Near-Field Aerodynamic Noise of Subway Trains: Comparative Mechanisms in Open Tracks vs. Confined Tunnels

Abstract

As the operational speeds of subway trains in China incrementally increase to 160 km/h, the enclosed nature of tunnel environments poses significant challenges by restricting free airflow. This limitation leads to intense airflow disturbances and turbulence phenomena within tunnels, consequently exacerbating aerodynamic noise issues. This study utilizes compressible Large Eddy Simulation (LES) and acoustic finite element methods to construct a computational model of aerodynamic noise for subway trains within tunnels. It employs this model to compare and analyze the near-field noise characteristics of subway trains traveling at 120 km/h on open tracks versus in infinitely long tunnels. The findings indicate that the distribution of sound pressure levels on the surfaces of trains within tunnels is comparatively uniform, overall being 15 dB higher than those on open tracks. The presence of a high blockage ratio in tunnels intensifies the cavity flow between two air conditioning units, making it the region with the highest sound pressure level. The surface sound pressure spectrum within the tunnel shows greater similarity across different segments, with low-frequency sound pressure levels notably enhanced and high-frequency levels attenuating more rapidly compared to open tracks. It is recommended that in tunnels with high blockage ratios, the positioning of subway train air conditioning should not be too high, overly concentrated, submerged, or without the use of sound-absorbing materials. Such adjustments can effectively reduce the sound pressure levels in these areas, thereby enhancing the acoustic performance of the train within the tunnel.

1. Introduction

According to statistics from the Ministry of Transport in January 2025, 54 cities across 31 provinces, autonomous regions, and municipalities, including the Xinjiang Production and Construction Corps, have operational urban rail transit lines totaling 325, covering a distance of 10,947.3 km. However, as the scale of operations continues to expand, the issue of train noise has become increasingly prominent. Currently, the majority of subway lines operate at speeds below 80 km/h, yet the noise levels within carriages of older lines have reached as high as 90 dBA [1], a figure nearing the indoor noise limit set by the “Urban Area Environmental Noise Standards”. With the acceleration of urbanization, the design speeds of new-generation subway trains have increased from 80 km/h to between 120 and 160 km/h. This increase in speed exacerbates the noise issues, with studies indicating that when subway trains travel at 160 km/h in tunnels, the noise levels inside increase by 11.2 to 18.7 dB(A) [2]. This high-intensity noise not only affects passenger comfort but may also lead to symptoms such as irritability and elevated blood pressure. Especially after the implementation of the “People’s Republic of China Pollution Prevention Law”, subway train noise pollution has become a focal point of public complaints. In recent years, environmental noise pollution has emerged as a key concern, with complaints about environmental noise accounting for approximately 45% of all complaints in 2024 [3].

Aerodynamic noise and wheel–rail noise are related to the square of the velocity to the power of 6–8 and 3 [4], respectively. In certain scenarios where speeds exceed 270 km/h, aerodynamic noise surpasses wheel–rail noise as the predominant source of noise [5,6,7,8]. When examining the mechanisms of noise generation, it is evident that subway train interior noise primarily arises from these two types of noise, with a notably greater increase in aerodynamic noise [9]. Compared to high-speed trains, subway train aerodynamic noise exhibits four distinctive characteristics: firstly, constrained by urban underground spaces and platform lengths, subway train fronts often feature short streamlined or blunt designs, with streamline lengths typically less than 4 m, significantly shorter than the approximately 10 m found in high-speed trains. Studies indicate a positive correlation between streamline length and aerodynamic performance [10], and shorter streamline designs significantly increase aerodynamic noise. Secondly, the blockage ratio inside tunnels for subway trains (typically 0.3–0.4) is notably higher than that of high-speed trains (0.12–0.14). The external pressure amplitude is directly proportional to the square of the train speed and increases with the blockage ratio, correlating positively with the train’s cross-sectional area raised to the power of 1.3 ± 0.25 [11]. A larger blockage ratio intensifies aerodynamic disturbances, thereby increasing the strength of the train’s inherent aerodynamic noise sources [12]. Furthermore, most subway lines operate in underground tunnels; data shows that at 350 km/h, the energy of aerodynamic noise sources within the tunnel is 3.2 times greater than that in open track scenarios [13,14]. When traveling at 60 km/h on a certain route, the noise inside the train in a tunnel environment is 9–12 dBA higher than in an open track environment [15]. Relative to high-speed trains, subway trains exhibit a more significant increase in aerodynamic noise source energy at comparable speeds [14,16]. Lastly, the equipment under subway trains is directly exposed to the air, which significantly enhances the intensity of the aerodynamic disturbances and, consequently, the strength of the undercarriage aerodynamic noise sources. In high-speed trains, such design features are typically mitigated through the use of equipment compartments and other enhancements [2].

In recent years, the issue of subway noise has garnered considerable attention among scholars. For instance, Deng Juming et al. [17] developed a subway tunnel noise intensity monitoring device to enhance the efficiency and accuracy of noise measurement in subway tunnels. Wen Xuewei et al. [18] provided a comprehensive review of current research on interior noise within vehicles internationally and domestically. They summarized potential factors influencing interior noise and evaluated various noise reduction strategies, offering insights and recommendations for future research aimed at mitigating interior noise. Li Fushu and Li Shuai [19] constructed a predictive model for vehicular radiated noise and analyzed its characteristics as well as the distribution of external noise fields around the vehicle. They identified that external noise primarily concentrates beneath the vehicle body and found that the overall distribution of external noise and wheel–rail noise field distributions are closely related, with wheel–rail interactions being a significant contributing factor. Negri et al. [20] explored the effects of train airflow speed through comprehensive full-scale experiments, analyzing how various train and infrastructure parameters influence the generation of shear flows when trains pass through tunnels. Rabani et al. [21] employed numerical simulations to study the impact of train speed on pressure waves, drag, and lateral forces. Zhou et al. [22] investigated the aerodynamic performance of trains passing through tunnels at three different speed regimes (constant 350 km/h, 350 to 300 km/h, and 350 to 250 km/h), discovering that a uniform deceleration of the train during tunnel passage resulted in a 15.8% reduction in peak pressure on the tunnel surfaces and a 12.8% reduction on the train surfaces. Liu et al. [23,24,25] conducted field measurements of surface pressures in tunnels, revealing that peak pressures increase with train speed and that the position of maximum pressure progressively shifts towards the tunnel entrance.

In the prevailing body of research, the majority of scholars have focused on the investigation of subway train noise through empirical vehicular tests, while numerical simulations have predominantly been employed to study the aerodynamic characteristics of subway trains. However, studies addressing the issue of aerodynamic noise emitted by subway trains are notably scarce. Aerodynamic noise, as an engineering challenge, becomes increasingly critical as the operational speeds of subway trains are pushed higher. It is important to note that the magnitude of aerodynamic noise is significantly lower—by more than three orders of magnitude—than that of pressure fluctuations caused by compression and expansion waves [26,27]. Consequently, to accurately simulate the propagation of aerodynamic noise within tunnels, simulation methods must utilize discretization schemes of at least third order. Under current computational constraints, achieving this level of accuracy is unattainable. Additionally, tunnel environments with a high blockage ratio are prone to numerical divergence issues. Therefore, developing a computational model for aerodynamic noise specific to tunnel environments and employing this model to investigate the acoustical properties of aerodynamic noise has profound implications for engineering applications.

2. Mathematical Model

The fundamental equation of classical acoustics in the time-domain differential form is presented as follows [28]:

$${\nabla }^2{p}^{\prime }-{\displaystyle \frac{1}{c_0^2}}{\displaystyle \frac{{\mathsf{\partial }}^2{p}^{\prime }}{{\mathsf{\partial }t}^2}}=-{\mathit{\rho }}_0{\displaystyle \frac{\mathsf{\partial }q}{\mathsf{\partial }t}}9$$

(1)

In this equation, ${\mathit{\rho }}_0$ and $c_0$ respectively denote the density and speed of sound in steady flow, where $p^{\prime }=p-p_0$ with $p$ and $p_0$ representing the pressure and steady flow pressure, respectively.

The aforementioned equation can be solved using the method of separation of variables, as demonstrated subsequently. Incorporating Equations (2) and (3) into Equation (1), we obtain

$$p^{\prime }=pj\left(x,y,z\right)·e^{j\mathit{\omega }t}$$

(2)

$$\mathrm{Q}=q_0\left(x,y,z\right)·e^{j\mathit{\omega }t}$$

(3)

Thus, the frequency-domain differential form of the basic equation of classical acoustics becomes

$${\nabla }^{2}p\left(x,y,z\right)-k^{2}p\left(x,y,z\right)=-j{\mathit{\rho }}_0\mathit{\omega }{q}_0\left(x,y,z\right)$$

(4)

Here, $k=\mathit{\omega }/c=2\mathit{\pi }f/c$ represents the wavenumber, $w=2\mathit{\pi }f$ denotes the angular frequency, and $f$ is the frequency $\left(\mathrm{H}\mathrm{z}\right)$. The corresponding wavelength is $\mathit{\lambda }=2\mathit{\pi }/k=2\mathit{\pi }c/\mathit{\omega }=c/f$.

To derive a unique solution, it is necessary to constrain certain variables within the equation, forming a closed system of equations. Such constraints are encapsulated by acoustic boundary conditions. These boundary conditions manifest in three primary forms: velocity boundary conditions for acoustic monopoles, pressure boundary conditions, and mixed boundary conditions (impedance boundary conditions), which are detailed in Equations (5)–(7), respectively. The physical interpretation of mixed boundary conditions involves the absorption efficiency or reflection coefficient of the acoustic boundary mesh.

$$v_n=\overline{v_n}$$

(5)

$$p=\overline{p}$$

(6)

$$Ap+B{v}_n=C$$

(7)

In these equations, A, B, and C represent known values that define the boundary conditions through the relationships between the velocity of acoustic monopoles and pressure at certain points on the acoustic boundary mesh.

The transformation of classical acoustic equations into acoustic finite element forms is as follows:

$$\left({\nabla }^{2}p\left(x,y,z\right)-k^{2}p\left(x,y,z\right)+j{\mathit{\rho }}_0\mathit{\omega }{q}_0\left(x,y,z\right)\right)dV=0$$

(8)

In this equation, $\tilde{p}$ represents the weight function, and V denotes the computational domain.

According to Gauss’s theorem, which delineates the relationship between volume integrals and surface integrals, the above equation is transformed to

$${\int }_V\left(\widetilde{\nabla p}·\nabla p\right)dV-{\mathit{\omega }}^2{\int }_V\left({\displaystyle \frac{1}{c^2}}\tilde{p}·p\right)dV={\int }_{V}j\tilde{p}{\mathit{\rho }}_0\mathit{\omega }{q}_{0}dV-{\int }_{S}j{\mathit{\rho }}_0\mathit{\omega }\tilde{p}v·ndS$$

(9)

Here, S represents the boundary of the computational domain V. The term $\tilde{p}={\displaystyle \frac{p}{‖p‖}}$ signifies the normalization of the matrix or vector, where “~” denotes normalization.

The aforementioned equation is discretized using a finite element mesh, and rearranged into a numerical form:

$$\left(K_a+j\mathit{\omega }{C}_a-{\mathit{\omega }}^2{M}_a\right)·p_i=Q_i+V_{ni}+P_i=F_{ai}$$

(10)

In this formulation, $Q_i$ represents the input acoustic source energy; $V_{ni}$ denotes the input vector of velocity of acoustic monopoles, corresponding to the velocity boundary; $P_i$ stands for the input acoustic pressure vector, which corresponds to the pressure boundary conditions; $F_{ai}$ is the acoustic excitation; $p_i$ is the solved nodal pressure at the mesh nodes. The term $K_a+j\mathit{\omega }{C}_a-{\mathit{\omega }}^2{M}_a$ represents the equation matrix, which is a sparse matrix. By processing the flow field output from CGNS data files with specified $Q_i$, $V_{ni}$, $P_i$, and $F_{ai}$ (the sources and boundary conditions), one can calculate the acoustic field.

The boundary element method offers dimensional reduction, high precision, and is suited for handling problems in infinite domains. In contrast, the finite element method accommodates complex geometrical shapes and boundary conditions, accurately simulating the low-frequency oscillatory characteristics of the acoustic field. Given the flexibility, controllable accuracy, and significant advantages in solving problems related to acoustic fields and acoustic radiation of the finite element method, this study employs finite element simulation analysis.

3. Numerical Calculation Model

3.1. Virtual.Lab Acoustics as a Multidisciplinary Simulation Platform

Virtual.Lab Acoustics is a comprehensive multidisciplinary simulation platform offering a wide range of advanced capabilities. It supports geometric modeling and parametric editing, enables multiphysics coupling analyses, and provides specialized engineering solutions. The platform features high-performance built-in solvers and covers structural mechanics, acoustics, fluid dynamics, and thermal analysis. It supports the simulation of composite materials as well as optimization workflows. To enhance computational efficiency, it incorporates Fast Multipole Boundary Element Method (FM-BEM) for accelerated boundary element analysis, and integrates Finite Element Method with Perfectly Matched Layer (FEM-PML) or Absorbing Matched Layer (AML) boundary technologies. In addition, it offers robust time-domain acoustic analysis capabilities.

With these features, the platform can address both conventional acoustic challenges and demanding scenarios such as transient engine noise prediction and high-frequency acoustic analysis. Through continuous technological innovation, Virtual.Lab Acoustics achieves significant gains in both simulation efficiency and computational accuracy.

When applied to computational aeroacoustics (CAA), the simulation process generally begins with a steady-state flow field calculation. Once the steady-state solution has converged, it is employed as the initial condition for subsequent transient simulations. In transient analyses, turbulence is typically modeled using Large Eddy Simulation (LES) or Detached Eddy Simulation (DES) approaches. The resulting time-domain pressure fluctuations obtained from the flow simulations are then transformed into the frequency domain via Fourier transformation, after which acoustic response analyses are performed. The overall workflow is illustrated in Figure 1.

3.2. Fluctuating Flow Field Model

The computational simulation employs a model of a subway train consisting of two carriages. This model includes a bogie system but excludes pantographs. The detailed structure of the model is depicted in Figure 2.

During operation on open tracks, the computational domain for the subway train is illustrated in Figure 3. To ensure adequate development of the flow field during the train’s operation, the dimensions of the computational area must meet specific requirements. Taking the height from the top of the train to the ground (i.e., the characteristic height) as 3.73 m, the computational domain on the open track is set to 287.5 m (length) × 30 m (width) × 15 m (height). These dimensions adhere to the fundamental criteria for flow simulation: the upstream region of the flow field is no less than eight times the characteristic height, and the downstream region is not less than sixteen times the characteristic height, thereby ensuring the accuracy and reliability of the computational results. The free-stream velocity is 120 km/h.

Within the tunnel, the computational domain for the subway train is shown in Figure 4. The tunnel has a fan-shaped cross-section with an area of 45.312 ${\mathrm{m}}^2$ and a blockage ratio of 0.23. The length of the tunnel used in this study is 287.5 m, with a distance of 50 m from the front of the train to the tunnel entrance and 200 m from the rear of the train to the tunnel exit.

3.3. Mesh Segmentation and Confidence Analysis

The mesh partitioning strategy primarily employs a hexahedral core mesh, supplemented by multi-layer mesh refinement techniques and boundary layer mesh technologies, to ensure a balance between computational accuracy and efficiency. Initially, the surface mesh is constructed using triangular meshes, aimed at facilitating joint analysis between two distinct software systems. Furthermore, considering that the flow within the boundary layers of the vehicle body, tunnel walls, and ground surfaces is a significant source of broadband noise, it is imperative to specifically incorporate boundary layer meshes in these regions to accurately capture the flow details within the boundary layers. Due to the severe variations in airflow velocity and pressure around the vehicle, during the mesh discretization process, the mesh around the vehicle region is appropriately refined. This refinement ensures that the thickness of the boundary layer mesh slightly exceeds the actual thickness of the boundary layer in the flow field, thereby enabling the more precise capture of the gas movement characteristics. Additionally, the flow field behind the vehicle tail is complex due to the presence of train wake vortices, necessitating appropriate mesh refinement in this area as well. Finally, to effectively control the mesh size and considering the smoother flow lines in the space far from the vehicle, a hexahedral mesh is utilized in these regions, while a pyramidal mesh is employed in the transition areas.

Under operating conditions on an open track, the mesh partitioning strategy has been meticulously designed based on the aerodynamic characteristics of different sections of the train. The leading and trailing cars employ a mesh scale of 40 mm, while the intermediate cars utilize a 50 mm mesh scale to balance computational accuracy with efficiency. For the streamlined sections of the leading and trailing cars, owing to their complex aerodynamic characteristics, the mesh scale is set at 20 mm. The bogie sections, subject to significant airflow disturbances, also adopt a 20 mm mesh scale to accurately capture the flow details in this region. In areas with pronounced surface curvature changes, the mesh density is appropriately increased to better conform to the variations in geometric shapes. The surface of the train body is equipped with 28 layers of prism mesh, with the first layer having a thickness of 0.04 mm and a mesh growth rate of 1.2, ensuring that the flow characteristics within the boundary layer are precisely captured. The ground tetrahedral mesh consists of 8 layers, with the first layer being 5 mm thick and having a growth rate of 1.2. Considering the variations in the flow field around the train, special attention has been given to mesh partitioning in regions where significant changes occur in the flow field downstream. The area extending five times the height of the train from the tip of the trailing car is a critical region for the generation and development of wake vortices. The lateral areas of the streamlined trailing car show significant mixing effects, and the airflow separation phenomena are readily apparent at the shoulders of the trailing car’s streamlined shape. For these regions, specific zones of densified mesh have been established to ensure accurate capture of complex flow phenomena such as wake vortices, mixing effects, and airflow separation, while also maintaining a reasonable control over the mesh size to enhance computational efficiency.

Figure 5 illustrates the computational mesh for the open-track environment, highlighting a refined near-wall boundary layer with graded growth (y+-targeted first layer) that transitions smoothly to a coarser core mesh to balance accuracy and cost. In tunnel environments, the mesh partitioning strategy surrounding the subway train mirrors that of the open track setting. However, key distinctions include a denser mesh at both the tunnel entrance and exit. Additionally, the inclusion of boundary layer meshes is required for the tunnel walls, floor, and underside of the train, as depicted in Figure 6.

In conducting high-precision LES, a rational grid distribution must meet two fundamental criteria, boundary layer grid distribution and spatial grid distribution, as well as the thickness of the boundary layer grid. The most critical parameter for the boundary layer grid is y+. Given that LES necessitates the accurate capture of quasi-ordered structures near the wall, which initially stem from low-speed streaks produced within the viscous sublayer (y+ < 10), it is imperative to arrange a sufficient number of grid layers within this sublayer. Typically, it is required that y+ be controlled to be less than 1. Figure 7 illustrates the specific distribution of y+ on the surface of trains under two different conditions: open track and inside a tunnel.

Regarding spatial grid distribution, the grid scale is the paramount parameter of consideration. Considering that small-scale eddies exhibit isotropic characteristics, the grid scale must reside within the local inertial subrange to ensure the subgrid model’s validity in simulating these small-scale eddies. The integral scale serves as a critical indicator to differentiate between the inertial subrange and the large-scale eddy zone; thus, the grid scale should be smaller than the local integral scale. The specific definition of the local integral scale is given by

$$l_t=C_0{k}^{3/2}/\mathit{\epsilon }$$

(11)

where $C_0$ is 0.2, $k$ is the turbulent kinetic energy, and $\mathit{\epsilon }$ is the dissipation rate, calculated as follows:

$$\mathit{\epsilon }=2{\upsilon }_t{\overline{S}}_{ij}{\overline{\mathrm{S}}}_{ij}$$

(12)

Equation (13) defines the equivalent grid length $l_{\mathit{\Delta }}$. The spatial distribution of $l_{\mathit{\Delta }}/l_t$ for a subway train is shown in Figure 8:

$$l_{∆}=V^{{\displaystyle \frac{1}{3}}}$$

(13)

where $V$ is the grid volume.

Figure 7 and Figure 8 demonstrate that the y+ values on the train surface and most of the grid’s $l_{\mathit{\Delta }}/l_t$ ratios are less than 1, thereby ensuring refined resolution of near-wall flow. Further comparative analysis with Figure 9 reveals that the thickness of the prismatic boundary layer is significantly greater than the actual thickness of the fluid boundary layer [29]. Overall, the grid configurations discussed herein are adequate to meet the precision requirements of large eddy simulations.

For the subway train operating under these two different conditions (open track and tunnel), differentiated boundary conditions were employed for numerical simulation calculations. The numerical simulation of the train’s flow field is divided into steady-state and transient computations. The steady-state computation aims to optimize the initial conditions for the subsequent transient analysis. Considering the different operating environments of the train and the computational efficiency, distinct approaches were adopted for the steady and transient phases. In the computational process, the time step was set at 5 × 10⁻⁵ s, with iterative calculations performed 30 times per time step, totaling 10,000 time steps. The specific computational methods and boundary conditions are summarized in the table below.

Table 1. Computational methods and boundary conditions.

Conditions	Open Track	Inside Tunnel
Steady State	SST kw model
Transient State	LES-wale
Algorithm	SIMPLE	Couple
Pressure Discretization Scheme	Second-order accuracy
Pressure-Velocity Coupling	PISO	Couple
Momentum, Turbulent Kinetic Energy, and Dissipation Rate	Second-order upwind discretization scheme
Inlet	Velocity inlet	Pressure far field
Outlet	Pressure outlet	Pressure outlet + acoustic non-reflective boundary
Computational Domain Side	Symmetry	Moving wall
Ground	Moving wall
Train Surface	Stationary boundary

summarizes the numerical setups for both operating environments, outlining the solvers used for steady and transient phases, key parameters (e.g., time step and iterations), and the differentiated boundary conditions applied to the open-track and tunnel cases.

3.4. Acoustic Field Model

As shown in Figure 10, the Automatically Matched Layer (AML) method is an innovative numerical simulation technique that has evolved from the Perfectly Matched Layer (PML) technology. Traditional PML approaches involve constructing a finite element acoustic mesh on the surface of a structure and manually setting the matching layer to analyze the sound pressure data transmitted to the matching layer through finite element discretization interpolation techniques. However, the PML method exhibits certain limitations in practical applications: the matching layer model must be manually constructed based on the geometric characteristics of the structure, a process that is not only complex, but also consumes considerable time and computational resources. In contrast, the AML method enhances this process through automation, significantly improving computational efficiency and applicability.

The AML method significantly enhances modeling efficiency through intelligent improvements. It requires only the specification of AML properties on the finite element acoustic mesh of the structure to automatically generate a PML between the acoustic mesh and the computational domain. This innovation not only substantially reduces the complexity of modeling but also demonstrates significant advantages in computational efficiency. Particularly in the study of the acoustic properties of subway trains, whether operating on open tracks or in tunnel conditions, the AML method exhibits exceptional computational performance. As illustrated in Figure 11, in open track conditions, setting the surface above the computational domain as an AML surface effectively reduces the computational scale; in tunnel conditions, setting the tunnel entrances and exits as AML surfaces allows for more accurate simulation of the acoustics of an infinitely long tunnel. This flexibility and efficiency make the AML method an ideal choice for complex acoustic simulations.

Prior to the advent of Finite Element Mesh Adaptive Optimization technology (FEMAO technology), it was a standard practice in finite element analysis of acoustics to divide each wavelength into at least six elements to ensure computational accuracy. The mesh size, L, must satisfy the following relationship:

$$\mathrm{L}={\displaystyle \frac{C_0}{fmax·6}}$$

(14)

where Fmax represents the highest frequency of interest, and $c_0$ is the speed of sound propagation.

The introduction of FEMAO technology has significantly enhanced both the efficiency and precision of computations. Studies have demonstrated that even with a comparatively coarse mesh division (e.g., encompassing only half an element per wavelength), this method still maintains the accuracy of the results. The FEMAO technology enables manual adjustment of mesh parameters and employs intelligent algorithms to automatically identify and refine key areas, thus substantially reducing the mesh requirements for acoustics. This optimization results in an exponential decrease in computational load and a substantial increase in computational efficiency. As depicted in Figure 12, the optimized acoustic mesh ensures computational accuracy while effectively reducing the mesh density.

4. Flow Field Structure

The structure of the flow field is characterized by the velocity field, which reflects the motion state of fluid particles, and the vorticity field, which reveals the rotational characteristics of the fluid. By analyzing the distribution and variations in the amplitude of velocity and vorticity, one can delve into complex phenomena such as energy transfer, vortex generation, and evolution within the flow field. Typically, the aerodynamic disturbances around a train can be determined by examining the contour plots of velocity amplitude and vorticity amplitude, as illustrated in Figure 13 and Figure 14, respectively.

The conversion formula for the velocity coefficient is given by

$${\mathrm{C}}_{\mathrm{v}}={\displaystyle \frac{{\mathrm{v}}_{\mathrm{f}}}{\mathrm{v}}}$$

(15)

where ${\mathrm{C}}_{\mathrm{v}}$ represents the velocity coefficient, ${\mathrm{v}}_{\mathrm{f}}$ is the airflow speed around the train, and v is the free-stream velocity.

According to the results depicted in Figure 13 and Figure 14, the flow field structures around the train in open track and tunnel environments exhibit considerable similarities. For instance, in the regions facing the wind near the leading car, underneath the train, and at the rear of the trailing car, there is a noticeable reduction in velocity due to airflow separation and thickening of the boundary layer, with significant spatial distribution changes. The areas around the bogie and downstream of the trailing car are characterized by intense vorticity zones with richly scaled vortex structures, including periodically shed multiscale vortices between the two air conditioning units. However, there are significant differences in their intensities and scales. Compared to open track conditions, the stagnation zone around the leading car in the tunnel is 0.5 times larger; the average airflow speeds at the bottom and top of the train in the tunnel increase by a factor of 1 and 0.5, respectively; the motion of air in the wake region of the tunnel is more intense, with the length of the wake vortices increasing by a factor of 5; the vorticity in the bogie area and downstream of the trailing car in the tunnel increases by 18–25%; and the strength of the vortex structures in the air conditioning area of the tunnel doubles.

5. Near-Field Noise

5.1. Intensity Characteristics

Figure 15 and Figure 16, respectively, illustrate the sound pressure level (SPL) distribution contours on the surface of the train and at various cross-sections on an open track. The cross-sections include the Y = 0 plane and the X-sections at four bogie locations (as indicated by the longitudinal dashed lines in Figure 16). Figure 17 depicts the SPL distribution curve along the Y = 0 plane indicated by the transverse dashed line in Figure 16.

On the open track, notable SPLs are observed on the surfaces of the train’s front and rear ends, the first and fourth bogies, and around the air conditioning units, with maximum values reaching 118.49 dB, 119 dB, 127 dB, 122 dB, and 117.3 dB, respectively. The SPLs in the vicinity of the train head, the first bogie, and the fourth bogie are significantly higher compared to other areas, with maximum values of 117 dB, 114 dB, and 103 dB, respectively. The longitudinal SPL distribution exhibits an explosive pattern, closely associated with the discontinuous nature of the train noise sources. The transverse SPL distribution is characterized by the highest levels at the bottom, followed by the sides, and the lowest in the middle, indicative of the typical radiation pattern of noise from the train’s underside. Intriguingly, between the two air conditioning units, two discontinuous areas of intense noise are observed on the roof’s surface, with peaks in these regions evident in the curve of Figure 17. This phenomenon is attributed to the oscillations in the flow field formed by the cavities around the two air conditioners, as derived from the analysis of the fluctuating flow field.

Figure 18 and Figure 19 show the SPL contours on the train body surface and at various cross-sections within an infinite-length tunnel. These sections include the y = 0 plane and the x-sections at four bogie locations (as indicated by the longitudinal dashed lines in Figure 19). Figure 20 presents the SPL distribution curve along the transverse dashed line in Figure 19.

Inside the tunnel, regions of high SPLs generally correspond to those observed on open tracks, yet the overall SPLs in the tunnel are higher than those in open track environments. Unlike on open tracks, between the two air conditioning units on the train, there is an additional area of intense sound pressure, with the central point reaching up to 120.1 dB, marking the strongest noise source on the train body. This phenomenon merits particular attention. One reason for this is the increased velocity of air flow in this region, which is accompanied by significantly enlarged scales and intensities of periodic vortex shedding, indicating oscillations in the flow field enhanced by the tunnel wall cavities. Another contributing factor is the multipath reflection of sound off the tunnel walls. When the train travels at high speeds through the tunnel, sound waves generated in the roof area undergo multiple reflections off the tunnel walls. The confined space of the tunnel causes these sound waves to superimpose repeatedly, preventing rapid dispersion of sound energy and resulting in a complex distribution of the acoustic field. This retention of sound energy causes a notable increase in SPLs in this area, becoming a prominent feature of the acoustic field distribution inside the tunnel.

In comparison to open tracks, there are several discontinuously distributed patches of intense sound pressure on both sides of the train body inside the tunnel, although these levels are lower than those between the air conditioning units. This phenomenon also warrants attention. The reason is the “piston effect” created as the train passes through the tunnel, which causes a rapid acceleration of airflow and instability in the boundary layer flow.

Upon comparing Figure 17 and Figure 20, it is evident that the propagation of aerodynamic noise within the tunnel exhibits a pronounced acoustic intensification effect. The distribution characteristics of the SPL along the tunnel demonstrate fundamental differences from those in open track conditions. Notably, above the middle section of the train’s roof within the tunnel, the maximum SPL reaches 116.4 dB, which is on average 15–16 dB higher than in open track conditions. This phenomenon primarily arises from the semi-enclosed structure of the tunnel, which leads to an accumulation of acoustic energy. In contrast, in open track conditions, where the train operates in an open space environment, the acoustic energy is able to disperse effectively. Consequently, the overall sound pressure level along the train exhibits a more gradual variation and even shows a slight decline in the tail section.

The bogie area, as a crucial source of aerodynamic noise at the bottom of the train, features high SPL values closely associated with phenomena such as vortex shedding and airflow separation. To address these high-noise regions, it may be beneficial to optimize the front-end design of the train, install fairings, or implement other noise reduction strategies to effectively lower the levels of aerodynamic noise and enhance the train’s acoustic performance. During tunnel operations, the structural characteristics between two air conditioning units further exacerbate the reflection and superposition effects of sound waves. By optimizing roof design to centralize air conditioners, submerging them, or employing sound-absorbing materials, the SPL in this area can be effectively reduced, thereby enhancing the acoustic performance of the train within the tunnel.

5.2. Frequency Characteristics

Figure 21 presents the SPL contour plots at frequencies of 50 Hz, 350 Hz, 650 Hz, and 950 Hz, for both open track and within a tunnel environment. The unit of measurement is dB.

A comparative analysis of the SPL contour plots from the above two scenarios reveals that although the overall SPL within the tunnel is consistently higher by approximately 15–20 dB compared to the open track, the trend of decreasing SPL with increasing frequency remains consistent in both environments. In the lower frequency range, high SPL zones on the open track are predominantly located around the leading car and the bogie areas. As the frequency increases, these high SPL zones gradually shift towards the middle and rear sections of the train, forming cluster-like high-value areas that expand upwards around the rear sides and bogies. Conversely, the distribution of SPL across different frequencies within the tunnel is more uniform, aligning with the characteristics of sound pressure distribution on the train surface in a reverberant space.

Figure 22 illustrates the locations of key measurement points for SPL spectra. Figure 23 then presents the corresponding SPL spectra at these points.

According to Figure 23, the frequency distribution characteristics of SPL vary significantly across different parts of the train on the open track. Notably, the SPL beneath the leading car significantly declines with increasing frequency, while the SPL around the trailing car and its wake exhibits a more complex relationship with frequency. Below 400 Hz, there is a slight decrease, and from 400 to 1000 Hz, there is a minimal increase. This variation is primarily due to the close association of the SPL in the leading car area with blunt-body aerodynamic interactions, which predominantly generate low-frequency noise. Meanwhile, the trailing car and its wake are situated within the boundary layer airflow. In this region, protruding structures such as the bogies not only facilitate the occurrence of turbulent bursting events within the boundary layer but also generate shedding vortices. The interaction between these phenomena can produce a substantial volume of multi-scale vortical structures, with the corresponding flow field structures predominantly generating frequencies between 100 and 2000 Hz.

Through the analysis of monitoring points surrounding the train within the tunnel, it has been observed that their SPL spectra exhibit considerable similarity, with notably enhanced low-frequency SPL compared to the open track, and a more rapid attenuation at higher frequencies. This phenomenon is primarily attributed to the low-frequency resonance effects within the tunnel environment, where sound waves repeatedly reflect off the tunnel surfaces and superimpose, thereby forming low-frequency standing waves. Particularly noteworthy is the mid-region of the train roof inside the tunnel, which exhibits a pronounced low-frequency standing wave effect, with SPL significantly higher than that on the open track, reaching peaks as high as 120.9 dB at certain low-frequency nodes.

In summary, there are marked differences in the distribution patterns and spectral characteristics of SPL around the train bodies on open tracks and inside tunnels. The open track environment, being relatively unenclosed, allows for less restricted propagation of aerodynamic noise, resulting in generally lower overall SPLs. Conversely, tunnels, as semi-enclosed spaces, constrain airflow against the tunnel walls, inhibiting the propagation of aerodynamic noise. Additionally, the accumulation of sound energy in the low-frequency range within the confined space further amplifies the differences in SPL.

6. Conclusions

This study delineates a refined simulation model of the fluctuating flow field within an infinitely long tunnel using the large eddy simulation framework, combined with acoustical non-reflective boundaries. Furthermore, an acoustic computation model for the near-field noise of the subway train is constructed employing finite element methods, the perfectly matched layer technique, and adaptive acoustic mesh technologies. This study conducts a comparative analysis of the near-field noise characteristics of subway trains traveling at 120 km/h on open tracks versus within an infinitely long tunnel, yielding the following conclusions:

(1)

The flow field structures around the trains on open tracks and within the tunnel exhibit similarities. However, there are significant differences in their intensities and scales. Notably, the cavity flow formed between two air conditioning units in the tunnel shows approximately a doubling in the intensity of the vortex structures.

(2)

There are substantial differences in the distribution of sound pressure levels on the surfaces of trains on open tracks. Specifically, the sound pressure levels are notably higher around the heads and tails of the intermediate cars, bogies 1 and 4, and near the shoulders of the air conditioning units. Conversely, the distribution of sound pressure levels on the surfaces of trains within the tunnel is more uniform, overall being 15 dB higher than on open tracks, with the highest levels occurring between the two air conditioners.

(3)

The frequency distribution of surface sound pressure levels on open track trains exhibits significant variability. The leading car area shows a marked decrease in sound pressure with increasing frequency, while the trailing car and its wake show a slight decrease in sound pressure below 400 Hz and a minor increase between 400 and 1000 Hz.

(4)

The spectral distribution of surface sound pressure levels within the tunnel is more homogenous. Low-frequency sound pressure levels are notably enhanced compared to those on open tracks, while high-frequency levels attenuate more rapidly.

(5)

In tunnels with a high blockage ratio, the positioning of subway train air conditioning units either too high, concentrated, submerged, or outfitted with sound-absorbing materials can effectively lower the sound pressure levels in these areas, thereby enhancing the acoustic performance of the train within the tunnel.

Based on the comparative analysis of near-field noise characteristics in open tracks versus confined tunnel environments, this study provides critical insights for optimizing acoustic design in underground transportation systems. The revealed intensified low-frequency noise propagation patterns and localized vortex-driven sound pressure amplification in high-blockage-ratio tunnels highlight the necessity of strategic noise control measures, such as aerodynamic component repositioning and targeted sound-absorbing material applications. These findings advance the development of comprehensive noise reduction strategies for underground infrastructure, offering actionable solutions to improve acoustic comfort while maintaining functional compactness in subway system design—a crucial advancement for sustainable urban underground mobility.