In this paper, an improved air discharge fluid model under non-uniform electric field is constructed based on the plasma module COMSOL Multiphysics with artificial stability term, and the boundary conditions developed in the previous paper are applied to the calculation of photoionization rate. Based on the modified model, the characteristics of low temperature sub-atmospheric air discharge under 13 kV direct current voltage are discussed, including needle-plate and needle-needle electrode structures. Firstly, in order to verify the reliability of the model, a numerical example and an experimental verification were carried out for the modified model respectively. Both verification results show that the model can ensure the accuracy and repeatability of the calculation. Secondly, according to the calculation results of the modified model, under the same voltage and spacing, the reduced electric field under low temperature sub-atmosphere pressure is larger than that under normal temperature and atmospheric pressure. The high electric field leads to the air discharge at low temperature and sub atmospheric pressure entering the streamer initiation stage earlier, and has a faster propagation speed in the streamer development stage, which shortens the overall discharge time. Finally, the discharge characteristics of the two electrode structures are compared, and it is found that the biggest difference between them is that there is a pre-ionization region near the cathode in the needle-needle electrode structure. When the pre-ionization level reaches 10¹³ cm⁻³, the propagation speed of the positive streamer remains unchanged throughout the discharge process, and is no longer affected by the negative streamer. The peak value of electric field decreases with the increase of pre-ionization level, and tends to be constant during streamer propagation. Based on the previous paper, this paper constructs the air discharge model under non-uniform electric field, complements with the previous paper, and forms a relatively complete set of air discharge simulation system under low temperature and sub atmospheric pressure, which provides a certain reference for future research.

在本文中，基于具有人工稳定项的等离子体模块 COMSOL Multiphysics 构建了改进的非均匀电场下的空气放电流体模型，并将前一篇论文中建立的边界条件应用于光电离率的计算。基于修正模型，讨论了13 kV直流电压下低温亚大气压空气放电的特性，包括针板和针针电极结构。首先，为了验证模型的可靠性，对修正后的模型分别进行了数值算例和实验验证。两个验证结果都表明该模型能够保证计算的准确性和可重复性。其次，根据修改后的模型计算结果，在相同的电压和间距下，低温亚大气压下的衰减电场大于常温常压下的电场强度。高电场导致低温、亚大气压下的空气放电较早进入流注引发阶段，在流注发展阶段传播速度较快，从而缩短了整体放电时间。最后比较了两种电极结构的放电特性，发现它们最大的区别在于针-针电极结构中阴极附近有一个预电离区。当预电离水平达到 10 低温亚大气压下的还原电场大于常温常压下的电场强度。高电场导致低温、亚大气压下的空气放电较早进入流注引发阶段，在流注发展阶段传播速度较快，从而缩短了整体放电时间。最后比较了两种电极结构的放电特性，发现它们最大的区别在于针-针电极结构中阴极附近有一个预电离区。当预电离水平达到 10 低温亚大气压下的还原电场大于常温常压下的电场强度。高电场导致低温、亚大气压下的空气放电较早进入流注引发阶段，在流注发展阶段传播速度较快，从而缩短了整体放电时间。最后比较了两种电极结构的放电特性，发现它们最大的区别在于针-针电极结构中阴极附近有一个预电离区。当预电离水平达到 10 高电场导致低温、亚大气压下的空气放电较早进入流注引发阶段，在流注发展阶段传播速度较快，从而缩短了整体放电时间。最后比较了两种电极结构的放电特性，发现它们最大的区别在于针-针电极结构中阴极附近有一个预电离区。当预电离水平达到 10 高电场导致低温、亚大气压下的空气放电较早进入流注引发阶段，在流注发展阶段传播速度较快，从而缩短了整体放电时间。最后比较了两种电极结构的放电特性，发现它们最大的区别在于针-针电极结构中阴极附近有一个预电离区。当预电离水平达到 10 发现它们之间最大的区别在于针-针电极结构中阴极附近有一个预电离区。当预电离水平达到 10 发现它们之间最大的区别在于针-针电极结构中阴极附近有一个预电离区。当预电离水平达到 10¹³ cm ^-3，正流光的传播速度在整个放电过程中保持不变，不再受负流光的影响。电场峰值随着预电离能级的增加而减小，在流注传播过程中趋于恒定。本文在前文的基础上，构建了非均匀电场下的空气放电模型，与前文相辅相成，形成了一套较为完整的低温亚大气压下空气放电模拟系统，提供了一定的参考用于未来的研究。