# Mathematical Modeling of Liquid-fed Pulsed Plasma Thruster

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model

#### 2.1. Equivalent Circuit Modeling

#### 2.2. Plasma Flow and Mass Modeling

#### 2.3. Dynamical Modeling

## 3. Implementation and Discussion of Mathematical Model

#### 3.1. Results for LPPT-1

#### 3.2. Results for LPPT-2

## 4. Optimization Suggestions for Liquid-fed PPTs

#### 4.1. Discharge Energy Variation

#### 4.2. Variation in Supplied Ablation Mass

#### 4.3. Circuit Parameters

## 5. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Operation of liquid propellant PPT [12].

**Figure 6.**Total impulse bit vs. Discharge energy: (

**A**) Simulation result; (

**B**) Experimental result [12].

**Figure 9.**Comparison of the numerical simulation for plasma mass with the high speed photographs [27].

Material | Mass (Amu) | 1st Ionization Energy (eV) | 2nd Ionization Energy (eV) | Heat of Vaporisation (J/Kg) | Heat Capacity (J/KgK) |
---|---|---|---|---|---|

Water | 18.02 | 40.8 | 75.9 | $2.4\times {10}^{6}$ | 4179 |

Teflon | 100 | 92.2 | 280.9 | $2.1\times {10}^{6}$ | 1250 |

Operation Parameter | Value |
---|---|

${L}_{1}$ | 0.88 |

Capacitor (C) | 3 $\mathsf{\mu}$F |

Discharge voltage (${V}_{o}$) | 3000 V |

Total mass supplied per discharge (${m}_{T}$) | 2.8 $\mathsf{\mu}$g |

Total discharge resistance (${R}_{T}$) | 82 m$\mathsf{\Omega}$ |

Total inductance (${L}_{t}$) | 84 nH |

Parameter | Simulation Result | Experimental Result |
---|---|---|

Discharge Voltage (V) | 3000 | 3000 |

Capacitor ($\mathsf{\mu}$F) | 3 | 3 |

Mean exhaust velocity (Km/s) | $27.2$ | $33.3$ |

Charged mass exit velocity (Km/s) | 49 | − |

Charged mass shot ($\mathsf{\mu}$g) | $1.46$ | − |

Neutral mass shot ($\mathsf{\mu}$g) | $1.34$ | − |

Impulse bit ($\mathsf{\mu}$N-s) | $78.2$ | $86.4$ |

Specific Impulse (s) | 2800 | 3400 |

Discharge Energy (J) | Charged Mass Shot ($\mathsf{\mu}$g) | Mean Exit Velocity (Km/s) | Impulse Bit ($\mathsf{\mu}$N-s) | Specific Impulse (s) |
---|---|---|---|---|

1.5 | $0.16$ | 3 | 8 | 306 |

6 | $0.6$ | 12 | 35 | 1224 |

13.5 | $1.4$ | $27.2$ | $78.2$ | 2800 |

21.6 | $2.2$ | 41 | 120 | 4183 |

Supplied Mass ($\mathsf{\mu}$g) | ${\mathit{I}}_{\mathbf{bit}}$ ($\mathsf{\mu}$N-s) | Exit Velocity (Km/s) | ${\mathit{I}}_{\mathit{sp}}$ (s) |
---|---|---|---|

2.0 | 78 | 39 | 3974 |

2.8 | 78.2 | 27.2 | 2800 |

6.8 | 82 | 12 | 1224 |

9.0 | 83 | 8.5 | 868 |

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Misra, K. Mathematical Modeling of Liquid-fed Pulsed Plasma Thruster. *Aerospace* **2018**, *5*, 13.
https://doi.org/10.3390/aerospace5010013

**AMA Style**

Misra K. Mathematical Modeling of Liquid-fed Pulsed Plasma Thruster. *Aerospace*. 2018; 5(1):13.
https://doi.org/10.3390/aerospace5010013

**Chicago/Turabian Style**

Misra, Kaartikey. 2018. "Mathematical Modeling of Liquid-fed Pulsed Plasma Thruster" *Aerospace* 5, no. 1: 13.
https://doi.org/10.3390/aerospace5010013