A breakup model of Jetting formation of Explosively Loaded Granular Shells
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A breakup model of Jetting formation of Explosively Loaded Granular Shells Kun Xue State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China. Nottingham Centre for Geomechanics, The University of Nottingham, Nottingham, NG7 2RD, UK. ABSTRACT This paper investigates the underlying physics governing the explosion driven expansion and fragmentation of spherical beds packed of partially saturated sand with varying mass fractions of interstitial oil. The breakup onset of the sand shells is characterized by the formation of fragments/agglomerates consisting of a large number of constituent grains, which in later time present themselves as prolific and regular jetting streams. Test data show a postponed jetting formation when sand shells are subject to the explosion with a higher detonation velocity, meanwhile a reduced jet mass scale is observed. A kinetic energy driven breakup model is proposed based on the instability criterion involving the opposing forces of stabilizing inertial pressures and destabilizing viscous resistance. This analytical model is capable of predicting the onset of granular material fragmentation as well as the characteristic fragment size, which is consistent with the experimental results. INTRODUCTION The particle layer subjected to the central explosion is observed to fragmentize into a number of fragments or agglomerates with the dimension much larger than the constituent grains [1-5]. These agglomerates later evolve into jetting streams which travel ballistically while shedding mass along the trajectories. Although previous studies often associated the jetting with the Rayleigh Taylor (RT) instability occurring at a material interface whenever a dense fluid is decelerated by a light fluid [1-3]. The multiphase explosion simulations carried out by Millen et al.[4] do not support RT instability as a plausible mechanism because it would take much longer time than observed for RT instability to grow to a discernable scale. In this work, an alternative kinetic energy driven fragmentation model is presented to estimate the onset of the jetting formation and resulting jet size. In this work, we begin with the experimental observations of the formation and development of jetting structures arising from dry sand layers surrounding the different types of central explosive charges with distinct detonation velocities. The critical diameters of the expanding sand shells at the onset of jetting and the ensuing characteristic mass of fragments have a strong correlation with the explosive. An analytical kinetic energy driven fragmentation model is then established to estimate the onset of sand shell breakup and resulting jet size. The predicted instability onset EXPERIMENT
The experiments were carried out using spherical explosive charges wrapped up by quartz sand with grains over a size range of 824-900 μm. The experimental shells consist of two thin plastic concentric spheres with the diameters of 40 mm and 130 mm, respectively. Two types of explosiv
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