Numerical investigation on the voltage fluctuation mechanism in an expansion channel of a DC hydrogen–nitrogen arc

A compressible magnetohydrodynamic model incorporating an inclined contact geometry was developed to study the transport and dynamic behavior of a DC arc in a hydrogen–nitrogen (7:3) mixture driven into an expanding channel by a transverse magnetic field. To disentangle the respective roles of geometric evolution and flow acceleration, physics-based criteria were introduced to quantify the arc morphology, force–flow alignment, and convective intensity. The results indicate that arc voltage fluctuations are primarily governed by flow acceleration arising from the competition between the Lorentz force and pressure gradient, whereas geometric evolution plays a secondary role owing to geometric confinement. Although increasing the external magnetic field does not eliminate the force competition, it drives the arc into a convection-saturated regime, thereby reducing the sensitivity of the electrical conductivity to velocity perturbations and effectively suppressing voltage fluctuations. Transient vortices were identified in the arc wake region. Analysis of the vorticity evolution indicates that these vortices are generated primarily by the baroclinic term and modulated by the compressibility term. This study identifies the dominant mechanisms governing arc voltage stability and provides guidance for the magnetic-field-assisted design of high-current DC contactors.