# Transient Flow Evolution of a Hypersonic Inlet/Isolator with Incoming Windshear

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## Abstract

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_{0}), the shock train first moves upstream and gradually couples with a cowl shock wave/boundary layer interaction, resulting in a more significant separation at the throat, and then moves downstream and decouples from the separation bubble at the throat. However, if the downstream backpressure increases to 140 p

_{0}, the shock train enlarges the separation bubble, forcing the inlet/isolator to fall into the unstart state, and it cannot be restarted. These findings emphasize the need to consider wind shear effects in the design and operation of hypersonic inlet/isolator.

## 1. Introduction

## 2. Introduction of the Hypersonic Inlet/Isolator and the Wind Shear Model

#### 2.1. Description of the Hypersonic Inlet/Isolator

_{cowl}, of 334.11 mm for a design Mach number of 6.0 is described. The external compression system contains an oblique shock with a deflection angle of 8.73 degrees and a series of compression waves to decelerate the incoming hypersonic flow with minimal total pressure loss. In essence, this is a design methodology for the hypersonic inlet/isolator that emphasizes high compression efficiency. Throughout the entire compression process, the entropy of the main flow outside the boundary layer remains constant. The throat has a minimum flow area of H

_{th}= 53 mm. The isolator has an expansion angle of 0.2 degrees and the value of L

_{iso}= 15.1H

_{th}. The main geometrical parameters of the inlet/isolator model are listed in Table 1. Note that the coordinate origin is set at the leading point of the ramp. The X-axis and Y-axis are shown in Figure 1.

#### 2.2. Model for the Wind Shear

## 3. Numerical Method

#### 3.1. Computational Method

#### 3.2. Grid Generation

^{+}, of less than or equal to one. Given the complexity of the flows at the lip and throat, the grid in these regions was also refined to clearly capture the shock waves and separation flow.

#### 3.3. Boundary Conditions

#### 3.4. Inlet/Isolator Performance Parameters

- (1)
- The total pressure recovery coefficient (TPR) is the ratio of total pressure at the inlet/isolator exit (P
_{out}*) to the freestream total pressure (P_{∞}*). The total pressure loss is the sum of shock and viscous losses. The total pressure at the exit is calculated with the mass-weighted average.$$\mathrm{T}\mathrm{P}\mathrm{R}=\frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}^{*}}{{\mathrm{P}}_{\mathrm{\infty}}^{*}}$$ - (2)
- The pressurization rate (PR) is one of the main indicators that characterize the compression characteristics of the inlet/isolator. It is defined as the ratio of inlet/isolator exit static pressure (P
_{out}) to inlet/isolator static pressure (P_{∞}). The static pressure at the exit is calculated with the mass-weighted average.$$\mathrm{P}\mathrm{R}=\frac{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{\infty}}}$$

#### 3.5. Validation of the Numerical Method and Grid Sensitivity

^{+}distribution curves corresponding to different grids are shown in Figure 6, and it can be seen that the y

^{+}values meet the requirement of the turbulence model [30]. Figure 7 shows the pressure distribution curves corresponding to different grids. After reaching a grid quantity of 150,000, noticeable changes in the positions of flow structures, such as separation and shock waves, can be observed compared with the coarser grid quantities. Figure 8 illustrates that, when the grid number is below 100,000, the separation bubble does not exhibit a triangular shape. Figure 9 compares the total pressure recovery (TPR) and pressurization rate (PR) results for the inlet/isolator with the six different grids. Only when the grid number exceeds 150,000 is the predicted shock wave structure insensitive to the grid number. While finer meshes require higher computational costs, the mesh with a grid number of 150,000 was selected for subsequent wind shear simulation calculations.

#### 3.6. Numerical Dissipation Verification

## 4. Results and Discussion

#### 4.1. Effect of Wind Shear on Hypersonic Inlet/Isolator under Unthrottled Conditions

#### 4.2. Effect of Wind Shear on Shock Train

_{0}) without wind shear. Once the backpressure exceeds this value, the shock train will be expelled out of the duct, and the inlet/isolator will fall into the unstart state. This section analyzes the impact of wind shear on the shock train under various throttling conditions.

_{0}, under incoming wind shear, the transient flowfield within the inlet/isolator is numerically analyzed. Figure 21 and Figure 22 present the Mach number and X-velocity contours of the inlet/isolator at different times. Wind shear induces the downstream shock train to continuously approach the throat, while the throat’s separation moves downstream. The reason is the compression strength of the external compression system decreases with wind shear. For the duct, the pressure at the entrance becomes smaller, while the exit remains unchanged, which eventually leads to the shock train being pushed upstream. At t = 45 ms, the lower wall separation zone of the shock train couples with the throat’s separation bubble. As the shock train moves upstream, the separation at the upper wall expands. This phenomenon happens because, as the shock train moves upstream, the shock causing separation changes from the right-running reflected shock to the left-running reflected shock [36].

_{0}, clearly showing that wind shear causes the shock train to move upstream and ultimately causes the unstart state. It can be seen that the separation point of the separation bubble at the throat moves upstream, which is further demonstrated in Figure 28. Moreover, the Cf value changes for the upper and lower walls, as shown in Figure 29 and Figure 30. This occurs because, as the shock train moves upstream, it approaches the upper wall, leading to a lower exit Mach number in Figure 31. At t = 40.6 ms, the downstream separation zone and separation bubble couple at the throat, and the separation bubble at the throat enlarges rapidly over time. The angle of attack change caused by wind shear begins to decrease after t = 50 ms, and the separation bubble at the throat starts to decouple from the downstream separation zone at t = 50.6 ms. However, unlike the condition when the backpressure is 0.675 times the limit back pressure, the Mach number contour at 52.2 ms clearly shows that the decoupling has failed, forcing the inlet/isolator to fall into the unstart state. Obviously, under this condition, the influence of wind shear on the inlet/isolator is profound, directly causing the inlet/isolator to fall into the unstart state, and it cannot be restarted.

## 5. Conclusions

_{0}), the shock train first moves upstream and gradually interacts with the cowl shock wave/boundary layer, apparently enlarging the separation bubble at the throat. As the shock train moves upstream, the separation at the upper wall expands because the shock that interacts with the shock train switches from the right-running reflected shock to the left-running reflected shock. Then, the shock train moves downstream and decouples from the separation bubble at the throat. Though the perturbation amplitude reduces to zero, because of the hysteresis effect, the flowfield in the inlet/isolator cannot fully recover to the initial state. When the downstream backpressure increases to 140 p

_{0}, the shock train expands the separation zone in both the upper and lower walls, ultimately forcing the inlet/isolator to fall into the unstart state, and it cannot be restarted. Therefore, it is necessary to pay more attention to the adverse effects of wind shear on inlet/isolator performance, which directly affects the internal flow.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Comparison of flow structures in the inlet and the isolator, where red circles indicate the separation zones.

Parameters | Value |
---|---|

$\delta ,\mathrm{d}\mathrm{e}\mathrm{g}$ | 17.13 |

$\beta ,\mathrm{d}\mathrm{e}\mathrm{g}$ | 8.73 |

H_{th}, mm | 53 |

${L}_{cowl}$ | $5.57{H}_{th}$ |

${y}_{th}$ | $5.3{H}_{th}$ |

${x}_{cowl}$ | $20.38{H}_{th}$ |

${y}_{cowl}$ | $6.3{H}_{th}$ |

${L}_{iso}$ | $15.1{H}_{th}$ |

Parameter | Value |
---|---|

On-design freestream Mach number | 6.0 |

Air model | Ideal gas |

Altitude, km | 30 |

Presser, Pa | 1197.003 |

Temperature, K | 226.509 |

Point | P1 | P2 | P3 | P4 | P5 | P6 | P7 | P8 | P9 | P10 |
---|---|---|---|---|---|---|---|---|---|---|

x, mm | 1411 | 1425 | 1433 | 1440 | 1444 | 1446 | 1455 | 1625 | 1792 | 2065 |

y, mm | 281 | 281 | 282 | 282 | 282 | 282 | 282 | 283 | 283 | 283 |

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**MDPI and ACS Style**

Gao, S.; Huang, H.; Meng, Y.; Tan, H.; Liu, M.; Guo, K.
Transient Flow Evolution of a Hypersonic Inlet/Isolator with Incoming Windshear. *Aerospace* **2023**, *10*, 1021.
https://doi.org/10.3390/aerospace10121021

**AMA Style**

Gao S, Huang H, Meng Y, Tan H, Liu M, Guo K.
Transient Flow Evolution of a Hypersonic Inlet/Isolator with Incoming Windshear. *Aerospace*. 2023; 10(12):1021.
https://doi.org/10.3390/aerospace10121021

**Chicago/Turabian Style**

Gao, Simin, Hexia Huang, Yupeng Meng, Huijun Tan, Mengying Liu, and Kun Guo.
2023. "Transient Flow Evolution of a Hypersonic Inlet/Isolator with Incoming Windshear" *Aerospace* 10, no. 12: 1021.
https://doi.org/10.3390/aerospace10121021