# Numerical Analysis of Unsteady Characteristics of the Second Throat of a Transonic Wind Tunnel

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## Abstract

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## 1. Introduction

## 2. Numerical Methods

^{+}≈1; additionally, the spacing ratio of adjacent grid points in the boundary layer along the vertical wall direction is about 1.2. The total number of grids is about 6 million cells. When modeling, the direction of airflow flow is the x-axis, and the vertical ground direction is the y-axis, while the z-axis is set according to the right-hand coordinate system. The center of the entrance to the test section is the coordinate origin. Other dimensions are shown in Table 1.

#### 2.1. Pulsating Pressure and Shock Position

^{−6}s and the total time is 1.0 s. Sub-iterations in each physical time step ensure that the residuals drop by four orders of magnitude so that the highly unsteady flow converges to the required accuracy.

#### 2.2. Governing Equation

#### 2.3. Boundary Conditions

#### 2.4. Algorithm Verification

## 3. Results and Discussion

#### 3.1. The Pressure Disturbance Frequency Is 5 Hz

#### 3.2. Pressure Disturbance Frequency Is 10 Hz~2500 Hz

## 4. Conclusions

- (1)
- Forced shock oscillations are caused by the propagation of a wavefront originating from downstream pressure perturbations that periodically alter the shock position and the flow field structure downstream of the shock, including boundary layer thickness, the size of the separation zone, and the size of the wake mixing zone. The shock boundary layer interference is very sensitive to the shock wave position. Due to the large shock wave displacement, a relatively long straight section needs to be provided in the second throat.
- (2)
- Compared with the outlet back pressure, the pressure change near the shock wave has a phase delay. The pressure disturbance shows a significant amplification effect; in particular, the closer the shock wave is, the more obvious it is. This leads to overshoot when the shock moves upstream or downstream. Under the same back pressure, the shock wave position in the unsteady state is different from the position in the steady state.
- (3)
- The variation trend in the second throat wall force, wavefront Mach number, and Mach number in the test section with time is consistent with the downstream disturbance, but does not have a complete follow-up effect. It shows that the pressure disturbance will propagate into the test section through the boundary layer or shock gap, but it is still recommended to use the second throat choking to control the Mach number stability of the test section.
- (4)
- The dynamic characteristics of shock oscillation are related to the amplitude and frequency of the applied pressure disturbance. The shock displacement decreases with the increase in the excitation frequency. When the frequency is higher than 125 Hz, the flow field is no longer sensitive to the forced excitation.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Mach number contour of symmetry plane in steady state when outlet pressure increases by 1%.

**Figure 11.**The power spectral density of the core flow along the x-direction under different disturbance frequencies.

Locations | y × z Cross-Sectional Size/mm | x-Coordinates/mm |
---|---|---|

test section entrance | 600 × 600 | (0, 0, 0) |

model area center of the test section | 600 × 600 | (1300, 0, 0) |

test section exit | 600 × 600 | (2350, 0, 0) |

support section exit | 680 × 680 | (2500, 0, 0) |

contraction section exit | Variable size × 680 | (3000, 0, 0) |

straight section exit | Variable size × 680 | (3600, 0, 0) |

diffuser section exit | 680 × 680 | (4500, 0, 0) |

computational domain exit | 860 × 860 | (18,000, 0, 0) |

Pressure Perturbation Amplitude | Frequency/Hz | Physical Time Step/s |
---|---|---|

1% | 5 | 5 × 10^{−4} |

1% | 10 | 2.5 × 10^{−4} |

1% | 25 | 1 × 10^{−4} |

1% | 50 | 5 × 10^{−5} |

1% | 125 | 2 × 10^{−4} |

1%, 2%, 5%, 10% | 500 | 5 × 10^{−6} |

1% | 2500 | 1 × 10^{−6} |

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**MDPI and ACS Style**

Cong, C.; Qin, H.; Yi, X.
Numerical Analysis of Unsteady Characteristics of the Second Throat of a Transonic Wind Tunnel. *Aerospace* **2023**, *10*, 956.
https://doi.org/10.3390/aerospace10110956

**AMA Style**

Cong C, Qin H, Yi X.
Numerical Analysis of Unsteady Characteristics of the Second Throat of a Transonic Wind Tunnel. *Aerospace*. 2023; 10(11):956.
https://doi.org/10.3390/aerospace10110956

**Chicago/Turabian Style**

Cong, Chenghua, Honggang Qin, and Xingyou Yi.
2023. "Numerical Analysis of Unsteady Characteristics of the Second Throat of a Transonic Wind Tunnel" *Aerospace* 10, no. 11: 956.
https://doi.org/10.3390/aerospace10110956