基于分形理论的尖-板电极短空气隙放电现象研究

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η 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.

Study on discharge phenomena of short-air-gap in needle-plate electrode based on fractal theory

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 η can always get from the previous data, but the range of the η will change under different experimental condition and there will exist differences in simulation results on fractal dimensions for different η, 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 η in this simulation model should accord with the experimental results, all the facts demonstrate that the value of η must lie between 0.04 and 0.05.