The aerodynamic noise of high-speed trains passing through a tunnel has gradually become an important issue. Numerical approaches for predicting the aerodynamic noise sources of high-speed trains running in tunnels are the key to alleviating aerodynamic noise issues. In this paper, two typical numerical methods are used to calculate the aerodynamic noise of high-speed trains. These are the static method combined with non-reflective boundary conditions and the dynamic mesh method combined with adaptive mesh. The fluctuating pressure, flow field and aerodynamic noise source are numerically simulated using the above methods. The results show that the fluctuating pressure, flow field structure and noise source characteristics obtained using different methods, are basically consistent. Compared to the dynamic mesh method, the pressure, vortex size and noise source radiation intensity, obtained by the static method, are larger. The differences are in the tail car and its wake. The two calculation methods show that the spectral characteristics of the surface noise source are consistent. The maximum difference in the sound pressure level is 1.9 dBA. The static method is more efficient and more suitable for engineering applications.

With the continuous development of high-speed railways, there are many operating environments for high-speed trains. Tunnels are one of the major routes of high-speed trains. When high-speed trains pass through tunnels, complex aerodynamic effects, along with noise problems will occur [

Current research mainly focuses on the identification of aerodynamic noise sources, including noise mechanisms and characteristics, and noise optimization when high-speed trains are running on open tracks [

The head and tail cars of high-speed trains have the same streamlined nose. However, their sound mechanisms are different [

Up to now, many scholars have studied the aerodynamic noise of high-speed trains passing through tunnels. However, most of the research focuses on the internal noise of the train, while relatively few studies address external noise and aerodynamic noise sources. Li et al. [

However, High-speed trains are affected by pressure waves when running in tunnels, and the flow around the train is more complex. It is difficult to numerically simulate the aerodynamic noise of high-speed trains running in tunnels. There are two typical methods. One is the numerical wind tunnel method based on the principle of relative motion combined with non-reflective boundary conditions. The non-reflective boundary conditions can effectively solve the problem of pseudo-reflected waves caused by the artificial truncation of the calculation domain, thereby eliminating the influence of the pressure wave in the tunnel on the characteristics of the surface noise source of the train. The other method is a dynamic mesh method, combined with an adaptive grid. This directly uses high-precision algorithms and high-quality grids to solve the fluctuating pressure characteristics of the train surface, when the high-speed train passes through the tunnel. In this paper, the above two different methods are used to study the flow structures and aerodynamic noise sources when the high-speed train is running in a tunnel.

Detached Eddy Simulation (DES) is a hybrid method that combines the advantages of Unsteady Reynolds Average Navier-Stokes (URANS) and Large Eddy Simulation (LES). URANS is used in the boundary layer, and the LES is used in the other regions. This reduces the required computing resources, while ensuring a high calculation accuracy. At present, improved delayed detached eddy simulation (IDDES) based on the SST k-ω turbulence model is widely used to simulate the turbulent flow around high-speed trains [

Lighthill acoustic analogy theory divides the sound sources into three categories, comprising monopole noise sources, dipole noise sources and quadrupole noise sources [

The relationship between the acoustic energy density of far-field aerodynamic noise and sound pressure is as follows

Treating the sound source as a point sound source, and neglecting the influence of the delay time at a low Mach number, the total sound power radiated by the sound source can be determined by

We define

Subsequently, we have

where the overline represents the average value of the physical quantity in the time domain,

The sound power per unit area (unit: W/m^{2}) described by the sound power level is expressed as
^{−12} W.

The sound pressure level is defined as
^{−5} Pa.

A typical high-speed train is chosen as the research object, with a simplified bogie cabin and pantograph. The streamlined nose and train body are unchanged. The simplified geometric model is shown in

The computational domain based on Method 1 is selected to test the mesh independence, in which different basic size discretization calculation domains were set, and three sets of grids with different grid quantities of 18.24 million, 21.44 million and 27.65 million were obtained.

The computational domain is discretized using an unstructured hexahedral grid of the same size. The computational mesh is shown in

When Method 1 is used to simulate the flow around trains, the procedure is as follows. First, the SST

In order to compare the two above methods, the implicit density solver is adopted. Meanwhile, the advection upstream splitting method+ (ASUM+) is adopted for the flux, and the flow and turbulence terms are all found using the second order upwind scheme (SOUS). In terms of time discretization, the implicit time step method is adopted. The physical time step adopts the second order Euler backward scheme (SOEBS), and the internal iteration adopts the implicit time-marching scheme (ITMS). The time steps are all set to 1 × 10^{−4} s. The maximum resolvable frequency is 5 kHz.

In order to verify the rationality and correctness of the numerical calculation method in this paper, a 1/8 scaled high-speed train aerodynamic noise wind tunnel test was carried out. During the wind tunnel test, 30 microphones were arranged on one side of the train model to measure the aerodynamic noise of the train. The distance between the microphone and the track centerline was 5.8 m. The test model was a smooth car body, and the bogie and pantograph areas were filled with blocking blocks, as shown in

The wind tunnel test can verify the correctness of the numerical static calculation method (Method 1). Therefore, the same numerical simulation calculation model as used in the wind tunnel test was set up.

The results will be discussed and analyzed in terms of surface pressure, flow field and aerodynamic noise source.

_{1} (the location is shown in _{1} in the figure represents the moment the head car enters the tunnel. At that moment, a compression wave will be generated and the amplitude of the surface pressure of the train will increase. Time _{2} represents when the tail car starts entering the tunnel. At this time, an expansion wave will be generated and the amplitude of the surface pressure of the train will decrease. The compression and expansion waves propagate back and forth in the tunnel at the speed of sound. When the train has completely entered the tunnel and the waves are not reflected at the exit, the time-averaged pressure amplitude on the train surface does not change significantly, seen in the pressure results during the time interval between 2.0 and 2.5 s.

The time-averaged pressure reflects the statistically stable value of the time-varying pressure over a period of time. In addition, the fast Fourier transform of the time-varying pressure data collected at the measurement point P_{1} within a certain period of time (2.0∼2.5 s) can obtain and analyze the frequency spectrum of the pulsating pressure. _{1} for the two methods during 0.5 s. It can be seen from the figure that the power spectral density (PSD) of the fluctuating pressure on the train surface is basically the same for both methods, but that there is a certain difference in the energy in the low frequency range. For Method 2, the pressure wave generated by the high-speed train entering the tunnel increases the energy of the surface pressure on the train in the lower frequency range.

Accurately predicting the fluctuating pressure on the train body is a key to the identification of the aerodynamic noise sources generated by the high-speed train. It can be evaluated by the physical quantities of the 0th, 1st and 2nd order of the flow field. The vorticity is a linear function of the first derivative of velocity, and the

The time-averaged vorticities around the train are shown in

The vortex structures around the train are shown in

The intensity of the dipole noise source can be characterized by the root mean square of the time gradient of the fluctuating pressure on the train surface. According to the intensity of the fluctuating pressure on the train surface, the sound power level of the train surface can be found, as shown in

The aerodynamic noises generated by the head and tail cars are calculated. The fluctuating pressure on the train surface within 0.5 s of the sound source data is extracted. Then, the sound pressure at the noise evaluation point R_{1} (position shown in _{1} noise measurement points. The aerodynamic noises of both head and tail cars show consistent trends for the two different methods. The main noise energy of the train is concentrated in the wide frequency range of 500 to 4000 Hz.

Noise source | Head (dBA) | Tail (dBA) | Whole train (dBA) |
---|---|---|---|

Method 1 | 109.4 | 108.1 | 111.8 |

Method 2 | 107.8 | 105.8 | 109.9 |

Difference | 1.6 | 2.3 | 1.9 |

The computational time spent by the two numerical calculation methods were recorded. The computational time using Method 1 is about 1/4 of that for Method 2.

Two different numerical methods are used to obtain the flow around and aerodynamic noise source of a high-speed train running in a tunnel. Method 1 is based on the principle of relative motion, whereas Method 2 uses a dynamic mesh, combined with adaptive mesh method. By comparing the train surface pressure, flow field structure and aerodynamic noise source characteristics obtained using the two methods, the following conclusions can be drawn.

When high-speed trains run in tunnels at speeds below 0.3

Both methods can effectively simulate the flow around and the aerodynamic noise source of the high-speed train, running in the tunnel. The difference in the sound pressure level between the two methods at the same noise measurement point is less than 2 dBA. Compared with Method 2, Method 1 has a higher efficiency and is more suitable for engineering applications.