# Study on Aerodynamic Drag Reduction by Plasma Jets for 600 km/h Vacuum Tube Train Sets

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Calculation Model

#### 2.1. Geometric Model and Simulation Conditions

#### 2.2. Validation of Numerical Plasma Simulation

^{−19}C; $\mathrm{\Delta}t$ is the unit cycle of the effective breakdown of air time, that is, discharge time, taken as 67; $E$ is the strength of the electric field; $\delta $ is the Dirac delta function, which is used to calculate the electric field’s range. When the electric field strength is greater than the threshold value of the degree of air breakdown, the Clarke function, which is used to calculate the range of the electric field, is taken as 1, and in the opposite case, it is taken as 0.

#### 2.3. Knudsen Number

#### 2.4. Dimensionless Coefficients

^{3}; $U$ represents the velocity of the distant incoming flow; $S$ is the area of the windward surface; $p$ is the pressure at a point in the flow field.

#### 2.5. Reliability Analysis and Mesh Partitioning Strategy

#### 2.6. Validation of Mathematical Techniques

## 3. Discussion

#### Determination of SDBD Position at the Rear of the High-Speed Train

## 4. Analysis of Results

#### 4.1. Position 1

#### 4.2. Position 2

#### 4.3. Position 3

#### 4.4. Position 4

#### 4.5. Comparison of Drag Reduction Effects at Four Positions

## 5. Conclusions

- (1)
- The flow control mechanism of plasma on rolling stock delays the flow separation by causing directional gas flow close to the wall, moving the flow separation point backward, reducing the size of the negative pressure zone at the end of the train’s body, and reducing the pressure difference drag between the front and rear of the train’s body to reduce the drag coefficient of the entire train.
- (2)
- The best drag reduction scheme can be obtained by studying the most effective way to reduce drag. The SDBD device is installed at the flow separation around the tip of the nose, and the drag reduction effect is maximized close to the excitation velocity ratio of V/U = 0.2, with the drag reduction ratio of about 0.88%; the drag reduction ratio of the rear car reaches the maximum at the excitation velocity ratio of V/U = 0.25, with the drag reduction ratio of 1.62%.
- (3)
- In the four positions of the excitation jet, position 4 produces the excitation jet when the rolling stock rear car wall shear stress reduction amplitude and range are larger than the other three positions to produce the excitation jet, and when the excitation velocity ratio of V/U = 0.1, the area of the low-stress zone at the nose tip of the rear car develops to its maximum, reaching the minimum value of wall shear stress, thereby more effectively reducing the surface friction drag of the train.
- (4)
- Vacuum tube moving train plasma excitation drag reduction is feasible, but the maximum drag reduction ratio is not more than 2%, so the effect is weak. Due to the fact that the vacuum tube belongs to a very narrow space, its internal flow field changes are more intense and variable, so using a simple plasma excitation jet to achieve the purpose of drag reduction effect is very limited.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Model grid scheme: (

**a**) surface grid division of high-speed train unit; (

**b**) grid division of the watershed near the rear car; (

**c**) internal grid division of vacuum tube; (

**d**) boundary layer grid.

**Figure 6.**Numerical model for wind tunnel test: (

**a**) numerical model and boundary conditions for wind tunnel test; (

**b**) fluid domain of wind tunnel simulation.

**Figure 12.**Variation surface pressure coefficient of the rear car with different excitation velocity ratios at position 1: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 13.**Position 1 center longitudinal profile rear train velocity contour and streamline diagrams: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 14.**Distribution of shear stress on the rear car’s wall surface at position 1: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 17.**Variation in rear car surface pressure coefficient for different excitation velocity ratios at position 2: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 18.**Velocity contour and streamline diagrams at z = 1.12 profile for position 2: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 19.**Distribution of shear stress on the rear car’s wall surface at position 2: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 22.**Variation in rear car surface pressure coefficient for different excitation velocity ratios at position 3: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 23.**Position 3 center longitudinal profile rear train velocity contour and streamline diagrams: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 24.**Position 3 velocity contour and streamline diagrams of the trailing train at z = 1.12 profile: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 25.**Distribution of shear stress on the rear car’s wall surface at position 3: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 28.**Variation in rear car surface pressure coefficient for different excitation velocity ratios at position 4: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 29.**Position 4 center longitudinal profile rear car velocity contour and streamline diagrams: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

**Figure 30.**Distribution of shear stress on the rear car’s wall surface at position 4: (

**a**) V/U = 0; (

**b**) V/U = 0.025; (

**c**) V/U = 0.05; (

**d**) V/U = 0.1; (

**e**) V/U = 0.15; (

**f**) V/U = 0.2; (

**g**) V/U = 0.25; (

**h**) V/U = 0.3.

Computational Domain | Boundary Condition | Calculation Settings |
---|---|---|

Tube inlet | Pressure far field | 0.489 Ma |

Tube outlet | Pressure outlet | 0 |

Train body | Wall | No-slip |

Tube | Wall | 167 m/s |

Computational Domain | Boundary Condition | Calculation Settings |
---|---|---|

Inlet | Velocity inlet | 2–10 m/s |

Outlet | Pressure outlet | 0 |

Side surface | Wall | symmetry |

Bottom surface | Wall | Fixed wall |

Mesh Density | Coarse | Medium | Fine |
---|---|---|---|

Mesh density (10^{6}) | 14 | 25 | 45 |

Aerodynamic drag coefficient ${\mathrm{C}}_{\mathrm{d}}$ | 0.5250 | 0.5130 | 0.5129 |

Grid Density (Million) | 9 | 16 | 28 | 33 | Experimental |
---|---|---|---|---|---|

Pneumatic drag coefficient ${\mathrm{C}}_{\mathrm{d}}$ | 0.321 | 0.3 | 0.318 | 0.343 | 0.335 |

inaccuracies | 4% | 10% | 5% | −2% | - |

Position Number | Excitation Position |
---|---|

Position 1 | Position of flow separation above the front windshield of the rear car, between the equal-section body and streamlined rear portion of a moving train |

Position 2 | Upstream flow separation on both sides of the tailgate windshield |

Position 3 | Flow separation around the tip of the nose |

Position 4 | nasal tip where the rear vortex falls off |

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## Share and Cite

**MDPI and ACS Style**

Li, A.; Cui, H.; Guan, Y.; Deng, J.; Zhang, Y.; Deng, W.
Study on Aerodynamic Drag Reduction by Plasma Jets for 600 km/h Vacuum Tube Train Sets. *Machines* **2023**, *11*, 1078.
https://doi.org/10.3390/machines11121078

**AMA Style**

Li A, Cui H, Guan Y, Deng J, Zhang Y, Deng W.
Study on Aerodynamic Drag Reduction by Plasma Jets for 600 km/h Vacuum Tube Train Sets. *Machines*. 2023; 11(12):1078.
https://doi.org/10.3390/machines11121078

**Chicago/Turabian Style**

Li, Ang, Hongjiang Cui, Ying Guan, Jichen Deng, Ying Zhang, and Wu Deng.
2023. "Study on Aerodynamic Drag Reduction by Plasma Jets for 600 km/h Vacuum Tube Train Sets" *Machines* 11, no. 12: 1078.
https://doi.org/10.3390/machines11121078