Session H5: Compressible Flow: Particle-shock Interactions and Explosions

The role of granular shocks in dust-layer dispersal by shock waves

Exactly how dust-layers are lifted and dispersed by shocks has been a longstanding question in compressible multiphase flow. Understanding the mechanism for this, however, is extremely important for early control of dust explosions. We address this problem by numerically solving a set of equations that couples a fully compressible representation of a gas with a kinetic-theory model for a granular medium (see Journal of Fluid Mechanics, (2016) 789:166-220) to simulate a shock propagating along the surface of a dust layer. The results show that the majority of the dispersed dust is lifted by hydrodynamic shear directly behind the shock wave. Simultaneously, large forces are produced behind the shock that compact the dust layer and create a granular shock. The effects from this granular shock on the surface of the dust layer destabilize the gas-dust boundary layer, which, in turn, enhances turbulence and the rate of dust dispersal.   

Simulations of Shock Wave Interaction with a Particle Cloud

Simulations of a shock wave interacting with a cloud of particles are performed in an attempt to understand similar phenomena observed in dispersal of solid particles under such extreme environment as an explosion. We conduct numerical experiments in which a particle curtain fills only 87{\%} of the shock tube from bottom to top. As such, the particle curtain upon interaction with the shock wave is expected to experience Kelvin-Helmholtz (KH) and Richtmyer-Meshkov (RM) instabilities. In this study, the initial volume fraction profile matches with that of Sandia Multiphase Shock Tube experiments, and the shock Mach number is limited to M$=$1.66. In these simulations we use a Eulerian-Lagrangian approach along with state-of-the-art point-particle force and heat transfer models. Measurements of particle dispersion are made at different initial volume fractions of the particle cloud. A detailed analysis of the evolution of the particle curtain with respect to the initial conditions is presented.   

Shock Interaction with Random Spherical Particle Beds

In this talk we present results on fully resolved simulations of shock interaction with randomly distributed bed of particles. Multiple simulations were carried out by varying the number of particles to isolate the effect of volume fraction. Major focus of these simulations was to understand 1) the effect of the shockwave and volume fraction on the forces experienced by the particles, 2) the effect of particles on the shock wave, and 3) fluid mediated particle-particle interactions. Peak drag force for particles at different volume fractions show a downward trend as the depth of the bed increased. This can be attributed to dissipation of energy as the shockwave travels through the bed of particles. One of the fascinating observations from these simulations was the fluctuations in different quantities due to presence of multiple particles and their random distribution. These are large simulations with hundreds of particles resulting in large amount of data. We present statistical analysis of the data and make relevant observations. Average pressure in the computational domain is computed to characterize the strengths of the reflected and transmitted waves. We also present flow field contour plots to support our observations.   

Shock Particle Interaction - Fully Resolved Simulations and Modeling

Currently there is a substantial lack of fully resolved data for shock interacting with multiple particles. In this talk we will fill this gap by presenting results of shock interaction with 1-D array and 3-D structured arrays of particles. Objectives of performing fully resolved simulations of shock propagation through packs of multiple particles are twofold, 1) To understand the complicated physical phenomena occurring during shock particle interaction, and 2) To translate the knowledge from microscale simulations in building next generation point-particle models for macroscale simulations that can better predict the motion (forces) and heat transfer for particles. We compare results from multiple particle simulations against the single particle simulations and make relevant observations. The drag history and flow field for multiple particle simulations are markedly different from those of single particle simluations, highlighting the effect of neighboring particles. We propose new models which capture this effect of neighboring particles. These models are called Pair-wise Interaction Extended Point Particle models (PIEP). Effect of multiple neighboring particles is broken down into pair-wise interactions, and these pair-wise interactions are superimposed to get the final model   

The Utility of Gas Gun Experiments in Developing Equations of State

Gas gun experiments have the potential to investigate material properties in various well defined shock conditions, making them a valuable research tool for the development of equations of state (EOS) and material response under shock loading. Gas guns have the ability to create shocks for loading to pressures ranging from MPa to GPa. A variety of diagnostics techniques can be used to gather data from gas gun experiments; resulting data from these experiments is applicable to many fields of study. The focus of this set of experiments is the development of data on the Hugoniot for the overdriven products EOS of PBX 9501 to extend data from which current computational EOS models draw. This series of shots was conducted by M-9 using the two-stage gas-guns at LANL and aimed to gather data within the 30-120 GPa pressure regime. The experiment was replicated using FLAG, a Langrangian multiphysics code, using a one-dimensional setup which employs the Wescott Stewart Davis (WSD) reactive burn model. Prior to this series, data did not extend into this higher range, so the new data allowed for the model to be re-evaluated. A comparison of the results to the experimental data reveals that the model is a good fit to the data below 40 GPa. However, the model did not fall within the error bars for pressures above this region. This is an indication that the material models or burn model could be modified to better match the data.   

A Scale Invariant Equation of State for Gruneisen Materials

Scale-invariant equations of state are required for the existence of the Noh, Sedov, and Guderley compressible flow similarity solutions in the general case. All of these problems are self-similar and their solutions are independent of space, time, and the hydrodynamic state of the system. This work establishes a new equation of state with hydrodynamic scaling properties that may be used to approximate Gruneisen materials. The Gruneisen equation of state is relevant for materials whose atoms are limited to small vibrations; however the Gruneisen EOS is shown to lack the form necessary to yield a scaling solution in the general case. A Virial EOS with coefficients reminiscent of Gruneisen materials is proposed and derived, and shown to possess the desired hydrodynamic scaling properties. The divergence of the approximation from the true Gruneisen EOS under strong shock conditions is discussed.   

Analysis of Computational Models of Shaped Charges for Jet Formation and Penetration

Shaped charges came into use during the Second World War demonstrating the immense penetration power of explosively formed projectiles and since has become a tool used by nearly every nation in the world. Penetration is critically dependent on how the metal liner is collapsed into a jet. The theory of jet formation has been studied in depth since the late 1940s, based on simple models that neglect the strength and compressibility of the metal liner. Although attempts have been made to improve these models, simplifying assumptions limit the understanding of how the material properties affect the jet formation. With a wide range of material and strength models available for simulation, a validation study was necessary to guide code users in choosing models for shaped charge simulations. Using PAGOSA, a finite-volume Eulerian hydrocode designed to model hypervelocity materials and strong shock waves developed by Los Alamos National Laboratory, and experimental data, we investigated the effects of various equations of state and material strength models on jet formation and penetration of a steel target. Comparing PAGOSA simulations against modern experimental data, we analyzed the strengths and weaknesses of available computational models. LA-UR-16-25639   

Physical and Electrical Measurements of Different Metals used in Exploding Wires

Implementation of the energy density metric has made it possible to better understand the physics of exploding wires. When applying the energy density metric to exploding wire experiments in a porous material bed, results suggest a link between characteristics of wire materials (e.g. their electrical properties during burst and the physical work done by the bursting wire). Previous work has focused on qualitative comparisons of current and voltage waveforms and the qualitative comparison of Schlieren images of wire shocks in air. In these experiments, the wires were all buried in a porous media allowing the simultaneous capture of accurate current and voltage to observe the energy density at burst, while simultaneously observing the amount of time the wire took to compress the porous media to a 1 mm deep crater. Observing the physical compression of the porous bed in time in concert with the energy density allows a link to be established between the measured electrical signals and the physical work done by the exploding wire. This research allows a more quantitative link to be established between the electrical energy and the physical energy expended by an exploding wire, allowing for the development of more accurate models and a better understanding of exploding wire physics.   

Jetting instability of a shocked cylindrical shell of solid particles.

Explosive dispersion of cylindrical or spherical shells of liquid or solid particles features jetting phenomena and the underlying mechanism generating these is not well understood. Previous studies have indicated that the jets originate from structures formed during a very short time interval after the passing of the shock wave. This study utilizes LES simulations to examine the jetting phenomena occurring during impulsive dispersal of solid particles. The problem considered is the dispersion of a ring of particles inside a Hele-Shaw cell by a shock-wave, as previously examined experimentally by [Rodriguez, V., Saurel, R., Jourdan, G., & Houas, L. (2013). Solid-particle jet formation under shock-wave acceleration. Physical Review E, 88(6), 063011]. Various degrees of coupling between the flow field and the solid particles are tested, and results are compared. The simpler case of replacing the shock-tube by a constant high pressure and high density region inside the solid particle ring is also examined and compared to the original problem.   

Analysis of Xrage and Flag High Explosive Burn Models with PBX 9404 Cylinder Tests

High explosives are energetic materials that release their chemical energy in a short interval of time. They are able to generate extreme heat and pressure by a shock driven chemical decomposition reaction, which makes them valuable tools that must be understood. This study investigated the accuracy and performance of two Los Alamos National Laboratory hydrodynamic codes, which are used to determine the behavior of explosives within a variety of systems: xRAGE which utilizes an Eulerian mesh, and FLAG with utilizes a Lagrangian mesh. Various programmed and reactive burn models within both codes were tested, using a copper cylinder expansion test. The test was based off of a recent experimental setup which contained the plastic bonded explosive PBX 9404. Detonation velocity versus time curves for this explosive were obtained from the experimental velocity data collected using Photon Doppler Velocimetry (PDV). The modeled results from each of the burn models tested were then compared to one another and to the experimental results using the Jones-Wilkins-Lee (JWL) equation of state parameters that were determined and adjusted from the experimental tests. This study is important to validate the accuracy of our high explosive burn models and the calibrated EOS parameters, which are important for many research topics in physical sciences.