# Study on the Influence of Nozzle Ablation on the Performance of the Solid Rocket Motor

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## Abstract

**:**

## 1. Introduction

## 2. Calculation Model and Method

#### 2.1. Physical Model

#### 2.2. Governing Equation

#### 2.3. Computational Methods and Boundary Conditions

_{K}is the generation term of turbulent kinetic energy K caused by average velocity gradient; and G

_{b}is the generation term of turbulent kinetic energy K caused by buoyancy. For incompressible fluid,${G}_{b}=0$; −ρε is a dissipation item; Y

_{M}is the compressibility correction term, which is the contribution of pulsation expansion in compressible turbulence; ${C}_{\epsilon 1}\frac{\epsilon}{K}{P}_{K}$ is the generated item of $\epsilon $; ${C}_{\epsilon 1}\frac{\epsilon}{K}{C}_{\epsilon 3}{G}_{b}$ is the buoyancy correction term; $-{C}_{\epsilon 2}\rho \frac{{\epsilon}^{2}}{K}$ is the dissipation term; ${S}_{K}$ and $S\epsilon $ are the source terms of K equation and ε equation, respectively; $c$ is the speed of sound; and ${\beta}_{T}$ is the coefficient of thermal expansion.

^{+}and y

^{+}needed to be extended:

_{w}is the wall temperature; and q

_{w}is the wall heat flux. The logarithmic law of velocity and temperature is expressed as:

#### 2.4. Model Verification

#### 2.4.1. Verification of Two-Phase Flow Model

#### 2.4.2. Verification of Grid Independence

## 3. Analysis of Calculation Results

#### 3.1. Analysis of Nozzle Ablation under Ground Condition

- (1)
- Influence of profile ablation on velocity field

- (2)
- Influence of profile ablation on the pressure field

- (3)
- Influence of profile ablation on the temperature field

- (4)
- Influence of profile ablation on nozzle performance

#### 3.2. Analysis on the Influence of Nozzle Ablation at Vacuum State

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**The profile of nozzle ablation after the experiment: (

**a**) schematic diagram of ground state nozzle ablation; (

**b**) the ablation of the ground state nozzle; (

**c**) schematic diagram of vacuum state nozzle ablation; (

**d**) the ablation of the vacuum state nozzle.

**Figure 10.**Comparison of pressure before and after nozzle ablation: (

**a**) pressure distribution of ground state nozzle before and after ablation; (

**b**) distribution of ground axis pressure ratio before and after ablation.

**Figure 12.**Comparison of flow field nephogram before and after ablation of vacuum state nozzle: (

**a**) static pressure; (

**b**) static temperature; (

**c**) speed; (

**d**) Mach number.

**Figure 13.**Axial velocity distribution on the axis of the vacuum state nozzle before and after ablation.

Parameters | Vacuum State Nozzle | Ground State Nozzle |
---|---|---|

Convergence ratio | 3 | 3 |

Expansion ratio | 48 | 13.4 |

Diameter of throat, m | 0.159 | 0.159 |

Diameter of exit, m | 1.102 | 0.582 |

Length of convergence, m | 0.095 | 0.095 |

Length of throat, m | 0.01 | 0.01 |

Length of divergence, m | 1.036 | 0.604 |

Curvature radius of arc, m | 0.080 | 0.080 |

Initial expansion half-angle, ° | 29 | 27 |

Expansion half-angle of exit, ° | 17 | 15 |

Working times, s | 50 | 50 |

Parameter | Initial Profile | Ablative Profile | Deviation |
---|---|---|---|

Mach number | 3.15783 | 3.05630 | 3.215% |

Total thrust, KN | 238.866 | 235.448 | 1.431% |

Specific impulse, m·s^{−1} | 2512.430 | 2476.471 | 1.431% |

Momentum thrust, KN | 196.750 | 192.706 | 2.055% |

Static thrust, KN | 17.049 | 18.004 | −5.602% |

Particle force, KN | 25.068 | 24.738 | 1.316% |

Outlet static temperature, K | 2100.965 | 2143.818 | −2.040% |

Parameter | Initial Profile | Ablative Profile | Deviation |
---|---|---|---|

Mach number | 4.024 | 3.897 | 3.156% |

Total thrust, KN | 251.405 | 249.505 | 0.756% |

Specific impulse, m·s^{−1} | 2644.288 | 2623.806 | 0.775% |

Momentum thrust, KN | 212.566 | 210.107 | 1.157% |

Static thrust, KN | 11.891 | 12.582 | −5.811% |

Particle force, KN | 26.948 | 26.815 | 0.494% |

Outlet static temperature, K | 1629.084 | 1673.599 | −2.733% |

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**MDPI and ACS Style**

Huang, W.; Wang, C.; Zhang, K.; Wang, Z.; Tian, W.
Study on the Influence of Nozzle Ablation on the Performance of the Solid Rocket Motor. *Aerospace* **2023**, *10*, 156.
https://doi.org/10.3390/aerospace10020156

**AMA Style**

Huang W, Wang C, Zhang K, Wang Z, Tian W.
Study on the Influence of Nozzle Ablation on the Performance of the Solid Rocket Motor. *Aerospace*. 2023; 10(2):156.
https://doi.org/10.3390/aerospace10020156

**Chicago/Turabian Style**

Huang, Weiqiang, Chunguang Wang, Kaining Zhang, Zhihong Wang, and Weiping Tian.
2023. "Study on the Influence of Nozzle Ablation on the Performance of the Solid Rocket Motor" *Aerospace* 10, no. 2: 156.
https://doi.org/10.3390/aerospace10020156