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

TL;DR

The paper addresses how external particle jets form on a spherical particle bed subjected to strong explosive loading, revealing a critical dependence on particle size. It employs a high-fidelity Eulerian–Lagrangian CMP-PIC framework with AMR to resolve gas–particle interactions and quantify jet formation via inner and outer radii $R_I$ and $R_O$, comparing small ($d_p$) and large particle regimes. The key finding is that drag-coupled dynamics dominate in the nonlinear stage, causing a larger velocity difference across the bed and pronounced jets for small particles, while large particles resist jetting due to higher inertia. A two-phase model combines a linear Gurney-based acceleration with a drag-dominated nonlinear deceleration to predict the evolution of $R_I$ and $R_O$ for both particle sizes, showing good agreement with simulations and aligning with experimental observations. This work provides mechanistic insight into jet formation under strong explosions and offers a framework extendable to cylindrical geometries and more complex material behaviors.

Abstract

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.

Figures (13)

• Figure 1: (a) Dispersal of FE-110 particles with average sizes $d_{p}=32.1~\mathrm{\upmu m}$goroshin2016measurement. Image courtesy of David Frost, private communication, 2025. (b) Schematic of the 3D explosive dispersal system set-up in the numerical simulation. (c) Numerical results for case DP50 at time $t = 5\mathrm{ms}$. The left panel displays the parcel distribution, colored by the parcel radial velocity, while the right panel shows the iso-surfaces of $|\boldsymbol\omega_{f}|=3\sqrt{\langle\Omega\rangle}$, mapped with the radial coordinate. Here $\Omega =|\boldsymbol\omega_{f}|^{2}/2$ denotes the enstrophy and $\langle\cdot\rangle$ represents the volume average over $\mathcal{D}$. Note that the visualized domain consists of two mirrored $1/8$-spherical sections, whereas the actual computation was performed only on a single $1/8$-spherical domain.
• Figure 2: Evolution of parcel distributions, characteristic radii and pressure fields in cases (a) DP50 and (b) DP450. Parcels are colored by the parcel radial velocity, with the inner radius $R_{I}$ and outer radius $R_{O}$ marked by blue and red dashed lines, respectively. The pressure contour is color-coded from white to blue within the range from $0.7$ to $1.4~\mathrm{bar}$. For clarity, the images at $t = 0~\mathrm{ms}$ are magnified six times.
• Figure 3: (a) Evolution of characteristic radii in cases DP50 (dashed lines) and DP450 (solid lines). (b) Evolution of the particle bed thickness.
• Figure 4: Shell-averaged flow field physical quantities distributed along the radial direction at time $t=2.5~\mathrm{ms}$. The blue and red dashed lines respectively mark the characteristic radius positions of cases DP50 and DP450.
• Figure 5: Scatter plots of the radial velocity and radial acceleration of parcels in the cases (a) DP50 and (b) DP450 at $t=2.5~\mathrm{ms}$. The dashed lines respectively mark the characteristic radius positions.