The fractal behavior of explosively driven product gasses with initial surface perturbation

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 impact of dominant initial surface perturbations, represented by a sinusoidal azimuthal variation in radius, is assessed. Perturbations of 10/π cycle/rad and 20/π cycle/rad were used, and a smooth, non-perturbed case was used as a baseline measurement. On the two tested charge masses of 105 g and 880 g, the effective angular wave numbers of the perturbations varied between k = 384.6 rad/m and k = 1574 rad/m. The early time product gas, or fireball, expansion was captured using high-speed cameras. Gas interface location profiles are extracted using automated image processing algorithms. The Hausdorff dimension was estimated using boxcounting algorithms on the extracted profiles. At microsecond time scales, the gas boundary develops fractal-like properties that show similar scaling to explosive fireball radius-time scaling. Despite apparent structural differences in fireball evolution, perturbations do not appear to have a significant effect on the evolution of the fractal dimension, with variations remaining inside the measurement uncertainty for the fractal dimension.