Typical view of positive streamer branching in a liquid dielectric. (a) Experimental image of a positive streamer initiated from a needle electrode 16,18,36 and (b) 3-D modeling result of a corresponding case (iso-surface plot of the electric field distribution). The streamer structures are qualitatively similar in experiments and simulations. The fractal structure of the streamer tree in the experimental image makes it possible to compare the modeling result also with other nodes of the tree including the one at the needle electrode tip.
IEC 60060 lightning impulse voltage (non-dimensional, ) with rise-time tr (10%–90% of peak voltage) versus non-dimensional time, generated with subtracting two exponential functions. 27 In this paper, the rise-time (tr ) varies in the range of 1 ns–100 ns, while the fall-time (τ 1 is set to 1 μs for all case studies).
Iso-surface plot of electric field distribution as modeling result of streamer is compared with corresponding experimental image in the inset image. Definite breakdown voltage, UDBD , for the modeling geometry (gaplength, d = 25 mm) is equal to 95 kV. The initiation voltage for the modeling geometry (electrode tip radius, ri = 40 μm) is 30 kV. In the experimental data, the applied voltages are expressed in terms of streamer initiation voltage, Vi , and 50% breakdown voltage, UBD , which is the impulse peak at which the dielectric breaks down in half of the discharge tests. For each panel the modeling data is expressed, followed by brief information about the related experiment in Table II .
Symmetrical streamer branching due to symmetric initial electron disturbance distribution (planes of symmetry are x = 0 and y = 0) showing that the numerical instabilities are minor enough to guarantee that the branching occurs due to physical inhomogeneities. The propagation direction of the main streamer column is in −z direction. The left panel shows iso-surface plots of the electric field generated by streamer branching from different view planes (xy, xz, and xy plane views).
Streamer head configuration. Three characteristic lengths, r a , r b , and d, are defined based on the volume charge density distribution (0.5ρmax to ρmax ) to study the streamer head instability growth, which ultimately causes the branching. Numerical modeling shows that the chance of branching increases as the head curvature ratio α = r a /d increases. Our previous studies show that increasing either applied voltage peak or applied voltage rate of rise would increase α.
Identification of streamer tree number of branches based on the streamer head geometry (characteristic lengths defined in Figure 6 ). Colors show the applied voltage rise-times: black (1 μs), blue (100 ns), purple (10 ns), and red (1 ns). Marker shapes indicate the applied voltage peaks: 130 kV (*), 200 kV (★), 250 kV (●), 300 kV (▼), 350 kV (▪), 400 kV (♦), and 500 kV (×). The points are obtained from taking average from ten different inhomogeneity distributions, but with the same inhomogeneity radius, maximum intensity, and density of 5 μm, 104 Cm−3, and 1011 m−3, respectively.
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