Optimization of C₁ Parameter in ARC Plasma Turbulence Simulation: Based on Energy Balance and Turbulence Characteristics

Arc in circuit breakers is a common and important phenomenon in the power system, and its characteristics play a crucial role in the safety and stability of electrical equipment. However, the high temperature, high-speed airflow, and instability of the arc make its simulation more complex. Turbulence is one of the main characteristics of arc behavior, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{k}-\varepsilon$</tex> turbulence model, as a kind of the classic turbulence model, is widely used in the field of engineering simulation. In this model, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> parameter directly affects the model's description of turbulent energy transfer, so its selection is crucial for the accuracy of simulation results. This article is based on the analysis of standard <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{k}-\varepsilon$</tex> turbulence models and focuses on the key role of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> parameter in the turbulence dissipation rate equation. Starting from energy transfer balance and turbulence characteristics, the influence of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> parameter on the turbulence characteristics of arc plasma is deeply studied. This article comprehensively considers the complexity of turbulent structures and the intensity of energy conversion and derives the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> parameter setting criteria in arc plasma simulation. To verify the proposed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> parameter setting criteria, different <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> values were selected. Arcing simulation tests were conducted under the conditions of 80kA current, the time constant of 120ms (T100a), and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> values of 1.1, 1.44, and 1.6, respectively. Comparing the simulation results, further confirms the influence of the selected <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{C}_{1}$</tex> parameter on the turbulence characteristics of arc plasma, thereby providing a more accurate turbulence simulation method and deepening the understanding of arc behavior under high current conditions. This study provides valuable references for the reliability and stability of power systems