Electric Field Simulation of Needle Tips with Different Shape Formations Using FEM Method

Abstract

Needle-plane (NP) electrode is the most widely-used geometry to study the characteristics of streamer in dielectric liquids. The arc angle, apex angle and the hyperbolic shape are identified as the key variables to describe a needle shape in the literature. Four different needle tip shape formations were adopted in this paper to study their effects on the needle tip electric field (NTEF). The calculation of NTEF was based on Laplace equation solved by finite element method (FEM). Mason equation was also used to calculate NTEF as a comparison. It was found that for a fixed NP electrode configuration with a needle tip radius (NTR) of 3 µm, the apex angle has an obvious effect. NTEF at a small apex angle of 10° is 4.6 times larger than NTEF at a large apex angle of 90°. Larger NTR leads to smaller variation of NTEF for different apex angles. Besides, NTEF of a hyperbolic needle tip is equal to that of a needle tip with a specific apex angle. This apex angle increases from around 30° to around 74° when NTR rises from 3 µm to 100 µm. Mason equation gives a good estimation of NTEF at small NTR in NP configuration when hyperbolic needle tip shape is taken. The difference of NTEF calculated by FEM and Mason equation for hyperbolic shape needles becomes larger with the increase of NTR.