A 2D Axisymmetric Multi-Domain DC Arc Model for Simulink Implementation

Abstract

This paper presents a multi-domain model for simulating direct current (DC) arcs by coupling thermal, fluid dynamics, and electromagnetic field equations. The magnetohydrodynamics (MHD) equations are first simplified to derive a two-dimensional (2D) axisymmetric model. The model is then discretized and implemented in MATLAB/Simulink to capture the spatial and temporal evolution of temperature, velocity, and magnetic fields within the arc column, surrounded by a stabilizing wall. Simulation results for arc currents in the range of 10-1500 A shows that the temperature distribution is strongly radial, with peak values along the central axis and rapid decay toward the surrounding walls. The velocity and magnetic field plots follow the expected physical patterns, validating the accuracy of the approach. Furthermore, the inverse current-voltage characteristic obtained aligns with classical arc models and experimental observations, while transient simulations confirm rapid voltage stabilization within milliseconds. The proposed model thus provides an approximate and simple-to-use model useful for studying DC arc behavior inside DC circuits and offers a foundation for extending arc simulations to systemlevel applications such as circuit breakers, welding systems, and plasma devices.