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Pantographs are important devices on high-speed trains. When a train runs at a high speed, concave and convex parts of the train cause serious airflow disturbances and result in flow separation, eddy shedding, and breakdown. A strong fluctuation pressure field will be caused and transformed into aerodynamic noises. When high-speed trains reach 300 km/h, aerodynamic noises become the main noise source. Aerodynamic noises of pantographs occupy a large proportion in far-field aerodynamic noises of the whole train. Therefore, the problem of aerodynamic noises for pantographs is outstanding among many aerodynamics problems. This paper applies Detached Eddy Simulation (DES) to conducting numerical simulations of flow fields around pantographs of high-speed trains which run in the open air. Time-domain characteristics, frequency-domain characteristics, and unsteady flow fields of aerodynamic noises for pantographs are obtained. The acoustic boundary element method is used to study noise radiation characteristics of pantographs. Results indicate that eddies with different rotation directions and different scales are in regions such as pantograph heads, hinge joints, bottom frames, and insulators, while larger eddies are on pantograph heads and bottom frames. These eddies affect fluctuation pressures of pantographs to form aerodynamic noise sources. Slide plates, pantograph heads, balance rods, insulators, bottom frames, and push rods are the main aerodynamic noise source of pantographs. Radiated energies of pantographs are mainly in mid-frequency and high-frequency bands. In high-frequency bands, the far-field aerodynamic noise of pantographs is mainly contributed by the pantograph head. Single-frequency noises are in the far-field aerodynamic noise of pantographs, where main frequencies are 293 Hz, 586 Hz, 880 Hz, and 1173 Hz. The farther the observed point is from the noise source, the faster the sound pressure attenuation will be. When the distance of two adjacent observed points is increased by double, the attenuation amplitude of sound pressure levels for pantographs is around 6.6 dB.

With the rapid development of high-speed trains, the running speed of trains is increased continuously, and train bodies are developed towards a lighter weight. Meanwhile, aerodynamic problems caused by high-speed trains become more and more significant. Especially, aerodynamic problems of pantographs have drawn immediate attention of scientific researchers.

Pantographs are an important device on the top of high-speed trains. When a train runs at a high speed, concave and convex parts on the train will cause serious disturbance on airflows and make them generate complicated flow separation, eddy shedding, and breakdown. As a result, a strong fluctuation pressure field will be caused and transformed into aerodynamic noises [

At present, researches on aerodynamic noises of pantographs are relatively underdeveloped compared with researches on the complete train structure and system. Researches on aerodynamic noises of pantographs are mainly completed by experimental test and numerical simulation. Experimental tests are divided into wind tunnel tests and full-scale model with real trains. Noger et al. [

In those published papers, just using wind tunnel or real-train tests has a high cost and low efficiency, while the repeatability of experimental results is poor. The problem has been solved very effectively by the reported numerical simulation. However, most researches fail to verify the numerical model using experimental test, and the reliability of studied results cannot be ensured. The approach of noise numerical simulation mainly depends on acoustic analogy theory and cannot conduct systematic researches on noise radiation characteristics. Aiming at these problems, this paper conducted an in-depth research on generation mechanism, sources, and radiation characteristics of aerodynamic noises for pantographs based on acoustic analogy theory and boundary element method. The reliability of numerical models is also verified by experimental test. Studied results prove that, in high-frequency bands, the far-field aerodynamic noise of pantographs is mainly contributed by the pantograph head. Single-frequency noises are in the far-field aerodynamic noise of pantographs, where main frequencies are 293 Hz, 586 Hz, 880 Hz, and 1173 Hz.

With the development of computer technologies, computational aeroacoustics have gradually developed into an important tool which explores aerodynamic noise mechanism, finds noise source positions, and predicts noises. The method of combining CFD and acoustic analog theory [

Aerodynamic noises are the result of interactions between fluid and structure when fluids flow through the solid surface. As universal fluid software, Fluent integrates strong computation ability for aerodynamic noises. By solving fluid dynamics equations, Fluent can directly achieve generation and propagation of acoustic waves. The direct computation method is called CAA (Computational Aero Acoustics). Viscidity and turbulence effects are simulated accurately through directly solving nonsteady N-S equations and Reynolds average RANS equations [

Based on the Lighthill equation, FW-H (Ffowcs Williams and Hawkings) applied the generalized Green function to generalize the Lighthill acoustic analogy theory into a flow noise issue with arbitrary solid boundaries, obtaining a FW-H equation which is widely applied at present [

Figure

Geometric model of pantographs in high-speed trains.

The computational domain is shown in Figure

The computational domain of pantographs in high-speed trains.

Trimmer meshes are used to divide meshes of the computational domain of pantographs. Boundary layer meshes are divided on the surface of pantographs. Meanwhile, refined mesh regions are set around the pantograph. The maximum mesh size on the surface of pantographs is 15 mm. Maximum size of space meshes is 500 mm. In order to control the mesh quality of around the pantograph, refined regions around the pantograph are divided into 2 blocks. The maximum mesh size of small block is 15 mm, and the maximum mesh size of big block is 30 mm, as shown in Figure

Refined meshes in the computational domain of pantographs.

Surface meshes and boundary layer meshes of pantographs.

In order to speed up the convergence, three-dimensional incompressible viscidity steady computation is conducted firstly. Then, steady results are taken as the initial value of transient computation in the transient flow field. Sound source information is extracted till the physical field becomes steady, and the extracted sound source information is stored in a neutral document. Finally, sound source information in the neutral document is read. FW-H equation is used to solve noise values of observed points in the acoustic field.

RNG

LES turbulence model is used for the transient computation. Smagorinsky-Lilly subgrid model based on hybrid length theory is used for simulating small-scale eddies. Second-order implicit expression is used as the time difference scheme. PISO algorithm is used for coupling between pressures and velocities. PRESTO format is used for separating continuous equations. Bounded Central Differencing is used to separate the momentum equation.

In addition, time step length

The computation model of flow field for pantographs is very complicated, so its reliability should be verified by experimental test. The pantograph studied in the paper is a standard structure, and relevant aerodynamic characteristics are tested by a lot of published papers. Li et al. [

Experimental test and comparison of aerodynamic resistance for pantographs.

The experimental test proves the reliability of the numerical model of pantographs. Therefore, the model can be used to study the subsequent contents. Contours of surface pressures of pantographs with running speed of 350 km/h are extracted, as shown in Figure

Contours of surface pressures.

Figure

Velocity distributions at center cross section.

Figure

Eddy distributions on center cross section of pantographs.

Figure ^{2}, 1000/s^{2}, 2000/s^{2}, 5000/s^{2}, 10000/s^{2}, and 20000/s^{2}. It is shown in Figure

Distribution contours of velocity isosurface based on Q-criterion for pantographs.

Velocity isosurface = 500/s^{2}

Velocity isosurface = 1000/s^{2}

Velocity isosurface = 2000/s^{2}

Velocity isosurface = 5000/s^{2}

Velocity isosurface = 10000/s^{2}

Velocity isosurface = 20000/s^{2}

Broadband Noise Sources Model in the software STAR-CCM+ is used to compute the distribution of noise sources on the surface of pantographs. Therefore, useful noise source information can be obtained and help to judge the parts which mainly generated noises. However, it cannot be used to predict the radiation of visible noises. Noise source distribution on the pantograph surface can be denoted by dipole noise sources, and the environment noise can be denoted by quadrupole noise sources.

Figure

Distribution of dipole noise sources.

Distribution of quadrupole noise sources for pantographs.

The longitudinal center symmetric plane

Location 0.2 m away from the longitudinal center plane

Location 0.4 m away from the longitudinal center plane

In order to study distribution characteristics of aerodynamic noises of pantographs in the far-field, 5 observed points are placed around the geometric center of pantographs along the horizontal direction. Two observed points satisfied duplation relations, where coordinates are as follows:

Distribution of observed points of aerodynamic noises in the far-field.

A-weighting is conducted on sound pressures of the aerodynamic noise at observed points. Hann window is selected for processing data. Overlap Factor is 0.5. Start point of data recording is 0.25 s. End point of data recording is 0.7 s. Therefore, based on the processed data, the highest frequency is 5000 Hz, and the frequency resolution is 2 Hz. Figure

Comparisons of frequency spectrums at observed points.

Observed point

Observed point

Observed point

Observed point

Observed point

The analyzed results prove that pantographs are a main aerodynamic noise source of high-speed trains. Therefore, this part mainly studies radiating characteristics of aerodynamic noises for pantographs which run at speed of 350 km/h. Time-domain signals of fluctuation pressures of pantographs are extracted in the flow field. The boundary element method is used to solve sound pressures on receiving points because it can compute the acoustic results more quickly. According to the rule of the boundary element mesh, one wave length should include six elements. The computational frequency is 5000 Hz, and the element size should be less than 11 mm. In this paper, the maximum element size is 10 mm. Therefore, there are 5021 elements and 5832 nodes. Acoustic software VIRTUAL.LAB is used to compute acoustic propagation on the pantograph surface [

Acoustic meshes of pantographs in high-speed trains.

Aerodynamic noise radiation of pantographs in high-speed trains.

The first main frequency = 293 Hz

The second main frequency = 586 Hz

The third main frequency = 880 Hz

The fourth main frequency = 1173 Hz

Results in Figure

The authors declare that there are not any conflicts of interest regarding the publication of this paper.

This work was supported by NSFC Projects of International Cooperation and Exchanges (Grant no. 71611530712) and by Fundamental Research Funds for the Central Universities of China (Grant no. 201713051).