J. Cent. South Univ. (2012) 19: 2061-2066

DOI: 10.1007/s11771-012-1245-5

Lateral aerodynamic performance and speed limits of double-deck container vehicles with different structures

LI Yan-fei(李燕飞)^1,2, Tian Hong-qi(田红旗)^1,2

1. Key Laboratory of Traffic Safety on Track of Ministry of Education

(Central South University), Changsha 410075, China;

2. School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: Based on 3D, steady N-S equations and k-ε turbulence model, Fluent was employed to do numerical simulation for lateral aerodynamic performance of 6-axis X2K double-deck container trains with two different loading forms, and speed limits of the freight trains were studied. The result indicates that under wind environment: 1) As for vehicles without and with cross-loaded structure, aero-pressure on the former is bigger, but air velocity around the latter is larger; 2) When sideslip angle θ=0°, the airflow is symmetry about train vertical axis; when θ>0°, the airflow is detached at the top of vehicles, and the air velocity increases above the separated line but decreases below it; 3) With θ increasing, the lateral force on the mid vehicle firstly increases but decreases as θ=75°; 4) When the 6-axis X2K flat car loads empty boxes of a 40 ft and a 48 ft at 120 km/h, the overturning wind speed is 25.19 m/s, and the train should be stopped under the 12th grade wind speed.

Key words: numerical simulation; 6-axis X2K flat car; loading form; lateral aerodynamic performance; speed limit

1 Introduction

To meet the requirements of heavy transportation, Chinese experts developed a 6-axis X2K flat car, which will be mainly used in double-deck container transport. To further increase the freight capacity, a cross-loaded structure is installed between two adjacent vehicles to add a 20ft container more. This design used in practice will greatly enhance the transport efficiency. Because most of the Chinese railroads pass through gale regions, we have to consider the lateral aerodynamic performance and running safety of the new 6-axis X2K double-deck container freight train under strong wind, especially after freight capacity expansion.

In recent years, many researchers have investigated important characteristics of the double-deck container for its safe running [1-5]. LIU and YANG [1] simulated the dynamics performance of 25 t axle double-deck container flat car with NUCARS 2.3, and got that the stability indexes and vibration acceleration of container vehicles increased with running speed increasing, and the hunting instability critical speed declined with the loading weight increasing. ALAM and WATKINS [2] studied experimentally the influence of Re on the aerodynamic coefficients of isolated freight train wagon to determine the effect of steady cross wind on double-stacked container wagons in order to assess the rollover risks. They found that the wind speed has negligible effects on aerodynamic coefficients at speeds over 40 km/h, and the C_d is independent on Reynolds number when the air speed is more than 60 km/h. They also showed that the side force and the rolling moment increased with yaw angle increasing, and the maximum values of these coefficients were obtained when the crosswind was at 90° yaw angle [2-3, 6-10].

However, the 6-axis X2K flat car loaded on double-deck containers is a new kind vehicle just designed and the form of the cross-loaded structure between two adjacent vehicles is also used. In this work the large software, Fluent, was employed to do the numerical simulation. For the lateral aerodynamic performance simulation results of the freight trains with and without the cross-loaded structure, by comparison and analysis, the reasonable loading form for the 6-axis X2K flat car under crosswind is summarized. Then, based on those research results above, speed limits of the freight trains were further studied. The results will be important and useful for the users and designers to utilize this kind of 6-axis X2K double-deck container vehicles.

2 Method of simulation

2.1 Mathematical model

Air flow around objects must obey the physical conservation laws and additional turbulence transport laws. In this work, we used standard k-ε model to simulate the turbulence equations. The governing equations contain mass conservation equation and momentum conservation equations, and the turbulence transport is described as k and ε equations. The detailed equations can be found in Refs. [11-12].

2.2 Simulation model

As Figs. 1-2 show, simulation models of the freight trains with different structures contained four cars, which were grouped by a locomotive and three vehicles. There were a 40 ft (1AA) box or two 20 ft boxes on every 6-axis flat car, and then a 48 ft box on the upper. Between two adjacent vehicles, there was a traction rod to connect them. For vehicles with cross-loaded structures, there was a 20 ft box placed on the structure. Every car in the model was defined respectively as locomotive, vehicle 1, vehicle 2, vehicle 3, and cross 1, cross 2.

Fig. 1 Double-deck container train without cross-loading structure

Fig. 2 Double-deck container train with cross-loading structure

2.3 Domain and boundary

Figure 3 demonstrated the simulation domain sizes and the coordinate system. To avoid the wake flow of trains impacting the export section, the domain length should be defined to make the downstream boundary away from the train as far as possible. For the domain width, it should be chosen to avoid yielding the phenomenon of blocking effects [13].

Boundary conditions are also crucial for airflow numerical simulation [14]. In this work, according to the specific calculation circumstances, wind speed with sideslip angle was divided into V_x and V_y separately along X and Y axis. Boundary conditions were decided as follows: 1) The top surface of the domain and surfaces of the train were set as no-slip surface walls; 2) The ground surfaces were set as slip boundary to reflect their relative motion to trains. And the slip speed was equal to V_x in value but opposite in the direction; 3) Planes ABCD and CDGH were both set as wind-import, and given the values of V_x and V_y, respectively; 4) Planes EFGH and ABEF were pressure-export, where the static pressure was equal to zero.

Fig. 3 Simulation domain and coordinate system

2.4 Calculation grid

The entire calculation domain was scattered about unstructured grids, where triangular grids were for material surfaces and tetrahedral grids were for volume and objects. The number of tetrahedral elements of the whole simulated model was about 3.1×10⁶. Figure 4 displays the body grids of a double-deck container vehicle.

Fig. 4 Body grids of double-deck container vehicle

3 Calculation result

In this work, under the synthesis speed of 30 m/s with different sideslip angles, lateral aerodynamic performances of the freight trains with and without cross-loaded structure were both simulated. From detailed analysis on results, we summarized lateral aerodynamic performances of double-deck container vehicles with two loaded structures. This laid a foundation for the following research on vehicle speed limits.

3.1 Pressure distribution

As Fig. 5 shows, except for the positive pressure on windward surface of vehicles, as well as part area of the front and the end surfaces near the windward surface, others were all covered with negative pressure. With the sideslip angle increasing, the positive pressure on windward surface gradually increased, and the maximum drifted from the front surface to the windward. When the sideslip angle was 90°, the maximum was the largest. But, when the angle was equal to 45°, the absolute value of negative pressure was the largest. Pressure on vehicles without cross-loaded structure was larger than that on vehicles with the structure.

3.2 Velocity distribution

Figure 6 shows speed contour lines around cross section of the mid-vehicle (namely vehicle 2) under different sideslip angles. From Fig. 6, we reached: 1) Airflow around the vehicle would become disordered with the sideslip angle increasing; 2) When the sideslip angle was 0°, airflow was symmetry about the vertical central axis of vehicle, and the airflow speed decreased gradually along the axis; 3) When the sideslip angle was larger than 0°, the airflow was no longer symmetrical, but separated at the top of double-deck container vehicle which was in a bluff-body shape. And air velocity above the separated line increased, but that below the line decreased; 4) There were a series of vortexes at the top and leeward side of the car body, so that negative pressure on the top and leeward surfaces increased; 5) For vehicles with cross-loaded structure, there were also some obviously complex vortexes above the separated line. The air velocity around vehicles with the structure was larger than that without it.

3.3 Aerodynamic force results

Figures 7 and 8 demonstrate the changing curves of lateral force and rolling moment of trains with sideslip angle increasing. To compare and analyze the lateral aerodynamic performance of the two different structure vehicles, we refined the curves of the mid-vehicle, as shown in Fig. 9.

As Figs. 7 and 8 showed, at the synthesis speed of 30 m/s with different sideslip angles, trains with two structures were both suffered positive lateral force and negative rolling moment. For the large cross area and large height of double-deck container, the lateral force and rolling moment of vehicles were both larger than those of the locomotive, and were reduced in the order of vehicle 1, vehicle 2, and vehicle 3. Suffered from the influence of inflow and wake flow, the lateral aerodynamic characteristics were different: with the sideslip angle increasing, the lateral force on locomotive and vehicle 3 increased, but that on vehicle 1, vehicle 2 and the two cross-loaded structures firstly increased and then decreased. Except for the rolling moment of vehicle 3 which increased with sideslip angle increasing, that of other cars and cross-loaded bodies all firstly increased and then decreased. From Fig. 9, when the sideslip angle was smaller than 75°, lateral force and rolling moment on the mid-vehicle both increased with the angle increasing, and the two forces of vehicle without the cross-loaded structure were larger than those of vehicle with the cross-loaded structure. When the sideslip was equal or larger than 75°, the lateral aerodynamic characteristics of the mid-vehicle were just opposite, the two lateral aerodynamic forces   decreased, and the forces of vehicles with cross-loaded structure were slightly larger than those without the cross-loaded structure.

Fig. 5 Pressure contours of double-deck container vehicles: (a) without cross-loaded structure; (b) with cross-loaded structure

Fig. 6 Velocity contour line around cross section of mid-vehicle: (a) Without cross-loaded structure; (b) With cross-loaded structure

Fig. 7 Changing curves of lateral force with sideslip angle: (a) Vehicle without cross-loaded structure; (b) Vehicle with cross-loaded structure

Fig. 8 Changing curves of rolling moment with sideslip angle: (a) Vehicle without cross-loaded structure; (b) Vehicle with cross-loaded structure

Fig. 9 Changing curves of aerodynamic forces with sideslip angle for mid-vehicle (vehicle 2): (a) Lateral force; (b) Rolling moment

3.4 Train-speed limits

For freight vehicles either with or without cross-loaded structure, the overturning wind speed for empty load must be lower than that for heavy load. Integrating the most unfavorable loaded circumstances, we chose the empty load form of a 40 ft box and a 48 ft box for the double-deck container vehicle without cross-loaded structure, to calculate the vehicle running speed limits under different wind grades.

In the running sections of the double-deck container vehicles, the minimum curve radius was 2 000 m, and the superelevation of outer rail on curve was 150 mm. According to GB/T 5599—1985, we chose the vehicle overturning factor D≤0.8 as the acceptable hazard rate. The impact of many forces needed to be considered in vehicle stability calculation. We can find the calculation equations from Ref. [15]. The calculation results are shown in Fig. 10 and Table 1. We can see that, in the process of train speed changing from 80 to 120 km/h, the critical wind speed decreased slightly. This was because the rolling moment growing effects caused by train speed increasing were nearly offset by the increasing of centrifugal force. When the 6-axis flat car was loaded of an empty 40 ft box and an empty 48 ft box at speed of 120 km/h, the overturning wind speed was 25.19 m/s (the 10th grade wind). And when wind reached the 12th grade, the 6-axis X2K double-deck container freight train should stop.

Fig. 10 Overturning wind speed for empty loaded double-deck container vehicle (40 ft and 48 ft) at different speeds

Table 1 Vehicle speed limits under different wind grade

4 Conclusions

1) For vehicles, except that windward surface suffered positive pressure, others are generally suffered negative one. With sideslip angle increasing, pressure on the front surface decreases, but that on the windward increases. Pressure on vehicles without cross-loaded structure is larger than that with the cross-loaded structure.

2) The airflow becomes disordered with the sideslip angle θ increasing: When θ=0°, the flow is symmetry about the car body vertical axis; When θ>0°, the flow is separated at the top of boxes into different-speed flow from the separated line; The air velocity around vehicles with cross-loaded structure is larger than that without the cross-loaded structure.

3) Lateral force F on cars is positive, but rolling moment M is negative. And the orders are in the order  of F_{vehicle 1}>F_{vehicle 2}>F_{vehicle 3}>F_Locomotive, M_{vehicle 1}>M_{vehicle 2}> M_{vehicle 3}>M_Locomotive.

4) For the mid-vehicle, the inflexion of lateral forces changing with the sideslip angle is θ=75°.

5) When the train speed is in the range of 80-120 km/h, the critical wind speed is increased. The freight train should stop when wind arrives at the 12th grade.

References

[1] LIU Hong-you, YANG Ai-guo. Dynamics performance simulation of double2deck container flat car [J]. Journal of Traffic and Transportation Engineering, 2004, 4(3): 20-24. (in Chinese)

[2] ALAM F, WATKINS S. Lateral stability of double stacked container wagon under crosswinds [C]// Proceedings of the International Conference on Mechanical Engineering (ICME2007). Dhaka, 2007: 79-85.

[3] HEMIDA H, BAKER C. Large-eddy simulation of the flow around a freight wagon subjected to a crosswind [J]. Computers and Fluids, 2010, 39(10): 1944-1956.

[4] FERREIRA A, VAZ P. Wind tunnel study of coal dust release from train wagons [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2004, 92(7/8): 565-577.

[5] BETTLE J, HOLLOWAY A, VENART J. A computational study of the aerodynamic forces acting on a tractor-trailer vehicle on a bridge in cross-wind [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2003, 91(5): 573-592.

[6] PASSMORE M, RICHARDSON S, IMAM A. An experimental study of unsteady vehicle aerodynamics [J]. Journal of Automobile Engineering, 2001, 215(7): 779-788.

[7] LIANG Xi-feng, HU Zhe-long, LIU Tang-hong. Analysis and comparison of aerodynamic performance of container flat wagon [J]. Journal of Central South University: Science and Technology, 2008, 39(4): 781-786. (in Chinese)

[8] KHIER W, BREUER M, DURST F. Flow structure around trains under side wind conditions: A numerical study [J]. Computers & Fluids, 2000, 29(3): 179-195.

[9] SUZUKI M, TANEMOTO K, MAEDA T. Aerodynamic characteristics of train/vehicles under cross winds [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2003, 91(1/2): 209-218.

[10] GAO Guang-jun, TIAN Hong-qi, ZHANG Jian. Cross-wind affection on double container train [J]. Journal of Traffic and Transportation Engineering, 2004, 4(2): 45-48. (in Chinese)

[11] WANG Fu-jun. Analysis of computational fluid dynamics [M]. Beijing: Tsinghua University Press, 2004: 7-12. (in Chinese)

[12] LI Yan-fei, Liang Xi-feng. Aerodynamic function and stability influence of high-speed moving EMUs on insulated boards [J]. Journal of Central South University: Science and Technology, 2009, 40(6): 1587-1592. (in Chinese)

[13] FINNEMORE E J, FRANZINI J B. Fluid mechanics with engineering applications [M]. Columbus: McGraw-Hill, 2002: 286-292.

[14] LI Yan-fei, LIANG Xi-feng. Comparison of aerodynamic performances between double container car and boxcar [J]. Journal of Central South University: Science and Technology, 2009, 40(1): 169-174. (in Chinese)

[15] GAO Guang-jun, TIAN Hong-qi, YAO Song, LIU Tang-hong. Effect of strong cross-wind on the stability of trains running on the Lanzhou-Xinjiang railway line [J]. Journal of the China Railway Society, 2004, 26(4): 36-40. (in Chinese)

(Edited by YANG Bing)

Foundation item: Project supported by Scholarship Award for Excellent Doctoral Student granted by Ministry of Education, China; Project(2012QNZT029) supported by the Fundamental Research Funds for the Central Universities of China; Project(CX2010B122) supported by Hunan Provincial Innovation Foundation for Postgraduate, China; Project(2010ybfz088) supported by the Foundation of Excellent Doctoral Dissertation of Central South University, China

Received date: 2011-04-18; Accepted date: 2011-09-09

Corresponding author: LI Yan-fei, PhD Candidate; Tel: +86-13107486861; E-mail: zhongnanyanfei@yahoo.com.cn