基于分形理论的SF_6/N_2混合气体放电仿真

Simulation of Discharge in SF_6/N_2 Gas Mixtures Based on Fractal Theory

为了研究SF_6/N_2混合气体电介质击穿现象,利用编写的Matlab程序对放电通道发展过程进行数值模拟,并结合分形几何原理计算放电树枝的分形维数。基于分形理论,建立了考虑空间电荷分布和引入物理时间的棒-板分形放电仿真模型,通过有限元方法(FEM)计算空间电场,并首次结合通量校正传输(FCT)法求解带电粒子连续性方程,研究了不同发展概率指数、不同放电阈值和SF_6含量变化下分形放电特性。结果表明:概率指数越大,SF_6含量越高,则分形维数越小,放电树枝分叉也越少;体积含量50%/50%的SF_6/N_2混合气体放电分形维数D=1.219 2,整个放电过程流注发展平均速度为1.15Mm/s,并得到了不同时刻空间电荷及轴向电场与电子浓度的分布。

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.