以磁流体动力学(magnetic hydro-dynamics，MHD)为基础建立了考虑电极烧蚀影响的低压断路器中电弧的数学模型。在传统的质量、动量和能量守恒方程的基础上增加了铜蒸气的浓度方程，考虑电极烧蚀对气体的热动力学特性和传输系数的影响，针对阴极和阳极不同特点分别建立了电弧与阴极和阳极作用的数学模型。利用基于有限容积法的商业软件对上述模型进行求解，得出灭弧室内温度场、浓度场、气流场、电位场的分布情况。仿真结果表明，由于电极附近“双漩涡”的存在，使得Cu蒸气浓度最大的区域位于弧根后方靠近电极的区域；考虑Cu蒸气影响时计算得到的电弧电压为比未考虑Cu蒸气影响时减小12.3%；考虑Cu蒸气影响所得到的电弧平均运动速度比未考虑Cu蒸气影响时减少21.3%。实验结果验证了仿真模型的合理性。

The mathematical model of 3-dimentional arc plasma considering the erosion of electrodes was set up based on magnetic hydro-dynamics (MHD). The Cu vapor mass concentration equation was introduced to the model on the basis of traditional mass, momentum and energy equations. The influence of electrodes erosion on the thermodynamic and transport properties was considered. The arc-cathode model and arc-anode model were built aiming at the difference of cathode and anode. By adopting the commercial computational fluid dynamics (CFD) package based on control-volume method, the above MHD model was solved and the distribution of temperature field, concentration field, flow field and electrical potential field in the arc chamber were calculated. The simulation results indicate that the maximal Cu vapor concentration locates at the region behind the arc root because of the existence of “double vortex” near electrodes. The simulated arc voltage considering the influence of Cu vapor is 12.3% lower than the result without considering the influence of Cu vapor. The simulated arc average speed considering the influence of Cu vapor is 21.3% lower than the result without considering the influence of Cu vapor. The experimental results prove the validity of the arc model.

国家自然科学基金项目(50477025，50537050，50525722)；教育部科学技术研究重点项目资助(10518)。