distri- bution around baffles with different angles in the knuckle- (b) upstream condition. When the angle is greater than 12, the flow field around the baffle basically no longer changes, which is consistent with the lift force. For the upper surface Sym of the baffle, the windward area becomes larger as the angle increases, and the positive pressure on the upper surface increase correspondingly. Therefore, the lift force of the upper surface keeps decreasing. Table 4 shows the aerodynamic forces of baffles and uplift force of the pantograph, including the isolated baffle and that installed in the pantograph. Numerically simulat- ing the baffle and its support separately, the lift forces of the baffle increase with the angle in the knuckle-down- stream condition, whereas the lift forces of the baffle decrease in the knuckle-upstream condition. Moreover, the lift force of the baffle increases linearly with the angle in the knuckle-downstream condition. In the knuckle-up- stream condition, the lift force of the baffle is also basically linear with the angle when the angle is less than 12. (c) As shown in Table 4, when the pantograph with the baffle is numerically simulated, the lift forces of the baffle also increase with the angle in the knuckle-downstream condition. Meanwhile, the lift forces of the baffle decrease as the angle increase in the knuckle-upstream condition, Knuckle downstream which is consistent with the result of numerically simu- Knuckle upstream lating the baffles separately. Therefore, it exists that the lift forces of the baffle considering the pantograph or not is different. The difference is due to some disturbances to the flow field around the baffle when there are other compo- nents around the baffle. However, the relationship between -20 the baffle lift force and the baffle angle can be used to 02468 10 12 14 16 18 deduce the variation of pantograph aerodynamic lift force Baffle angle (°) with the existence of the baffle. The pantograph baffle can be optimized according to the conclusions above. It can be Fig. 8 Models and lift forces of baffles: a baffles with different angles; b computational domain for the baffle (unit: m); c lift forces of obtained that the aerodynamic uplift forces of the pan- baffles tograph with the 5.8 baffle in the knuckle-downstream and knuckle-upstream conditions are equal. Therefore, baffles the amplitude of the positive pressure also increases. with 5 different angles including 4,5,6,7 and 8 are Consequently, the lift of the lower surface improves. The selected to be installed on the pantograph for the following increment of the baffle angle leads to an increase in the numerical simulations. attack angle. Therefore, the air velocity above the upper surface of the baffle increases, and the negative pressure Rail. Eng. Science (2022) 30(1):117–128 Sym Sym Inlet Outlet Ground Lift force of the baffle (N) 4 Numerical simulation and optimization of aerodynamic uplift force of a high-speed pantograph 125 (a) (b) 40 15 Upper face Upper face Lower face Lower face -15 -30 -20 02 4 6 8 10 12 14 16 18 02468 10 12 14 16 18 Baffle angle (°) Baffle angle (°) Fig. 9 Lift force of the upper and lower surfaces of the baffle: a knuckle-downstream condition; b knuckle-upstream condition Fig. 10 Pressure and streamlines around the baffle in the knuckle-downstream operating condition: a 0; b 4; c 8; d 12; e 14; f 17 5.3 Optimization on the aerodynamic uplift force the aerodynamic uplift force of the pantograph shown in Fig. 12b is completely consistent with the lift force of the Based on the above research results, the angle interval is baffle shown in Fig. 12a. However, the aerodynamic uplift reduced to 4–8. In this section, pantograph models force of the pantograph is obtained by means of multibody equipped with 4,5,6,7 and 8 baffles are established simulation. The consistency of the results also indicates the for numerical simulation, and the lift forces of baffles in the accuracy of the computational fluid dynamics and multi- knuckle-downstream and knuckle-upstream conditions are body simulation in this study. The two curves in Fig. 12b obtained, as shown in Fig. 12a. Figure 12b shows the intersect at about 4.75, indicating that the aerodynamic aerodynamic uplift forces of the pantograph obtained by uplift forces of the pantograph in the knuckle-downstream the multibody simulation. and knuckle-upstream operating conditions are equal at the It can be seen from Fig. 12a that the lift force of the angle, and the aerodynamic uplift force is 48 N. Moreover, baffle increases linearly with the angle in the knuckle- the static uplift force is 80 N, and the pantograph–catenary downstream condition, and the lift force of the baffle contact force is 128 N correspondingly. basically decreases linearly with the increment of the angle According to the conclusion, the pantograph equipped in the knuckle-upstream operation, whereas the decreasing with a 4.75 baffle is numerically simulated to obtain the trend slows down when the angle is larger. The variation of aerodynamic forces and moments of each component of the Rail. Eng. Science (2022) 30(1):117–128 Lift force of the baffle (N) Lift force of the baffle (N) 126 Z. Dai et al. Fig. 11 Pressure and streamlines around the baffle in the knuckle-upstream operating condition: a 0; b 4; c 8; d 12; e 14; f 17 Table 4 Aerodynamic forces of baffles and uplift force of the pantograph Condition Baffle angle () Lift force of the Lift force of the baffle Aerodynamic isolated baffle (N) installed at the pantograph (N) uplift force (N) Knuckle-downstream 0 16.13 37.63 10.56 17 79.15 160.77 132.50 Knuckle-upstream 0 17.91 36.16 81.47 17 -10.26 -20.74 26.15 (a) (a) (b) (b) 110 110 80 80 100 100 Knuckle downstream Knuckle downstream 70 70 90 90 Knuckle upstream Knuckle upstream 80 80 60 60 70 70 Knuckle downstream Knuckle downstream Knuckle upstream Knuckle upstream 10 10 50 50 0 0 40 40 -10 -10 30 30 4567 4567 88 45 45 66 77 88 Baffle angle (°) Baffle angle (°) Baffle angle (°) Baffle angle (°) Fig. 12 Lift force and aerodynamic uplift force: a lift force of baffles with different angles; b uplift force of pantographs with different baffles pantograph, and then the multibody simulation is per- the requirements in the standard EN50367:2012, the pan- formed to obtain the aerodynamic uplift force of the pan- tograph–catenary contact force should be in the range of tograph, as shown in Table 5. 110–180 N when the operating speed is 350 km/h. The The pantograph–catenary contact force is 128.89 N in optimization result satisfies the requirements of the the knuckle-downstream condition, and the contact force is standard. 129.15 N in the knuckle-upstream condition. According to Rail. Eng. Science (2022) 30(1):117–128 Lift force of the baffle (N) Lift force of the baffle (N) Up-lift force of the pantograph (N) Up-lift force of the pantograph (N) Numerical simulation and optimization of aerodynamic uplift force of a high-speed pantograph 127 Table 5 Aerodynamic uplift forces of the original and optimized pantographs Condition Baffle angle () Lift force of the baffle Aerodynamic Pantograph–catenary and its support (N) uplift force (N) contact force (N) Knuckle downstream No baffle – -27.10 52.9 4.75 76.35 48.89 128.89 Knuckle upstream No baffle – 46.18 126.18 4.75 1.89 49.15 129.15 Open Access This article is licensed under a Creative Commons 6 Conclusions Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as The aerodynamic performance of the pantograph is long as you give appropriate credit to the original author(s) and the numerically simulated by computational fluid dynamics, source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this and then the multibody simulation is performed to obtain article are included in the article’s Creative Commons licence, unless the aerodynamic uplift force of the pantograph. According indicated otherwise in a credit line to the material. If material is not to the results, the pantograph baffles are optimized, and the included in the article’s Creative Commons licence and your intended following conclusions are obtained: use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright (1) The lift force of the baffle increases linearly with the holder. To view a copy of this licence, visit http://creativecommons. org/licenses/by/4.0/. angle in the knuckle-downstream condition. The lift force of the baffle basically decreases linearly with the increment of the angle in the knuckle-upstream operation, while the decreasing trend slows down References when the angle is greater than 12. (2) It is determined that the optimal installation angle of 1. Pombo J, Ambro´sio J, Pereira M et al (2009) Influence of the the baffle is 4.75. The pantograph–catenary contact aerodynamic forces on the pantograph–catenary system for high- forces in the knuckle-downstream and knuckle-up- speed trains. Veh Syst Dyn 47(11):1327–1347 2. Song Y, Wang Z, Liu Z et al (2021) A spatial coupling model to stream operating condition are 128.89 N and study dynamic performance of pantograph–catenary with vehicle- 129.15 N, respectively. The values are nearly equal track excitation. Mech Syst Signal Process 151:107336 and both meet standard requirements. 3. 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Veh Syst Dyn all speed levels, and the optimal model under the corre- 38(6):393–414 sponding speed level can be obtained by this method, the 7. Kim H, Hu Z, Thompson D (2020) Effect of cavity flow control work does not develop a specific relationship between the on high-speed train pantograph and roof aerodynamic noise. optimal model and speed. Therefore, the relationship Railw Eng Sci 28(1):54–74 8. Tian H (2019) Review of research on high-speed railway aero- between the optimal angle of the baffle and the operating dynamics in China. Transport Saf Environ 1(1):1–21 speed need further study to improve the overall perfor- 9. Li X, Tan Y, Qiu X, Gong Z, Wang M (2021) Wind tunnel mance of pantographs. measurement of aerodynamic characteristics of trains passing each other on a simply supported box girder bridge. Railw Eng Sci 29(2):152–162 Acknowledgements This project was supported by National Key Research and Development Program of China (No. 10. 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Railway Engineering Science – Springer Journals
Published: Mar 1, 2022
Keywords: High-speed pantograph; Aerodynamic uplift force; Baffle; Numerical simulation; Multibody simulation
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