Formation of external particle jets on a spherical particle bed subjected to strong explosive loading

We report the mechanism for the formation of external particle jets on a spherical particle bed subjected to strong explosive loading, revealing a critical dependence on particle size. Under strong explosive loading, the formation of external particle jets is primarily driven by a drag-coupled mechanism. We conducted Eulerian-Lagrangian simulations, with up to $2048^3$ effective cells and $1.8$ million tracked parcels on an adaptive mesh, for both small- and large-particle cases. Pronounced jets are observed only with small particles, alongside accelerated bed thickening. By defining characteristic inner and outer radii, the particle bed thickness evolution is quantified, showing an initial linear growth followed by a nonlinear deceleration. Particle dynamics analysis indicates that drag force dominates particle motion and jet formation during the nonlinear stage. The initial angular non-uniformity of the particle bed induces a non-uniform gas radial velocity. Through drag coupling, this flow asymmetry generates a radial velocity difference in small particles, thereby promoting pronounced jet formation, whereas large particles resist this drag-induced effect. The greater drag-induced deceleration on smaller particles leads to an increased velocity difference across the particle bed, explaining the accelerated thickening. A characteristic radius model that integrates the Gurney model for the linear stage with a drag-dominated deceleration model for the nonlinear stage is established and shows good agreement with numerical results across different particle sizes.