# An Aero-Optical Effect Analysis Method in Hypersonic Turbulence Based on Photon Monte Carlo Simulation

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Transmission Process of Photons in Turbulence

#### 2.1. Refraction and Reflection of Photons

#### 2.2. Absorption and Scattering of Photons

## 3. Design of MC-AOEA

- (a)
- Photon transmission is seen as the refraction, reflection, absorption, and scattering of a group of photons in turbulence, excluding the photon-stimulated radiation.
- (b)
- The absorption and scattering of photons are determined by the absorption coefficient, scattering coefficient, and phase function reflecting the scattering distribution (used to determine the direction of scattering).
- (c)
- The polarization and interference of photons are ignored, and only the transmission of photon energy in turbulent molecules is tracked.

#### 3.1. Photon Probability Function and Photon Step Size

#### 3.2. Update of Photon Position

#### 3.3. Update of Photon Direction

#### 3.4. Update of Photon Weight

#### 3.5. Grid Boundary of Photon Transmission

#### 3.6. Physical Description of Aero-Optical Effects Based on MC-AOEA

- (1)
- Photon statistical optical path difference (PS-OPD)

- (2)
- Energy loss of photons (${E}_{loss}$)

## 4. Simulation and Analysis

#### 4.1. Hypersonic Turbulence by LES

^{2}.The optical sensor receiving size was 80 × 80 mm

^{2}.

^{−7}s. In order to ensure the accuracy of simulation, we used a 256-core high-performance server to calculate the hypersonic turbulence, as shown in Figure 9.

#### 4.2. Simulation Analysis of MC-AOEA

^{3}, as shown in Figure 10. ${\mathit{x}}_{w}-{\mathit{y}}_{w}-{\mathit{z}}_{w}$ represents the window coordinate system. Additionally, the photon simulation threshold was divided into $480\times 480\times 800$ grid cells. The initial condition of the light source was set as a parallel light source. The initial incidence angle was 90 degrees; the wavelength was 572 nm; the initial number of photons for each photon packet was $1\times {10}^{6}$; and there were $1\times {10}^{12}$ photons in total.

#### 4.3. Aero-Optical Effects under Different Flight Conditions

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 11.**Simulation results without considering absorption and scattering: (

**a**) OPD of the traditional ray tracing; (

**b**) PS-OPD of the MC-AOEA.

**Figure 12.**Simulation results considering absorption and scattering: (

**a**) PS-OPD of the MC-AOEA; (

**b**) PS-OPD of the MC-AOEA.

**Figure 15.**Hypersonic turbulence at the same altitude and different speeds: (

**a**) 2 Ma, 20 km; (

**b**) 3 Ma, 20 km; (

**c**) 5 Ma, 20 km; (

**d**) 10 Ma, 20 km.

**Figure 16.**Hypersonic turbulence at the same speed and different altitudes: (

**a**) 3 Ma, 5 km; (

**b**) 3 Ma, 10 km; (

**c**) 3 Ma, 20 km; (

**d**) 3 Ma, 40 km.

**Figure 17.**Offset angle in different receiving planes under different flight conditions: (

**a**) the same altitude and different speeds; (

**b**) the same speed and different altitudes.

Simulation Conditions | Ray-Tracing | MC-AOEA | Relative Error of Offset Angle | ||
---|---|---|---|---|---|

Offset Angle | Time | Offset Angle | Time | ||

3 Ma, 5 km | 101.8 μrad | 14.12 s | 92.3 μrad | 5011.45 s | 9.35% |

3 Ma, 10 km | 52.1 μrad | 12.89 s | 48.5 μrad | 5041.56 s | 6.99% |

3 Ma, 20 km | 25.4 μrad | 13.30 s | 24.1 μrad | 5096.20 s | 5.11% |

3 Ma, 40 km | 4.8 μrad | 12.65 s | 4.7 μrad | 5012.99 s | 1.08% |

2 Ma, 20 km | 10.9 μrad | 12.54 s | 10.5 μrad | 4953.10 s | 3.82% |

5 Ma, 20 km | 47.7 μrad | 13.61 s | 44.0 μrad | 4991.28 s | 7.76% |

10 Ma, 20 km | 60.9 μrad | 12.98 s | 55.6 μrad | 5014.04 s | 8.67% |

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**MDPI and ACS Style**

Yang, B.; Yu, H.; Liu, C.; Wei, X.; Fan, Z.; Miao, J.
An Aero-Optical Effect Analysis Method in Hypersonic Turbulence Based on Photon Monte Carlo Simulation. *Photonics* **2023**, *10*, 172.
https://doi.org/10.3390/photonics10020172

**AMA Style**

Yang B, Yu H, Liu C, Wei X, Fan Z, Miao J.
An Aero-Optical Effect Analysis Method in Hypersonic Turbulence Based on Photon Monte Carlo Simulation. *Photonics*. 2023; 10(2):172.
https://doi.org/10.3390/photonics10020172

**Chicago/Turabian Style**

Yang, Bo, He Yu, Chaofan Liu, Xiang Wei, Zichen Fan, and Jun Miao.
2023. "An Aero-Optical Effect Analysis Method in Hypersonic Turbulence Based on Photon Monte Carlo Simulation" *Photonics* 10, no. 2: 172.
https://doi.org/10.3390/photonics10020172