Theoretical calculation and numerical simulation of different static airtightness of trains

Abstract

With increasingly stringent requirements for the airtightness of high-speed train bodies, determining appropriate airtightness levels has become critically important. To calculate the airtightness of high-speed train bodies more accurately, based on one-dimensional isentropic flow theory, this study derives cabin pressure calculation models for both positive and negative pressure conditions during static airtightness tests of high-speed train bodies. Since the flow coefficient, which is closely related to the leakage characteristics of the carriage, is influenced by multiple factors including operating pressure conditions (positive/negative), leakage path cross-sectional shape, and size, a flow coefficient calibration method is proposed to achieve high-precision and efficient calibration of the flow coefficient for trains with varying leakage properties. This method generates a series of flow coefficient values for circular and square cross-sectional shapes under both positive and negative pressure conditions across various cross-sectional areas. Furthermore, functional relationships between flow coefficient and leakage path area under positive/negative pressure are established through curve fitting. Using these functional relationships and the cabin pressure calculation model, the pressure variation curves for a static airtightness test are simulated. Specifically, for circular cross-sectional shapes, the theoretical curves under positive and negative pressure conditions exhibited R² values of 0.9936 and 0.9931, respectively, when compared to experimental data, and for square cross-sectional shapes, the corresponding R² values are 0.9928 and 0.9932, validating the accuracy of the proposed theoretical model. The proposed theoretical model effectively evaluates the airtightness of high-speed train bodies with varying performance levels during static airtightness tests, providing a robust theoretical reference for optimizing high-speed train airtightness design.

Keywords

train airtightness / static leak / flow rate coefficient / high-speed train / computational fluid dynamics

References

[1] He D-hua. The study of pressure comfort criterion for high-speed train [J]. Railway Locomotive & Car, 2016, 36(3): 1-610

[2] Mei Y-g, Zhang C-y, Zhou Z-het al.. Research on the aural discomfort when a single train passes through a super long tunnel [J]. Journal of Mechanical Engineering, 2015, 51(14): 100-107 in Chinese)

[3] Wang Q-x, Hu Z-l, Liang X-fet al.. Relationship among internal pressure, body air tightness and external pressure of rail vehicle [J]. Journal of Traffic and Transportation Engineering, 2018, 18(4): 103-111(in Chinese)

[4] Zhang Y-l, Zhang Z-c, Yang W-cet al.. The human comfort degree analysis of high speed trains intersection at the same speed in the tunnel [J]. Journal of Zhengzhou University (Engineering Science), 2017, 38(2): 26-29(in Chinese)

[5] Huang J, He H, Yang W-cet al.. Influence of altitude on transient pressure and ride comfort in railway tunnel [J]. Journal of Railway Science and Engineering, 2022, 19(3): 608-615(in Chinese)

[6] Li W-x, Xu S-d. The air-tightness technology and standards of high-speed multiple unit and passenger cars [J]. Railway Quality Control, 2013, 41(5): 10-12(in Chinese)

[7] Mei Y-g, Wang Z-j, Lyu Bet al.. Full-scale experiment on pressure changes inside and outside high-speed trains in tunnels [J]. Journal of Traffic and Transportation Engineering, 2023, 23(2): 183-198(in Chinese)

[8] Mei Y-g, Ma Y, Wang L. Numerical simulation study on dynamic air-tightness thresholds characteristics of high-speed train body in mountain area high speed railway [J]. Journal of Mechanical Engineering, 2020, 56(12): 196-206 in Chinese)

[9] Du Q, Du Y-c, Yang Ret al.. Full-scale test on internal and external pressure wave characteristics of high-speed trains in long, steep tunnels and tunnel group environments [J]. Tunnel Construction, 2024, 44(7): 1454-1464(in Chinese)

[10] Wan Y-c, Zhou X-x, Mei Y-g. Characteristics of pressure wave inside and outside high-speed train passing through high-elevation and large gradient tunnels [J]. China Railway Science, 2023, 44(1): 167-176(in Chinese)

[11] Wang Z-j, Mei Y-g. Field study of pressure comfort environment characteristics of high-speed train [J]. Acta Aerodynamica Sinica, 2021, 39(5): 170-180(in Chinese)

[12] Zhang F-t, Li W-b, Li B. Technical discussion of the EMU air-tightness [J]. Railway Locomotive & Car, 2015, 35(6): 44-4672

[13] Xia Y-t, Chen X-d, Liu T-het al.. A study on the airtightness of a high-speed train using a reduced-scale method [J]. Measurement, 2022, 188: 110610

[14] Xia Y-t, Liu T-h, Wang X-ret al.. Piecewise linear representation of pressure wave data of high-speed trains traveling through tunnels [J]. Journal of Central South University, 2023, 30(7): 2411-2426

[15] Fang F-y, Liu T-h, Xia Y-tet al.. Aerodynamic effects of trains circulating through a bifurcated tunnel [J]. Journal of Central South University, 2024, 31(3): 1017-1031

[16] Liu T-h, Geng S-g, Chen X-det al.. Numerical analysis on the dynamic airtightness of a railway vehicle passing through tunnels [J]. Tunnelling and Underground Space Technology, 2020, 97: 103286

[17] Guo Z-j, Liu T-h, Zhou L. Study of differences in train-induced slipstream characteristics with different platform configurations [J]. Journal of Central South University (Science and Technology), 2023, 54(5): 2039-2048(in Chinese)

[18] Zhou M-m, Liu T-h, Xia Y-tet al.. Comparative investigations of pressure waves induced by trains passing through a tunnel with different speed modes [J]. Journal of Central South University, 2022, 29(8): 2639-2653

[19] Zeng H-y, Liu T-h, Chen X-det al.. Study on the influence of asymmetric mountain structures at tunnel portals on the aerodynamics of intersecting trains [J]. Transportation Safety and Environment, 2025, 7: tdaf016

[20] Zhang J, Zhang M-l, Han Set al.. A novel asymptotic linear method for micro-pressure wave mitigation at high-speed maglev tunnel exit: A case study with various open ratios on tunnel hoods [J]. Journal of Central South University, 2025, 32(5): 1955-1972

[21] Zhou D, Li J-z, Li X-fet al.. Experimental study on ventilation shaft locations for alleviating transient pressure induced by high-speed trains passing through underground station [J]. Journal of Central South University, 2023, 30(7): 2427-2440

[22] Liu Z, Liu F, Yao S-bet al.. Research on numerical simulation of transient pressure for high-speed train passing through the most unfavourable length tunnel [J]. Transportation Safety and Environment, 2023, 5(3): tdac059

[23] Xue R-d, Xiong X-h, Wang K-wet al.. Influence of variable cross-section on pressure transients and unsteady slipstream in a long tunnel when high-speed train passes through [J]. Journal of Central South University, 2023, 3031027-1046

[24] Chen C-j, Nie X-c, Tang M. Transfer function model of the air pressure inside CRH2 EMU under outside air pressure [J]. China Railway Science, 2013, 34(4): 84-88(in Chinese)

[25] Mu B-y, Chen C-j, Yang L. Model of interior pressure fluctuation in high-speed trains considering the dynamic characteristics of variable air volume systems [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2025, 258: 106021

[26] Chen C-j, Feng Y-p, He Z-yet al.. Primary study on variation law of tightness and dynamic air tightness model of high-speed train [J]. Journal of the China Railway Society, 2021, 43(9): 18-23(in Chinese)

[27] Chen C-j, He Z-y, Feng Y-pet al.. Semi-empirical model of internal pressure for a high-speed train under the excitation of tunnel pressure waves [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2022, 236(7): 803-815

[28] Yang L, Chen C-j, Wang X-ret al.. Internal pressure fluctuation modelling and passenger pressure comfort analysis of high-speed trains passing through extreme tunnels [J]. Building and Environment, 2024, 251: 111200

[29] Chen C-j, Cao Y-x, He Z-yet al.. Iterative learning control of interior pressure under excitation of tunnel pressure wave with fixed form [J]. Journal of Southwest Jiaotong University, 2024, 59(1): 20-28(in Chinese)

[30] Xu L-z, Liang X-f, Liu T-het al.. Pressure variation test inside full-scale high-speed train running in open area [J]. Journal of Central South University (Science and Technology), 2014, 45(8): 2878-2884(in Chinese)

[31] Li T, Dai Z-y, Zhang J-yet al.. Theoretical model and calculation of static leakage for train air tightness [J]. Journal of Traffic and Transportation Engineering, 2020, 20(1): 150-158(in Chinese)

[32] Luo J-j. Aerodynamic effect induced by high-speed train entering into tunnel in high altitude area [J]. Journal of Southwest Jiaotong University, 2016, 51(4): 607-614(in Chinese)

[33] Liu A-h, Zhou X-y, Xu C-cet al.. Quantitative study on orifice leakage flow coefficient of urban gas pipeline [J]. Journal of Safety and Environment, 2024, 24(5): 1701-1709(in Chinese)

[34] Wan B-m, Cao J, Li C-cet al.. Experiment on discharge coefficients for outlet lateral dilated hole [J]. Journal of Aerospace Power, 2021, 36(11): 2325-2330(in Chinese)

RIGHTS & PERMISSIONS

Central South University