2-D and 3-D Radiative Transfer Calculation in Arc Plasmas Burning in Environmentally Friendly High-Voltage Switchgear

This contribution reports on the radiation transfer calculation in high-voltage switching arcs burning in CO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> + O<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and C<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub>F<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sub>N+CO<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> in a self-blast circuit breaker. The discrete ordinates method (DOM) is applied to a cylindrical arc column with a radius of 0.01 m and a length of 0.04 m to calculate the effect of radiation in a 3-D space in terms of radiative flux divergence. Then, a simplified yet much faster 2-D model is tested for its ability to approximate the accurate radiation transfer results. The calculation covers a broad frequency spectrum, from mid-infrared to extreme ultraviolet bands. The filling gas pressure is six bar absolute, and the arc column corresponds to the currents in the range of 15–50 kA. Typical temperature profiles are used, and the calculation results are presented and analyzed. The 2-D model uses about 20% of the calculation time by 3-D DOM. With the cases under investigation, it has been shown that while the 2-D model produces results within only 60% proximity to those of the 3-D model, it does capture the crucial features and patterns of the 3-D model, such as the ratio of net emission to net absorption in the radial direction and the start and end temperature of the net absorption region across the arc radius. Both models predict an absorption ratio between 40% and 72%, and the start temperature of the net absorption region is 0.66T<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> to 0.83T<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub>, where T<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> is the highest temperature located on the axis of the arc column.