Fractal Analysis of Positive Streamer Patterns in Transformer Oil-Based TiO2 Nanofluid

In this paper, prebreakdown streamers in transformer oil and transformer oil-based TiO
₂
nanofluid were observed by the schlieren method under positive lightning impulse voltage. Streamers in the nanofluid have numerous branches with much shorter length, whereas in the pure oil, they exhibit only certain filaments with longer length. The discrepancy in positive streamer pattern of both oils is further investigated under a range of applied voltages. The complexity of streamer patterns was quantitatively described using the fractal analysis method. Results indicate that the fractal dimension of streamer patterns shows different changing tendencies in both oils, and it keeps higher value in the nanofluid than that in pure oil during the whole propagation process, well corresponding with streamer propagating structures. Moreover, a new parameter, the ratio of fractal dimension to propagation length (D/L), is introduced to classify the complex streamer patterns for the first time. Three propagation zones in both nanofluid and pure oil are clearly categorized by the value of D/L, providing a quantitative way to distinguish the streamer patterns.