We report reactive molecular dynamics simulations using the ReaxFF reactive force field to examine shock-induced hot-spot formation followed by detonation initiation in realistic (2.7 million atoms) models of polymer bonded explosives (PBX) with nonplanar interfaces. We considered here two energetic materials (EMs) pentaerythritol tetranitrate (PETN), a common EM for PBX, and silicon pentaerythritol tetranitrate (Si-PETN), which is so extremely sensitive that it has not been possible to characterize its shock properties experimentally. In each case the EM was embedded in a hydroxyl-terminated polybutadiene (HTPB) based polymer binder matrix to form a model of PBX that has a periodic sawtooth nonplanar interface. For the cases in which the shock wave propagates from the EM to polymer (EM→poly), we observed that a hot spot arises from shear localization at the convex polymer asperity. For the case in which the shock direction is inverted (shock wave propagates from the polymer to the EM, EM←poly), we find t...

Highly Shocked Polymer Bonded Explosives at a Nonplanar Interface: Hot-Spot Formation Leading to Detonation

We investigate the Richtmyer-Meshkov instability (RMI) in converging geometries analytically and computationally. The linear, or small amplitude, regime is first covered as it is the onset to subsequent non-linear stages of the perturbation growth. While the plane interaction of a shock with a slightly perturbed density interface is classically viewed as a single interface evolving as baroclinic vorticity have been initially deposited on it, we propose a simple but more complete model characterizing the early interaction between the interface and the receding waves produced by the shock-interface interaction, in the case of a reflected shock. A universal time scale representing the time needed by the RMI to reach its asymptotic growth rate is found analytically and confirmed by ideal gas computations for various incident shock Mach numbers MI and Atwood ratios A, and could be useful especially for experimentalists in non-dimensionalizing their data. Considering again linear perturbations, we then obtain a general analytical model for the asymptotic growth rate reached by the instability during the concentric interaction of an imploding/exploding cylindrical shock with a cylindrical interface containing three-dimensional orthogonal perturbations, in the azimuthal and axial directions. Stable perturbations, typical of the converging geometry, are discovered. Comparisons are made with simulations where the effects of compressibility, wave reverberations, and flow convergence are isolated. Azimuthal and axial perturbation evolution are compared with results obtained for the plane RMI at comparable initial wavelengths. A second interaction occurs when the transmitted shock, produced by the incident converging shock impacting the interface, converges to the axis and reflects to reshock the initially accelerated interface. This leads to highly non-linear perturbation growth. To isolate the complex wave interaction process, the interface is considered initially unperturbed so that the flow is radially symmetric. An accurate visualization procedure is performed to characterize the underlying physics behind the reshock event. We study extensively the cylindrical and spherical geometry, for various MI and for the air → SF6 (A=0.67) and SF6 → (A=-0.67) interactions, and draw important differences with the equivalent plane configuration. A hybrid, low-numerical dissipation/shock-capturing method, embedded into an adaptive mesh refinement framework is optimized in order to achieve large-eddy simulations of the self-similar cylindrical converging shock-driven RMI and the turbulent mixing generated by the reshock. Computations are produced for MI=1.3 and 2.0, and for air -> SF6 SF6 -> air interfaces. We develop statistics tools to study extensively the growth of the turbulent mixing zone using cylindrical averages as well as various measures such as probability density functions of the mixing and turbulent power spectra, with the objectives of understanding the turbulent mixing in this particular geometry.

Richtmyer-Meshkov Instability in Converging Geometries

This review is devoted to cumulative hydrodynamic processes in a plasma and to the possibility of using them for controlled thermonuclear fusion. The cumulation of convergent shock waves and the mechanisms of their limitation are discussed in greatest detail. Results are presented of study of non-one-dimensional cumulative shock waves, which had practically not yielded to analysis until recently.

Hydrodynamic cumulative processes in plasma physics

The behaviour of an initially planar shock wave propagating into a linearly convergent wedge is investigated experimentally and numerically. In the experiment, a 25° internal wedge is mounted asymmetrically in a pressure-driven shock tube. Shock waves with incident Mach numbers in the ranges of 1.4–1.6 and 2.4–2.6 are generated in nitrogen and carbon dioxide. During each run, the full pressure history is recorded at fourteen locations along the wedge faces and schlieren images are produced. Numerical simulations performed based on the compressible Euler equations are validated against the experiment. The simulations are then used as an additional tool in the investigation.

The linearly convergent geometry strengthens the incoming shock repeatedly, as waves reflected from the wedge faces cross the interior of the wedge. This investigation shows that aspects of this structure persist through multiple reflections and influence the nature of the shock-wave focusing. The shock focusing resulting from the distributed reflected waves of the Mach 1.5 case is distinctly different from the stepwise focusing at the higher incoming shock Mach number. Further experiments using CO_2 instead of N_2 elucidate some relevant real-gas effects and suggest that the presence or absence of a weak leading shock on the distributed reflections is not a controlling factor for focusing.

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Shock focusing in a planar convergent geometry: experiment and simulation

Spherical converging shock waves are produced in a conventional shock tube with a circular cross-section. Initially, plane shocks are transformed into the shape of a spherical cap by means of a smo ...

Energy concentration by spherical converging shocks generated in a shock tube

The behaviour of an initially plane, strong shock wave propagating into a conical convergence is investigated experimentally and theoretically. In the experiment a 10° half-angle cone is mounted on the end of a pressure-driven shock tube. Shock waves with initial Mach numbers varying from 6.0 to 10·2 are generated in argon a t a pressure of 1·5 Torr. During each run local shock velocities a t several positions along the cone axis are measured using a thin multi-crystal piezoelectric probe inserted from the vertex. This technique produces accurate velocity data for both the incident and reflected shock waves. In the corresponding analysis, a simplified characteristics method is used to obtain an approximate solution of the axisymmetric diffraction equations derived by Whitham (1959).
Both the shock velocity measurements and the axisymmetric diffraction solution confirm that the incident shock behaviour is dominated by cyclic diffraction processes which originate at the entrance of the cone. Each diffraction cycle is characterized by Mach reflexion on the cone wall followed by Mach reflexion on the axis, These cycles evidently persist until the shock reaches the cone vertex, where the measured velocity has increased by as much as a factor of three. Real-gas effects, enhanced in the experiment by increasing the initial Mach number and decreasing the pressure, apparently alter the shock wave behaviour only in the region near the vertex. Velocity measurements for the reflected shock within the cone show that the shock velocity is nearly constant throughout most of the convergence length.

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Erik Storm

Papers

An investigation of shock strengthening in a conical convergent channel