Characteristics analysis of near-field and far-field aerodynamic noise around high-speed railway bridge

Abstract

The aerodynamic noise around the high-speed railway bridge is studied by the train-bridge-flow field numerical model and theory analysis. With the background of the Beijing-Shanghai high-speed railway line in China, based on the broadband noise sources method and acoustic analogy theory, both the intensity characteristics of near-field aerodynamic noise sources of the train and the spatial distribution characteristics of far-field aerodynamic noise around the bridge are analyzed. The results show that there is the largest sound source energy on the nose tip of the high-speed train; the fluctuating pressure between air and train surface contributes the most to aerodynamic noise; along the longitudinal direction of the bridge, the aerodynamic noise energy near the junction of train tail and body is the strongest; along the transverse direction of the bridge, the aerodynamic noise energy decreases gradually with the distance from the centerline of the railway; along the vertical direction, the aerodynamic noise energy is the strongest at a location of 1.2 m above the top surface of the rail; the train speed, train type, and the height variation of the bridge pier can affect the distribution of far-field aerodynamic noise.

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Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgments

The authors wish to thank all the experts who give guidance and help to the research, and also thank the grant of Beijing Natural Science Foundation (8202040) and 111 Project of China (B13002).

Funding

The research is supported by the grant of the Beijing Natural Science Foundation (8202040) and 111 Project of China (B13002).

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Authors

Contributions

Yanmei CAO, Zhe LI, and Meng MA developed the idea of the study, participated in its design and coordination and drafted the manuscript. Wei JI and Yanmei CAO contributed to the acquisition and interpretation of data. Zhe LI and Meng MA provided critical review and substantially revised the manuscript. All authors read and approved the final manuscript.

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Correspondence to Zhe Li.

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Appendices

Appendix 1

If the right side of Eq. (2) is regarded as the sound source term F(x, t), Eq. (2) is a typical acoustic wave equation:

$$ \left(\frac{1}{c_0^2}\frac{\partial^2}{\partial {t}^2}-{\nabla}^2\right)\left[{Hc}_0^2\left(\rho -{\rho}_0\right)\right]=F\left(x,t\right) $$
(9)

which can be solved using Green’s function.

When the high-speed train is running, the ground can be approximated as an interface with good sound reflection, so the sound field induced by the train is a semi-free field, and its Green’s function can be expressed as (Goldstein 1974):

$$ G\left(\mathbf{x},\mathbf{y};t-\tau \right)=\frac{\delta \left(t-\tau -\left|\mathbf{x}-\mathbf{y}\right|/{c}_0\right)}{4\uppi \left|\mathbf{x}-\mathbf{y}\right|}+\frac{\delta \left(t-\tau -\left|\mathbf{x}-\tilde{\mathbf{y}}\right|/{c}_0\right)}{4\uppi \left|\mathbf{x}-\tilde{\mathbf{y}}\right|} $$
(10)

where x = {x1, x2, x3}andy = {y1, y2, y3} are the receiving point vector and the source point vector in the Cartesian coordinate system, respectively; τ and t respectively represent the time emitted at the sound source point should be standardized form y and received at the receiving point x; \( \tilde{\mathbf{y}}=\left\{{y}_1,{y}_2,-{y}_3\right\} \) is symmetrical with y = {y1, y2, y3} about the ground.

Herein, the variables ρ = ρ − ρ0 and p = p − p0 are introduced. Based on Eq. (10) of Green’s function, Eq. (11) can be derived from Eq. (9):

$$ {\displaystyle \begin{array}{c}H{c}_0^2\left(\rho -{\rho}_0\right)=H{p}^{\prime}\left(x,t\right)={\iiint}_V{\int}_{-\infty}^{\infty }F\left(y,t\right)G\left(x,y;t-\tau \right)\mathrm{d}\tau \mathrm{d}V\\ {}=\frac{\partial^2}{\partial {x}_i\partial {x}_j}{\iiint}_V\left[{T}_{ij}\right]\frac{\mathrm{d}V}{2\uppi R}-\frac{\partial }{\partial {x}_i}{\oint}_S\left[\rho {u}_i\left({u}_j-{v}_j\right)+{p}_{ij}\right]\frac{\mathrm{d}{S}_j(y)}{2\uppi R}\\ {}+\frac{\partial }{\partial t}{\oint}_S\left\{\left[\rho \left({u}_j-{v}_j\right)+{\rho}_0{u}_j\right]\right\}\frac{\mathrm{d}{S}_j(y)}{2\uppi R}\\ {}\approx -\frac{\partial }{\partial {x}_i}{\oint}_S\left[\rho {u}_i\left({u}_j-{v}_j\right)+{p}_{ij}\right]\frac{\mathrm{d}{S}_j(y)}{2\uppi R}\end{array}} $$
(11)

where S and V are the integral surface and integral space, respectively; R is the distance from the sound source point y to the receiving point x; other mathematical symbols are as mentioned above.

By simplifying and solving Eq. (11), the theoretical prediction of Eq. (3) for the far-field aerodynamic noise can be obtained.

Appendix 2

Fig. 23
figure23

The discretization and grid of computational domain

Fig. 24
figure24

Two different types of train models. a CRH2. b CR400-BF

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Cao, Y., Li, Z., Ji, W. et al. Characteristics analysis of near-field and far-field aerodynamic noise around high-speed railway bridge. Environ Sci Pollut Res (2021). https://doi.org/10.1007/s11356-021-12417-8

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Keywords

  • Aerodynamic noise
  • High-speed railway bridge
  • Near-field noise
  • Far-filed noise
  • Spatial distribution
  • Influence factors