基于有限元弱解式的棒-板长空气间隙先导放电空间电场仿真研究

对棒-板长空气间隙先导放电过程的空间电场分布以及带电离子浓度等特征参数进行仿真计算研究。建立棒-板长空气间隙放电的二维模型，导出流注-先导放电的二阶偏微分方程，通过有限元弱解形式(weak form)数值计算方法求解先导放电过程中产生的电子、正、负离子浓度与空间电场的大小。仿真结果显示：气体放电所产生的空间电荷对空间电场分布影响显著；间隙距离1.5 m的棒-板长空气间隙下，外加500 kV、250/2 500 ms正极性操作电压时的先导放电起始条件为，流注头部带电离子浓度达到4′1013 cm-3数量级，空间电场最低达到10 kV/cm；先导放电形成后，先导通道内电场约为1~2 kV/cm，先导起始时间在400 ms左右且以3′104 m/s速度传播；有限元弱解形式能有效消除计算离子流中的数值振荡，使偏微分方程求解迅速收敛。

Simulation Study on Electric Field of a Long Rod-plane Air Gap During Leader Discharge Based on Weak Form of Finite Element Method

This paper conducts a simulation analysis on the electric field distribution and charged ion density of a long rod-plane air gap during the leader discharge stage. The two-dimensional model of the rod-plane gap is established, from which the second-order partial differential equations (PDEs) of the leader discharge are derived. The electron density, the negative and positive ion density and the space electric field are all calculated by the weak form of finite element method (FEM). The results show that the space electric field is greatly influenced by space charge; the initial conditions of the leader discharge of 1.5m long rod-plane air gap under 500kV, 250/2500ms positive switching impulse are that the charged ion density of electron, positive and negative ion at the stream head are about 4′1013cm-3, and the electric field value at the stream head is above 10kV/cm; with leader discharge beginning at the time of 400ms, the electric field value in the leader channel is about 1~2 kV/cm and the leader channel propagates from rod electrode to plane electrode at a speed of 3′104 m/s; the weak form of FEM can effectively reduce the numerical oscillation and let PDE converge rapidly.