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A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis^{ †}

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*DSMC and Related Simulations*, Proceedings of the 30th International Symposium on Rarefied Gas Dynamics, Victoria, BC, Canada, 10–15 July 2016; Ketsdever, A.; Struchtrup, H., Eds.; AIP Publishing, Melville, NY, USA; Volume 1786, 050006.[...]

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Non-Equilibrium Navier–Stokes–Fourier Equations

#### 2.2. Energy Transfers

#### 2.3. Departure from the Continuum Regime

## 3. Results and Discussion

#### 3.1. Mach 11.3 Blunted Cone

#### 3.2. Mach 20 Cylinder

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**–

**c**) Stagnation line profiles, and (

**d**–

**f**) surface quantities along the blunted cone; (

**a**) normalised temperature; (

**b**) normalised mass density; (

**c**) normalised velocity; (

**d**) pressure coefficient; (

**e**) friction coefficient; (

**f**) Stanton number.

**Figure 4.**Computational fluid dynamics-direct simulation Monte Carlo (CFD-DSMC) flow-field comparisons for run number 2. In (

**b**–

**d**): the dsmcFoam solution is represented in the upper half and the hy2Foam solution in the lower half. (

**a**) Local gradient-length Knudsen number; (

**b**) Mach number; (

**c**) trans-rotational temperature; and (

**d**) vibrational temperature.

**Figure 5.**(

**a**–

**c**): Stagnation line profiles. CFD run 1:

**black**lines, run 2:

**red**lines, run 3:

**blue**lines. (

**d**–

**f**): surface quantities around the cylinder. (

**a**) Mach number; (

**b**) temperature; (

**c**) number density; (

**d**) pressure coefficient; (

**e**) skin-friction coefficient; (

**f**) surface heat flux.

Quantity | Value | Unit |
---|---|---|

Free-stream velocity, ${U}_{\infty}$ | 2764.5 | m/s |

Free-stream pressure, ${p}_{\infty}$ | 21.9139 | Pa |

Free-stream density, ${\rho}_{\infty}$ | $5.113\times {10}^{-4}$ | kg/m${}^{3}$ |

Free-stream temperature, ${T}_{\infty}$ | 144.4 | K |

Free-stream mean-free-path, ${\lambda}_{\infty}$ | $1.01\times {10}^{-4}$ | m |

Overall Knudsen number, $K{n}_{ov}$ | 0.002 | - |

Wall temperature, ${T}_{w}$ | 297.2 | K |

Quantity | Value | Unit |
---|---|---|

Free-stream velocity, ${U}_{\infty}$ | 6047 | m/s |

Free-stream pressure, ${p}_{\infty}$ | 0.89 | Pa |

Free-stream density, ${\rho}_{\infty}$ | $1.363\times {10}^{-5}$ | kg/m${}^{3}$ |

Free-stream temperature, ${T}_{\infty}$ | 220 | K |

Free-stream mean-free-path, ${\lambda}_{\infty}$ | $4.45\times {10}^{-3}$ | m |

Overall Knudsen number, $K{n}_{ov}$ | 0.0022 | - |

Wall temperature, ${T}_{w}$ | 1000 | K |

Run Number | V–T Transfer | Electronic Mode | CV Model | Rates |
---|---|---|---|---|

1 | MWP | no | CVDV | QK |

2 | SSH | no | CVDV | QK |

3 | MWP | no | Park TTv | Park |

Reaction Rate | Reaction | Arrhenius Law Constants | ||
---|---|---|---|---|

Colliding Partner | A | β | ${\mathit{T}}_{\mathit{a}}$ | |

Quantum-Kinetics (QK) | N_{2} | $2.47\times {10}^{18}$ | −0.62 | 113,500 |

N | $6.02\times {10}^{18}$ | −0.68 | 113,500 | |

Park | N_{2} | $7.0\times {10}^{21}$ | −1.6 | 113,200 |

N | $3.0\times {10}^{22}$ | −1.6 | 113,200 |

CFD Run Number | ${\mathit{C}}_{\mathit{D}}$ | ${\mathit{C}}_{\mathit{H}}(\mathbf{kW})$ | ||
---|---|---|---|---|

CFD | DSMC | CFD | DSMC | |

NR | 1.3 | 1.286 | 106 | 115 |

1 | 1.302 | 1.284 | 81.0 | 63.3 |

2 | 1.302 | 80.5 | ||

3 | 1.304 | 88.1 |

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**MDPI and ACS Style**

Casseau, V.; Espinoza, D.E.R.; Scanlon, T.J.; Brown, R.E.
A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis. *Aerospace* **2016**, *3*, 45.
https://doi.org/10.3390/aerospace3040045

**AMA Style**

Casseau V, Espinoza DER, Scanlon TJ, Brown RE.
A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis. *Aerospace*. 2016; 3(4):45.
https://doi.org/10.3390/aerospace3040045

**Chicago/Turabian Style**

Casseau, Vincent, Daniel E. R. Espinoza, Thomas J. Scanlon, and Richard E. Brown.
2016. "A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis" *Aerospace* 3, no. 4: 45.
https://doi.org/10.3390/aerospace3040045