# Shock Waves Asymmetry in a Symmetric Nozzle

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. CFD Simulations

## 4. Measurement Cases

## 5. Results

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Shock wave asymmetry in nozzle flows. (

**a**) Asymmetric nozzle with flat bottom wall (

**b**) Symmetric nozzle.

**Figure 2.**Thrust force in supersonic nozzle. (

**a**) Symmetric shock system (

**b**) Asymmetric shock system.

**Figure 8.**Normalized height and the zones of symmetry for divergence angle values of 3°, 4.5°, 6.54°.

**Figure 9.**Symmetrical and asymmetrical shock wave. (

**a**) Symmetric shock system. (

**b**) Asymmetric shock system.

M (-) | δ (°) | Experimental | CFD |
---|---|---|---|

1.31 | 4.5 | ✓ | ✗ |

1.32 | 6.54 | ✓ | ✓ |

1.36 | 3 | ✓ | ✗ |

1.36 | 4.5 | ✓ | ✗ |

1.40 | 3 | ✓ | ✗ |

1.40 | 4.5 | ✓ | ✗ |

1.45 | 4.5 | ✓ | ✗ |

1.57 | 6.54 | ✓ | ✗ |

1.59 | 6.54 | ✗ | ✓ |

M (-) | δ (°) | Experimental | CFD | ||||||
---|---|---|---|---|---|---|---|---|---|

h1/a | h2/b | Flow | Diff. | h1/a | h2/b | Flow | Diff. | ||

1.31 | 4.5 | 0.3187 | Symmetric | ||||||

1.32 | 6.54 | 0.615 | 0.622 | Asymmetric | 1.1% | 0.531 | 0.524 | Asymmetric | 1.3% |

1.36 | 3 | 0.4611 | Symmetric | ||||||

1.36 | 4.5 | 0.64 | 0.632 | Asymmetric | 1.3% | ||||

1.40 | 3 | 0.5075 | Symmetric | ||||||

1.40 | 4.5 | 0.6377 | 0.6377 | Asymmetric | 0% | ||||

1.45 | 4.5 | 0.6451 | 0.6451 | Asymmetric | 0% | ||||

1.57 | 6.54 | 0.763 | 0.767 | Asymmetric | 0.5% | ||||

1.59 | 6.54 | 0.795 | 0.798 | Asymmetric | 0.4% |

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**MDPI and ACS Style**

Telega, J.; Szwaba, R.; Doerffer, P.
Shock Waves Asymmetry in a Symmetric Nozzle. *Symmetry* **2019**, *11*, 1477.
https://doi.org/10.3390/sym11121477

**AMA Style**

Telega J, Szwaba R, Doerffer P.
Shock Waves Asymmetry in a Symmetric Nozzle. *Symmetry*. 2019; 11(12):1477.
https://doi.org/10.3390/sym11121477

**Chicago/Turabian Style**

Telega, Janusz, Ryszard Szwaba, and Piotr Doerffer.
2019. "Shock Waves Asymmetry in a Symmetric Nozzle" *Symmetry* 11, no. 12: 1477.
https://doi.org/10.3390/sym11121477