T. L. Jackson

Shock interaction with one-dimensional array of particles in air

In this paper, we present axisymmetric numerical simulations of shock propagation in air over an aluminum particle for Mach numbers up to 10. The numerical method is a finite-volume based solver on a Cartesian grid that allows for multi-material interfaces and shocks. Validation of the solver is demonstrated by comparing to existing experimental data. We compute the unsteady inviscid drag coefficient as a function of time, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with Mach number. Furthermore, for supercritical Mach numbers, we show that the inviscid steady-state drag asymptotes to a non-zero value due to the presence of a bow shock formed just upstream of the particle. Using this information, we also present a simplified point-particle force model that can be used for mesoscale simulations. Finally, we investigate the dynamics of a shock propagating over a 1-D array of particles aligned in the flow direction. We show that the maximum drag coefficient ...

Pore collapse in an energetic material from the micro-scale to the macro-scale

We examine a pore in an energetic material whose collapse following the passage of a strong genesis shock wave, the subsequent ignition of reactive gases within it produced by pyrolysis at the pore boundary, and the emission of shock waves as a consequence of this ignition, can lead to a detonation. The interest in such a problem arises from the interest in knowing the sensitivity and therefore the safe-handling protocol of energetic materials. We follow the initial pore collapse, before melting occurs, using rational analytical strategies, but to describe the later stages, with full coupling between the physics in the condensate and those in the pore cavity, we describe a numerical strategy. The results provide a description of the power deposition into the energetic material and lead to a power deposition model for the macro-scale, one that encompasses a number of pores. For suitable parameter choices, shock waves generated by the pores interact to form a detonation upstream of the genesis shock.

Third-order thermo-mechanical properties for packs of Platonic solids using statistical micromechanics

Obtaining an accurate higher order statistical description of heterogeneous materials and using this information to predict effective material behaviour with high fidelity has remained an outstanding problem for many years. In a recent letter, Gillman & Matouš (2014 Phys. Lett. A 378, 3070–3073. ()) accurately evaluated the three-point microstructural parameter that arises in third-order theories and predicted with high accuracy the effective thermal conductivity of highly packed material systems. Expanding this work here, we predict for the first time effective thermo-mechanical properties of granular Platonic solid packs using third-order statistical micromechanics. Systems of impenetrable and penetrable spheres are considered to verify adaptive methods for computing n-point probability functions directly from three-dimensional microstructures, and excellent agreement is shown with simulation. Moreover, a significant shape effect is discovered for the effective thermal conductivity of highly packed composites, whereas a moderate shape effect is exhibited for the elastic constants.

Numerical investigation of shock interaction with one-dimensional transverse array of particles in air

In this paper, we present numerical simulations of shock propagation in air over a one-dimensional transverse array of particles. Simulations are carried out by varying the particle spacing and shock Mach number. We compute the unsteady inviscid drag coefficient as a function of time and make relevant comparisons to that for a single particle. We find that deviations in the drag coefficient in time from that of a single particle can be correlated to the acoustic-particle interaction time. Finally, we investigate and classify the interaction of the bow shocks in front of the transverse array of particles.

Numerical simulation of fluid flow through random packs of cylinders using immersed boundary method

The macroscopic properties of two-dimensional random periodic packs of monomodal and bimodal cylinders are investigated by means of numerical methods. We solve the unsteady, two-dimensional Navier-Stokes equations on a staggered Cartesian grid and use the immersed boundary method to treat internal flow boundaries. A number of verification problems for the numerical method are presented. The effects of porosity, diameter ratio, large-to-total particle ratio, and Reynolds number on the macroscopic permeability are studied. For small Reynolds numbers, we show that the permeability can be correlated to the underlying microstructure by means of a suitably defined statistical descriptor, the mean shortest Delaunay edge. With proper scaling, the results for bimodal cylinders collapse onto the data for monomodal cylinders, which can then be fitted with a universal curve. For larger Reynolds numbers we show that a modified Forchheimer equation can characterize the flow.

Density-based kinetics for mesoscale simulations of detonation initiation in energetic materials

In this work we present one- and two-dimensional mesoscale simulations of detonation initiation in energetic materials. We solve the reactive Euler equations, with the energy equation augmented by a power deposition term. The reaction rate at the mesoscale is modelled using a density-based kinetics scheme, adapted from standard ‘Ignition and Growth’ models. The deposition term is based on previous results of simulations of void collapse at the microscale, modelled at the mesoscale as hot spots. For an isolated hot spot in a homogeneous medium, it is found that a critical size of the hot spots exists. If the hot spots exceed the critical size, initiation of detonation can be achieved. For sub-critical hot-spot sizes, we show that it takes a collection of hot spots to achieve detonation. We also carry out two-dimensional mesoscale simulations of random packs of HMX crystals in a binder, and show that the transition between no detonation and detonation depends on the number density of the hot spots, the initial radius of the hot spot, the post-shock pressure of an imposed shock, and the amplitude of the power deposition term.

Shock interaction with deformable particles using a constrained interface reinitialization scheme

In this paper, we present axisymmetric numerical simulations of shock propagation in nitromethane over an aluminum particle for post-shock pressures up to 10 GPa. We use the Mie-Gruneisen equation of state to describe both the medium and the particle. The numerical method is a finite-volume based solver on a Cartesian grid, that allows for multi-material interfaces and shocks, and uses a novel constrained reinitialization scheme to precisely preserve particle mass and volume. We compute the unsteady inviscid drag coefficient as a function of time, and show that when normalized by post-shock conditions, the maximum drag coefficient decreases with increasing post-shock pressure. We also compute the mass-averaged particle pressure and show that the observed oscillations inside the particle are on the particle-acoustic time scale. Finally, we present simplified point-particle models that can be used for macroscale simulations. In the Appendix, we extend the isothermal or isentropic assumption concerning the p...

Direct detonation initiation with thermal deposition due to pore collapse in energetic materials – towards the coupling between micro- and macroscale

In this work we investigate the initiation of detonations in energetic materials through thermal power deposition due to pore collapse. We solve the reactive Euler equations, with the energy equation augmented by a power deposition term. The deposition term is partially based on previous results of simulations of pore collapse at the microscale, modelled at the macroscale as hotspots. It is found that a critical size of the hotspots exists. If the hotspots exceed the critical size, direct initiation of detonation can be achieved even with a low power input, in contrast to the common assumption that a sufficient power is necessary to initiate detonation. We show that sufficient power is necessary only when the size of the hotspots is below the critical size. In this scenario, the so-called ‘explosion in the explosion’, the initial ignition does not lead to a detonation directly, but detonation occurs later as a result of shock-to-detonation transition in the region processed by the shock wave generated by the initial ignition.

Numerical simulation of fluid flow through random packs of polydisperse cylinders

The macroscopic properties of two-dimensional random periodic packs of polydisperse cylinders are investigated by means of numerical methods. We solve the unsteady, two-dimensional Navier-Stokes equations on a staggered Cartesian grid and use the immersed boundary method to treat internal flow boundaries. The effects of porosity, polydispersity, and Reynolds numbers on the macroscopic permeability are studied. For small Reynolds numbers, we show that the permeability can be correlated to the underlying microstructure by means of a suitably defined statistical descriptor, the mean shortest Delaunay edge. With proper scaling, the results for polydisperse cylinders collapse onto the data for monodisperse cylinders, which can then be fitted with a universal curve. We also carry out a statistical analysis of the permeability computed for 500 samples and show that rare events, where the permeability lies outside the mean plus/minus three times the standard deviation, are possible. Finally, for larger Reynolds numbers, we show that a modified Forchheimer equation can characterize the flow.

Numerical simulation of fluid flow through random packs of ellipses

The effect of particle shape on permeability is investigated by means of numerical methods of fluid flow through two-dimensional, periodic, random packs of ellipses. We solve the unsteady Navier-Stokes equations on a Cartesian grid and use the immersed boundary method to treat internal flow boundaries. The effect of porosity, aspect ratio, and Reynolds number on the macroscopic permeability and tortuosity is studied. For small Reynolds numbers, it is shown that an area-preserving deformation of a pack of disks, generating a pack of ellipses, can lead to significant variations in the permeability. However, if the ellipses are randomly packed, so that the alignment of their axes is random, the shape effect is small. Irrespective of orientation, the aspect ratio has a strong effect on the tortuosity at all values of the porosity. We also show that the parameters in the Carman-Kozeny equation are not constant but are functions of porosity and aspect ratio. For larger Reynolds numbers, we show results for random packs of bidisperse and polydisperse cylinders, as well as for ellipses. We find that a modified Forchheimer equation can well characterize the flow.