A 2D Axisymmetric Multi-Domain DC Arc Model for Simulink Implementation
This paper presents a validated 2D axisymmetric multi-domain model implemented in MATLAB/Simulink that successfully simulates the coupled thermal, fluid, and electromagnetic dynamics of DC arcs across a 10–1500 A range, offering a robust tool for analyzing arc behavior in applications like circuit breakers and welding.
Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer
Electric arcs are the brilliant, humming bridges of electricity that form when current jumps through a gap in the air, turning the gas into a superheated, conducting fluid known as plasma. We see them in the sparks of a welding torch or the sudden flash of a short circuit, but they are also the invisible force that powers everything from industrial lighting to the safety mechanisms in our power grids. While these arcs are useful tools, they can also be dangerous, capable of melting metal or causing fires if they behave unpredictably. To keep our systems safe and efficient, engineers need to understand exactly how these arcs move, heat up, and interact with magnetic fields. For a long time, the best ways to study them were either too simple to capture the full picture or so complex that they required massive supercomputers, making it hard to use them in real-world design software.
A team of engineers and researchers has now created a new way to simulate these electric arcs that strikes a balance between accuracy and practicality. They developed a model that treats the arc not just as a line of electricity, but as a three-dimensional column of hot gas that flows and swirls inside a tube. By simplifying the complex physics of how heat, fluid motion, and magnetism interact, they were able to build a digital version of an arc that runs on standard engineering software used to design power systems. This approach allows them to watch, in a computer simulation, how the temperature rises in the center of the arc, how the gas moves, and how the magnetic field wraps around the current, all while the arc is held steady by the walls of a container.
The researchers focused on direct current arcs, which are common in solar power systems, electric vehicles, and modern microgrids. They set up a virtual experiment where an electric arc forms between two metal electrodes inside a cylindrical tube filled with air. The tube acts as a stabilizer, keeping the arc from wandering off. In their simulation, they tracked the behavior of the plasma as it heated up, flowed, and reacted to magnetic forces generated by the electricity itself. They did not just guess at the results; they solved the fundamental laws of physics that govern how fluids move and how heat spreads, but they did so in a way that breaks the problem down into small, manageable steps that a computer can solve quickly.
When they ran the simulation with currents ranging from a small 10 amps up to a powerful 1,500 amps, the results revealed a clear and predictable pattern. The hottest part of the arc was always right in the center, like the core of a flame, with the temperature dropping off sharply as it moved toward the cooler walls of the tube. The gas in the center moved along the length of the tube, while the magnetic field wrapped around the column, creating a force that helped squeeze the arc tight. The model showed that the arc reaches a stable state very quickly, settling into a steady voltage within a few thousandths of a second. This rapid stabilization is a crucial detail for engineers who need to know how fast a safety device must react to cut off a dangerous arc.
One of the most important findings was how the voltage of the arc changed as the current increased. In many electrical systems, higher current means higher voltage, but with an electric arc, the opposite happens. As the current gets stronger, the arc becomes a better conductor, and the voltage required to keep it going actually drops. The researchers found that their simulation matched this well-known behavior perfectly. They also tested arcs of different lengths, from 5 millimeters to 100 millimeters, and found that longer arcs required higher voltages to sustain the same current, a result that aligns with both classical theory and real-world measurements.
To ensure their model was reliable, they compared their simulation results against a famous mathematical formula used to describe arc behavior for decades. The numbers from their new, detailed simulation fit the old formula almost exactly, giving them confidence that their simplified approach captures the essential physics without needing the heavy computational power of more complex methods. This means the model can be used to study how arcs behave in real electrical circuits, such as those found in circuit breakers or welding machines, without needing to build a physical prototype first.
The work demonstrates that it is possible to create a detailed, physics-based picture of an electric arc that is simple enough to be used in everyday engineering tools. By capturing the way heat, flow, and magnetism work together, the researchers have provided a new tool for designing safer and more efficient power systems. Their model can help engineers predict how an arc will behave under different conditions, allowing them to design better protection systems for electric vehicles and solar farms. While the simulation is a digital representation and not a physical experiment, the consistency of its results with established laws and experimental data suggests it is a robust way to understand these powerful phenomena. This advancement offers a clearer path for managing the risks and harnessing the benefits of electric arcs in the growing world of direct current power.
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