In order to understand the mechanism by which a pantograph can generate aerodynamic noise and grasp its far-field characteristics, a simplified double-strip pantograph is analyzed numerically. Firstly, the unsteady flow field around the pantograph is simulated in the frame of a large eddy simulation (LES) technique. Then the location of the main noise source is determined using surface fluctuating pressure data and the vortex structures in the pantograph flow field are analyzed by means of the Q-criterion. Based on this, the relationship between the wake vortex and the intensity of the aerodynamic sound source on the pantograph surface is discussed. Finally, the far-field aerodynamic noise is calculated by means of the Ffowcs Williams-Hawkings (FW-H) equation, and the contribution of each component to total noise and the frequency spectrum characteristics are analyzed. The results show that on the pantograph surface where vortex shedding or interaction with the wake of upstream components occurs, the pressure fluctuation is more intense, resulting in strong dipole sources. The far-field aerodynamic noise energy of the pantograph is mainly concentrated in the frequency band below 1500 Hz. The peaks in the frequency spectrum are mainly generated by the base frame, balance arm and the rear strip, which are also the main contributors to the aerodynamic noise.

With the continuous increase in train operation speed, train noise pollution becomes more and more serious. The noise radiated by high-speed trains seriously affects the life of residents along the line. It is urgent to take effective measures to reduce the noise levels of high-speed trains. The high-speed train noise mainly includes wheel/rail rolling noise and aerodynamic noise. It is generally believed that the aerodynamic noise increases with the speed faster than the wheel/rail rolling noise. According to the test results in Europe, when the speed exceeds 300 km/h, the aerodynamic noise will exceed the wheel/rail noise and occupy a dominant position [

There are two main methods for pantograph aerodynamic noise research, experiment and numerical simulation. In terms of experimental research, Noger et al. [

Although the aerodynamic noise results of pantograph under real conditions can be obtained by experimental research, the cost of experimental research is high and the flow field information can be obtained is limited. With the rapid development of computing technology, computational fluid dynamics (CFD) technology is gradually applied to the prediction of aerodynamic noise. More comprehensive flow field information can be obtained through numerical simulation, which can help people understand the mechanism of aerodynamic noise more deeply. In the aspect of numerical simulation, Yu et al. [

The purpose of this paper is to analyze the relationship between the vortex structures in the pantograph area and the pressure fluctuation(dipole source) on the surface of the pantograph to explore the generation mechanism of pantograph aerodynamic noise and master the far-field aerodynamic noise characteristics of the pantograph, including the spatial distribution characteristics of the far-field noise, the noise contribution of each component, the spectrum characteristics and the inflow velocity dependent regularity. Therefore, a simplified double-strip pantograph is taken as the research object. The unsteady flow field around the pantograph is simulated by LES model, and the far-field aerodynamic noise is calculated by FW-H equation. The arrangement of the paper is as follows. In

As the large eddy simulation (LES) model has a strong ability to capture vortices, it is first used to calculate the flow field around the pantograph to obtain accurate sound source data. Then the FW-H equation is used to calculate the far-field aerodynamic noise of the pantograph.

Large eddy simulation is a kind of spatial averaging of turbulent fluctuations. Its basic idea is to separate the large-scale vortices and small-scale vortices through filtering function, the large scale vortices are solved directly, while small scale vortices are solved by modeling. The governing equations employed for LES are filtered Navier-Stokes equations, which are as follows:

_{ij} is the viscous stress tensor, and _{t} is the sub-grid viscosity coefficient and _{ij} is Kronecker tensor, and the viscosity coefficient of sub-grid turbulence can be expressed as:_{s} is the mixed length of the grid, _{s} is the Samagorinsky constant, and

In 1969, Fwowcs Williams and Hawkings extended Lighthill and Curle’s results to consider the influence of the moving solid boundary by introducing generalized functions, and obtained a more general result-FW-H equation, as shown in _{0} is the sound speed, ^{′} is the sound pressure, _{0} is the density of the fluid at the undisturbed area, _{n} is the normal velocity component of the sound source surface, _{ij} is the Lighthill stress tensor.

If the right hand of _{e} indicates that the relevant variables are evaluated at restarted time _{e}, and _{e} = _{0}, _{j} is the unit outward normal vector of a point on the sound source surface, and _{0} is the pressure of the fluid in the undisturbed area. It should be noted that the influence of air flow on sound propagation is not considered when

A simplified full scale double-strip pantograph model is used as the research object, and its geometry model is shown in

A rectangular computational domain in

The maximum inflow velocity is 400 km/h and the corresponding Mach number is 0.327. There are two main reasons for still considering air as incompressible gas in this paper. One is that Mach number is still close to 0.3, and the compressibility of gas is not strong; the other is that it is difficult to accept the computing resources and time cost required for using the compressible model, and the incompressible gas model has better convergence and calculation efficiency. The inlet of the computational domain is set as velocity inlet boundary and flow velocity is input, the outlet of the computational domain is set as pressure outlet boundary, the static pressure is 0, the two sides and the top of the computational domain are set as symmetrical boundary condition, the bottom of the computational domain and the pantograph surface are set as the static wall with no slip.

The steady flow field computation combined the Realizable

The convergent steady-state results provide initial field for transient simulation. The time step of transient calculation is 10^{−4} s, according to Nyquist theorem, the corresponding maximum analysis frequency being 5000 Hz. Each time step has 20 iterations to ensure convergence. During the transient calculation, the first 1500 time steps ensure flow field achieve statistical stability, and the next 2500 time steps record the fluctuating pressure data on the pantograph surface as the calculation input of far-field noise.

Aerodynamic drag | Sound pressure level (p1) | Sound pressure level (p7) | Sound pressure level (p13) | |
---|---|---|---|---|

Coarse | 2700.1 N | 99.2 dB | 100.6 dB | 105.8 dB |

Medium | 2746.2 N | 100.7 dB | 100.2 dB | 105.7 dB |

Fine | 2740.1 N | 100.8 dB | 100.3 dB | 105.4 dB |

According to the solution setup mentioned above, the aerodynamic noise generated by a cylinder with a diameter of 10 mm at inflow velocity of 72 m/s is simulated. This case is also used to verify the calculation method in other literatures on pantograph aerodynamic noise research [^{−5} s, and the sampling time is 0.25 s, corresponding to the frequency resolution of 4 Hz, which is the same as that of the experiment. It can be seen that the time-averaged pressure coefficient obtained by numerical simulation and the experimental results agree well, and the numerical simulation could capture the peak value caused by periodic vortex shedding. In general, the simulation results are in good agreement with the experimental results, which verifies the reliability of the calculation methods in this paper.

Since the value of viscous stress is small and _{0} = 0, in _{ij} ≈ _{ij}. Then, according to _{rms} on pantograph surface at the speed of 400 km/h. It can be seen from

According to the results in ^{6}, that of sound velocity in air is 10^{2}, that of distance ^{1}∼10^{2}, and that of fluctuating pressure on pantograph surface is 10^{3}∼10^{4}. To sum up, in the brackets of ^{2}∼10^{3}, and the order of the second term is 10^{−1}∼10^{2}. Therefore, the far-field aerodynamic noise of pantograph mainly depends on the change rate of fluctuating pressure on the pantograph surface with time and (∂_{rms} can be used to characterize the aerodynamic sound source intensity on the pantograph surface. In fact, this is just as Curle pointed out: for far-field noise, when the distance between the sound source and the receiving point is far greater than the sound wave length, the first term in the bracket of

According to the results of

It can be seen from

In other words, the vortex shedding and the wake impact of upstream components will aggravate the pressure fluctuation on the pantograph surface, thus enhancing the aerodynamic noise generated by the pantograph. Therefore, in order to reduce the aerodynamic noise of pantograph, it is necessary to reduce the flow separation in the pantograph area and avoid the interaction between the wake vortices of the upstream components and the downstream components.

The layout of far-field noise measuring points is shown in

The directivity curves shown in

According to the calculation results of q1–q7 measuring points, the attenuation characteristics of far-field noise of pantograph are shown in

Strip1 | Balance arm | Strip2 | Upper arm | Lower arm | Base frame | Insulator1 | Insulator2 | Insulator3 | |
---|---|---|---|---|---|---|---|---|---|

p1 | 66.3 | 96.1 | 95.1 | 74 | 89.1 | 97.6 | 82.1 | 80.7 | 86.9 |

p4 | 74.1 | 91.7 | 92 | 78.8 | 88.1 | 96.6 | 84 | 84.3 | 88.8 |

p7 | 75.9 | 93.8 | 89.8 | 82.9 | 86.3 | 96 | 87.2 | 85.6 | 91.1 |

p10 | 72.4 | 93.1 | 91.2 | 84.6 | 85.8 | 101 | 86.5 | 84 | 91 |

p13 | 68.6 | 98.6 | 95.5 | 79.1 | 76.4 | 102.9 | 83.3 | 82.4 | 89.6 |

Velocity | Frequency1 | Frequency2 | Frequency3 | Frequency4 |
---|---|---|---|---|

200 km/h | 81 | 175 | 354 | 525 |

250 km/h | 98 | 218 | 435 | 653 |

300 km/h | 119 | 261 | 525 | 799 |

350 km/h | 141 | 308 | 611 | 919 |

400 km/h | 158 | 346 | 692 | 1047 |

Since p7 is the measuring point located at the track side that usually used for noise evaluation, the sound pressure level at p13 is the highest and the peaks in its spectrum is the most obvious, p7 and p13 are taken as examples to further analyze the source of peaks in the spectrum of pantograph aerodynamic noise. The spectrum of p7 and p13 is calculated with each component as the sound source at the inflow velocity of 400 km/h, as shown in

It can also be found from

In high-speed railway engineering, A-weighted sound pressure level is usually used to evaluate the far-field noise.

In this study, a LES/FW-H hybrid method is used to investigate the aerodynamic noise characteristics of a simplified double-strip pantograph. The location of the main sound source on the pantograph surface is determined by the CFD results. The vortex structures in the pantograph flow field are studied based on Q-criterion. The relationship between them is discussed to reveal the generation mechanism of pantograph aerodynamic noise and provide guidance for noise reduction. The characteristics of far-field aerodynamic noise are also studied.

The results show that the aerodynamic noise of pantograph surface is mainly related to the change rate of the surface pressure with time on pantograph surface. (∂_{rms} can be used as an index to characterize the sound source intensity on pantograph surface and determine the main source location.

The aerodynamic sound source on the surface of the pantograph is closely related to the vortex structures of the pantograph. The pressure fluctuates violently where the vortex sheds or impacted by the wake of the upstream components and these areas are the main sound sources location. Therefore, in order to control the aerodynamic noise of pantograph, it is necessary to reduce the flow separation on the surface of pantograph and avoid the interference of the upstream components wake on the downstream components.

The aerodynamic noise of pantograph mainly radiates backward. When the transverse distance is greater than 5 m, it’s attenuation characteristics is similar to the far field attenuation characteristics of a point source in free field. The far-field aerodynamic noise energy of pantograph is mainly concentrated in the frequency band below 1500 Hz. The peak value of the frequency spectrum is mainly generated by the base frame, balance arm and the rear strip. They are also the components that contribute the most to the far-field aerodynamic noise. The linear weighted sound pressure level and A-weighted sound pressure level of the far-field aerodynamic are approximately linear with the logarithm of the inflow velocity. For the linear weighted sound pressure level, the proportion coefficient is about 50∼60, which is similar to the velocity dependence regularity of a dipole source. For A-weighted sound pressure level, as the main frequencies of the pantograph aerodynamic noise move to high frequency band with the increase of inflow velocity and the attenuation after weighting decreases, so it increases faster with the inflow velocity.