# Reynolds Number Effect on Aerodynamic and Starting Characteristics of a Two-Dimensional Hypersonic Inlet

^{1}

^{2}

^{*}

## Abstract

**:**

^{6}to 9.71 × 10

^{4}with model scaling increases from 1 to 1/50, the relative boundary layer thickness at the entrance of the inlet increases from 10.4% to 21.2%; as the flight altitude increases from 25.5 km to 36.5 km, which causes the Reynolds number to decrease from 5.67 × 10

^{6}to 1.07 × 10

^{6}, the relative boundary layer thickness at the entrance of the inlet increases from 9.8% to 13.2%. Finally, the Reynolds number effect on the aerodynamics and starting characteristics caused by these two different factors are compared. The results show that the effect of scaling the model is similar to the effect of changing the altitude. As the relative boundary layer thickness increased by 1.0%, the total pressure recovery at the throat section decreased by 0.8%, and the inlet starting Mach number increased by 0.1.

## 1. Introduction

_{c}≈ 10

^{7}) to investigate the Reynolds number effect on the airfoil flow fields. They qualitatively predicted the decrease in boundary layer thickness and increase in lift coefficient with the Reynolds number effect, and that a thin boundary layer thickness induces the backward displacement of the shock wave in a transonic case.

## 2. Methods

^{+}is smaller than 1. The mesh and boundary conditions of the two-dimensional hypersonic inlet are shown in Figure 2. The inflow Mach number is 6.0 at an altitude of 26.5 km. The pressure farfield and pressure outlet boundary conditions are set according to the inflow conditions. The non-slip adiabatic wall boundary condition is used. The ideal gas model is used, and the viscosity is calculated based on the Sutherland equation. The convergence of simulation is determined by a decrease of at least 3 orders of magnitude in the residual of each equation, and the flow quantities are stable at critical sections [17].

## 3. Results

#### 3.1. Model Scaling on Two-Dimensional Hypersonic Inlet Aerodynamic Characteristics

^{4}to 4.86 × 10

^{6}at different model scaling ratios are shown in Table 1.

^{4}, the expansion fan disappears, and the separation bubble at the shoulder induces a separation shock, which causes the static pressure to increase in this area. As the separation reattaches, an expansion fan occurs, and the static pressure decreases mildly.

^{5}to 6.0 × 10

^{6}, the total pressure recovery coefficient of the throat section increases from 0.59 to 0.64, and the variation is approximately 7%. During the curve fitting of the total pressure recovery and mass flow ratio in Figure 8, the results below 1 × 10

^{5}are discarded because the flow pattern at this condition (Figure 4b) is different from other states.

#### 3.2. Inflow Conditions on Two-Dimensional Hypersonic Inlet Aerodynamic Characteristics

^{6}to 1.07 × 10

^{6}. The Reynolds number variation induced by the flight altitude is smaller than that of model scaling. Therefore, its impact on the hypersonic inlet would be milder. According to the static pressure along the ramp side at different altitudes (Figure 10), the flow acceleration phenomenon at the inlet shoulder exists at different flight altitudes, and there is no flow separation.

^{6}to 1.0 × 10

^{6}, the total throat pressure recovery coefficient decreases from 0.64 to 0.61, and the variation is approximately 4%.

## 4. Discussion

^{5}, the value of the parameters is quite different from other Reynolds numbers. The main reason is that the flow field is significantly different from other Reynolds numbers. As illustrated in Figure 4b, an obvious separation bubble appears at the inlet shoulder at this Reynolds number. As shown in Figure 18, the unit Reynolds number varies at different flight trajectories. The symbols with solid lines represent the flight trajectory and the unit Reynolds number at dynamic pressures of 30 kPa. The symbols with dash lines represent the flight trajectory and the unit Reynolds number at dynamic pressures of 50 kPa. The unit Reynolds number of the inflow is between 1.0 × 10

^{6}and 2.0 × 10

^{7}during flight conditions. Therefore, the Reynolds number at flight conditions would be larger than 1.0 × 10

^{5}. Based on this fact, we discard the value when the Reynolds number is lower than 1.0 × 10

^{5}.

## 5. Conclusions

- The inflow Reynolds number decreased from 4.86 × 10
^{6}to 9.71 × 10^{4}as the model scaling increased from 1 to 1/50. This resulted in an increase in the relative boundary layer thickness of the inlet entrance section from 10.4% to 21.2%. Thus, the inlet shoulder separation bubble size increased gradually, and the total pressure recovery at the inlet throat section decreased from 0.64 to 0.55. The starting Mach number increased from 3.45 to 4.50 with model scaling. - The inflow Reynolds number decreased from 5.67 × 10
^{6}to 1.07 × 10^{6}as the flight altitude increased from 25.5 km to 36.5 km. This resulted in an increase in the relative boundary layer thickness of the entrance section from 9.8% to 13.2%. Thus, the inlet shoulder separation bubble size increased gradually, and the total pressure recovery at the inlet throat section decreased from 0.64 to 0.61. The starting Mach number increased from 3.40 to 3.70 with flight altitude. - The effect of the Reynolds number effect caused by the model scaling and flight altitude on the aerodynamic characteristics of the hypersonic inlet has been compared. The results show that the relative boundary layer thickness at the entrance section, mass flow ratio, total pressure recovery coefficient at the throat section and starting Mach number are almost the same under the same Reynolds number.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Comparison of the static pressure along the ramp and cowl of the hypersonic inlet between the numerical simulation and experimental test [18].

**Figure 4.**Mach number contour at two different model scalings: (

**a**) Baseline model; (

**b**) Scale 1:50 model.

**Figure 6.**Velocity profile at different model scales: (

**a**) Inlet entrance section; (

**b**) Throat section.

**Figure 9.**Numerical schlieren at starting Mach number of different scales: (

**a**) Baseline model numerical schlieren at Ma 3.45; (

**b**) Scale 1:50 model numerical schlieren at Ma 4.5.

**Figure 11.**Inlet velocity profile at different shrinkage ratio scales: (

**a**) Inlet entrance section; (

**b**) Throat entrance section.

**Figure 14.**Numerical schlieren at the starting Mach number of different flight altitudes: (

**a**) H = 25.5 km numerical schlieren at Ma 3.4; (

**b**) H = 36.5 km numerical schlieren at Ma 3.7.

Scale | Re |
---|---|

1 | 4.86 × 10^{6} |

1/2 | 2.43 × 10^{6} |

1/5 | 9.71 × 10^{5} |

1/10 | 4.86 × 10^{5} |

1/20 | 2.43 × 10^{5} |

1/50 | 9.71 × 10^{4} |

Scale | Starting Mach Number |
---|---|

1 | 3.45 |

1/2 | 3.55 |

1/5 | 3.70 |

1/10 | 3.85 |

1/20 | 4.05 |

1/50 | 4.50 |

Altitude (km) | Starting Mach Number |
---|---|

25.5 | 3.40 |

26.5 | 3.45 |

28.5 | 3.50 |

30.5 | 3.55 |

32.5 | 3.60 |

36.5 | 3.70 |

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**MDPI and ACS Style**

Liu, J.; Chen, J.; Yuan, H.
Reynolds Number Effect on Aerodynamic and Starting Characteristics of a Two-Dimensional Hypersonic Inlet. *Aerospace* **2022**, *9*, 811.
https://doi.org/10.3390/aerospace9120811

**AMA Style**

Liu J, Chen J, Yuan H.
Reynolds Number Effect on Aerodynamic and Starting Characteristics of a Two-Dimensional Hypersonic Inlet. *Aerospace*. 2022; 9(12):811.
https://doi.org/10.3390/aerospace9120811

**Chicago/Turabian Style**

Liu, Jun, Jingzhe Chen, and Huacheng Yuan.
2022. "Reynolds Number Effect on Aerodynamic and Starting Characteristics of a Two-Dimensional Hypersonic Inlet" *Aerospace* 9, no. 12: 811.
https://doi.org/10.3390/aerospace9120811