The fractal scaling of explosively driven gas clouds

Characterization of the interface between explosive product gases and ambient air in an explosion is a complicated task due to the turbulent mixing and inherently three-dimensional expansion of the interface. This study aims to quantify the evolution of the interface as a temporally-varying fractal dimension. The Hausdorff or fractal dimension of the two-dimensional slices of an explosively driven gas cloud has been measured from multiple angles for explosions at varying scales. Experimental studies were conducted with explosives from the gram scale to the kilogram scale. Gas cloud profiles are extracted using automated image processing algorithms. The Hausdorff dimension is estimated using boxcounting algorithms on the extracted profiles. Variations in explosive charge mass are used to identify scaling for the Hausdorff dimension. When scaled with time, the fractal dimension evolution as a function of time appears to collapse to a single curve. Following an initial expansion, the fractal dimension tends toward a value of 4/3 before plateauing. Luminous early time fireballs collapse well to this curve, and demonstrate axial symmetry in estimated fractal dimension for symmetric charges. Late time fireballs do not appear to collapse to the same curve, indicating a change in underlying expansion and mixing regime for the product gases.