Complexity

Volume 2018, Article ID 5858415, 19 pages

https://doi.org/10.1155/2018/5858415

## Characteristics and Mechanism Analysis of Aerodynamic Noise Sources for High-Speed Train in Tunnel

Key Laboratory of Traffic Safety on Track, Ministry of Education, Central South University, Changsha, Hunan Province 410075, China

Correspondence should be addressed to Zhi-Gang Yang; nc.ude.usc@qdw_dnuos

Received 21 May 2018; Revised 2 September 2018; Accepted 25 September 2018; Published 9 December 2018

Academic Editor: Mohammad Hassan Khooban

Copyright © 2018 Xiao-Ming Tan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We aim to study the characteristics and mechanism of the aerodynamic noise sources for a high-speed train in a tunnel at the speeds of 50 m/s, 70 m/s, 83 m/s, and 97 m/s by means of the numerical wind tunnel model and the nonreflective boundary condition. First, the large eddy simulation model was used to simulate the fluctuating flow field around a 1/8 scale model of a high-speed train that consists of three connected vehicles with bogies in the tunnel. Next, the spectral characteristics of the aerodynamic noise source for the high-speed train were obtained by performing a Fourier transform on the fluctuating pressure. Finally, the mechanism of the aerodynamic noise was studied using the sound theory of cavity flow and the flow field structure. The results show that the spectrum pattern of the sound source energy presented broadband and multipeak characteristics for the high-speed train. The dominant distribution frequency range is from 100 Hz to 4 kHz for the high-speed train, accounting for approximately 95.1% of the total sound source energy. The peak frequencies are 400 Hz and 800 Hz. The sound source energy at 400 Hz and 800 Hz is primarily from the bogie cavities. The spectrum pattern of the sound source energy has frequency similarity for the bottom structure of the streamlined part of the head vehicle. The induced mode of the sound source energy is probably the dynamic oscillation mode of the cavity and the resonant oscillation mode of the cavity for the under-car structure at 400 Hz and 800 Hz, respectively. The numerical computation model was checked by the wind tunnel test results.

#### 1. Introduction

High-speed trains have become the preferred vehicle for middle- and long-distance travel. They are critical in social economic development and cultural exchange and have attracted wide attention worldwide [1, 2]. However, with the further increase in their operating speed (>300 km/h), the problem of environmental pollution of high-speed trains due to aerodynamic noise has become an urgent problem that needs to be solved by producers and operators. The comprehensive and accurate understanding of aerodynamic noise characteristics and its generation mechanism is the basis of aerodynamic noise control of high-speed trains. After more than 20 years of wind tunnel tests, field running tests, and numerical simulations, researchers have attained a comprehensive and accurate understanding of the aerodynamic noise characteristics and the generation mechanism of high-speed trains.

Before the previous century, it was widely believed that the operating speed of 300 km/h was the acoustic transition speed [3, 4] of high-speed trains. However, with the gradual application of noise reduction techniques such as the streamlined head shape and the smooth car body in high-speed train design, the acoustic conversion speed of high-speed trains is increased to 350 km/h [5–7]. The speed of acoustic conversion is defined as the operating speed of high-speed trains when the contributions of the aerodynamic noise and rolling noise are the same.

The dominant noise sources of different high-speed trains are not identical, but the bogie area and the pantograph area are generally recognized as the dominant sources of exterior noise. In the field running test, Mellet et al. [8] used the acoustic imaging technology to identify the dominant noise sources for the ICE high-speed train, which were the streamline part of head/tail car, the bogie area, the pantograph area, and the ventilation area, but did not include the intercoach windshield area; He et al. [9] also used the similar method to identify the dominant noise sources for a type of Chinese high-speed train, which were the bogie area, the pantograph area, and the intercoach windshield area; Deng et al. [10] also utilized the similar method to identify the dominant noise sources for another type of Chinese high-speed train, which included the streamline part of the head, the intercoach windshield area, the bogie area, and the pantograph area.

The spectrum characteristics and propagation characteristics of the aerodynamic noises in the bogie area, the pantograph area, and the intercoach windshield area have gradually become the focus of research in recent years. In 2000, Frémion et al. [11] used coherent output power technology to analyze the spectral characteristics of the aerodynamic noises in the intercoach windshield area and the bogie area of the full-size French TGV train. They found that the radiated noise in the intercoach windshield area was primarily tonal and distributed in the low-frequency range, but had little influence on the total aerodynamic noise. The bogie area had a variety of uncorrelated sound sources. The external radiation was insignificant from the sound source at the bottom of the bogie, but was relatively obvious from the upstream and the downstream of the wheel arches. The dominant frequency distribution range was 500–1000 Hz for the noises radiated from the upstream and downstream of the wheel arches. The spectrum of the sound source located downstream of the wheel arches had multipeak frequencies near 600 Hz. In 2012, Lauterbach et al. [12] studied the Reynolds number effect of aerodynamic noise on a 1/25 scale model of a high-speed train in the aeroacoustic wind tunnel of the German Aerospace Center in Brunswick and in the cryogenic wind tunnel of the DNW (German-Dutch wind tunnels) in Cologne. They found that the aerodynamic noise in the bogie area at 1 : 25 1 : 25 was primarily distributed below 5000 Hz and can be described by the cavity excitation mode. The aerodynamic noise in the pantograph area was primarily distributed above 5000 Hz and has the Strouhal number similarity. In 2015, Lee et al. [13] numerically analyzed the contribution of the pantograph’s various components to the aerodynamic noise energy at 400 km/h in the closed state and indicated that the aerodynamic noise at (60–400 Hz), (600–800 Hz), (1 kHz–2 kHz), and (2 kHz–5 kHz) was primarily derived from the bottom frame area, the panhead area, the knuckle area between the upper and lower arms, and the whole pantograph, respectively. In 2017, Iglesias et al. [14] discovered that the trailing edge of the bogie cavity contributed highly to the noise radiated from the bogie cavity using sound source imaging technology in the anechoic wind tunnel test of the Japan Railway Technology Research Institute. Their results are consistent with the conclusion of Yamazaki and Ido [15].

Sound analogy theory is the dominant theoretical basis for the current research on the aerodynamic noise generation mechanism of high-speed trains. Dipole noise sources are generally considered to be the dominant noise source [16] for high-speed trains and can be described by the fluctuating pressure [17] on the train surface. The fluctuating pressure on the train surface is closely related to the structure of the flow field and the induced mechanism of the flow field structure in the different areas for the high-speed train. For the head car part, the combination of the effect of airflow, the airflow separation and reattachment of streamlined shoulder, the airflow blending in the cowcatcher area, and vortex shedding creates a unique flow field structure [18] in the area. For the middle train, the hairpin vortex in the turbulent boundary layer dominates the momentum transmission on the train surface, which is an important mechanism for the generation and dissipation of turbulence in the area [19]. For the tail car part, the streamlined shoulder flow has a large-scale separation and reattachment, and the vortex structures produced by the tail car and its upstream components are highly mixed in the recirculation zone, forming the flow field characteristics of the wake region with high turbulence intensity, large turbulent kinetic energy, and a pair of oppositely directed large-scale drag vortex structures [20–22]. For the intercoach windshield area, the cavity vocalization is its dominant vocal mechanism [23, 24]. For the pantograph area, the airflow separation and the vortex shedding from the rod and their interactions are the dominant reasons for the flow field structure in this area [17, 25, 26]. For the bogie area, the flow pattern of the cavity and the bluff body flow pattern such as the wheelset and axle are combined in the narrow space of the bogie cavity, which is the dominant inducing mechanism of the complex flow field structure in this area [27, 28].

It is noteworthy that the research results above are all directed to high-speed trains on the open track and lack the detailed studies on the aerodynamic noise characteristics and the mechanism of the high-speed trains in tunnels. The flow field structure-induced mechanism on an open track and the wave interference mechanism in a tunnel cause the flow structure of the high-speed train in the tunnel to be complicated. The sliding grid method is the dominant research method for the current aerodynamics problems of high-speed trains crossing tunnels [29, 30]. However, the most significant drawback of this method is the interpolation error of the data exchange surface, resulting in inconsistent flow fluxes on both sides, and thus, the flow spectrum jumps on the data exchange surface. This jump has little influence on the aerodynamic issues such as drag, lift, and torque. However, it has a significant influence on the calculation of the fluctuating quantity of the flow field. Therefore, the sliding grid method is generally not recommended in aeroacoustic calculations [31]. Currently, numerical models of high-speed train’s aerodynamic noise on an open track tends to be mature and can accurately predict the aerodynamic noise of high-speed trains. This paper attempts to introduce a nonreflective boundary condition based on the numerical model of aerodynamic noise calculation for high-speed trains on an open track to study the flow field structure, the aerodynamic noise source intensity distribution characteristics/spectral characteristics, and their mutual relations in an infinite tunnel. The Reynolds numbers based on vehicle height and incoming velocity are , respectively. This paper is structured as follows: Section 2 introduces the turbulence model, acoustic reflection-free boundary, and acoustic equations used herein. Section 3 establishes and verifies the numerical model of the aerodynamic noise of a high-speed train in a tunnel. Section 4 discusses the flow field structure of high-speed trains in tunnels. Section 5 analyzes the distribution/spectrum characteristics and velocity dependence law of the noise source on the high-speed train in tunnels. Section 6 analyzes the aerodynamic noise mechanism of high-speed trains in tunnels using the flow field structure and the cavity flow-sound theory. Section 7 presents the conclusion.

#### 2. Mathematical Physical Model

##### 2.1. Large Eddy Simulation (LES) Model

Although the running Mach number of high-speed trains herein is less than 0.3, the influence of the change in air density on the flow field around the train in the tunnel cannot be ignored. Therefore, the three-dimensional, unsteady, compressible, and viscous Navier-Stokes (N-S) equations are used herein. The LES model can well capture the vortices and flow field fluctuating information and thus is suitable for refined flow field simulations. LES is a special filtering method used to filter the compressible N-S equations to obtain the compressible numerical simulation control equations describing the large-scale vortex motion, while the subgrid scale model is used to solve the small-scale vortices to avoid the direct simulation of the full-scale eddy motion of the flow field. The Favre filtering method is a relatively simple and practical filtering method, which uses the common physical space filtering for density and pressure and density-weighted filtering for speed, temperature, and internal energy. The compressible numerical simulation control equation filtered by the Favre filtering [32] method is as follows: where “” represents the physical space filtering, “” represents the density-weighted filtering, and are the minor scales, is the air density, is the pressure, is the flow speed, is the dynamic viscosity coefficient, is the thermal conductivity, is the internal energy, and is the temperature. The equations for , , and are shown as follows:

The density-weighted filtered state equation is where is the gas constant.

To close the system of equations, the subgrid scale (SGS) model proposed by Smagorinsky is introduced to the subgrid stress [33, 34].

##### 2.2. Nonreflecting Boundary Condition

The nonreflective boundary condition can effectively solve the problem of the pseudoreflected waves caused by the artificial truncated computational domain, thereby enabling the simulation of the flow field around the high-speed train in an infinitely long tunnel. By reconstructing the Euler equations based on the wave characteristics, a set of equations acoustically describing nonreflective boundary conditions can be obtained [35–37] as follows:

The coordinate system is a local Cartesian coordinate system based on a nonreflective boundary, where the -axis is perpendicular to the boundary and points outward; is the speed of sound. The formula for each coefficient is as follows:

##### 2.3. Aeroacoustic Equation

The Lighthill’s sound analogy theory [16, 38] divides the sound sources into three types: monopole, dipole, and quadrupole. In practical applications, the dominant types of sound sources are selected for integration, which facilitates engineering applications. Herein, the train is a stationary rigid solid wall, and the velocity of airflow passing through its surface is subsonic. Therefore, the Curle acoustics integral formula [39] can be used to study the aerodynamic sound from the train. The Curle acoustics integral formula is as follows: where is the sound pressure, and are, respectively, the spatial location vectors of the far-field receiver and the sound source, is the sound speed in the far field, is the angle between the surface normal vector of the sound source and the vector from the sound source to the far-field receiver, is the distance from the sound source to the far-field receiver, is the retarded time, is the surface area of the sound source, and is the fluctuating pressure on the train surface.

Using (6), the acoustic energy density of the far-field aerodynamic noise can be approximated as follows: where the overline represents the average values of the physical quantities in the time domain.

In the far field, the size of the sound source is negligible. It can be regarded as a point sound source. Subsequently, is approximately equal to . Again, the flow rate is a low Mach number such that the effect of delay time can be ignored. Thus, the total acoustic power radiated from the sound source can be expressed as follows: where is the sphere radius of the acoustic energy integral surface.

In (8), represents the intensity of the sound source, and represents the projection of the intensity of the sound source in the direction from the sound source to the receiver. Therefore, from the aspect of engineering application, we may define the acoustic power of the sound source as follows:

We define

Subsequently, where the right superscript represents the time derivative, is the acoustic power of the sound source, and is the fluctuating force.

It is noteworthy that the calculation formula of the acoustic power of the sound source does not consider the sound source radiation characteristics, and that this paper studies only dipole noise sources. Herein, (11) will be applied to calculate the percentage of the sound source energy from each component of the high-speed train in the total sound source energy.

#### 3. Numerical Computation Model

##### 3.1. Model Preparation

The geometric model used herein is a high-speed train with three cars, with bogies and without pantographs at a scale of 1 : 8. The full-size model has a length of 79.6 m, a height of 4.08 m, and a width of 3.36 m. The names of the various parts of the model are as follows: the bogies from the upstream to the downstream are named the first bogie to the sixth bogie, sequentially; the three cars from the upstream to the downstream were named the head car, the mid-car, and the tail car, sequentially. The streamlined parts of the head car and the tail car are named independently. The bottom of each carriage is independently named. A schematic view of the train is shown in Figure 1.