# Numerical Investigation on the Effect of Electrical Parameters on the Discharge Characteristics of NS-SDBD

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical modeling

#### 2.1. Plasma Fluid Model

^{−23}J·K

^{–1}), and $q$ represents elementary positive charge (1.6 × 10

^{−19}C).

^{−12}F·m

^{−1}) and the relative permittivity of the dielectric material, respectively; and $\varphi $ represents the electric potential.

_{2}, N

_{2}

^{+}, O

_{2}, O

_{2}

^{+}, O

_{2}

^{−}, and electrons. The model assumes that the initial neutral air is a mixture of N

_{2}and O

_{2}with a molar fraction ratio of 4:1. (The temperature is set at 300 K, and the gas pressure is set at 760 Toor.) The chemical reactions in the plasma fluid model are shown in Table 1, and the Townsend coefficient and reaction rate coefficients are obtained through other works from the literature [24,25] and two Boltzmann solvers, BOLSIG+ [26].

^{13}/m

^{3}. In order to maintain electrical neutrality in the discharge space, the initial value of positive ion density should be equal to the electron density, and the initial average energy of electrons is set to 4 eV. The initial values of other particles are all set to 0. In addition, secondary electron emission and ion bombardment of the electrode are important supplementary sources of electrons in the plasma discharge process. Therefore, the surface electron emission from the high-voltage electrode and dielectric is also considered, with the secondary electron emission coefficient set to 0.01 for both the electrode and dielectric surfaces; the surface reaction equations are shown in Table 2. The model assumes that the plasma is non-continuous, ignoring the microstructure and details inside the plasma and regarding it as a continuous medium composed of electrons, ions, and neutral particles. In the simulation, the plasma is assumed to reach local thermodynamic equilibrium within the simulation timescale; that is, the temperature of the plasma is evenly distributed and meets the Boltzmann distribution.

#### 2.2. Boundary Conditions

#### 2.3. Simulation Setup

^{−11}) and the relative tolerance (10

^{−10}) indicate the time step that will be used. Each integration step is considered to have converged if the predicted local errors are smaller than both tolerances, which are set by the user. Therefore, during the pulse stage, the time step is nearly 1 × 10

^{−12}s.

## 3. Results and Discussion

#### 3.1. Analysis of Discharge Characteristics

#### 3.1.1. Analysis of Voltage–Current (V-A) Characteristics

#### 3.1.2. Analysis of the Evolution of Discharge Particles

^{18}/m

^{3}. The number of free electrons and ions in the plasma starts to decline as the voltage drops, the electric field becomes weaker, and the ionization process slows down, but they keep moving forward for a while due to their inherent inertia of motion. This is supported by the electron density nephogram at 104 ns, which indicates that while the spatial distribution area continues to expand, the electron density value declines. At this point, the electric field strength returns to a low level, and the residual charge in space mostly determines its amplitude and distribution.

#### 3.1.3. Analysis of Spectrum Characteristics

#### 3.2. Influence of Electrical Parameters on Discharge Characteristics

#### 3.2.1. Effect of Voltage Amplitude on Discharge Characteristics

#### 3.2.2. Effect of Pulse Width on Discharge Characteristics

#### 3.2.3. Effect of Rise Time on Discharge Characteristics

#### 3.2.4. Effect of Fall Time on Discharge Characteristics

#### 3.3. Discussion

- The voltage amplitude has a significant impact on the discharge behavior. Higher voltage amplitudes result in a higher discharge current and electron density. Higher voltage amplitudes generate stronger electric field intensities, facilitating ionization and excitation processes, thereby increasing energy transfer efficiency.
- The pulse width affects the characteristics of the second discharge. A longer pulse width increases the current and electron density of the second discharge, but it has almost no effect on the first discharge. A longer pulse width provides more time for electrons to acquire energy, thereby enhancing the excitation and ionization processes.
- The rise time has an impact on the first discharge but has a smaller effect on the second discharge. A longer rise time leads to a decrease in the peak current and electron density of the first discharge, as well as a delay in the discharge initiation. The results of total power deposition indicate that a longer rise time reduces the energy conversion efficiency of the first discharge but increases the peak value of total power deposition for the second discharge.
- The fall time has an impact on the second discharge but does not affect the discharge characteristics during the voltage-rise process. A longer fall time increases the chance of electron collisions with gas molecules, leading to an increase in electron energy loss. As a result, the peak current and electron density of the second discharge decrease, and the wave form becomes smoother.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Sequence | Reaction Equations | Rate Coefficient |
---|---|---|

R 1 | e + N_{2} => e + N_{2} | α_{1} |

R 2 | e + O_{2} => e + O_{2} | α_{2} |

R 3 | e + 2O_{2} => O_{2} + O_{2}^{−} | α_{3} |

R 4 | e + O_{2} => O_{2}^{+} + 2e | α_{4} |

R 5 | e + N_{2} => N_{2}^{+} + 2e | α_{5} |

R 6 | e + O_{2} => O_{2}^{−} | α_{6} |

R 7 | e + N_{2}^{+} => N_{2} | 4.65 × 10^{10} × (T_{e})^{−0.5} |

R 8 | e + N_{2}^{+} => N_{2} | 2.4 × 10^{6} |

R 9 | O_{2}^{+} + O_{2}^{−} => 2O_{2} | 1.2 × 10^{11} |

R 10 | 2e + N_{2}^{+} => N_{2} + e | 2.6 × 10^{9} × (T_{e})^{−4.5} |

R 11 | 2e + O_{2}^{+} => O_{2} + e | 2.6 × 10^{9} × (T_{e})^{−4.5} |

R 12 | O_{2}^{+} + O_{2}^{−} + O_{2} => 3O_{2} | 7.25 × 10^{10} |

R 13 | O_{2}^{+} + O_{2}^{−} + N_{2} => 2O_{2} + N_{2} | 7.25 × 10^{10} |

Sequence | Reaction Equations | Sticking Coefficient |
---|---|---|

R 1 | N_{2}^{+} => N_{2} | 1 |

R 2 | O_{2}^{+} => O_{2} | 1 |

R 3 | O_{2}^{−} => O_{2} | 1 |

R 4 | O => 0.5O_{2} | 1 |

R 5 | O^{+} => 0.5O_{2} | 1 |

R 6 | O^{−} => 0.5O_{2} | 1 |

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**MDPI and ACS Style**

Liang, S.; Yu, Y.; Zheng, B.; Mao, Y.
Numerical Investigation on the Effect of Electrical Parameters on the Discharge Characteristics of NS-SDBD. *Coatings* **2023**, *13*, 1237.
https://doi.org/10.3390/coatings13071237

**AMA Style**

Liang S, Yu Y, Zheng B, Mao Y.
Numerical Investigation on the Effect of Electrical Parameters on the Discharge Characteristics of NS-SDBD. *Coatings*. 2023; 13(7):1237.
https://doi.org/10.3390/coatings13071237

**Chicago/Turabian Style**

Liang, Sijia, Yang Yu, Borui Zheng, and Yuepeng Mao.
2023. "Numerical Investigation on the Effect of Electrical Parameters on the Discharge Characteristics of NS-SDBD" *Coatings* 13, no. 7: 1237.
https://doi.org/10.3390/coatings13071237