Abstract: Understanding the aerodynamic and dynamic characteristics of unloaded freight trains in crosswinds is pivotal for ensuring their operational safety and reliability. The dynamic performance of unloaded gondola cars under varying windbreak heights is therefore investigated in this study, revealing distinct differences in lateral stability and safety indicators, and enabling the determination of an optimal windbreak height. A 3D unsteady aerodynamic model was developed using the improved delayed detached eddy simulation (IDDES) method and an overset numerical mesh. Also leveraging a multi-body dynamics (MBD) model of a three-wagon freight car configuration, we investigate time-averaged aerodynamic forces, transient flow field distributions, and nonlinear dynamic responses. Parametric analyses reveal a non-monotonic relationship between the height of the windbreak and the stability of the train. A windbreak with a critical height of 2 m (0.74 relative to the car body height) results in 76%, 64%, and 81% lower values of the derailment coefficient C_D, wheel unloading ratio R, and overturning coefficient C_O, respectively. Notably, when the height of the windbreak exceeds 2 m, vortices within the gondola induce an adverse pressure coefficient distribution (C_p=-2.17) on the leeward internal wall, intensifying the lateral force and overturning moment. Furthermore, frequency-domain analysis reveals that the lateral sway and overturning vibration mode are associated with low-frequency (1.61 Hz) lateral vibrations under crosswind conditions. This study provides a theoretical foundation for the design and optimization of railway windbreaks.

基于计算流体力学和多体动力学的横风下空载敞车挡风墙结构对比研究

[1]AnderssonE, HäggströmJ, SimaM, et al., 2004. Assessment of train-overturning risk due to strong cross-winds. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 218(3):213-223.

[2]CheliF, CorradiR, RocchiD, et al., 2010. Wind tunnel tests on train scale models to investigate the effect of infrastructure scenario. Journal of Wind Engineering and Industrial Aerodynamics, 98(6-7):353-362.

[3]DaiZY, LiT, ZhangWH, et al., 2024. Investigation on aerodynamic characteristics of high-speed trains with shields beneath bogies. Journal of Wind Engineering and Industrial Aerodynamics, 246:105666.

[4]FlynnD, HemidaH, BakerC, 2016. On the effect of crosswinds on the slipstream of a freight train and associated effects. Journal of Wind Engineering and Industrial Aerodynamics, 156:14-28.

[5]GaoGJ, DuanLL, 2011. Height of wind barrier on embankment of single railway line. Journal of Central South University (Science and Technology), 42(1):254-259 (in Chinese).

[6]GaoGJ, LiP, 2011. Runing stability of container car in Qinghai—Tibet railway line. Journal of Central South University (Science and Technology), 42(2):533-538 (in Chinese).

[7]GaoHR, LiuTH, ChenXD, et al., 2024. Flow characteristics induced by a multiform windbreak in complex terrains with and without a train: a simplified method for calculating aerodynamic loads. Physics of Fluids, 36(12):125115.

[8]GaoHR, LiuTH, ChenXD, et al., 2025. Aerodynamic and dynamic behaviour of a train in cutting-viaduct-cutting sections with windbreaks in complex terrains under crosswinds: key factors. Engineering Structures, 328:119728.

[9]GeX, LingL, GuoLR, et al., 2022. Dynamic derailment simulation of an empty wagon passing a turnout in the through route. Vehicle System Dynamics, 60(4):1148-1169.

[10]GolovanevskiyVA, ChmovzhVV, GirkaYV, 2012. On the optimal model configuration for aerodynamic modeling of open cargo railway train. Journal of Wind Engineering and Industrial Aerodynamics, 107-108:131-139.

[11]GuoZJ, LiuTH, LiuZ, et al., 2021. An IDDES study on a train suffering a crosswind with angles of attack on a bridge. Journal of Wind Engineering and Industrial Aerodynamics, 217:104735.

[12]HashmiSA, HemidaH, SoperD, 2019. Wind tunnel testing on a train model subjected to crosswinds with different windbreak walls. Journal of Wind Engineering and Industrial Aerodynamics, 195:104013.

[13]HeWT, HuYL, GeX, et al., 2025. Research on operational safety of empty gondola cars in freight trains subjected to crosswind. Engineering Mechanics, 42(1):249-258 (in Chinese).

[14]HuX, DengZG, ZhangWH, 2021. Effect of cross passage on aerodynamic characteristics of super-high-speed evacuated tube transportation. Journal of Wind Engineering and Industrial Aerodynamics, 211:104562.

[15]HuYL, GeX, LingL, et al., 2025. Dynamic performance of a high-speed train exiting a tunnel under crosswinds. Journal of Zhejiang University-SCIENCE A, 26(1):21-35.

[16]LiC, BurtonD, KostM, et al., 2017. Flow topology of a container train wagon subjected to varying local loading configurations. Journal of Wind Engineering and Industrial Aerodynamics, 169:12-29.

[17]LiNX, LiT, DaiZY, et al., 2024. Effect of streamlined nose length on aerodynamic performance of high-speed train with a speed of 400 km/h. Journal of Zhejiang University-SCIENCE A, 25(7):525-540.

[18]LiT, QinD, ZhangJY, 2019. Effect of RANS turbulence model on aerodynamic behavior of trains in crosswind. Chinese Journal of Mechanical Engineering, 32(1):85.

[19]LiT, LiangH, ZhangJ, et al., 2023. Numerical study on aerodynamic resistance reduction of high-speed train using vortex generator. Engineering Applications of Computational Fluid Mechanics, 17(1):e2153925.

[20]LiT, LiYF, WeiL, et al., 2025. Comparative study on lateral vibration characteristics of the head and tail cars of high-speed trains under unsteady aerodynamic loadings. Vehicle System Dynamics, 63(3):518-536.

[21]LiangH, SunY, LiT, et al., 2023. Influence of marshalling length on aerodynamic characteristics of urban emus under crosswind. Journal of Applied Fluid Mechanics, 16(1):9-20.

[22]LiuTH, WangL, GaoHR, et al., 2022. Research progress on train operation safety in Xinjiang railway under wind environment. Transportation Safety and Environment, 2(4):tdac005.

[23]MalekiS, BurtonD, ThompsonMC, 2017. Assessment of various turbulence models (ELES, SAS, URANS and RANS) for predicting the aerodynamics of freight train container wagons. Journal of Wind Engineering and Industrial Aerodynamics, 170:68-80.

[24]MalekiS, BurtonD, ThompsonMC, 2019. Flow structure between freight train containers with implications for aerodynamic drag. Journal of Wind Engineering and Industrial Aerodynamics, 188:194-206.

[25]MalekiS, BurtonD, ThompsonMC, 2020. On the flow past and forces on double-stacked wagons within a freight train under cross-wind. Journal of Wind Engineering and Industrial Aerodynamics, 206:104224.

[26]MenterFR, 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 32(8):1598-1605.

[27]MohebbiM, RezvaniMA, 2019. Analysis of the effects of lateral wind on a high speed train on a double routed railway track with porous shelters. Journal of Wind Engineering and Industrial Aerodynamics, 184:116-127.

[28]MohebbiM, MaY, MohebbiR, 2025. Enhancing high-speed train stability: unraveling the influence of sloping crosswind shields on aerodynamic characteristic. Engineering Structures, 326:119569.

[29]MoukalledF, ManganiL, DarwishM, 2016. The Finite Volume Method in Computational Fluid Dynamics. Springer, Cham, Germany.

[30]NiuJQ, ZhouD, LiangXF, 2018. Numerical investigation of the aerodynamic characteristics of high-speed trains of different lengths under crosswind with or without windbreaks. Engineering Applications of Computational Fluid Mechanics, 12(1):195-215.

[31]NiuJQ, ZhangYC, LiR, et al., 2022. Aerodynamic simulation of effects of one- and two-side windbreak walls on a moving train running on a double track railway line subjected to strong crosswind. Journal of Wind Engineering and Industrial Aerodynamics, 221:104912.

[32]NoguchiY, SuzukiM, BakerC, et al., 2019. Numerical and experimental study on the aerodynamic force coefficients of railway vehicles on an embankment in crosswind. Journal of Wind Engineering and Industrial Aerodynamics, 184:90-105.

[33]NRA (National Railway Administration of the People’s Republic of China), 2016. Code for Design of Railway Earth Structure, TB10001-2016. National Standards of the People’s Republic of China(in Chinese).

[34]NRA (National Railway Administration of the People’s Republic of China), 2017. Code for Design of Railway Line, TB10098-2017. National Standards of the People’s Republic of China(in Chinese).

[35]PanYM, LiZP, WangXF, et al., 2025. Effect of side track height on aerodynamic characteristics of a high-speed high-temperature superconducting maglev train under crosswind. Journal of Zhejiang University-SCIENCE A, 26(10):983-996.

[36]QuaziA, CrouchT, BellJ, et al., 2023. A field study on the aerodynamics of freight trains with different stacking configurations. Journal of Wind Engineering and Industrial Aerodynamics, 232:105245.

[37]RAIB (Rail Accident Investigation Branch), 2009. Detachment of Containers from Freight Wagons Near Cheddington and Hardendale, 1 March 2008. Rail Accident Report, RAIB, UK.

[38]SAMR (State Administration for Market Regulation), 2019. Specification for Dynamic Performance Assessment and Testing Verification of Rolling Stock, GB/T5599-2019. National Standards of the People’s Republic of China(in Chinese).

[39]ShurML, SpalartPR, StreletsMK, et al., 2008. A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. International Journal of Heat and Fluid Flow, 29(6):1638-1649.

[40]SunZ, DaiHY, GaoH, et al., 2019. Dynamic performance of high-speed train passing windbreak breach under unsteady crosswind. Vehicle System Dynamics, 57(3):408-424.

[41]SunZ, DaiHY, HemidaH, et al., 2020. Safety of high-speed train passing by windbreak breach with different sizes. Vehicle System Dynamics, 58(12):1935-1952.

[42]SuzukiM, TanemotoK, MaedaT, 2003. Aerodynamic characteristics of train/vehicles under cross winds. Journal of Wind Engineering and Industrial Aerodynamics, 91(1-2):209-218.

[43]TianHQ, 2015. Determination method of load balance ranges for train operation safety under strong wind. Journal of Central South University, 22(3):1146-1154.

[44]WangG, LiQZ, LiuY, 2021. IDDES method based on differential Reynolds-stress model and its application in bluff body turbulent flows. Aerospace Science and Technology, 119:107207.

[45]WenJC, LiQ, LuZG, 2024. Safety of an express freight train running over a bridge in crosswind. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 238(1):89-101.

[46]XueRD, XiongXH, ChenG, et al., 2025. Numerical comparison of aerodynamic performance between stationary and moving trains with varied-height windbreak wall under crosswind. Alexandria Engineering Journal, 110:540-556.

[47]YangF, LiuTH, ShiZL, et al., 2021. Influence of height of earth embankment type windbreak wall on flow field characteristics and catenary wind-induced displacement. Engineering Applications of Computational Fluid Mechanics, 15(1):672-691.

[48]ZhangD, GuoZH, NiYQ, et al., 2023. Correlation between cargo properties and train overturning safety for a high-speed freight train under strong winds. Engineering Applications of Computational Fluid Mechanics, 17(1):221308.

[49]ZhangJ, LiangXF, LiuTH, et al., 2011. Optimization research on aerodynamic shape of passenger car body with strong crosswind. Journal of Central South University (Science and Technology), 42(11):3578-3584 (in Chinese).

[50]ZhangQY, ZhouSQ, XuG, et al., 2024. Integrated CFD and MBD methods for dynamic performance analysis of a high-speed train transitioning through varied windbreak corridor designs. Journal of Wind Engineering and Industrial Aerodynamics, 250:105755.

[51]ZhaoL, YangWC, LiuYK, et al., 2024. Effects of windbreak types on aerodynamics of high-speed trains traversing from flat ground to semi-cutting and semi-embankment under crosswinds. Physics of Fluids, 36(7):075115.

[52]ZhouD, YuDZ, WuLL, et al., 2023. Numerical investigation of the evolution of aerodynamic behaviour when a high-speed train accelerates under crosswind conditions. Alexandria Engineering Journal, 72:51-66.

[53]ZhuFT, XieJW, LvDZ, et al., 2024. Transient aerodynamic behavior of a high-speed Maglev train in plate braking under crosswind. Physics of Fluids, 36(3):035133.

[54]ZhuangYQ, LuXY, 2015. Numerical investigation on the aerodynamics of a simplified high-speed train under crosswinds. Theoretical and Applied Mechanics Letters, 5(5):181-186.