Investigation on aerodynamic noise generated from the simplified high-speed train leading cars

Abstract

The aerodynamic noise behavior of flow passing the simplified leading car and nose car scale models of a high-speed train is investigated through the vortex sound theory and acoustic analogy approach. The unsteady flow developed around the geometries is solved numerically and the data are applied to study the near-field quadrupole sound source and calculate the far-field noise radiated. It is found that the turbulent flow developed around the leading car is characterized by multi-scale vortices separated from the geometries. The intensity of volume dipole source is much larger than that of volume quadrupole source and the volume dipole source becomes the predominate source of the near-field quadrupole noise. The flow is separated noticeably in the regions of the nose, bogies, bogie cavities, and train tail of the leading car where the pressure fluctuations are generated largely upon the solid surfaces and correspondingly a dipole noise of high level is produced. By comparison, the noise contribution from the leading bogie and bogie cavity is larger than that from the other components. Moreover, the numerical and experimental results of train nose car model demonstrate that the flow around the bogie region is the dominant aerodynamic sound source. Therefore, the flow-induced noise generated from the leading cars may be reduced efficiently within a certain frequency range and specific direction by mitigating the flow interactions around the areas of leading bogie and bogie cavity.

Keywords

High-speed train leading car train nose car aerodynamic noise flow behavior noise prediction

Introduction

With an increasing of running speed over 300 km/h for a high-speed train, the aerodynamic noise becomes predominant due to strong interaction between the moving body and the induced flow.^1–3 In recent years, many studies have used numerical methods to investigate the flow-induced noise of a high-speed train and its components as the computer resources become increasingly available. Motivated by seeking for noise reduction methods for the pantograph of high-speed train, Liu et al.⁴ analyzed the flow and flow-induced noise produced from square bars by introducing spanwise waviness along them. Results showed that strong crossflow vortices were developed around the bars, which suppressed the primary vortex shedding of the separated flow associated with the tonal noise generation. The flow-induced noise produced by the square bars was reduced effectively. Tan et al.⁵ simulated the vortex structure of the pantograph based on large-eddy simulation (LES) and investigated the sound directivity of the flow-induced noise introduced by the geometry. The results may provide theoretical guidance to optimize the main components of a pantograph for noise-control design. Liu et al.⁶ investigated the characteristics of sound pressure level (SPL), spectra, and speed dependence law of the aerodynamic noise produced from the pantograph of the high-speed train through numerical simulation. It was found that the flow-induced noise of the pantograph was narrow-band and its main energy was distributed in the frequency range of 100–700 Hz. Zhao et al.⁷ investigated the aerodynamic noise of high-speed train pantograph based on the Ffowcs Williams–Hawkings (FW-H) method and acoustic perturbation equation (APE) approach. For the contribution to the far-field radiated noise, the dipole source was dominated and the quadrupole source was negligible. The flow around the components of the base-frame, panhead, groove, upper-arm, horn, lower-arm, and rod-insulator were the main sound sources of the pantograph structure. Zhu et al.⁸ investigated the turbulent flow and aerodynamic noise of a simplified train bogie structure. It was found that the wall pressure fluctuations on the solid surfaces introduced from the unsteady flow separated around the geometries were the main reason for the flow-induced noise generation of a bogie. Gao et al.⁹ compared the aerodynamic noise behavior of a high-speed train model based on the flow data calculated by LES. The far-field radiated noise was predicted by FW-H method and verified by the wind-tunnel measurements. The near-field noise was solved by APE approach. Results showed that the overall sound pressure level (OASPL) of the near-field noise produced from the bogie area was higher than the other regions. Minelli et al.¹⁰ studied the characteristics of the flow and flow-induced noise produced by a bogie cavity model of a simplified high-speed train (ICE3) leading car. Results showed that the underbody jet flow was produced by the gap between the snow-plow and the ground, and a shear layer was separated laterally from the snow-plow leading edge. The jet flow had an influence on the ground surface as well as the structures underneath the train, and the shear flow affected the lateral side surfaces of the bogie cavity and the train. The two main flow structures caused the dominant noise generations around the leading bogie. Zhu et al.¹¹ calculated the aerodynamic forces and far-field aerodynamic noise of a scaled high-speed train model with three coaches using detached-eddy simulation (DES) and acoustic analogy method. It was found that the flow-induced noise produced from a train had the feature of dipole-type and the leading bogie region generated the main noise. Masson et al. ¹² studied the aeroacoustic behavior of the power car of a high-speed train of TGV (train à grande vitesse) at full scale using numerical simulation by lattice-Boltzmann method. Results showed that the bogies and pantographs produced the main aerodynamic noise of a high-speed train. The aerodynamic noise generated by a train would be reduced potentially through applying the geometrical optimization approaches. Based on acoustic analogy and lattice-Boltzmann method using wall-function approach, Meskine et al.¹³ calculated the aerodynamic noise produced from a simplified full-scale high-speed train to predict the radiated noise levels and explore the noise reduction methods without experimental verification. The main sound sources including bogies, pantographs, and gaps between two coaches were applied to obtain the far-field sound power and by-pass noise levels. Results suggested that the sound sources of the leading bogie area at low frequencies and the pantograph at high frequencies should be optimized to control the flow-induced noise from a high-speed train.

Thus, in most of the numerical simulations on the flow-induced noise of a high-speed train performed earlier, unstructured grids were utilized to do CFD (computational fluid dynamics) simulation of the flow due to the complexity of train structures. Then the radiated noise was predicted using the flow data close to the train through acoustic analogy approach. Thereafter, the aerodynamic noise behavior and its variation in time and frequency domain were investigated. More recently, the acoustic analogy method has been successfully used for aerodynamic noise predictions on the high-speed train and its main components.^14–16 However, the mechanism of the aerodynamic noise generated by the flow interaction of the incoming flow and the geometries needs to be revealed. Since the radiated noise is calculated by the equivalent sound sources at near field, the acoustic analogy approach cannot be used to clarify the relation between the vortex motion and the flow-induced noise. Meanwhile, the quadrupole sound source at low Mach numbers used to be ignored because it was relatively small compared to the dipole source. Numerical simulations of aerodynamic noise generated from a high-speed train require a large amount of computation resources. Due to the complexity of the turbulent flow developed around the key regions (such as the leading bogie, bogie cavity, and pantograph) of the train, it is still quite hard to obtain the accurate flow field around the train numerically. This will lead to the inaccuracy of the noise prediction on these geometries with complex configurations. Thereby for numerical investigation using unstructured grids, it is essential to keep the flow field calculation accurate to obtain the flow fluctuations which are generally small compared to flow hydrodynamic quantities, yet responsible for introducing the aerodynamic noise. By comparison, the noise prediction for simplified geometries can be simulated through structured grids with good quality to improve the numerical accuracy and allow a detail investigation of the flow and flow-induced noise behavior.

Therefore, in order to reveal the generating mechanism of flow-induced noise produced by a high-speed train and to explore the efficient noise control methods, this study aims to analyze the behavior of the unsteady flow and flow-induced noise produced around the high-speed train leading car and nose car models through numerical simulations and wind tunnel measurements. Based on acoustic analogy approach and vortex sound theory, the aerodynamic noise generating mechanism is revealed. The sound radiation directivity and noise contribution of each part are studied to provide the theoretical foundation for a configuration optimization and low-noise design of the key components of a high-speed train.

Noise prediction and sound source analysis

The aerodynamic noise can be predicted numerically through the compressible Navier–Stokes equations principally. However, such direct method will use large computational resources to solve the nonlinear differential equations and is not suitable for industrial applications. Generally, high-speed trains are operating at low Mach numbers and the compressibility effects may be neglected in studying the flow hydrodynamics. Thereby, the Navier–Stokes equations of incompressible form are utilized for CFD simulation with affordable computational cost.⁸ In acoustic analogy approach, the near-field flow provides the source data to calculate the far-field radiated noise through the Ffowcs Williams–Hawkings equation.¹⁷ The solution to FW-H equation is written as

\begin{array}{l} p^{′} (x, t) = \frac{\partial}{\partial t} \int_{f = 0} {[\frac{Q_{i} n_{i}}{4 π | x - y |}]}_{τ_{e}} d S - \frac{\partial}{\partial x_{i}} \int_{f = 0} {[\frac{L_{i j} n_{j}}{4 π | x - y |}]}_{τ_{e}} d S \\ + \frac{\partial^{2}}{\partial x_{i} x_{j}} \int_{f > 0} {[\frac{T_{i j}}{4 π | x - y |}]}_{τ_{e}} d V, \end{array}

(1)

where

x_{i}

and

x_{j}

represent the three Cartesian coordinates

(i = 1,2,3, j = 1,2,3)

n_{i}

is the component of unit normal vector pointing outward to the surface.

{[]}_{τ_{e}}

means evaluating at emission time

τ_{e}

. The control surface “

S

” is represented by

f (x, t) = 0

. The sound pressure

p^{′} (x, t)

is predicted at a far-field observer at position

x

with an observer time of

t

. The source terms of

Q_{i}

and

L_{i j}

are the thickness and loading noises;

T_{i j}

is the Lighthill stress tensor.¹⁸ The FW-H equation may be solved numerically by the Farassat’s Formulation 1A.^19,20

In order to investigate the flow-induced noise introduced by vortex motion in the turbulent flow developed around the leading car, the characteristics of the volume sound source of quadrupole noise produced in the flow field are investigated based on the theory of vortex sound. ^21,22 For isentropic flow at low velocity, the vortex sound equation can be expressed as

\nabla^{2} p^{′} - \frac{1}{c_{0}^{2}} \frac{\partial^{2} p^{′}}{\partial t^{2}} = \nabla \cdot [ρ_{0} (ω \times v)] + \nabla^{2} (\frac{1}{2} ρ_{0} {| v |}^{2}),

(2)

in which

p^{′}

represents the sound pressure.

ρ_{0}

is the non-perturbed density and

c_{0}

is the sound speed in the uniform medium.

ω

and

v

are the vorticity vector and velocity vector, respectively, and

(ω \times v)

is the Lamb vector. The vortex sound equation links the vorticity in the flow with the aerodynamic noise generation. There are two sound source terms situated at the right-hand side of the equation. The first term (

\nabla \cdot [ρ_{0} (ω \times v)]

) associated with the divergence of the Lamb vector

(ω \times v)

, representing a dipole distribution, denotes the volume dipole source produced from the stretching and breaking up of the turbulent eddies in the flow field. The second term

(\nabla^{2} (\frac{1}{2} ρ_{0} {| v |}^{2}))

represents the volume quadrupole source formed by uneven distribution of the fluid kinetic energy. When the solid bodies exist in the flow, the interaction between the turbulent eddies and the solid boundaries will produce pressure fluctuations on the flow in proximity to the walls. The aerodynamic force fluctuates with time and induces the formation and radiation of the dipole sound source produced on the solid boundaries. Thus, the vorticity is the ultimate source of the aerodynamic noise introduced by the solid objects moving at low Mach numbers. The generation mechanism of flow-induced noise can be studied based on the vortex motion through vorticity dynamics. The flow-induced noise of the cases of rod-aerofoil and rectangular cavity was simulated based on the vortex sound theory and verified by the experimental measurements.²³ This noise prediction approach was beneficial for revealing the generating mechanism of noise produced by the unsteady flow developed around the geometries.

A simplified high-speed train leading car model

The high-speed train leading car model (1:25 scale) used in this study includes the nose, carbody, two bogies, and tail, as shown in Figure 1. The back of the car is modified to mimic the nose to allow correct wake structures behind the geometry. Taking into account a more general case, the nose shape of the current leading car model is less streamlined to see its influence on the aerodynamic noise generation. The geometric dimensions of length, width, and height are 1.02 m, 0.105 m, and 0.145 m. For simplicity, the ground is represented by a flat plane. Since the track structures of rails and sleepers are neglected, the gap between wheel bottom and ground is set as 0.01 m. The open source package OpenFOAM is used to calculate the governing equations ⁸. The convection term uses a total variation diminishing scheme and the temporal discretization follows a second-order implicit scheme. A pressure implicit with split operator (PISO) algorithm is applied for the pressure–velocity coupling term.

Figure 1.

Simplified leading vehicle model.

Simulation setup

For saving the computational resources, half of the leading car symmetrical along the carbody longitudinal central plane is built for numerical simulation.¹³ Figure 2 displays the computational domain with dimensions of $22.4 H$ (streamwise x), $3.8 H$ (vertical y), and $2.6 H$ (spanwise z), where $H$ is the train height. The blockage ratio (defined as the ratio of the projected leading car area to the domain cross-sectional area) is 3.1%, which is well within the range of 5% with very low influence on wall surface pressure distributions for passenger car flow ²⁴. Thereby, the side and outlet boundaries are far from the geometries and will not affect the flow developed close to the leading car. The inflow speed ( $U_{\infty}$ ) is 30 m/s with a low turbulence intensity (less than $0.5 %$ ); the top and side boundaries are represented as symmetry (equivalent to a zero-shear slip wall); the downstream exit boundary is set as a pressure outlet; the ground is defined as a moving wall with the inflow velocity; the leading car surfaces are defined as stationary no-slip walls except the wheelset surfaces are set as moving walls through imposing the corresponding rotation velocity on the wheel surfaces to implement the rotation effect. The Reynolds number ( $R e$ ) of the leading car model is 300,000 based on the inflow speed, height of leading car, and kinematic viscosity of $1.4607 \times 10^{- 5}$ m²/s.

Figure 2.

Computational domain of the leading car model (not to scale). (a) Side view (b) Front view.

A mesh-refinement study for a complex configuration as the leading car is hard to carry out due to large flow simulations required. Moreover, structured grids generating on complicated geometries are extremely challenging and time-consuming. Considering the aerodynamic noise predictions on the high-speed train bogie and bogie-inside-cavity cases performed earlier by the authors in which the numerical calculations agreed well with the experimental measurements,^8,25 the same grid generation technique with the similar resolution between different scales is applied for the mesh generation around the bogies of the current leading car case. Thus the grid-independent study is performed on an isolated carbody case by removing the bogie configurations and covering the bogie cavity to save the computational resources and improve the simulation efficiency. The boundary conditions are same as those mentioned above except all surfaces of the carbody are defined as stationary walls (no-slip). A fully structured mesh is generated around three mesh-refinement cases with different mesh resolutions. The spatial resolution has been compared through coarse, medium, and fine meshes by using different grids along x, y, and z directions to see its influence. Compared with medium mesh, the coarse mesh is reduced by a factor of 1.2 and the fine mesh is increased by a factor of 1.2 in grid number. For all cases, the near-wall spacing

y^{+}

is kept less than 1 for carbody surfaces. In order to ensure an adequate temporal resolution for flow simulation, the Courant–Friedrichs–Lewy (CFL) number is kept less than 1 in most regions of the computational domain during each iteration. The mesh size for grid-independence study and the influence of mesh resolution on mean and root-mean-square (RMS) values of aerodynamic force coefficients are displayed in Table 1. The lift coefficient (

C_{L}

) and drag coefficient (

C_{D}

) are non-dimensionalized by (

\frac{1}{2} ρ_{0} U_{\infty}^{2} A

), where

A

is the projected frontal cross-section area of half carbody. It shows that the variations of the mean and RMS values between the cases of medium and fine meshes are less than 5% and the differences between them are smaller than those between the cases of coarse and medium meshes. This indicates that the unsteady flow simulation is independent of the grid distribution and reaches reliable accuracy when the computational domain is meshed by medium grids. Considering the leading car case having the bogie and bogie cavity configurations underneath the carbody compared to the isolated carbody case, the fine mesh scale deduced from the grid-independence study is used to guide the mesh generating of the leading car case together with the mesh topology technique and an implicit time-marching scheme with similar CFL number applied in the bogie and bogie-inside-cavity cases performed in Refs. 8 and 25.

Table 1.

Comparisons of force coefficients obtained from different meshes.

Mesh	Grid points (M)	$\bar{C_{L}}$	$C_{L, r m s}$	$\bar{C_{D}}$	$C_{D, r m s}$
Coarse	20	0.2465	0.0061	0.165	0.00168
Medium	24	0.225	0.0067	0.1564	0.00182
Fine	29	0.233	0.007	0.1602	0.0019

Based on the mesh-refinement study mentioned above and mesh size with the similar resolution used in the bogie and bogie-inside-cavity cases performed earlier,^8,25 the fully structured grids with good mesh quality are generated around the leading car as shown in Figure 3. The delayed detached-eddy simulation (DDES) using Spalart–Allmaras (S-A) turbulence model is used to solve boundary layer and calculate the flow separated outside near-wall regions.²⁶ The value of $y^{+}$ is kept less than 1 for all surfaces to ensure that the boundary layer is resolved properly by considering low-Reynolds number effects inside viscous sublayer. A fully block-structured mesh with 56 million grid points is generated in the computational domain. Simulations are run with a physical timestep size of $1 \times 10^{- 5}$ s to ensure that the maximum CFL number is less than 1 within most computational domain to give a stable temporal resolution for implicit time marching scheme.

Figure 3.

Structured grids around the leading car. (a) Nose car surface (b) Around the nose car.

The flow was run

3 \times 10^{4}

timesteps to remove the initial large unsteadiness and transit to full development. Then another

3 \times 10^{4}

timesteps were run to obtain the time series of the aerodynamic force coefficients of the leading car. Table 2 displays the mean and RMS results from three sections of 50% overlapping. Results show that the variations of mean and RMS values of different sections are as small as less than 7%. This indicates that the temporal convergence has been achieved and the flow field becomes statistically stable. Thus, the simulation was run further for

3 \times 10^{4}

timesteps to obtain statistics and sound source data. It would be very challenging to run simulation of a large case with complex geometries to obtain detail flow behavior with boundary layer solved.

Table 2.

Mean and root-mean-square values of force coefficients of the leading car.

	Section 1(0.30-0.45 $s$ )	Section 2(0.375-0.525 $s$ )	Section 3(0.45-0.60 $s$ )	Total length(0.30-0.60 $s$ )
$\bar{C_{L}}$	0.432	0.4326	0.4332	0.4326
$\bar{C_{D}}$	0.3622	0.3606	0.3632	0.3626
$C_{L, r m s}$	0.0243	0.025	0.026	0.0248
$C_{D, r m s}$	0.017	0.0169	0.018	0.0178

Flow field

In order to visualize the flow structure with eddy formation and distribution in the turbulent flow evolved around the leading car, Figure 4 displays the instantaneous spanwise vorticity field ( $ω_{z} = (\partial V / \partial x - \partial U / \partial y) D / U_{\infty}$ , where $D$ is the diameter of wheel) in a vertical plane along the wheel mid-span. It can be seen that multi-scale vortices are generated in regions around two bogies and train tail as a consequence of flow interacting strongly with the geometries.

Figure 4.

Instantaneous spanwise vorticity field.

The turbulent vortices with a high velocity magnitude level are evolved behind the leading bogie, especially around the rear wall area of the bogie cavity. These eddies detached from the bogie cavity leading edge, having a strong flow interaction with the components of bogie structure and impinging on the rear walls of the bogie cavity. The vortices are significantly deformed and merged, before being convected downstream behind the bogie cavity. Compared to the leading bogie, the turbulence evolution in the rear bogie is much weaker and affected largely by the configuration of the train tail. Different to the turbulent wake behind the leading bogie which is concentrated and mainly developed underneath the train, the flow developed behind the rear bogie is transported upward and evolved into the train wake. The vortices are convected downstream beneath the train carbody and are merged with the vortices produced from the bogie structures. Correspondingly, the turbulent eddies with large scales are generated and have a strong interaction with the vortices produced around the tail region. The vortices introduced from the rear bogie and the train tail interact with each other and are pushed downward by the large-scale vortices generated from the rear roof of the leading car. All the vortices are amalgamated close to the ground behind the leading car and interact strongly with the ground surface flow. Therefore, the eddy evolution in the wake of the leading car is complex and is affected by the flow generated from the different regions of rear bogie, train tail, and ground. The vortices with different scales and strong flow oscillations generated in the train wake may cause large pressure fluctuating on the rear wall surfaces of the train tail of the leading car.

Lift and drag coefficients

Since the dominant noise produced at low Mach numbers is dipole sound source introduced from the wall pressure fluctuations and corresponds to the aerodynamic forces exerting back on the fluid close to the solid boundaries, the fluctuating forces of different components of the leading car are investigated to shed light on the aerodynamic sound source distribution of the configuration. Figure 5 shows the power spectral densities (PSDs) of the lift and drag coefficients of the front and rear bogies and the carbody with the frequency bin width of 6 Hz and three averages. It can be seen that compared to two bogies, the aerodynamic force coefficients of carbody are much larger in the frequency range below 4 kHz. This is due to the incoming flow impinging on the leading car nose, the turbulence impact on the front and rear bogie cavity walls, and the flow interacting between the large-scale eddies produced in the train wake. Additionally, the force coefficient of the front bogie (leading bogie) is larger than rear bogie above 200 Hz owing to a stronger flow interaction introduced in the leading bogie region as the first obstacle in the flow underneath the train.¹² The different aerodynamic force characteristics of various parts of the leading car will have a strong influence on aerodynamic noise generation in these regions.

Figure 5.

Power spectral densities of force coefficients for different components of leading car. (a) Lift efficient (b) Drag coefficient.

Near-field volume sound source

Based on the vortex sound theory, the density represented in the two sound source terms at the right-hand side of the vortex sound equation (2) is a constant ( $ρ_{0}$ =1.225 kg/m³) which may be omitted to facilitate the calculation. The volume dipole and volume quadrupole sources produced in the flow around the leading car are presented in the same order of magnitude of the intensity to compare the two sound sources of near-field quadrupole noise. Figures 6 and 7 show, respectively, the instantaneous distributions of volume dipole and volume quadrupole sources around the leading car along the wheel vertical mid-span. Results show that the two volume sources mainly exist in the regions of two bogies and train wake, the gap between the carbody bottom and the ground, and the train tail of the leading car. The volume dipole is much stronger than the volume quadruple and exists in a large region within the flow. Figure 8 presents the volume sound source distributions (shown in Figure 8(b)) of the leading car along the streamline (shown in Figure 8(a)) in the axle vertical mid-plane at the cross-section of 1/4 axle length to compare the intensity of sound source quantitatively. It can be seen that the strongest volume sound sources are located within the leading bogie cavity, especially in the flow separation area close to the front axle (the nose tip being located at x=0 m). The intensity of the volume dipole source is about 5 times of magnitude larger than the volume quadrupole source, indicating that the volume quadrupole source can be a negligible sound source compared to the volume dipole source. This is due to the flow separation, the turbulent eddy motion, and the vortex stretching as well as breaking up developed around the near-wall region of the high-speed train configurations producing strong flow interactions with the structures.¹³ Thus the formed volume dipole sound source converts flow energy into acoustic energy much more efficiently and becomes the main sound source of the near-field quadrupole noise generated around the train.²² Therefore, the Lamb vector $(ω \times v)$ presented in the vortex sound equation constitutes the main sound source of the near-field quadrupole noise. When the Lamb vector associated with a given point changes with time, the corresponding region of the fluid will radiate sound.

Figure 6.

Contours of instantaneous volume dipole source distribution of leading car along the wheel vertical mid-span.

Figure 7.

Contours of instantaneous volume quadrupole source distribution of leading car along the wheel vertical mid-span.

Figure 8.

Instantaneous volume sound source distribution of leading car along the streamline in the axle vertical mid-plane at the cross-section of 1/4 axle length. (a) Streamline (b) Volume sound source distribution.

Far-field radiated noise

When the flow becomes statistically steady, the aerodynamic noise can be calculated based on near-field flow data through FW-H approach. The SPL of the radiated noise is calculated by Welch’s method²⁷ using a Hanning window from the predicted pressure time series through the code developed in Ref. 28. Then an overall sound pressure level can be obtained for far-field receivers and the noise directivities may be analyzed. As a symmetry plane is applied and the flow data from half leading car are used for noise prediction, the SPL of the noise produced from the whole leading car is calculated by $L_{p} = 10 log (10^{\frac{L p 1}{10}} + 10^{\frac{L p 2}{10}})$ , where $L_{p_{1}}$ and $L_{p_{2}}$ are the SPLs of two receivers situated symmetrically along the longitudinal symmetry plane of the leading car. In the calculation of far-field noise directivity, the FW-H integration surfaces are placed on the solid wall surfaces to account for the dipole sources which are the main flow-induced noise for the current cases. The receivers are distributed uniformly along a circumference with a radius of 1 m at an interval of 5° in the horizontal plane and centered at the carbody center for the leading car as the noise source or at the bogie center for the bogie as the noise source. Figure 9 shows the sketch of the receiver locations used for the directivity calculation of the noise radiated from the bogie section in the horizontal plane. The carbody center for noise directivity calculation is located at the same height of the bogie center. Figure 10 presents the noise directivities of the leading car, front, and rear bogies. It can be seen that the flow-induced noise of the leading car has a relatively uniform directivity in all directions of the horizontal plane, shaped as a circle. This is mainly because a large number of irregular vortices of different scales are generated around the leading car and introduce the aerodynamic noise. By comparison, the development of the flow interaction between the flow and the bogie structure is limited by the configurations of bogie cavity vertically and longitudinally, resulting in the lateral dipole pattern of the noise directivity radiated from the front and rear bogies. The noise level of the front bogie is 4–7 dB higher than the rear bogie, corresponding to the stronger flow interaction evolved around the leading bogie.

Figure 9.

Sketch of receiver locations in the horizontal plane (top view).

Figure 10.

Far-field noise directivity in the horizontal plane.

In the current numerical wind-tunnel case, the leading car is kept stationary and the inlet flow passes it at the supposed train running speed. For simulating the noise radiated from the leading car passing by a fixed receiver located at the trackside region, probes are distributed evenly along the train at the interval of 0.03 m within the distance from 1 m ahead of the leading car to 1 m behind it, and are located 0.3 m from the bogie center laterally and 0.048 m from the rail top surface vertically, as sketched in Figure 11. Thus, the OASPL value of each probe is linked consecutively to obtain the time-series signals when the leading car passes by these probes set in the trackside regions (neglecting the Doppler effect, which is reasonable for the current case at low Mach numbers).

Figure 11.

Locations of trackside probes (not to scale). (a) Side view (b) Front view.

Figure 12 shows the OASPL of the flow-induced noise generated by different components of the leading car when it passes by the probe located 1 m ahead of it, the first probe in the left side illustrated in Figure 11. To facilitate the comparison and analysis, the influence of the sound reflection from the ground is not included here. Results show that two dominant peaks in the pass-by time series correspond to the aerodynamic noise generated from the leading bogie and rear bogie, respectively, demonstrating that the front bogie is the dominant sound source with the OASPL about 6 dB higher than the rear bogie. Moreover, there are two peaks shown in the OASPL curve of the carbody, happening just after the bogie cavities passing by the observer. Compared with the pass-by time series of the leading bogie, the amplitude of the first peak is smaller and occurs later, pointing to the noise generated from the cavity of leading bogie. Correspondingly, the second peak refers to the noise generated from the cavity of rear bogie with the amplitude level higher than the noise from the rear bogie due to the noise generating from both the rear bogie cavity and the train tail. Thus the carbody also generates a fair amount of noise due to the flow impact occurring on the rear wall surfaces of the bogie cavities and the flow separation formed at the rear region of the leading car. Furthermore, two peaks with high amplitude value appear in the time series of the pass-by OASPL of the leading car with the front peak much higher than the rear one. This demonstrates that the aerodynamic noise produced by the upstream region of the leading car contributes more than the areas of the tail and the rear bogie. As mentioned above, this is because the intensive turbulence evolution and flow interaction occurring in the leading bogie cavity, together with the flow separation from the nose region, introduce the strong aerodynamic noise. Therefore, mitigating the flow impact and vortex separation around the regions of the leading bogie and nose will effectively reduce the generation and radiation of flow-induced noise generated from the leading car of a high-speed train.

Figure 12.

Pass-by overall sound pressure level from different parts of the simplified leading car.

A simplified high-speed train nose car model

The numerical investigation on the high-speed train leading car model shows that the leading bogie region is the main aerodynamic sound source. Thereafter, a high-speed train nose car model at 1:3 scale (shown in Figure 13) is built to study further the flow behavior and aerodynamic noise characteristics around the leading bogie based on the numerical calculation and experimental measurement. The nose car model including the structures of the nose, snowplough, leading bogie, carbody, bogie cavity, and tail has the dimensions of 5.8 m (length), 1.1 m (width), and 1.4 m (height), respectively. The train tail is streamlined to avoid the flow-induced noise generated by the flow separation occurring at the train tail. The blockage ratio of the nose car model is close to 5%. The Reynolds number of the nose car model is 6,600,000 according to the inflow speed of 69.5 m/s $(U_{\infty})$ and height of nose car $(H)$ . The configurations of the nose car model are fairly complex containing the structures of bogie and bogie cavity in which many components with little or no streamlining. Thereby, LES with the wall-adapting local-eddy viscosity subgrid-scale model which has been validated by the fundamental flow cases is applied for the flow calculation to save computation resources and improve iteration convergence. Based on the mesh topologies of the carbody and pantograph of high-speed train,⁷ the adaptive unstructured trim grids with a number of 1.2×10⁸ are generated around the geometries after the mesh-refinement study has been performed. The mid-span mesh of the train nose car model is displayed in Figure 14. Simulations are run with a physical timestep size of $5 \times 10^{- 5}$ s to keep the maximum CFL number less than 0.5 within most computational domain. The near-field flow data obtained from the CFD simulation are used for calculating the far-field radiated noise. The aerodynamic noise predictions are verified against the wind tunnel experiments.

Figure 13.

Train nose car model.

Figure 14.

Mesh topology around the nose car mid-span.

Flow simulation

In order to visualize the flow structure with eddy formation and distribution in the turbulent flow evolved around the leading bogie of the nose car model, Figure 15 shows the instantaneous vortex structure represented by the iso-surfaces of normalized Q-criterion value of 1500 (based on $Q / [{(U_{\infty} / H)}^{2}]$ , where $Q$ is the second invariant of the velocity gradient). They are colored by the velocity magnitude normalized with freestream velocity. It is shown that the turbulent vortices with a high velocity magnitude level are evolved behind the leading bogie, especially around the front wheelset bottom and the rear wall region of bogie cavity. All the vortices are amalgamated close to the ground and interact strongly with the boundary layer developed from the ground, introducing the complex wake behind the leading bogie. Moreover, Figure 16 presents the contours of the mean TKE (turbulent kinetic energy, $k = \frac{1}{2} (\bar{u' u'} + \bar{v' v'} + \bar{w' w'}) / U_{\infty}^{2}$ , where $u^{'}$ , $v^{'}$ , and $w'$ are velocity fluctuation components in x, y, and z directions, respectively, and the overbar denotes a time average) in the nose car mid-span from a side view. It can be seen clearly that the eddies are detached from the leading edge of the bogie cavity, interacting with the components of the bogie structure and impinging on the rear walls of the bogie cavity. The vortices are concentrated and mainly developed in the gap between the train bottom and the ground, and are significantly deformed and merged before being convected downstream behind the bogie cavity.

Figure 15.

Iso-surfaces of the instantaneous normalized Q-criterion.

Figure 16.

Contours of the mean turbulent kinetic energy in nose car mid-span.

Aerodynamic noise prediction

The characteristics of the aerodynamic noise radiated by the nose car are analyzed in frequency domain. Figure 17 displays the far-field receivers located in a plane parallel to the longitudinal center-plane of the train model with a distance of 6 m and distributed at the height of 0.6 m from the ground. As two typical locations of bogie cavity configuration, receiver 1 is located from the bogie center laterally and receiver 2 situated opposite to the bogie cavity rear corner with 0.67 m downward from receiver 1. The FW-H method is used to calculate the far-field noise, and the integration surfaces are the wall surfaces. Figure 18 shows the far-field noise 1/3 octave spectra of receiver 1. Results show that in the frequency range below 3 kHz, the OASPL of the noise radiated from the nose car is 87.4 dB(A) in which 83.6 dB(A) produced from the leading bogie and 84.3 dB(A) generated from the carbody. The OASPL of the noise generated from the leading bogie and the carbody is quite similar since the structures of bogie itself and bogie cavity (situated in the carbody) produce the main aerodynamic noise.

Figure 17.

Location of far-field receivers.

Figure 18.

Far-field noise spectra.

Wind tunnel experimental measurements

The experimental measurements of the aerodynamic noise produced by a high-speed train nose car model at 1:3 scale (presented in Figure 19) are conducted in Shanghai automotive wind tunnel center at Tongji University. The wind tunnel is equipped with an open-jet and a semi-anechoic chamber except for the ground. The nozzle area is 27 m², and the blockage ratio of the train model is less than 5%. The inflow velocity is 69.5 m/s. The train nose car model is fixed on the support floor in the test section of the wind tunnel. The support columns located between the carbody and the floor are covered by aerofoils to reduce flow interfering. The laser orientator is used to ensure the train model being located precisely along the nozzle longitudinal centerline. The sound pressure of far-field noise is measured by the microphones placed outside the core flow. A 120-channel planar microphone array with dimensions of 1.8 m*1.8 m (length*width) was set out-of-flow with a distance of 5.8 m from train model centerline and opposite to the bogie cavity, as shown in Figure 19. In the measurements of identifying the sound source, the sound pressure signals acquired by the microphone array, in which the microphones are distributed in a spiral shape, have a certain delay depending on their spatial angle. The sound source localization can be realized through reconstructing the sound source signals at each space angle by the delay-and-sum method to enhance the signals generated from the sound source direction and weaken the signals produced from the other directions. The algorithm for sound source location using the conventional beamforming method in matrix form can be expressed as

B (m, w) = g^{H} (m, w) C (w) g (m, w),

(3)

where

B (m, w)

is the source auto-power. g(m,w) is the steering vector representing the time delay and amplitude attenuation from the point source of unit strength located at

m

to each microphone of the array.

C (w)

is the cross-spectral matrix of acoustic pressure signals obtained by the microphones.²⁹

Figure 19.

Train nose car model in the wind tunnel.

Figure 20 displays the spectra of the noise radiated from the train nose car model at two far-field receivers shown in Figure 17. The noise spectra curves correspond well between the numerical simulations and experimental measurements, especially at the frequency range with high amplitude levels. The OASPL of the radiated noise below 3 kHz obtained from numerical prediction is 0.5 dB(A) higher and 0.1 dB(A) lower than the experimental result at receivers 1 and 2 accordingly. Thereby, the wind tunnel measurements have verified the numerical predictions. Furthermore, the sound source distribution of the nose car model at the inflow velocity of 69.5 m/s measured by the microphone array is presented in Figure 21. Results show that the bogie region is the dominant aerodynamic sound source of the train nose car. This is in good agreement with the wind tunnel measurements carried out by Lauterbach et al.³⁰ and the field tests performed by Mellet et al.³

Figure 20.

Comparisons of far-field noise spectra. (a) Receiver 1 (b) Receiver 2.

Figure 21.

Sound source map of train nose car model.

Conclusions

The flow and flow-induced noise behavior of a scaled leading car of a high-speed train have been studied numerically based on the theory of vortex sound and acoustic analogy method. Results show that strong flow separation occurs at two bogies, rear wall surfaces of bogie cavities, and train tail of the leading car. The vortex motion evolves intensively in the flow field close to the solid walls of the geometries. The volume dipole source is formed with intensity much higher than the volume quadrupole source and becomes the dominant sound source of the near-field quadrupole noise. The far-field noise directivity in the horizontal plane is uniform-directional. The sound directivities of the front and rear bogies show a pattern of lateral dipole with the main radiation to the trackside direction. The noise generated from the front bogie region is much higher than that produced from the rear bogie and train tail, and becomes the dominant aerodynamic sound source. The strong aerodynamic noise is produced by the carbody due to the intensive flow interaction generated on the bogie cavity walls (especially the rear walls). Moreover, the numerical and experimental results obtained from a train nose car model demonstrate that the leading bogie and its bogie cavity are the dominant aerodynamic noise regions. Therefore, the flow developed around the leading bogie and bogie cavity is the key region of aerodynamic sound source of a high-speed train. The aerodynamic noise generated around the leading car of a high-speed train can be effectively reduced by mitigating the flow impact and flow interaction occurring around the regions of the leading bogie and the rear walls of bogie cavity. The findings based on the simplified leading car and nose car models are expected to be helpful to understand the train aeroacoustic behavior and seek the noise control methods for high-speed train in future research.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by National Natural Science Foundation of China (51875411, 11772230), National Natural Science Foundation of Hunan Province, China (2020JJ5631), and Shanghai Professional Technical Service Platform Program (19DZ2290400).

ORCID iD

Jianyue Zhu

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