# Evaluation of Sonic Boom Shock Wave Generation with CFD Methods

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. CFD Approach

#### 2.2. Computational Domain

#### 2.3. CS1 Test Case

- Range $\ge 7200$ km;
- Passengers $\ge 120$;
- MTOW ≤ 200,000 kg;
- Cruise @ Mach 2.

#### Computational Grid

#### 2.4. CS3 Test Case

#### Computational Grid

#### 2.5. Solver Setup

## 3. Results

#### 3.1. CS1 Noise Performances

#### 3.2. CS3 Noise Performances

#### 3.3. Comparison

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

NASA | National Aeronautics and Space Administration |

$\mu $ | Mach angle |

$\theta $ | Misalignment angle |

ICAO | International Civil Aviation Organization |

MORE&LESS | MDO and REgulations for Low-boom and Environmentally Sustainable Supersonic Aviation |

CFD | Computational Fluid Dynamic |

ISA | subscript for International Standard Atmosphere |

SPL | Sound Pressure Level |

PLdb | Perceived Noise Level |

a | Speed of sound, m/s |

$H/L$ | Height over length ratio for extraction |

${C}_{L}$ | Lift coefficient |

${C}_{D}$ | Drag coefficient |

M | Mach number |

${p}_{s}$ | Static Pressure |

${p}_{0}$ | Free-stream pressure condition |

$\alpha $ | Angle of attack, deg |

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**Figure 3.**Hybrid grid approach: inner unstructured mesh (pink) and outer structured inclined mesh (blue).

**Figure 6.**CS1 computational grid, overall grid domain (

**left**), and particular cells around the aircraft (

**right**).

**Figure 7.**CS1 mesh grid, comparison between aeroacoustic (

**left**) and aerodynamic (

**right**) mesh construction approaches.

**Figure 14.**CS1 pressure signature in radial position around the aircraft at $H/L=3$ on the left, values in dB on the right, for mission point 1.

**Figure 17.**CS1 pressure signature in radial position around the aircraft at $H/L=3$ on the left, values in dB on the right, for mission point 2.

**Figure 19.**CS1 pressure signature at $H/L=3$ for mission point 3, Mach 2.0, AoA 3.5, altitude 18,500 m.

**Figure 20.**CS1 pressure signature in radial position around the aircraft at $H/L=3$ on the left, values in dB on the right, for mission point 3.

Characteristic | Value |
---|---|

Design GTO Mass [kg] | 179,849 |

OEW [kg] | 79,460 |

Design fuel weight [kg] | 85,289 |

Design Payload weight | 15,200 |

Wing Surface [m^{2}] | 358 |

Aircraft Length [m] | 61.7 |

Wingspan [m] | 25.6 |

Design Range [km] | 6500 |

Cruise Altitude [m] | 18,000 |

Thrust to weight ratio (dry at TO) | 0.4 |

Wing Loading [kg/m^{2}] | 494 |

Lift over drag ratio | 7 |

Max Mach | 2.2 |

Required Runway Length [m] | 3400 |

Operating Conditions | Mission Point 1 | Mission Point 2 | Mission Point 3 |
---|---|---|---|

Mach number | 1.5 | 1.5 | 2.0 |

Angle of attack [deg] | 4.0 | 4.5 | 3.5 |

Altitude [m] | 17,500 | 15,000 | 18,500 |

Pressure [Pa] | 8120.51 | 12,044.6 | 6935.86 |

Temperature [K] | 216.6 | 216.6 | 216.6 |

Characteristic | Value |
---|---|

Overall length [m] | 75.16 |

Wingspan [m] | 41.0 |

Reference lifting surface [m^{2}] | 2000 |

Internal Volume Arrangement [m^{3}] | 8000 |

Available fuel volume [m^{3}] | 1582 |

Payload capacity [kg] | 26,400 |

Reference Range [km] | 19,000 |

MTOW [kg] | 288,400 |

OEW [kg] | 150,000 |

Available fuel mass [kg] | 112,000 |

Mach Number | Altitude [km] | Pressure [Pa] | Temperature [K] | Mission Point |
---|---|---|---|---|

4.0 | 31.0 | 1008.23 | 227.650 | 1 |

4.2 | 31.0 | 1008.23 | 227.650 | 2 |

4.4 | 31.0 | 1008.23 | 227.650 | 3 |

4.6 | 31.0 | 1008.23 | 227.650 | 4 |

4.8 | 31.0 | 1008.23 | 227.650 | 5 |

5.0 | 31.0 | 1008.23 | 227.650 | 6 |

5.0 | 28.0 | 1586.29 | 224.650 | 7 |

Scheme | ${\mathit{C}}_{\mathit{L}}$ | ${\mathit{C}}_{\mathit{D}}$ |
---|---|---|

AUSM | 0.05690 | 0.01129 |

ROE-FDs | 0.05704 | 0.01136 |

AUSM Finer Grid | 0.05690 | 0.01132 |

Aerodynamic | 0.05674 | 0.01121 |

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## Share and Cite

**MDPI and ACS Style**

Graziani, S.; Petrosino, F.; Jäschke, J.; Glorioso, A.; Fusaro, R.; Viola, N.
Evaluation of Sonic Boom Shock Wave Generation with CFD Methods. *Aerospace* **2024**, *11*, 484.
https://doi.org/10.3390/aerospace11060484

**AMA Style**

Graziani S, Petrosino F, Jäschke J, Glorioso A, Fusaro R, Viola N.
Evaluation of Sonic Boom Shock Wave Generation with CFD Methods. *Aerospace*. 2024; 11(6):484.
https://doi.org/10.3390/aerospace11060484

**Chicago/Turabian Style**

Graziani, Samuele, Francesco Petrosino, Jacob Jäschke, Antimo Glorioso, Roberta Fusaro, and Nicole Viola.
2024. "Evaluation of Sonic Boom Shock Wave Generation with CFD Methods" *Aerospace* 11, no. 6: 484.
https://doi.org/10.3390/aerospace11060484