Fractal Analysis of Positive Pulsed Streamer Patterns in Supercritical Carbon Dioxide

Abstract

A positive pulsed prebreakdown in a needle-to-plane gap at CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> phases up to supercritical (SC) condition was observed by means of Schlieren imaging method. Our observations confirmed that the pattern of positive prebreakdown discharge was a treelike streamer independent of medium phase and that the SC phase led to streamer branches of higher complexity than those in the gas and liquid phases. Both streamer branches' complexity and fractal dimension variation of the developing streamer were quantitatively assessed by means of fractal analysis. Experimental results are summarized as follows: 1) SC carbon dioxide (SCCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) led to the greatest complexity of streamer branching in comparison with gas and liquid phases; 2) the fractal dimensions of gas, liquid, and SC phases of CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> were estimated to around D = 1.47, 1.60, and 1.73 with a coefficient of determination R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> >; 0.99; and 3) the fractal dimension D in SCCO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> stayed constant at around D = 1.7 during the streamer growth phase.