# Dynamic Characteristics of Unsteady Aerodynamic Pressure on an Enclosed Housing for Sound Emission Alleviation Caused by a Passing High-Speed Train

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Methodology

#### 2.1. Geometry

_{T}) of 203 m and a width (W) and height (H) of 3.38 m and 3.7 m, respectively. Figure 1b shows the geometry of the enclosed housing for sound emission alleviation. The model is the preliminary design of a project in a high-speed railway line. The length of the enclosed housing for sound emission alleviation is 840 m, the radius of the cross-section is 6.913 m, the height is 9.637 m, the track spacing is 5.0 m and the cross-sectional area of the enclosed housing for sound emission alleviation is 110.5 m

^{2}. A universal beam (H 500 × 300 × 12 × 25) is set up every two meters inside the housing for sound emission alleviation.

#### 2.2. Computational Domain and Mesh

_{S}) of 840 m. The boundary conditions of the computational domain are defined as shown in Figure 2a. The bottom surface is ground and set as a no-slip solid wall, while the other five surfaces are atmospheric condition and set as outlets with zero pressure [26,29]. The surfaces of the train body and the housing for sound emission alleviation are set as no-slip solid walls. The entire computational model uses a hybrid grid of tetrahedral unstructured grids and prismatic grids. In addition, the meshes on the train body and wall of the housing for sound emission alleviation are refined to improve the calculation accuracy.

^{2}at the location of −250 m (the entrance of the housing for sound emission alleviation is at the location of 0 m) and reaches the design speed at the location of −152.78 m, −152.78 m before the head coach enters the housing for sound emission alleviation, then passes through the housing for sound emission alleviation with a constant speed of 350 km/h, and finally exits the housing for sound emission alleviation. Figure 5 shows the speed strategy of the train model.

#### 2.3. Numerical Method

^{−6}. This approach considers the influence of vortex factors and low Reynolds number effects in a turbulent flow and adds an extra term to the ε equation of the standard k-ε model to effectively improve the accuracy. The governing equations are presented as below [25,43]:

#### 2.4. Layout of Measurement Points

## 3. Validation

_{T_MAX}variations between the numerical simulation and the experimental results of VT1 and VT2, which are 0.5 m and 38.5 m away from the tunnel inlet, respectively. U

_{T_MAX}is set to as 3.0 m/s. The comparison results show that the numerical calculation and the experimental results are in good agreement. Although the train speed of the validation case is much lower than that of the current work, the comparison results indicate that the numerical method adopted in this research is accurate to simulate the moving object-induced aerodynamic pressure and unsteady flow inside a tunnel structure. In addition, Liu et al. [45] and Izadi et al. [46] had used a similar method to simulate the aerodynamic pressure inside tunnels and obtained reasonable results. It indicates that the numerical method adopted in this research is accurate for obtaining the main characteristics of the flow field and aerodynamic pressure fluctuation when a high-speed train passes the housing for sound emission alleviation.

## 4. Results and Discussion

#### 4.1. Wave Propagation

_{N}) is the running trajectory of the train head, the green dotted line (marked by T

_{R}) is the running trajectory of the train rear, the blue solid lines (marked by C

_{W}) present the propagation trajectory of the compression waves, and the blue dotted lines (marked by E

_{W}) are the propagation trajectory of the expansion waves. The results show that a compression wave is generated at the instant the train head enters the housing for sound emission alleviation and then propagates inside the housing for sound emission alleviation at sound velocity. When the compression wave reaches section S9 at t

_{1}, the monitored aerodynamic pressure first rapidly and then steadily increases. When the train tail enters the housing for sound emission alleviation, an expansion wave is generated and propagates inside the housing for sound emission alleviation at the sound velocity. When the expansion wave reaches S9 at t

_{2}, the aerodynamic pressure begins to rapidly decrease. When the compression and expansion waves propagate to the exit of the housing for sound emission alleviation, they are reflected back as expansion and compression waves, respectively. At instant t

_{3}, the reflected expansion wave reaches S9, and the aerodynamic pressure continues to rapidly decrease. At instant t

_{4}, the reflected compression wave reaches S9, the aerodynamic pressure increases. When the train head passes section S9 at t

_{5}, the aerodynamic pressure decreases. After that, multiple compression and expansion waves are transmitted to section S6, and the pressure increases and decreases accordingly. The transmission of the aerodynamic pressure waves in the enclosed housing for sound emission alleviation is also consistent with those in tunnels, as reported by Liu et al. [47] and Ji et al. [48]. Figure 12 shows the pressure distribution on the wall of the housing for sound emission alleviation when t = 6 s. The video of the train transition with pressure shown is given in the attachment.

#### 4.2. Extreme Pressure, Duration of Extreme Pressure and Impact Effects

_{pmax}is the positive-extreme pressure, P

_{nmax}is the negative-extreme pressure, and the peak-to-peak pressure is the absolute difference of P

_{pmax}and P

_{nmax}(P

_{pmax}– P

_{nmax}). The results show that the extreme pressures are almost symmetrical against section S6, the middle section. The extreme aerodynamic pressure at the central region is always higher than those close to the entrance/exit. In particular, the negative extreme pressure drastically increases in the range of 150 m to 350 m from the entrance/exit and reaches −2153 Pa at the middle section, more than two times higher than that at the entrance/exit sections. Different from the negative peak, the positive extreme pressure gradually increases from the entrance/exit to the middle section and reaches the maximum value of 1298 Pa at the middle section. The maximum peak-to-peak pressure is calculated as 3451 Pa.

_{d}, and the change rate of aerodynamic pressure, $\overline{P}$ and P

_{pmax}and P

_{nmax}, as Figure 13 shows.

_{d}is defined as the time when the aerodynamic pressure is higher than 85% of extreme pressure and the extreme pressure appears:

#### 4.3. Dominant Frequency and Decay Rate of the Aerodynamic Pressure after the Train Exits

_{K}is a pressure extreme in the process of pressure decay, A

_{K+}

_{1}is the next pressure extreme after a cycle. The definition of the decay rate of the aerodynamic pressure is similar to that of a damped free vibration.

## 5. Conclusions

- (1)
- The unsteady aerodynamic pressure is complicated and aperiodic when the train is running in the enclosed housing for sound emission alleviation. The reasons for the variation in the aerodynamic pressure are clearly caused by the propagation of the aerodynamic pressure wave, similar to that in a tunnel.
- (2)
- The extreme aerodynamic pressure at the central region is always higher than those close to the entrance and exit. In particular, negative and positive extreme pressures appearing in the middle section are −2153 Pa and 1298 Pa, respectively. The maximum peak-to-peak pressure is 3451 Pa.
- (3)
- To further quantify the dynamic characteristics of the train-induced aerodynamic pressure on the housing for sound emission alleviation, an ideal model of aerodynamic pressure is proposed using the duration of the extreme aerodynamic pressure and the pressure change rate. The longest duration of the extreme aerodynamic pressure appears in the middle section, and the highest pressure change rate occurs at the entrance section. In other sections, the pressure change rate is relatively close. The ideal model is much simpler than the original aerodynamic pressure and can be adopted to calculate the structural responses of the housing for sound emission alleviation. The rationality of the parameters in the ideal model needs further studies.
- (4)
- For the special enclosed housing for sound emission alleviation, the longest durations of the positive and negative extreme aerodynamic pressures are calculated as 1.41 s and 1.04 s, respectively. The highest positive and negative pressure change rates are calculated as 9.881 kPa/s and −10.415 kPa/s, respectively. In other sections, the average pressure change rate is calculated as 5.4 kPa/s and −5.9 kPa/s.
- (5)
- After the train exits the housing for sound emission alleviation, the aerodynamic pressure reverts to periodic decay curves. The pressure amplitude at the central region is always higher than those close to the entrance/exit. To better understand the aerodynamic pressure in this process, the dominant frequency and decay rate are proposed to express the dynamic characteristics. For the special enclosed housing for sound emission alleviation, the dominant frequency is identified as 0.2 Hz, and the decay rate is calculated as 0.262.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Computational models and surface meshes. (

**a**) Train model. (

**b**) Enclosed housing for sound emission alleviation.

**Figure 2.**Overview and cross-section of the computational domain. (

**a**) Overview of the computational domain. (

**b**) Cross-section of the computational domain.

**Figure 6.**Measuring point distribution on the enclosed housing for sound emission alleviation. (

**a**) Schematic diagram of the overall monitoring cross-sectional arrangement. (

**b**) Layout of the measuring points on a monitoring cross-section.

**Figure 8.**Comparison of Cp variations between the numerical simulation and the experimental results. (

**a**) PT1. (

**b**) PT2. (

**c**) PT3. (

**d**) PT4.

**Figure 9.**Comparison of u/U

_{T_MAX}between the numerical and the experimental results. (

**a**) VT1. (

**b**) VT2.

**Figure 11.**Pressure variations of P3 on the housing for sound emission alleviation section S9 and the propagation process of the pressure waves when the train passing through the housing for sound emission alleviation: (

**a**) Time history of wind pressure of P3 at S9; (

**b**) Propagation process of the pressure waves (The black dotted line in (

**b**) represents the test section of (

**a**), the red solid line is the running trajectory of the train head, marked by T

_{N}; the green dotted line is the running trajectory of the train rear, marked by T

_{R}; the blue solid lines present the propagation trajectory of the compression waves, marked by C

_{W}; and the blue dotted lines are the propagation trajectory of the expansion waves, marked by E

_{W}).

**Figure 12.**The pressure distribution on the wall of the housing for sound emission alleviation when t = 6 s.

**Figure 14.**Ideal aerodynamic pressure at different sections. (

**a**) S1. (

**b**) S3. (

**c**) S6. (

**d**) S9. (

**e**) S11.

**Figure 17.**Pressure curves of different measuring points for the train passing through the housing for sound emission alleviation. (

**a**) S1. (

**b**) S3. (

**c**) S6. (

**d**) S9. (

**e**) S11.

**Figure 18.**Pressure curves of different measuring points for the train passing through the housing for sound emission alleviation. (

**a**) S1. (

**b**) S3. (

**c**) S6. (

**d**) S9. (

**e**) S11.

**Figure 19.**Pressure wave attenuations of different sections. (

**a**) S1. (

**b**) S3. (

**c**) S6. (

**d**) S9. (

**e**) S11.

**Table 1.**Distribution of the extreme pressure in the longitudinal direction of the housing for sound emission alleviation.

Sections | P_{pmax} (Pa) | P_{nmax} (Pa) | Peak-to-Peak (Pa) |
---|---|---|---|

1 | 1090 | −1020 | 2110 |

2 | 1047 | −1088 | 2135 |

3 | 1145 | −1607 | 2752 |

4 | 1237 | −2076 | 3312 |

5 | 1285 | −2111 | 3396 |

6 | 1298 | −2153 | 3451 |

7 | 1277 | −2023 | 3300 |

8 | 1227 | −1963 | 3190 |

9 | 1170 | −1212 | 2382 |

10 | 944 | −909 | 1853 |

11 | 799 | −936 | 17 |

Sections | P_{pmax} | P_{nmax} | ||
---|---|---|---|---|

T_{d} (s) | $\overline{\mathit{P}}$ (kPa/s) | T_{d} (s) | $\overline{\mathit{P}}$ (kPa/s) | |

S1 | 0.222 | 9.881 | 0.154 | −10.415 |

S3 | 1.379 | 3.288 | 0.347 | −5.488 |

S6 | 1.410 | 5.780 | 1.041 | −6.569 |

S9 | 1.059 | 6.227 | 0.719 | −5.842 |

S11 | 0.356 | 6.366 | 0.526 | −5.609 |

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## Share and Cite

**MDPI and ACS Style**

Jing, H.; Ji, X.; He, X.; Zhang, S.; Zhou, J.; Zhang, H.
Dynamic Characteristics of Unsteady Aerodynamic Pressure on an Enclosed Housing for Sound Emission Alleviation Caused by a Passing High-Speed Train. *Appl. Sci.* **2022**, *12*, 1545.
https://doi.org/10.3390/app12031545

**AMA Style**

Jing H, Ji X, He X, Zhang S, Zhou J, Zhang H.
Dynamic Characteristics of Unsteady Aerodynamic Pressure on an Enclosed Housing for Sound Emission Alleviation Caused by a Passing High-Speed Train. *Applied Sciences*. 2022; 12(3):1545.
https://doi.org/10.3390/app12031545

**Chicago/Turabian Style**

Jing, Haiquan, Xiaoyu Ji, Xuhui He, Shifeng Zhang, Jichao Zhou, and Haiyu Zhang.
2022. "Dynamic Characteristics of Unsteady Aerodynamic Pressure on an Enclosed Housing for Sound Emission Alleviation Caused by a Passing High-Speed Train" *Applied Sciences* 12, no. 3: 1545.
https://doi.org/10.3390/app12031545