基于不连续有限元的短间隙气体放电仿真算法及其应用

Discontinuous Galerkin Method for Short Air Gap Discharge Simulations and Its Applications

我国超、特高压输电工程建设亟需空气间隙放电理论的支撑。作为长间隙放电研究的基础,短间隙放电是间隙放电研究的重要内容与切入点。仅靠现有实验手段与实验结果无法构建这些放电过程的完整物理图像,使得数学建模与仿真,成为研究短间隙放电的重要方法。为此,概述了描述短间隙气体放电过程的流体模型,提出了基于不连续有限元的仿真算法:引入罚因子不连续有限元离散Poisson方程;提出了加权不连续有限元用于求解粒子输运方程,提出了圆柱坐标系下的多层重构算法用于抑制高阶格式可能引起的数值振荡。实现了基于上述算法的短间隙气体放电仿真程序,利用该程序研究了碰撞电离系数、附着系数、粒子迁移率等放电参量对流注发展的影响,电子碰撞电离系数与电子迁移率影响最大,电子附着系数与电子扩散系数有一定影响,离子迁移率基本没有影响。通过考虑Townsend放电中的光发射机制,成功预测了一定长度范围内平板间隙中Townsend放电击穿电压曲线,验证了将数值仿真应用于气体放电研究的可行性。

The support of air gap discharge theory is urgently required in the construction of the UHV/EHV power systems. Up to now, the existing experiment data are insufficient to build a clear picture of the short gap discharge process, which makes numerical simulation an important way for short gap gas discharge research. We briefly introduced the fluid model of short air gap discharge, and proposed a simulation method based on discontinuous Galerkin method. Interior penalty Galerkin method was adopted to discritize the Poisson＇ s equation, the Runge- Kutta weighted discontinuous Galerkin method was proposed to discretize the particle transport equation, and a Hierarchical Reconstruction algorithm in cylindrical coordinate system was proposed to eliminate the possible numerical oscillations. Based on the above methods, a simulation program is implemented. The effect of micro- coefficients, such as collision ionization, recombination, and particle drift, on the streamer discharge was well compared. The breakdown voltage of Townsend discharge in a parallel-plate air gap was predicted successfully, which shed a light to the application of numerical simulation in air gap discharge research.