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气体放电的发展过程非常复杂, 实验观测结果表明非均匀场短空气隙放电过程中经常产生随机并伴有分岔现象的放电通道. 由于这些放电现象的整体结构表现出一定的自相似性, 因此, 结合经典流注放电与分形理论而建立的介质击穿模型成为描述气体中放电通道分岔现象的一种有效的分析方法, 而放电通道的复杂程度可以用分形维数表征. 为了明确此模型参数中发展概率指数的取值, 本文对直流高压作用下的10 mm针板电极空气隙放电通道图像进行了分析、处理和分形计算, 并与理论模型的仿真结果对比. 由于空气隙主放电通道的亮度明显高于其他弱分支, 导致各放电通道的宽度各异, 需要对所拍摄图像进行灰度变换和边界识别处理, 最后运用盒维数法计算出分形维数. 研究结果表明在其他参数与实验条件相同条件下, 调整理论模型中的发展概率指数, 使得仿真结果与实验结果相吻合, 依据本文实验条件下和理论模型分析, 发展概率指数 在0.04-0.05范围. 本文的研究印证了尖-板电极短空气隙放电复杂现象的可测性并提供了一种分析方法.The process of gas discharge is very complicated and experimental observations indicate that streamers in short gap under non-uniform electric fields always exhibit irregularity and self-similarity, so a dielectric breakdown model, which is the combination of the random fractal method and the traditional streamer theory, can simulate this phenomenon.In this paper, a stochastic model with the growth probability index at any point proportional to the power of the electric field is utilized to quantify the channel tortuosity, and the space charge effect is taken into account as well. The potential distribution is solved by the Poisson's equation which is calculated iteratively by finite difference method; and the box counting method is used to characterize the channel tortuosity and estimate the fractal dimensions of the discharge channels. Based on this, an idea is proposed that the analysis of the experimental results, which in turn provide the appropriate parameters for the model, can better elucidate this phenomenon.The growth probability index can always get from the previous data, but the range of the will change under different experimental condition and there will exist differences in simulation results on fractal dimensions for different , so the limitation of the previous studies is its possible lack of generalizability. In order to define the range of the growth probability index in this model, the bifurcation phenomenon of plasma channels generated by the discharge, affected by HVDC (high-voltage direct current) of short-air-gap in a needle-plate electrode, is captured by ICCD. Before estimating the fractal dimensions of discharge channels, experimental images are saved as a binarized (black and white) image, and the gray-level transformation and boundary identification algorithm will be conducted to remove the apparent thickness of the discharge channel caused by the magnitude of the flowing currents through different branches. Experimental results show that the range of fractal dimensions in the box counting method for the discharge channel is 1.40-1.55. Under the same condition that other factors remain the same but the adjusted growth probability index in this simulation model should accord with the experimental results, all the facts demonstrate that the value of must lie between 0.04 and 0.05.
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Keywords:
- fractal dimension /
- image processing /
- probability index /
- bifurcation
[1] Sun X, Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese) [孙霞, 吴自勤 2001 物理学报 50 2126]
[2] Huo Y L, Zhang G S, Lv S H, Yuan P 2013 Acta Phys. Sin. 62 059201 (in Chinese) [火元莲, 张广庶, 吕世华, 袁萍 2013 物理学报 62 059201]
[3] Sun K Y, Zhao X Y, Zhang G L, Zang H M 2014 Acta Phys. Sin. 63 029204 (in Chinese) [孙柯岩, 赵小莹, 张功磊, 臧洪明 2014 物理学报 63 029204]
[4] Jia Z D, Le B, Jiang X W 1999 High Voltage Engineering 25 1 (in Chinese) [贾志东, 乐波, 蒋雄伟 1999 高电压技术 25 1]
[5] Niemeyer L, Pietronero L, Wiesmann H J 1984 Phys. Rev. Lett. 52 12
[6] Wiesmann H J, Zeller H R 1986 J. Phys. D: Appl. Phys. 60 1770
[7] Noskov M D, Kukhta V R, Lopatin V V 1995 J. Phys. D: Appl. Phys. 28 1187
[8] Veldhuizen E M, Kemps P C M, Rutgers W R 2002 IEEE Trans. Plasma Sci. 30 162
[9] Kupershtokh A L, Charalambakos V, Agoris D 2001 J. Phys. D: Appl. Phys. 34 936
[10] Hallac A, Georghiou G E, Metaxas A C 2005 IEEE Trans. Plasma Sci. 33 266
[11] Qing X, Anton Y N, Xin P L 2011 IEEE Trans. Plasma Sci. 39 2094
[12] Luque A, Ebert U 2012 J. Comput Phys. 231 904
[13] Dulan A, Upul S A, Marcus B B, Vernon C 2015 J. Electrostat. 73 33
[14] Ren S P, Chi J P, Zhuang H C 1998 Chinese Journal of Space Science 18 363 (in Chinese) [任顺平, 迟建平, 庄洪春 1998 空间科学学报 18 363]
[15] Gu T, Yan P, Zhang S C 2006 High Voltage Engineering 32 1 (in Chinese) [谷探, 严萍, 张适昌 2006 高电压技术 32 1]
[16] Hong C 2007 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [洪川 2007 博士学位论文 (重庆: 重庆大学)]
[17] He H X, He J J, Qian G J 2008 High Voltage Engineering 34 2047 [贺恒鑫, 何俊佳, 钱冠军 2008 高电压技术 34 2047]
[18] Gallimberti I, Bacchiega G, Bondiou C A 2002 C. R. Physique 3 1335
[19] Dulan A, Upul S 2008 J. Natl Sci Found SR. 36 137
[20] Niemeyer L, Ullrich L, Wiegart N 1989 IEEE Trans. Electr Insul. 24 309
[21] Wang J T, Yang J M 2013 Complex Systems and Complexity Science 0 1 (in Chinese) [王江涛, 杨建梅 2013 复杂系统与复杂性科学 0 1]
[22] Canny J 1986 IEEE Trans. Pattern Anal. 8 679
[23] Nobuyuki O 1979 IEEE SMC Society 9 62
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[1] Sun X, Wu Z Q 2001 Acta Phys. Sin. 50 2126 (in Chinese) [孙霞, 吴自勤 2001 物理学报 50 2126]
[2] Huo Y L, Zhang G S, Lv S H, Yuan P 2013 Acta Phys. Sin. 62 059201 (in Chinese) [火元莲, 张广庶, 吕世华, 袁萍 2013 物理学报 62 059201]
[3] Sun K Y, Zhao X Y, Zhang G L, Zang H M 2014 Acta Phys. Sin. 63 029204 (in Chinese) [孙柯岩, 赵小莹, 张功磊, 臧洪明 2014 物理学报 63 029204]
[4] Jia Z D, Le B, Jiang X W 1999 High Voltage Engineering 25 1 (in Chinese) [贾志东, 乐波, 蒋雄伟 1999 高电压技术 25 1]
[5] Niemeyer L, Pietronero L, Wiesmann H J 1984 Phys. Rev. Lett. 52 12
[6] Wiesmann H J, Zeller H R 1986 J. Phys. D: Appl. Phys. 60 1770
[7] Noskov M D, Kukhta V R, Lopatin V V 1995 J. Phys. D: Appl. Phys. 28 1187
[8] Veldhuizen E M, Kemps P C M, Rutgers W R 2002 IEEE Trans. Plasma Sci. 30 162
[9] Kupershtokh A L, Charalambakos V, Agoris D 2001 J. Phys. D: Appl. Phys. 34 936
[10] Hallac A, Georghiou G E, Metaxas A C 2005 IEEE Trans. Plasma Sci. 33 266
[11] Qing X, Anton Y N, Xin P L 2011 IEEE Trans. Plasma Sci. 39 2094
[12] Luque A, Ebert U 2012 J. Comput Phys. 231 904
[13] Dulan A, Upul S A, Marcus B B, Vernon C 2015 J. Electrostat. 73 33
[14] Ren S P, Chi J P, Zhuang H C 1998 Chinese Journal of Space Science 18 363 (in Chinese) [任顺平, 迟建平, 庄洪春 1998 空间科学学报 18 363]
[15] Gu T, Yan P, Zhang S C 2006 High Voltage Engineering 32 1 (in Chinese) [谷探, 严萍, 张适昌 2006 高电压技术 32 1]
[16] Hong C 2007 Ph. D. Dissertation (Chongqing: Chongqing University) (in Chinese) [洪川 2007 博士学位论文 (重庆: 重庆大学)]
[17] He H X, He J J, Qian G J 2008 High Voltage Engineering 34 2047 [贺恒鑫, 何俊佳, 钱冠军 2008 高电压技术 34 2047]
[18] Gallimberti I, Bacchiega G, Bondiou C A 2002 C. R. Physique 3 1335
[19] Dulan A, Upul S 2008 J. Natl Sci Found SR. 36 137
[20] Niemeyer L, Ullrich L, Wiegart N 1989 IEEE Trans. Electr Insul. 24 309
[21] Wang J T, Yang J M 2013 Complex Systems and Complexity Science 0 1 (in Chinese) [王江涛, 杨建梅 2013 复杂系统与复杂性科学 0 1]
[22] Canny J 1986 IEEE Trans. Pattern Anal. 8 679
[23] Nobuyuki O 1979 IEEE SMC Society 9 62
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