Numerical method for micro-pressure wave noise prediction based on turbulence model evaluation and time window optimization

Abstract

The micro-pressure waves (MPWs) generated by a high-speed train entering a tunnel are a significant noise source affecting the acoustic environment near tunnel exits. Accurate prediction of MPW noise strongly depends on the selection of turbulence models and the treatment of transient impulsive sources. In this study, the generation of MPWs induced by a high-speed metro train was numerically simulated using delayed detached eddy simulation (DDES), based on the k-epsilon (k-ε), Shear stress transport k-omega (SST k-ω), Spalart-Allmaras (S-A) turbulence models, and large eddy simulation (LES). The comparison indicates that the DDES (SST k-ω) model achieves an appropriate balance between computational accuracy and efficiency, accurately reproducing the waveform and pressure gradient characteristics of MPWs. Furthermore, based on these results, the far-field radiation from MPW noise was computed using the acoustic finite element method (FEM). In the MPW noise, dipole noise dominated, with its energy concentrated below 20 Hz and a peak frequency of 4 Hz. An optimal time window method was also proposed, encompassing 95% of the total MPW energy. This criterion effectively minimizes acoustic energy loss caused by overly short windows. It avoids waveform smoothing caused by excessively long windows, thereby improving the accuracy of MPW noise prediction. Finally, the time window method was verified using on-site test data. The findings offer practical guidance for accurately predicting and effectively controlling MPW noise in the rail transit system.

Keywords

tunnel portal / micro-pressure wave / turbulence models / micro-pressure wave noise / time window optimization

References

[1] Wang H-l, Vardy A E, Bi H-quan. Characteristics of pressure waves radiated from tunnel portals in cuttings [J]. Journal of Sound and Vibration, 2022, 521: 116664

[2] Wang H-l, Vardy A E, Bi H-quan. Micro-pressure wave radiation from tunnel portals in deep cuttings [J]. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 2023, 237(2): 166-178

[3] Zhang J, Wang Y-g, Han S, et al.. A novel arch latticeshell of enlarged cross-section hoods for micro-pressure wave mitigation at exit of maglev tunnels [J]. Tunnelling and Underground Space Technology, 2023, 132: 104859

[4] Wang K-w, Chen G, Wen C-y, et al.. Mitigation mechanism of porous media hood for the sonic boom emitted from maglev tunnel portals [J]. Physics of Fluids, 2024, 36(10): 106134

[5] Meng S, Zhou D, Xiong X-h, et al.. The effect of the nose length on the aerodynamics of a high-speed train passing through a noise barrier [J]. Flow, Turbulence and Combustion, 2022, 108(2): 411-431

[6] Saito S, Fukuda T. Design of a tunnel entrance hood for high-speed trains [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2020, 206: 104375

[7] Xiang X-t, Xue L-p, Wang B-l, et al.. Mechanism and capability of ventilation openings for alleviating micro-pressure waves emitted from high-speed railway tunnels [J]. Building and Environment, 2018, 132: 245-254

[8] Li T, Shao M-y, Ma W-b, et al.. Influence of segmented linings on the micro-pressure wave of tunnels [J]. Advances in Civil Engineering, 2023, 2023: 9451361

[9] Li W-h, Liu T-h, Huo X-s, et al.. Influence of the enlarged portal length on pressure waves in railway tunnels with cross-section expansion [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2019, 190: 10-22

[10] Miyachi T, Kikuchi K, Hieke M. Multistep train nose for reducing micro-pressure waves [J]. Journal of Sound and Vibration, 2022, 520: 116665

[11] Zhang J, Guo B-j, Wang Y-g, et al.. Influence of arch lattice-shell hood length on micro-pressure waves at portal of a high-speed maglev tunnel [J]. Physics of Fluids, 2024, 36(9): 096105

[12] Shi J-w, Zhang J-y, Li T. Numerical study on aerodynamic noise reduction of high-speed pantograph using base-frame fairing [J]. Railway Engineering Science, 2026, 34(2): 314-332

[13] Bodony D J, Lele S K. Current status of jet noise predictions using large-eddy simulation [J]. AIAA Journal, 2008, 46(2): 364-380

[14] Liu K, Zhou S-q, Li X-x, et al.. Flow-induced noise simulation using detached eddy simulation and the finite element acoustic analogy method [J]. Advances in Mechanical Engineering, 2016, 8(7): 1687814016655683

[15] Zhang L, Gao Y, Lin T-t, et al.. Comparative analysis of crosswind influence on aerodynamic characteristics of superconducting and normal-conducting high-speed maglev trains [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2025, 265: 106182

[16] Menter F R, Kuntz M. Adaptation of eddy-viscosity turbulence models to unsteady separated flow behind vehicles [C]. The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains, 2004, Berlin, Heidelberg, Springer339-352

[17] Sui Y, Niu J-q, Ricco P, et al.. Impact of vacuum degree on the aerodynamics of a high-speed train capsule running in a tube [J]. International Journal of Heat and Fluid Flow, 2021, 88: 108752

[18] Qin D, Li T, Zhou P, et al.. Effect of model scale and airflow velocity on aerodynamic noise prediction for high-speed train leading car and bogie [J]. Engineering Applications of Computational Fluid Mechanics, 2024, 18(1): 2384445

[19] Zhou P-h, Shen L, Han Y, et al.. A novel three-dimensional yaw wake analytical model and experimental validation using particle image velocimetry [J]. Energy, 2026, 344: 139885

[20] Saito S. Alleviation of micro-pressure waves radiated from tunnel hoods [J]. Tunnelling and Underground Space Technology, 2024, 147: 105703

[21] Lin T-t, Yang M-z, Zhang L, et al.. Influence of bionics shark gills tunnel portal on the micro-pressure wave at the tunnel exit [J]. Tunnelling and Underground Space Technology, 2024, 144: 105542

[22] Kikuchi, Lida, Takasaki, et al.. Field measurement of wayside low-frequency noise emitted from tunnel portals and trains of high-speed railway [J]. Noise Notes, 2006, 5(3): 5-18

[23] Tebbutt J A, Vahdati M, Carolan D, et al.. Numerical investigation on an array of Helmholtz resonators for the reduction of micro-pressure waves in modern and future high-speed rail tunnel systems [J]. Journal of Sound and Vibration, 2017, 400: 606-625

[24] Luo W-f, Wang H-l, Wu Y-d, et al.. Numerical studies on the radiation of micro-pressure wave noise at the tunnel exits [J]. Physics of Fluids, 2024, 36(9): 097154

[25] Ji P, Wang T-t, Wu F. Calculation grid and turbulence model for numerical simulating pressure fluctuations in high-speed train tunnel [J]. Journal of Central South University, 2019, 26(10): 2870-2877

[26] Spalart P R, Deck S, Shur M L, et al.. A new version of detached-eddy simulation, resistant to ambiguous grid densities [J]. Theoretical and Computational Fluid Dynamics, 2006, 20(3): 181-195

[27] Tan X-m, Yang Z-gang. Investigation on aerodynamic noise reduction for snow-plough of high-speed train [J]. Journal of Central South University, 2022, 29(5): 1735-1748

[28] Li Q-l, Li W, Hao X-w, et al.. Aerodynamic noise control of rearview mirror by steady and unsteady jets [J]. Applied Acoustics, 2022, 192: 108739

[29] Ffowcs Williams J E, Hawkings D L. Sound generation by turbulence and surfaces in arbitrary motion [J]. Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences, 1969, 264(1151): 321-342

[30] Qin D, Li T, Zhou N, et al.. Numerical study on the quadrupole sound source in aerodynamic noise of high-speed pantographs [J]. International Journal of Rail Transportation, 2025, 13(2): 313-331

[31] Thompson L L. A review of finite-element methods for time-harmonic acoustics [J]. The Journal of the Acoustical Society of America, 2006, 119(3): 1315-1330

[32] Wang K-w, Xiong X-h, Wen C Y, et al.. Formation and propagation characteristics of a weak shock wave in maglev tube [J]. Physics of Fluids, 2024, 36(3): 036120

[33] Berenger J P. A perfectly matched layer for the absorption of electromagnetic waves [J]. Journal of Computational Physics, 1994, 114(2): 185-200

[34] Hu X, Deng Z-g, Zhang J-w, et al.. Effect of tracks on the flow and heat transfer of supersonic evacuated tube maglev transportation [J]. Journal of Fluids and Structures, 2021, 107: 103413

[35] Wang T-t, Hu C, Zhang L, et al.. Research on the mechanism of micro-pressure waves in a high-speed train passing through a high geo-temperature tunnel [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2022, 226: 105031

[36] Ma W-b, Wen G-c, Zhu H-z, et al.. Sonic boom and alleviated measurements in Wan’an tunnel of Beijing-Hong Kong high-speed railway [J]. Tunnel Construction, 2024, 44(7): 1431-1439(in Chinese)

[37] Iyer R S, Kim D H, Kim H D. Effect of air chambers on the compression wave propagating along a high-speed railway tunnel [J]. Journal of Mechanical Science and Technology, 2023, 37(2): 793-805

[38] Zhang G, Kim T H, Kim D H, et al.. Prediction of micro-pressure waves generated at the exit of a model train tunnel [J]. Journal of Wind Engineering and Industrial Aerodynamics, 2018, 183: 127-139

RIGHTS & PERMISSIONS

Central South University

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.