Abstract:In this paper, the model of dielectric breakdown in SF6/N2 mixed gas is simulated by using the Matlab programs. This rod-plane model is established considering the distribution of space charge and introducing physical time, based on the fractal theory. The finite element method (FEM) is used to solve the electric field, and particle continuity equations are solved by the flux corrected transport (FCT) algorithm. Moreover, the characteristics of fractal discharge under various scenarios are analyzed, such as different probability exponents, different discharge thresholds, and different percentages of SF6 and so on. The simulation results show that the number of branches and fractal dimension decrease with the increasing of probability exponent and the percentage of SF6. The discharge fractal dimension D of 50%/50% SF6/N2 gas mixture equals to 1.219 2, and the average velocity during the discharge process of streamer propagation is 1.15Mm/s. Moreover, the distributions of charge density in space, electric field alone the axis, and electrons density alone the axis are calculated.
李敏, 汪沨, 许松枝, 陈晓林, 黄墀志, 谢望君. 基于分形理论的SF6/N2混合气体放电仿真[J]. 电工技术学报, 2016, 31(24): 88-95.
Li Min, Wang Feng, Xu Songzhi, Chen Xiaolin, Huang Chizhi, Xie Wangjun. Simulation of Discharge in SF6/N2 Gas Mixtures Based on Fractal Theory. Transactions of China Electrotechnical Society, 2016, 31(24): 88-95.
[1] 汪沨, 肖晓林, 张宪标, 等. 基于PIC法SF 6 /N 2 混合气体中绝缘子沿面放电特性研究[J]. 电工技术学报, 2011, 26(8): 220-226. Wang Feng, Xiao Xiaolin, Zhang Xianbiao, et al. Research on the insulator surface discharge characte- ristics in SF 6 /N 2 gas mixture using PIC method[J]. Transactions of China Electrotechnical Society, 2011, 26(8): 220-226. [2] 赵虎, 李兴文, 贾申利. SF 6 及其混合气体临界击穿场强计算与特性分析[J]. 西安交通大学学报, 2013, 47(2): 109-115. Zhao Hu, Li Xingwen, Jia Shenli. Calculation and characteristic analysis of critical breakdown field strength of SF 6 and the mixtures[J]. Transactions of China Electrotechnical Society, 2013, 47(2): 109- 115. [3] 汪沨, 李锰, 潘雄峰, 等. 基于FEM-FCT算法的SF 6 /N 2 混合气体中棒-板间隙电晕放电特性的仿真研究[J]. 电工技术学报, 2013, 28(9): 261-267. Wang Feng, Li Meng, Pan Xiongfeng, et al. Corona discharge simulations of rod-plate gap in SF 6 /N 2 gas mixtures using FEM-FCT method[J]. Transactions of China Electrotechnical Society, 2013, 28(9): 261- 267. [4] Mandelbrot B B. The fractal geometry of nature[M]. New York, USA: W. H. Freeman and Company, 1982. [5] 陈庆国, 张乔根, 邱毓昌, 等. SF 6 气体放电通道的分形特征及计算机模拟[J].西安交通大学学报, 2000, 34(4): 1-4. Chen Qingguo, Zhang Qiaogen, Qiu Yuchang, et al. Fractal characteristics and computer simulation of the discharge channel in SF 6 gas[J]. Journal of Xi’an Jiaotong University, 2000, 34(4): 1-4. [6] 贾志东, 乐波, 蒋雄伟, 等. 分形几何在电介质科学中的应用[J]. 高电压技术, 1999, 25(3): 1-3. Jia Zhidong, Le Bo, Jiang Xiongwei, et al. Fractal geometry and its application in the science of diele- ctrics[J]. High Voltage Engineering, 1999, 25(3): 1-3. [7] Cisse H T, Ablart G. The frequency response of a fractal photolithographic structure[J]. IEEE Transa- ctions on Dielectrics and Electrical Insulation, 1997, 4(3): 321-326. [8] Niemeyer L, Pietronero L, Wiesmann H J. Fractal dimension of dielectric breakdown[J]. Physical Review Letters, 1984, 52(12): 1033-1036. [9] Wiesmann H J, Zeller H R. A fractal model of dielectric breakdown and prebreakdown in solid dielectrics[J]. Journal of Applied Physics, 1986, 60(5): 1770-1773. [10] Karpov D I, Kupershtokh. A L. Models of streamers growth with "physical" time and fractal characterics of streamer structures[C]//Conference Record of the 1998 IEEE International Symposium on Electrical Insulation, Arlington, VA, 1998: 607-610. [11] Ding H Z, Varlow B R. Thermodynamic model for electrical tree propagation kinetics in combined electrical and mechanical stresses[J]. IEEE Transa- ctions on Dielectrics and Electrical Insulation, 2005, 12(1): 81-89. [12] 贺恒鑫, 何俊佳, 钱冠军, 等. 棒-板长间隙正极性流注生长概率模型及应用[J]. 高电压技术, 2008, 34(10): 2047-2053. He Hengxin, He Junjia, Qian Guanjun, et al. Stochastic model of streamer growth in air for a rod-plate gap and its application[J]. High Voltage Engineering, 2008, 34(10): 2047-2053. [13] 谭震宇, 万基磊, 李清泉. 基于分形理论的水中流注放电仿真[J]. 高电压技术, 2012, 38(7): 1556- 1561. Tan Zhenyu, Wan Jilei, Li Qingquan. Fractal simu- lation of streamer discharge in liquid water[J]. High Voltage Engineering, 2012, 38(7): 1556-1561. [14] 陈伟根, 汪万平, 夏青. 绝缘子污秽放电泄漏电流的多重分形特征研究[J]. 电工技术学报, 2013, 28(1): 50-56. Chen Weigen, Wang Wanping, Xia Qing. Research on multi-fractal characteristics of leakage current for contamination discharge of insulators[J]. Transa- ctions of China Electrotechnical Society, 2013, 28(1): 50-56. [15] Morrow R, Lowke J J. Streamer propagation in air[J] . Journal of Physics D: Applied Physics, 1997, 30(4): 614-627. [16] 庄池杰, 曾嵘. 短间隙流注放电数值仿真方法研究进展[J]. 中国电机工程学报, 2012, 32(22): 157-166. Zhuang Chijie, Zeng Rong. Research and deve- lopment on short gap streamer discharge simulation methods[J]. Proceedings of the CSEE, 2012, 32(22): 157-166. [17] Georghiou G E, Morrow R, Metaxas A C. A two- dimensional, finite-element, flux-corrected transport algorithm for the solution of gas discharge pro- blems[J]. Journal of Physics D: Applied Physics, 2000, 33(19): 605-620. [18] Lohner R, Morgan K, Peraire J, et al. Finite element flux-corrected transport (FEM-FCT) for the Euler and Navier-Stokes equation[J]. International Journal for Numerical Methods in Fluids, 1987, 10(7): 1093- 1109. [19] Georghiou G E, Morrow R, Metaxasan A C. An improved finite-element flux-corrected transport algorithm[J]. Journal of Computational Physics, 1999, 148(2): 605-620. [20] 汪沨, 李敏, 李锰, 等. 基于ETG-通量校正传输法的短间隙SF 6 /N 2 混合气体流注放电数值仿真[J]. 电工技术学报, 2016, 31(6): 234-241. Wang Feng, Li Min, Li Meng, et al. Numerical simulation of short gap streamer discharge in SF 6 /N 2 gas mixtures based on Euler-Taylor-Galerkin-flux corrected transport method[J]. Transactions of China Electrotechnical Society, 2016, 31(6): 234-241. [21] Georghiou G E, Morrow R, Metaxas A C. Two- dimensional simulation of streamers using the FE- FCT algorithm[J]. Journal of Physics D: Applied Physics, 2000, 33(3): 27-32. [22] Biller P. Fractal streamer models with physical time[C]//Proceedings of IEEE 11th International Conference on Conduction and Breakdown in Dielectric Liquids, Baden-Dattwil, Switzerland, 1993: 199-203. [23] Noskov M D, Kuktha V R, Lopatin V V. Simulation of the electrical discharge development in inho- mogeneous insulators[J]. Journal of Physics D: Applied Physics, 1995, 28(6): 1187-1194. [24] Pancheshnyi S V, Starikovskaia S M, Yu Starikovskii A. Role of photoionization processes in propagation of cathode-directed streamer[J]. Journal of Physics D: Applied Physics, 2001, 34(1): 105-115. [25] 孙鹏程, 王帮田, 洪文芳, 等. SF 6 /N 2 混合气体绝缘特性的实验研究[J]. 中国电力, 2012, 45(12): 71-75. Sun Pengcheng, Wang Bangtian, Hong Wenfang, et al. Experimental studies on electrical insulation performances of SF 6 /N 2 gas mixtures[J]. Electric Power, 2012, 45(12): 71-75.