Study of the Aerodynamic Performance of Pantograph Bowhead with Serrated Lower Surface in the Thermal Management Systems of the High-Speed Train Electrical Devices

Abstract

The thermal management problems of traction drive systems for high-speed trains are of great importance for the operation reliability of high-speed trains. The thermal performance of transformer and traction rectifier are mainly affected by the aerodynamic performance of pantograph. Nine bowheads with different sawtooth structures on the lower surface are proposed and a CFD numerical model is built with Transition SST turbulence model. The influence of the number and height of sawteeth on the aerodynamic characteristics of the bowhead flow field are investigated. The results show that compared with the rectangular bowhead, the aerodynamic drag of the 5w3h-shaped bowhead is reduced by 8.6%, 8.7%, and 9.9% at train speeds of 250 km/h, 300 km/h, and 350 km/h, respectively. The promotion of aerodynamic performance of pantograph is beneficial to improve the thermal characteristics of traction drive systems for high-speed trains.

1. Introduction

With the fast development of high-speed railways, the heat management problems of the traction drive system for high-speed trains are given increasing attention, leading to a serious operation reliability crisis [1]. The traction drive system for high-speed trains consists of five parts, namely, pantograph, traction transformer, four-quadrant converter, traction inverter and traction motor, as shown in Figure 1. The pantograph transmits the high voltage to the traction transformer, which reduces the high voltage and then transfers it to the traction converter. The traction converter rectifies, filters, and inverts the input current, and outputs three-phase AC to drive the traction motor to rotate. During this current transmission process the electrical components of traction transformer, traction converter, and traction motor will generate much heat, which will cause the electrical components to experience high temperature and may even cause insulation failure, fire damage and shortening of service life [2]. The improvement of the current collection quality of the pantograph can improve the working performance of the transformer, converter, and motor, thus having a positive effect on the thermal management of electronic components [3]. Therefore, the improvement of the aerodynamic characteristics of the pantograph is important to ensure the reliability of train operation and traction drive system.

Some researchers investigated the influence of aerodynamic effect on the pantograph–catenary system [4]. M. Carnevale [5] investigated the pantograph features that mainly affect its aerodynamic behavior, and their influence on the mean value of the contact force. Y. Song [6,7] analyzed the effect of contact wire irregularity and crosswind on high-speed railway pantograph-catenary interactions. M. Tur [8] put forward the concept of contact wire irregularity and studied the influence of contact wire irregularity on the pantograph and catenary current collection quality. M. Bocciolone [9] performed a wind tunnel test and numerical simulation were used to calculate the lift coefficient and drag coefficient of four different shapes of pantograph head slide plates, and the change law of pantograph contact force was obtained. The results show that the aerodynamic force has a significant influence on the mean value and standard deviation of the contact force between pantograph and catenary. X. Li [10] used the time-delayed vortex separation method to study the unsteady aerodynamic characteristics of pantograph under four different cross-wind flow directions of 0°, 10°, 20°, and 30°. The simulation results show that the asymmetry of the spatial flow field distribution of the pantograph increases with the increase of the angle of cross-wind flow.

For the aerodynamic characteristics of pantographs of high-speed trains, many investigations have been conducted by researchers. Wu Yan et al. [11] established the aerodynamic numerical model of the pantograph system, analyzed the aerodynamic performance of the pantograph, and obtained the mechanical parameters of the pantograph at a speed of 250 km/h. During the development of the DSA350S high-speed pantograph, W. Herbert [12] developed a controllable and movable air deflector, which actively controls the relationship between air inflow angle and height. Yao Yuan et al. [13] studied the different mechanical characteristics of the pantograph when it is operated in open- and closed-port mode and investigated the lift and drag forces of the pantograph under two operation modes. Zhang Liang et al. [14] made a study on the installation position and opening direction of the pantograph, analyzed the speed distribution and the change of aerodynamic lift, and found that the pantograph has the best aerodynamic characteristics when it is installed in the middle of the tail car. Yang Kang et al. [15] used fluid simulation software to calculate the aerodynamic characteristics of the pantograph during high-speed operation and concluded that the bowhead is the main force component of the pantograph. The improvement of aerodynamic characteristics by optimizing the pantograph structure and shape has also been effective. Xiao Yougang et al. [16] studied and optimized the cross-sectional shape of pantograph insulators, and the best results were obtained when the windward cross-section was elliptical, and the long axis was the same as the airflow direction. Kaike Qi et al. [17] machined the bowhead and other rods into teardrop-shaped cross-sections, and the optimized teardrop-shaped pantograph reduced the resistance by 136.4 N and the aerodynamic noise by 4 dB. Yeongbin Lee et al. [18] proposed a new pantograph shape with a passive flow control strategy using holes on the surface of the column of the head, and the aerodynamic performance of the optimized head was improved. Mitsuru IKEDA [19] proposed a bowhead shape whose profile is connected by a set of discrete nodes, and this structure can change the windward angle of the bowhead with the change in the train running speed. By analyzing its aerodynamic characteristics and the law of lift variation, it is proved that this structure effectively reduces the aerodynamic lift.

Based on the pantograph head with rectangular cross-section that is commonly used at present, nine pantograph heads with serrated structure on the lower surface are proposed. The simplified two-dimensional pantograph head cross-section is simulated and compared by the computational fluid dynamics method using ANSYS Fluent 19.0. The influence of the structural parameters on the aerodynamic and mechanical properties of the pantograph head is investigated, and a sawtooth shape with better aerodynamic performance is obtained. This work provides a theoretical foundation and practical experience for further development and utilization of thermal management of high-speed train traction drive systems and promotes the function improvement of its thermal management technology.

2. 2 Numerical Modeling of the Air Flow Field around the Bowhead

The numerical modeling of the air flow field for rectangular bowhead and different nine structures of serrated bowhead was built to analysis their aerodynamic force characteristics. The accuracy of numerical modeling was verified by comparing the resistance coefficient with the experimental results. Grid non-correlation verification was conducted to ensure the accuracy of numerical modeling.

2.1. Transition SST Model

Transition SST model [20,21], also known as $\gamma -R{e}_{\theta }$ model, is a four-equation transitional model obtained by coupling the SST transport equation with the $\gamma -R{e}_{\theta }$ transport equation and empirical formulation.

In this expression $\gamma$ is the intermittency factor which acts on the turbulent kinetic energy equation and controls the generation of turbulent kinetic energy. $R{e}_{\theta }$ is the Reynolds number of the boundary layer momentum thickness. $\gamma -R{e}_{\theta }$ has been used extensively in aerodynamic directions to predict boundary layer transitions and separation phenomena [22].

This is example (1)–(3) of the model intermittent transport equation γ.

$$\frac{\partial \left(\rho \gamma \right)}{\partial t}+\frac{\partial \left(\rho U_j\gamma \right)}{\partial x_j}=P_{\gamma 1}-E_{\gamma 1}+P_{\gamma 2}-E_{\gamma 2}+\frac{\partial }{\partial x_j}\left[\left(\mu +\frac{{\mu }_t}{{\sigma }_{\gamma }}\right)\frac{\partial \gamma }{\partial x_j}\right]$$

(1)

$$P_{\gamma 1}=C_{a1}{F}_{length }\rho S{\left[\gamma F_{onset }\right]}^{c_{\gamma 3}}, E_{\gamma 1}=C_{e1}{P}_{\gamma 1}\gamma$$

(2)

$$P_{\gamma 2}=C_{a2}\rho \Omega \gamma F_{turb }, E_{\gamma 2}=C_{e2}{P}_{\gamma 2}\gamma$$

(3)

where: $S$—Strain rate $F_{length}$—Length of turning area

$\mathsf{\Omega }$—Vortex intensity $P_{\gamma 1}$, $E_{\gamma 1}$—Turning source term

$P_{\gamma 2}$—Rupture coefficient $E_{\gamma 2}$—Re-attachment coefficient

Where the model constant for the intermittent equation $\gamma$ is: $C_{a1}$ = 2 $C_{e1}$ = 1 $C_{a2}$ = 0.06 $C_{e2}$ = 50 $c_{\gamma 3}$ = 0.5 ${\sigma }_{\gamma }$ = 1, $F_{onset}$ is used to trigger the intermittency coefficient generation term. $F_{turb}$ is a function of the viscosity coefficient ratio. The momentum thickness Reynolds number $R{\tilde{e}}_{\theta t}$ equation is given in Equations (4) and (5):

$$\frac{\partial \left(\rho R{\tilde{e}}_{\theta t}\right)}{\partial t}+\frac{\partial \left(\rho U_{j}R{\tilde{e}}_{\theta t}\right)}{\partial x_j}=P_{\theta t}+\frac{\partial }{\partial x_j}\left[{\sigma }_{\theta t}\left(\mu +{\mu }_t\right)\frac{\partial R{\tilde{e}}_{\theta t}}{\partial x_j}\right]$$

(4)

$$P_{\theta t}=c_{\theta t}\frac{\rho }{t}\left(R{e}_{\theta t}-R{\tilde{e}}_{\theta t}\right)\left(1.0-F_{\theta t}\right)$$

(5)

$F_{\theta t}$—Source term control parameters $c_{\theta t}$ = 0.03.

2.2. Two-Dimensional Physical Model Building

The CX-NG pantograph head is used as the research object, and the three-dimensional model is shown in Figure 2. The two-dimensional model is established with the windward section of the collector strip for simulation analysis, as shown in Figure 2, and the size of rectangular collector strip section of bowhead is 25 mm × 35 mm.

In order to investigate the effect of structural parameter changes of the lower surface serrated shape on fluid motion and vortex shedding at the tail vortex, three groups of serrated structure bowheads are proposed for simulation. As shown in Figure 3, each group of parameters includes 3, 5, 7 sawtooth numbers and 1 mm, 2 mm, 3 mm sawtooth heights, a total of nine bowhead models to compare the effects of different sawtooth numbers and sawtooth heights on aerodynamic parameters. Among them, all parameters except the lower surface are kept the same as the length and width of the rectangular bowhead. The naming rules for serrations bowheads is according to the number and the height of sawtooth with the letters “w” and “h”. For example, the definition of 5w3h is that the serrated bowhead has five sawteeth and the sawtooth height is 3 mm.

2.3. Meshing and Boundary Condition Setting

In order to ensure the complete development of the wake vortex behind the bowhead and capture the development of the flow field near the bowhead, as well as to combine the computational resources and computational costs, the flow field range is determined to be 28D × 8D, the bowhead is 5D from the entrance, and the bowhead is 3.5D from the upper and lower flow fields. The meshing is performed using ICEM with an unstructured grid with ≥80,000 grids and y+ ≤ 1. The cross region in the computational domain where the bowhead is located is meshed with encryption [23]. The details of the rectangular, 3w1h-shaped bowhead boundary layer meshing are shown in Figure 4.

According to the actual operation, the left boundary of the flow field is set as velocity inlet with velocity of 250 km/h, 300 km/h and 350 km/h, and the right boundary is a pressure outlet with pressure of 0 Pa. The upper and lower boundaries are symmetrical boundaries, which can exclude the influence of the wall boundary on the flow field calculation. The bow head is a non-slip wall surface.

The accuracy of numerical results is significantly affected by the mesh quality and grid number. Then the simulation results of resistance coefficient were compared under three different grid numbers for Re = 2.2 × 10⁴ shown in

Table 1. Simulation results of resistance coefficient under different grid number.

Grid Number	50,000	70,000	150,000
${\mathit{C}}_{\mathit{d}}$	1.65	1.86	1.88

. It is found that the variation of resistance coefficient is small when the grid number is larger than 70,000. Thus, the grid numbers for the simulation models are larger than 80,000.

To verify the accuracy of the numerical model, the simulation results of the square column disturbance model at different Reynolds numbers are given in

Table 2. Simulation results of flow around a square column.

Reynolds Count	Data Comparison	${\mathit{C}}_{\mathit{d}}$	${\mathit{S}}_{\mathit{t}}$
2.2 × 104	Reference [24] Simulation results	2.06 1.86	0.132 0.124
1 × 105	Reference [25] Simulation results	2.13 1.92	0.127 0.123
3 × 105	Reference [26] Simulation results	2.04 2.21	0.126 0.132

. The simulation results are in general agreement with the experimental data.

3. Analysis of the Air Flow Field on the Outer Surface of the Bowhead

In order to compare with the serrated bowhead, the aerodynamic force performance for the rectangular bowhead was analyzed first at different flow rates. The variation of rectangular bowhead lift and drag coefficient was studied over time with different flow rates.

3.1. Analysis of the Flow Field Outside the Rectangular Bowhead at Different Flow Rates

The variation of the air pressure field around the rectangular bowhead at different velocities is shown in Figure 5. The maximum pressure is at the stationary point in front of the bowhead, and the minimum pressure appears at the upper and lower sides of the bowhead. When the speed is 250 km/h, the maximum pressure of the air around the bowhead is about 3590 Pa, and when the speed increases to 350 km/h, the maximum pressure is about doubled to 6830 Pa. When the speed increases, the pressure at the windward side of the bowhead and the stationary point also increases, but the pressure at the low-pressure area at the leeward side of the bowhead gradually decreases. Therefore, the difference between the pressure at the front and rear of the bowhead increases gradually with the increase of speed, and the resulting pressure difference is the main source of pneumatic resistance during the operation of the pantograph.

The velocity contour of the rectangular bowhead operating at 250 km/h, 300 km/h and 350 km/h speed conditions are shown in Figure 6. The air separates at the windward side of the bowhead, so that the pressure at the front stationing point is maximum and the speed becomes small. After the air separated by the upper and lower sides the velocity became sharply larger, and a low velocity zone was generated near the bow head, which was due to the formation of two vortices with opposite rotation directions on the upper and lower surfaces, and backflow occurred. The formation of a continuous vortex behind the bow head will increase the loss of mechanical energy. In addition, the maximum velocity of air around the bowhead increases with the increase of velocity.

Figure 7 shows the time course curves of the lift and drag coefficients of the rectangular bowhead. Both the lift and drag coefficients of the bowhead show regular periodic fluctuations, which are closely related to the tail vortex that is periodically shed at the rear of the bowhead. The drag coefficient shows a trend of decreasing, then increasing and finally leveling off with time, while the lift coefficient fluctuates with time firstly increasing and then gradually remaining constant. In addition, the average value of the drag coefficient increases with the increase in velocity, and the amplitude of fluctuation of the drag and lift coefficient also increases. This is because, as the velocity increases, the pressure on the windward side of the bowhead increases, while the pressure on the leeward side decreases, resulting in an increase in the differential pressure drag on the bowhead.

3.2. Analysis of the Air Flow Field on the Outer Surface of the Serrated Bow Head

Taking the speed of 350 km/h as an example, the pressure distribution of the flow field of the nine serrated bowheads is shown in Figure 8. The maximum pressure of the three sets of bowheads with 1 mm sawtooth height is about 6820 pa, which is smaller than that of the rectangular bowhead. Compared with the pressure difference of the rectangular bowhead, the pressure difference of 5w1h bowhead is smaller than that of the rectangular bowhead, which is about 17,520 Pa. The difference between 3w1h tooth bowhead and 7w1h bowhead, and rectangular pressure difference is not significant. The low-pressure area of the three groups of bowheads was reduced more obviously after the sawtooth height was increased to 2 mm. The maximum pressure was 6930 Pa, 6860 Pa, and 6650 Pa, respectively, which was larger than that of the rectangular bowhead. The maximum pressure of the three groups of bowheads with 3 mm saw tooth height is about 6830 Pa, 6710 Pa, and 6680 Pa, which are smaller than that of the rectangular bowhead. The minimum pressure is about −13,600 Pa, −15,200 Pa, and −11,100 Pa respectively. The maximum pressure difference is smaller than that of the rectangular bowhead, which is 17,780 Pa.

Therefore, the bowhead pressure difference decreases with increasing sawtooth height, which is due to the vortex generated by the air flow over the sawtooth structure, which consumes part of the flow energy and reduces the turbulent dissipation energy within the wake vortex. In addition, as the tooth height increases, the turbulent energy consumed by the sawtooth structure increases and the drag reduction capacity is enhanced.

The velocity distribution of the air flow field for the nine serrated bowheads is shown in Figure 9. The tail flow area of the bowhead becomes smaller as the number of teeth increases when the tooth height is 1 mm. Compared with the rectangular bowhead, due to the serrated groove structure on the lower surface, the return phenomenon of air reattachment occurs after the boundary layer separation in the near-wall area of the groove, which eases the turbulent separation and makes the air in the flow field reattach in the groove, effectively reducing the kinetic energy loss.

The velocity distribution of the flow field for 1 mm and 2 mm sawtooth heights is approximately the same, and the 3w2h structure has an enhanced effect on suppressing premature vortex shedding compared to the 3w1h structure, which is reflected in the reduction of the low-speed vortex region. The 5w2h and 7w2h structures have an insignificant effect on suppressing vortex development in the wake region.

For the bowhead model with a sawtooth height of 3 mm, the 3w3h and 5w3h structures have an enhanced effect on suppressing premature air separation on the lower surface, and the 7w3h structure has the tendency to accelerate the vortex shedding, which is because the notch depth is too large, leading to the poor condition of air adhesion in the notch, so that the vortex that should be at the notch is prematurely shed.

4. Analysis of Unsteady Aerodynamic Characteristics of Bowhead

4.1. Analysis of Aerodynamic Lift of Different Bowhead Structures

The bowhead lift force plays an important role in the stable operation of the pantograph. Under different operating conditions, the smaller the change of lift force on the bowhead, the higher the quality of the pantograph head and the stronger the resistance to wear. Figure 10 shows the variation curves of lift force with speed for rectangular and serrated pantograph heads. As the speed increases, the lift force of the rectangular head increases slowly and then decreases. Moreover, with the increase of air flow velocity, the variation amplitude of 5w1h, 3w1h, and 5w3h bowheads are smaller than that of other shapes of bowheads. With the increase of the height of the sawtooth for a given sawtooth number, the lift force gradually decreases, which is because the sawtooth structure inhibits the shedding of the tail vortex on the lower surface of the bow head.

4.2. Analysis of Aerodynamic Resistance of Different Bowhead Structures

Figure 11 shows the variation curves of resistance with velocity for the rectangular bowhead and the serrated bowhead. The formula for pneumatic resistance $F_d$ can be expressed as follows:

$$F_d=\frac{1}{2}{C}_d\rho S{V}^2$$

(6)

where: $C_d$—Air resistance coefficient $S$—Windward area of bowhead V—the train speed $\rho —$the density of air.

With the increase of wind velocity, the drag forces increase for both rectangular and serrated bowheads. The aerodynamic drag of the bowheads with the serrated structure is smaller than that of the rectangular bowhead, which indicates the better performance on drag reduction effect of the serrated bowhead. In Figure 11, with increasing the sawtooth height the drag force decreases. This is because the air flows through serrated structure and the kinetic energy is partially consumed, which leads to suppression of the shedding of tail vortex. In addition, with an increase of the number of sawteeth, the drag force decreases first for three and five sawteeth and then increases for seven sawteeth.

In summary, the 7w2h bowhead has better aerodynamic characteristics, and the resistance is reduced by 8.5%, 8.9%, and 7.9% in the three speeds in Figure 11b, respectively, and the 5w3h bowhead performs best when the saw tooth height is increased to 3 mm in Figure 11c, and its drag is reduced by 8.6%, 8.7%, and 9.9% at the three speeds, respectively. In conclusion, the 5w3h bowhead has the lowest aerodynamic drag among the nine serrated bowheads.

Then, Figure 12 compares the variation of aerodynamic forces with speed for rectangular and 5w3h-shaped bowheads. With the train speed increasing the variation of the drag coefficient is small for both rectangular and 5w3h-shaped bowhead, and the drag force of 5w3h-shaped bowhead is smaller than that of the rectangular bowhead at three train speeds, as shown in Figure 12a. At the three speeds, the drag coefficient is reduced by 8.59%, 8.71%, and 9.77% using the 5w3h-shaped bowhead, respectively. In Figure 12b, the lift coefficient for rectangular bowhead is increased first and then decreases with increase of velocity, and the lift coefficient for 5w3h-shaped bowhead decreases first and then increases with increasing train speed. Moreover, at train speed of 300 km/h the lift force on the 5w3h-shaped bowhead is smaller than that on the rectangular bowhead, and there is a small difference in train speeds of 250 km/h and 350 km/h.

5. Conclusions

The performance and heat dissipation characteristics of traction drive systems are influenced by the aerodynamic characteristics and current collection quality of pantograph bowhead. In order to improve the current transmission efficiency of traction power system and the thermal characteristics of traction drive systems, nine serrated head structures are proposed and the flow field model of the head before and after optimization is numerically simulated using Transition SST turbulence model and the following conclusions are drawn:

• When the air flows through the bowhead, the air pressure at the windward stationary point increases and the air velocity decreases. Meanwhile, the air near the bow head backflows and mixes with the incoming air, thus producing vortex shedding. With the increase of speed, the frequency of bowhead vortex shedding accelerates and the resistance increases. The average value of the drag coefficient increases with the increase in velocity, and the amplitude of fluctuation of the drag and lift coefficient also increases.
• The optimized serrated groove structure on the lower surface suppresses the separation of the boundary layer and provides conditions for the separated fluid to reattach, and the complete separation bubble is formed in the groove before flowing downward, effectively reducing energy dissipation.
• For the bowhead with the same height of serrated teeth, the effect of reducing aerodynamic resistance is not obvious when the tooth height is 1 mm. The drag of the seven-tooth bowhead with 2 mm tooth height is reduced by 7.9%. The effect of optimizing the five-tooth bowhead is obvious when the tooth height is 3 mm, and the drag is reduced by 9.9% at 350 km/h. The improvement of aerodynamic performance of the bowhead could increase the current collection efficiency and heat dissipation performance of traction drive systems.
• For bowheads with the same number of teeth, the aerodynamic performance of three- and five-tooth bowheads is improved with the increase in tooth height. Seven-tooth bowheads with a certain height increase in tooth height accelerate the phenomenon of sharp vortex shedding at the tip of the serrated teeth, and the aerodynamic performance becomes worse.
• The 5w3h-shaped bowhead has the best aerodynamic performance. Compared with the rectangular bowhead, the running resistance is optimized by 8.6%, 8.7%, and 9.9% at the three speeds, respectively. The drag coefficients are reduced by 8.59%, 8.71%, and 9.77%, respectively. The improvement of aerodynamic characteristics of the pantograph is beneficial in promoting the thermal performance of traction drive systems for high-speed trains.