# Burn Time Correction of Start-Up Transients for CAMUI Type Hybrid Rocket Engine

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## Abstract

**:**

## 1. Introduction

#### 1.1. CAMUI Hybrid Rocket Engine and Simulator

#### 1.2. Problematic of Start-Up Transient

## 2. Methodology

## 3. Results

## 4. Discussion

- Error reduction (delta error RMS) = error RMS ($tb$) – error RMS($t{b}_{eq}$);
- Burnt time ratio = $tb$ (simulated)/$tb$ (analysed);
- Transient time ratio = $tt$ (analysed)/$tt$ (simulated).

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CAMUI | Cascaded Multi-stage Impinging Jet |

LOX | Liquid Oxygen |

a | Empirical constant |

H | Height (between fore- and back-end surfaces) (m) |

$nu$ | Empirical constant (fore-end surface) |

${D}_{p}$ | Port diameter (m) |

${H}_{i}$ | Initial height (m) |

$Re$ | Reynolds number |

${D}_{pi}$ | Initial port diameter (m) |

$md$ | Empirical constant (back-end surface) |

${R}_{fd}$ | Total regression back-end surface (m) |

F | Force of engine thrust (N) |

$mp$ | Empirical constant (port) |

${R}_{fp}$ | Total regression port (m) |

${F}_{steadystate}$ | Force of engine thrust at steady state (N) |

$mu$ | Empirical constant (fore-end surface) |

${R}_{fu}$ | Total regression fore-end surface (m) |

${G}_{p}$ | Propellant mass flux (kg/s/m^{2}) |

$nd$ | Empirical constant (back-end surface) |

${r}_{fd}$ | Regression rate back-end surface (m) |

${r}_{fp}$ | Regression rate port (m) |

${r}_{fu}$ | Regression rate fore-end surface (m) |

$tb$ | Burn time (seconds) |

${t}_{{b}_{eq}}$ | Equivalent burn time (m) |

## References

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**Figure 4.**CAMUI simulator concept: Constants analyser Module (

**top**) and Regression Simulator Module (

**bottom**).

**Figure 6.**

**Top**: overshoot and undershoot errors, using nominal burn time derived constants (conceptual).

**Bottom**: overshoot error, using equivalent burn time derived constants (conceptual).

**Figure 8.**Accuracy of simulation for analysis of Low and High Reynold’s number engines using nominal $tb$ and $t{b}_{eq}$, port only: (

**a**) 100 Lo, (

**b**) 200 Lo, (

**c**) 230 Hi and (

**d**) 200 Hi.

**Figure 9.**Accuracy of simulation for analysis of Low and High Reynold’s number engines using nominal $tb$ and $t{b}_{eq}$: (

**a**) 100 Lo, (

**b**) 200 Lo, (

**c**) 230 Hi, (

**d**) 200 Hi.

a | function of $\mathit{O}/\mathit{F}$ | H | Height (between fore- and back-end surfaces) (mm) | $\mathit{n}\mathit{u}$ | Empirical constant (fore-end surface) |

${D}_{p}$ | Port diameter (mm) | ${H}_{i}$ | Initial height (mm) | $Re$ | Reynolds number |

${D}_{pi}$ | Initial port diameter (mm) | $md$ | Empirical constant (back-end surface) | ${R}_{fd}$ | Total regression back-end surface (mm) |

F | Force of engine thrust (N) | $mp$ | Empirical constant (port) | ${R}_{fp}$ | Total regression port (mm) |

${F}_{steadystate}$ | Force of engine thrust at steady state (N) | $mu$ | Empirical constant (fore-end surface) | ${R}_{fu}$ | Total regression fore-end surface (mm) |

${G}_{p}$ | Propellant mass flux (kg/s/m${}^{2}$) | $nd$ | Empirical constant (back-end surface) | ${r}_{fd}$ | Regression rate back-end surface (mm) |

${r}_{fp}$ | Regression rate port (mm) | ${r}_{fu}$ | Regression rate fore-end surface (mm) | $tb$ | Burn time (s) |

$t{b}_{eq}$ | Equivalent burn time (s) |

Engine Name | Number of Fuel Blocks per Engine | Fuel Outer Diameter (mm) | Nominal Thrust Level (kN) | Burn Times (s) | Burn Time Category | Re Number ·${10}^{4}$ |
---|---|---|---|---|---|---|

100 Lo | 10 | 100 | 2.5 | 2–5 | short | 1–5 |

230 Hi | 10 | 230 | 10 | 5–10 | medium | 10–20 |

200 Lo | 7 | 200 | 2 | 5–25 | long | 1–5 |

200 Hi | 8 | 200 | 4 | 5–10 | medium | 10–20 |

Engine Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

$tb$ | 5.3 | 4.2 | 2.2 | 2.2 | 2.3 | 3 | 3.2 |

$t{b}_{eq}$ | 4.7 | 3.5 | 2 | 2.1 | 2 | 2.6 | 2.6 |

% $tb$ reduction | 11% | 17% | 10% | 5% | 13% | 13% | 19% |

Engine Number | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

$tb$ | 10.2 | 5.5 | 6.9 | 5.3 | 4.8 | 5 |

$t{b}_{eq}$ | 10 | 5.1 | 6 | 4.9 | 4.3 | 4.4 |

% $tb$ reduction | 2% | 7% | 13% | 8% | 10% | 12% |

Analysis Baseline Engine | 100 Lo | 230 Hi | ||
---|---|---|---|---|

Simulated engine | 100 Lo | 200 Lo | 230 Hi | 200 Hi |

Simulated engine | 100 Lo | 200 Lo | 230 Hi | 200 Hi |

Error RMS $tb$ | 15% | 41% | 14% | 27% |

Error RMS $t{b}_{eq}$ | 47% | 18% | 24% | 24% |

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**MDPI and ACS Style**

Viscor, T.; Isochi, H.; Adachi, N.; Nagata, H.
Burn Time Correction of Start-Up Transients for CAMUI Type Hybrid Rocket Engine. *Aerospace* **2021**, *8*, 385.
https://doi.org/10.3390/aerospace8120385

**AMA Style**

Viscor T, Isochi H, Adachi N, Nagata H.
Burn Time Correction of Start-Up Transients for CAMUI Type Hybrid Rocket Engine. *Aerospace*. 2021; 8(12):385.
https://doi.org/10.3390/aerospace8120385

**Chicago/Turabian Style**

Viscor, Tor, Hikaru Isochi, Naoto Adachi, and Harunori Nagata.
2021. "Burn Time Correction of Start-Up Transients for CAMUI Type Hybrid Rocket Engine" *Aerospace* 8, no. 12: 385.
https://doi.org/10.3390/aerospace8120385