Numerical study of breakdown voltage calculation and discharge characteristics of millimeter-level short air gap with a single water droplet

Abstract Water droplets in the short air gap significantly affect the breakdown voltage. Currently, there is a lack of computational studies on the breakdown voltage and discharge process of short air gaps containing water droplets. In this paper, we establish a plasma dynamics-based model for the discharge in a millimeter-scale short air gap containing a single water droplet under ambient pressure and propose a breakdown voltage calculation method. We discuss typical discharge processes, calculate breakdown voltages for different gap lengths, validate the model through discharge phenomena and breakdown voltage, and analyze the impact of droplet parameters on discharge characteristics. The results show that negative streamer discharge in the cathode-side gap and positive streamer discharge in the anode-side gap occur sequentially, consistent with reported experimental results, with the positive streamer discharge being the primary process leading to gap breakdown. The average error rate between the calculated breakdown voltages for 4–8 mm gaps and reported experimental results is 4.85%, indicating good agreement. The observed streamer branching phenomenon may explain the difference between calculated and experimental breakdown voltages for the 10 mm gap. Under the influence of surface charges, low-conductivity droplets cause the discharge channel to propagate along the droplet surface. In contrast, high-conductivity droplets confine the discharge channel within the two gap sections. Increasing droplet diameter reduces breakdown voltage, with a critical value where the reduction becomes significant. Increased droplet deformation degree raises the breakdown voltage. This effect is related to the deviation of the positive streamer from the axial development and the reverse streamer generated on the droplet’s surface in different cases. The closer the droplet is to the electrode, the higher the breakdown voltage. The discharge is facilitated by the streamers generated on the droplet’s lower surface when it is close to the anode.