Numerical study on uniformity of atmospheric helium gas dielectric barrier discharge on non-smooth surface regulated by sinusoidal clipping voltage

Liu Kai; Fang Ze; Dai Dong

doi:10.7498/aps.72.20230385

Abstract

In practical applications of dielectric barrier discharges under atmospheric pressure, plasma usually acts on non-smooth surfaces. The electric field distortion and uneven surface charge distribution caused by its surface morphology will create an adverse effect on the uniformity and stability of the discharge. In this paper, we establish a simulation model of atmospheric pressure helium dielectric barrier discharge on a wavy lower dielectric plate, and use a sinusoidal clipping voltage to regulate the discharge uniformity. The results show that the discharge uniformity is improved compared with the unclipped case, and the discharge mode is changed from columnar mode to quasi-uniform mode. This can be attributed to the incomplete discharge dissipation caused by the reduction of air gap voltage; the subsequent electron backflow process neutralizes the the residual space electrons with the surface charge, which limits the accumulation of surface charges. With the increase of clipping ratio, the surface charge distribution becomes more uniform, and the radial fluctuation of electric field distribution weakens. In addition, the discharge efficiency is improved in a certain clipping range. This study reveals the mechanism of clipping voltage influence on non-smooth surface discharge, and provides a new idea for regulating the uniformity of dielectric barrier discharge.

Keywords:

Authors and contacts

School of Electric Power, South China University of Technology, Guangzhou 510641, China

Corresponding author: Dai Dong, ddai@scut.edu.cn

Funds: Project supported by the National Key Research and Development Program of China (Grant No. 2021YFE0114700) and the National Natural Science Foundation of China (Grant No. 51877086).

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References

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[43]	Cheng H, Liu X, Liu D W, Lu X P 2016 High Volt. 1 62 Google Scholar
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[46]	Lazarou C, Koukounis D, Chiper A S, Costin C, Topala I, Georghiou G E 2015 Plasma Sources Sci. Technol. 24 035012 Google Scholar
[47]	Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722 Google Scholar
[48]	Purwins H G, Stollenwerk L 2014 Plasma Phys. Control. Fusion 56 123001 Google Scholar
[49]	Ellis H W, Pai R Y, McDaniel E W, Mason E A, Viehland L A 1976 At. Data Nucl. Data Tables. 17 177 Google Scholar
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Cited By

图 1 w-DBD仿真模型的几何结构

Figure 1. Geometry of w-DBD simulation model.

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图 2 削波电压波形

Figure 2. Waveform of clipping voltage.

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图 3 稳态下DBD在外施电压周期内其平均电子密度的空间分布 (施加10 kHz, 1.5 kV正弦电压)　(a)平滑表面DBD; (b) w-DBD

Figure 3. Spatial distribution of average electron density on DBD over one period of applied voltage at steady state (The voltage source is 10 kHz, 1.5 kV sinusoidal voltage): (a) Smooth surface DBD; (b) w-DBD.

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图 4 不同p_c下, 放电达到稳态后一个外施电压周期内的平均电子密度的空间分布　(a) p_c = 50%; (b) p_c = 55%; (c) p_c = 60%; (d) p_c = 65%; (e) p_c = 70%

Figure 4. Spatial distribution of average electron density over one period of applied voltage at steady state under different p_c: (a) p_c = 50%; (b) p_c=55%; (c) p_c = 60%; (d) p_c = 65%; (e) p_c = 70%.

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图 5 不同p_c下, 放电达到稳态后一个外施电压周期内的外施电压V_a, 气隙电压V_g和电流密度J　(a) p_c = 0; (b) p_c = 50%; (c) p_c = 55%; (d) p_c = 60%; (e) p_c = 65%; (f) p_c = 70%

Figure 5. Temporal profiles of applied voltage V_a, gap voltage V_g and current density J over one period of applied voltage at steady state under different p_c: (a) p_c = 0; (b) p_c = 50%; (c) p_c = 55%; (d) p_c = 60%; (e) p_c = 65%; (f) p_c = 70%.

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图 6 p_c不同时, 放电达到稳态后一个外施电压周期内的电压电流波形(a), (c), (e)和t₁—t₅时刻对应的电子密度空间分布(b), (d), (f). 正负号表示该时刻的气隙电压极性　(a), (b) p_c = 0; (c), (d) p_c = 55%; (e), (f) p_c = 70%

Figure 6. Voltage and current waveform (a), (c), (e) and spatial distribution (b), (d), (f) of electron density corresponding to t₁ to t₅ over one period of applied voltage at steady state under different p_c. Plus and minus signs indicate air gap voltage polarity at this time: (a), (b) p_c = 0; (c), (d) p_c = 55%; (e), (f) p_c = 70%.

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图 7 p_c分别为0, 55%, 70%时, t₁ (a)和t₄ (b)时刻对应的净表面电荷密度ρ_s

Figure 7. Net surface charge density ρ_s at t₁ (a) and t₄ (b) under p_c of 0, 55% and 70% respectively.

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图 8 p_c分别为0, 55%, 70%时　(a1), (b1) t₁和t₄时刻对应的轴向平均电场强度|E_z|; (a2) t₁时刻距上介质板表面0.05 mm附近的径向电场强度E_r; (b2) t₄时刻距下介质板表面0.05 mm附近的径向电场强度E_r

Figure 8. Under p_c of 0, 55% and 70%: (a1), (b1) Axial average electric field |E_z| at t₁ and t₄ respectively; (a2) radial electric field E_r near surface of 0.05 mm upper dielectric plate at t₁; (b2) radial electric field E_r near surface of 0.05 mm lower dielectric plate at t₄.

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图 9 p_c分别为0, 55%, 70%时, 介质板表面附近的电子通量Γ_e　(a) t₁时刻上介质板表面附近(r = 0—8 mm, z = 2—3 mm区域); (b) t₄时刻下介质板表面附近(r = 0—8 mm, z = 0.9—2.0 mm区域)

Figure 9. Electron flux Γ_e near dielectric plate at p_c of 0, 55% and 70%: (a) Near upper dielectric plate (r = 0–8 mm, z = 2–3 mm) at t₁; (b) near lower dielectric plate (r = 0–8 mm, z = 0.9–2.0 mm) at t₄.

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图 10 p_c分别为0, 55%, 70%时, t₁ (a)和t₄ (b)时刻对应的轴向平均种子电子密度n_e

Figure 10. Axial average seed electron density n_e at t₁ (a) and t₄ (b) under p_c of 0, 55% and 70% respectively.

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图 11 p_c分别为0, 55%, 70%时, 正击穿过程中(从预电离阶段开始的半个外施电压周期)局部强放电处的轴向切线的电子密度时空分布, 以及气隙电压极性反转时刻的电子密度n_e, 离子密度n_i和轴向电场|E_z|的轴向分布　(a) p_c = 0; (b) p_c = 55%; (c) p_c = 70%

Figure 11. Spatial-temporal distribution of electron density at axial tangent of the partial strong discharge during positive breakdown (half of applied voltage period starting from pre-ionization stage), and axial distribution of electron density n_e, ion density n_i and axial electric field |E_z| at the time of polarity reversal of the air gap voltage under different p_c: (a) p_c = 0; (b) p_c = 55%; (c) p_c = 70%.

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图 12 电子回流开始和结束时刻下表面电荷密度分布　(a) p_c = 55%; (b) p_c = 70%

Figure 12. Lower surface’s charge density distribution at beginning and the end of electron backflow: (a) p_c = 55%; (b) p_c = 70%.

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图 13 p_c分别为0, 55%, 70%时, 5个周期内局部强放电的击穿强度(以轴向平均电子密度表示, 其中削波电压下选取的正负击穿位置不同)

Figure 13. Strength of local intense discharge or discharge column within five periods under p_c of 0, 55% and 70% respectively (Which is expressed as axial average electron density, and selected positions of positive and negative breakdown under the clipping voltage are different).

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图 14 p_c分别为0, 55%, 70%时, 放电达到稳态后一个外施电压周期内的彭宁电离速率

Figure 14. Penning ionization rates over one period of applied voltage at steady state under p_c of 0, 55% and 70% respectively.

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图 15 不同p_c下, 放电达到稳态后预电离阶段的轴向平均电场强度|E_z|和轴向平均种子电荷密度(n_e + n_i)_avg

Figure 15. Axial average electric field |E_z| and axial average seed charge density (n_e + n_i)_avg at pre-ionization stage after discharge reaches steady state under different p_c.

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图 16 不同p_c下, 放电达到稳态后一个外施电压周期内的时间平均功率密度P_av和时间平均电子密度n_eav

Figure 16. Time-averaged power density P_av and time-averaged electron density n_eav over one period of applied voltage at steady state under different p_c.

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表 1 等离子体模型的边界条件

Table 1. Boundary conditions of plasma model.

边界	表达式	备注
AB	V = V_am	高压电极
GH	V = 0	接地
BC, CD, EF, FG	$- {\boldsymbol{n}} \cdot D = 0$	零电荷
DE	$- {\boldsymbol{n} } \cdot { {\boldsymbol{\varGamma } }_{\text{e} } } = 0$	绝缘
DE	$- {\boldsymbol{n} } \cdot { {\boldsymbol{\varGamma } }_{ \text{ε}} } = 0$	绝缘
DJ, EI	Eq. (10)—Eq. (12), Eq. (14), Eq. (15)	介质表面
HIJA	${ {\partial V}/{\partial r} } = 0$	对称轴

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表 2 模型中输入的初始值

Table 2. Initial parameters applied in model.

参数	初始值
电子数密度/m^–3	2.2×10¹³
He⁺数密度/m^–3	1.0×10¹³
$ {\text{He}}_2^ + $数密度/m^–3	1.0×10¹³
$ {\text{N}}_2^ + $数密度/m^–3	1.0×10¹²
$ {\text{N}}_4^ + $数密度/m^–3	1.0×10¹²
He^*摩尔分数	1.0×10^–9
$ {\text{He}}_2^* $摩尔分数	1.0×10^–9
N₂摩尔分数	100×10^–6
平均电子/eV	4
气体温度/K	300
压强/Torr	760

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map

[1]	梅丹华, 方志, 邵涛 2020 中国电机工程学报 40 1339 Google Scholar Mei D H, Fang Z, Shao T 2020 Chin. Soc. Elec. Eng. 40 1339 Google Scholar
[2]	戴栋, 宁文军, 邵涛 2017 电工技术学报 32 1 Google Scholar Dai D, Ning W J, Shao T 2017 Trans. Chin. Elc. Soc. 32 1 Google Scholar
[3]	李和平, 于达仁, 孙文廷, 刘定新, 李杰, 韩先伟, 李增耀, 孙冰, 吴云 2017 高电压技术 42 3697 Google Scholar Li H P, Yu D L, Sun W T, Liu D X, Li J, Han X W, Li Z Y, Sun B, Wu Y 2017 High Voltage Eng. 42 3697 Google Scholar
[4]	Adamovich I, Agarwal S, Ahedo E, et al. 2022 J. Phys. D: Appl. Phys. 55 373001 Google Scholar
[5]	Larouss M, Bekeschus S, Bogaerts A, Keidar M, Bogaerts A, Fridman A, Lu B X 2022 IEEE Trans. Radiat. Plasma Med. Sci. 6 127 Google Scholar
[6]	Sanito R C, You S J, Wang Y F 2021 J. Environ. Manage. 288 112380 Google Scholar
[7]	Laroussi M, Lu X, Keidar M 2017 J. Appl. Phys. 122 020901 Google Scholar
[8]	Gaunt L F, Beggs C B, Georghiou G E 2006 IEEE Trans. Plasma Sci. 34 1257 Google Scholar
[9]	Ouyang J T, Li B, He F, Dai D 2018 Plasma Sci. Technol. 20 103002 Google Scholar
[10]	Fang Z, Qiu Y, Zhang C, Kuffel E 2007 J. Phys. D:Appl. Phys. 40 1401 Google Scholar
[11]	Wang Q, Ning W J, Dai D, Zhang Y H, Ouyang J T 2019 J. Phys. D: Appl. Phys. 52 205201 Google Scholar
[12]	Zhang Y H, Ning W J, Dai D, Wang Q 2019 Plasma Sources Sci. Technol. 28 075003 Google Scholar
[13]	Zhang Y H, Neyts E C, Bogaerts A 2016 J. Phys. Chem. C 120 25923 Google Scholar
[14]	Hao Y P, Zheng B, Liu Y G 2014 Phys. Plasmas 21 013503 Google Scholar
[15]	Zhang P, Kortshagen U 2006 J. Phys. D: Appl. Phys. 39 153 Google Scholar
[16]	Zhang J, Wang Y H, Wang D Z 2015 Phys. Plasmas 22 043517 Google Scholar
[17]	Brauer I, Punset C, Purwins H G, Boeuf J P 1999 J. Appl. Phys. 85 7569 Google Scholar
[18]	Boeuf J P, Bernecker B, Callegari T, Blanco S, Fournier R 2012 Appl. Phys. Lett. 100 244108 Google Scholar
[19]	Zhang Y H, Ning W J, Dai D, Wang Q 2019 Plasma Sci. Technol. 21 074003 Google Scholar
[20]	Huang Z M, Hao Y P, Han Y Y, Yang L, Tang L, Liao Y F, Li L C 2017 Phys. Plasmas 24 113506 Google Scholar
[21]	Ye Q Z, Wu Y F, Li X W, Chen T, Shao G W 2012 Plasma Sources Sci. Technol. 21 065008 Google Scholar
[22]	Motrescu I, Ciolan M A, Sugiyama K, Kawamura N, Nagatsu M 2018 Plasma Sources Sci. Technol. 27 115005 Google Scholar
[23]	Wang X X, Luo H Y, Liang Z, Mao T, Ma R L 2006 Plasma Sources Sci. Technol. 15 845 Google Scholar
[24]	Brandenburg R 2017 Plasma Sources Sci. Technol. 26 053001 Google Scholar
[25]	Heinlin J, Morfill G, Landthaler M, Stolz W, Isbary G, Zimmermann J L, Shimizu T, Karrer S 2010 J. Dtsch. Dermatol. Ges. 8 968 Google Scholar
[26]	Buendia J A, Venkattraman A 2015 Europhys. Lett. 112 55002 Google Scholar
[27]	Fu Y Y, Zhang P, Verboncoeur J P, Christlieb A J, Wang X X 2018 Phys. Plasmas 25 013530 Google Scholar
[28]	Fu Y Y, Zhang P, Verboncoeur J P 2018 Appl. Phys. Lett. 113 054102 Google Scholar
[29]	Levko D, Raja L L 2015 J. Appl. Phys. 117 173303 Google Scholar
[30]	Go D B, Venkattraman A 2014 J. Phys. D: Appl. Phys. 47 503001 Google Scholar
[31]	Venkattraman A, Garg A, Peroulis D, Alexeenko A A 2012 Appl. Phys. Lett. 100 083503 Google Scholar
[32]	Cheng H, Liu X, Lu X P, Liu D W 2016 Phys. Plasmas 23 073517 Google Scholar
[33]	Cheng H, Xu M Y, Pan S H, Lu X P, Liu D W 2018 Plasma Sci. Technol. 20 044006 Google Scholar
[34]	Wang Q, Ning W J, Dai D, Zhang Y H 2019 Plasma Process. Polym. 17 1900182 Google Scholar
[35]	Mujahid Z, Korolov I, Liu Y, Mussenbrock T, Schulze J 2022 J. Phys. D: Appl. Phys. 55 495201 Google Scholar
[36]	Babaeva N Y, Tian W, Kushner M J 2014 J. Phys. D: Appl. Phys. 47 235201 Google Scholar
[37]	Babaeva N Y, Kushner M J 2013 J. Phys. D:Appl. Phys. 46 025401 Google Scholar
[38]	Lin A, Biscop E, Gorbanev Y, Smits E, Bogaerts A 2021 Plasma Process. Polym. 19 e2100151 Google Scholar
[39]	Zhang Y H, Ning W J, Dai D, Wang Q 2019 Plasma Sources Sci. Technol. 28 104001 Google Scholar
[40]	Kong M G, Deng X T 2003 IEEE Trans. Plasma Sci. 31 7 Google Scholar
[41]	Fridman G, Friedman G, Gutsol A, Shekhter A B, Vasilets V N, Fridman A 2008 Plasma Process. Polym. 5 503 Google Scholar
[42]	Ning W J, Dai D, Li L C 2018 Plasma Sources Sci. Technol. 27 08LT01 Google Scholar
[43]	Cheng H, Liu X, Liu D W, Lu X P 2016 High Volt. 1 62 Google Scholar
[44]	Lazarou C, Belmonte T, Chiper A S, Georghiou G E 2016 Plasma Sources Sci. Technol. 25 055023 Google Scholar
[45]	力伯曼, 里登伯格著 (蒲以康等译) 2018 等离子体放电与材料工艺原理: 第2版 (北京: 电子工业出版社) 第6—7页 Lieberman M A, Lichtenberg A J (translated by Pu Y K, et al.) 2018 Principles of Plasma Discharges and Materials Processing (2nd Ed.) (Beijing: Publishing House of Electronics Industry) pp6–7 (in Chinese)
[46]	Lazarou C, Koukounis D, Chiper A S, Costin C, Topala I, Georghiou G E 2015 Plasma Sources Sci. Technol. 24 035012 Google Scholar
[47]	Hagelaar G J M, Pitchford L C 2005 Plasma Sources Sci. Technol. 14 722 Google Scholar
[48]	Purwins H G, Stollenwerk L 2014 Plasma Phys. Control. Fusion 56 123001 Google Scholar
[49]	Ellis H W, Pai R Y, McDaniel E W, Mason E A, Viehland L A 1976 At. Data Nucl. Data Tables. 17 177 Google Scholar
[50]	Yan W, Xia Y, Bi Z H, Song Y, Wang D Z, Sosnin E A, Skakun V S, Liu D P 2017 J. Phys. D: Appl. Phys. 50 345201 Google Scholar
[51]	Hagelaar G J M 2000 Phys. Rev. E 62 1452 Google Scholar
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