Effects of Initial Perturbations in the Early Moments of an Explosive Dispersal of Particles

Abstract

Recent experiments have shown that when a dense layer of solid particles surrounding a high-energy reactive material is explosively dispersed, the particles cluster locally leading to jetlike patterns. The formation of these coherent structures has yet to be fully understood and is believed to have its origin in the early moments of the explosive dispersal. This paper focuses on the early moments of an explosive dispersal of particles. In particular, the effect of initial perturbations on both the gas and particulate phase is investigated, considering heavy particles with a low initial particle volume fraction. Two-dimensional simulations are carried out, and results suggest that a distinctive heterogeneity in the form of a single wavelength perturbation in the rapidly expanding detonation products does not have a significant impact on the early evolution of neither the gas phase nor the cloud of particles. In contrast, the equivalent distinctive heterogeneity in the initial particle volume fraction distribution lingers for the duration of our simulations. Developing instabilities in the gas phase and at the inner- and outer-most front of the particle bed display a dominant wavelength equal to the wavelength of the initial perturbation in the particle volume fraction.

Effect of a bimodal initial particle volume fraction perturbation in an explosive dispersal of particles

“…We restrict ourselves to a two dimensional domain by considering only a unit cell in the axial direction. The r-θ plane (with a maximum radius of 0.6 m) is identical to the one described in [8] with a 512 x 512 cell Cartesian mesh contorted into an inner cylinder of radius 0.0038 m that contains the explosive (pentaerythritol tetranitrate -PETN) charge. Surrounding the charge we have a polar mesh with 1050 and 2048 cells in the r and θ directions respectively.…”

“…For the particles, x p i and u p i are the position and velocity vectors, T p i is the particle temperature, m p i is the particle mass and C p i is the specific heat of the particle. The physical models for F gp i , F pp i , G gp i and Q gp i are identical to those used in [8], where their specific definitions can be found. Note that the models for the quasi-steady and viscous-unsteady forces which make up part of the gas-particle interaction force are functions of the Reynolds number, Mach number and local particle volume fraction.…”

“…The fluxes are computed using a second order accurate AUSM+ scheme [10] and the gradients are modified using a WENO reconstruction technique (see reference in [8]). The time integration is carried out using a third order accurate Runge-Kutta scheme.…”

“…Their results showed that a single mode initial perturbation in particle volume fraction was sustained at much later times (500 μs after detonation). Here, we extend the study in [8] considering two mode perturbations (as opposed to a single mode) while retaining the same particle and mass ratio constraints. Of particular interest is the modal interaction that is known to promote growth and transition to turbulence in classic RT and RM instability.…”

“…Previously, Annamalai et al [8] investigated the effects of single mode perturbations on the particle cloud. They considered large particles and a particle to explosive mass ratio much greater than one.…”