Cole Yarrington

A physically-based Mie–Grüneisen equation of state to determine hot spot temperature distributions

A physically-based form of the Mie–Grüneisen equation of state (EOS) is derived for calculating 1d planar shock temperatures, as well as hot spot temperature distributions from heterogeneous impact simulations. This form utilises a multi-term Einstein oscillator model for specific heat, and is completely algebraic in terms of temperature, volume, an integrating factor, and the cold curve energy. Moreover, any empirical relation for the reference pressure and energy may be substituted into the equations via the use of a generalised reference function. The complete EOS is then applied to calculations of the Hugoniot temperature and simulation of hydrodynamic pore collapse using data for the secondary explosive, hexanitrostilbene (HNS). From these results, it is shown that the choice of EOS is even more significant for determining hot spot temperature distributions than planar shock states. The complete EOS is also compared to an alternative derivation assuming that specific heat is a function of temperature alone, i.e. cv(T). Temperature discrepancies on the order of 100–600 K were observed corresponding to the shock pressures required to initiate HNS (near 10 GPa). Overall, the results of this work will improve confidence in temperature predictions. By adopting this EOS, future work may be able to assign physical meaning to other thermally sensitive constitutive model parameters necessary to predict the shock initiation and detonation of heterogeneous explosives.

Reactive nanolaminate pulsed-laser ignition mechanism: Modeling and experimental evidence of diffusion limited reactions

Al/Pt nanolaminates with a bilayer thickness (tb, width of an Al/Pt pair-layer) of 164 nm were irradiated with single laser pulses with durations of 10 ms and 0.5 ms at 189 W/cm2 and 1189 W/cm2, respectively. The time to ignition was measured for each pulse, and shorter ignition times were observed for the higher power/shorter pulse width. Videographic images of the irradiated area shortly after ignition show a non-uniform radial brightness for the longer pulse, while the shorter pulse shows uniform brightness. A diffusion-limited single step reaction mechanism was implemented in a finite element package to model the progress from reactants to products at both pulse widths. The model captures well both the observed ignition delay and qualitative observations regarding the non-uniform radial temperature.

A Mie-Grüneisen EOS with non-constant specific heat

A complete and consistent equation of state based on Mie-Gruneisen assumptions was developed. This EOS assumes constant Gruneisen coefficient, but a variable specific heat that is modeled using Einsteins theory of heat capacities using two oscillators. The shock velocity particle velocity Hugoniot (Us-up) was derived from density functional theory molecular dynamics (DFT-MD). The EOS was formatted as a tabular EOS and checked for consistency using one-dimensional impact simulations in CTH.

Shock interactions with heterogeneous energetic materials

The complex physical phenomenon of shock wave interaction with material heterogeneities has significant importance and nevertheless remains little understood. In many materials, the observed macroscale response to shock loading is governed by characteristics of the microstructure. Yet, the majority of computational studies aimed at predicting phenomena affected by these processes, such as the initiation and propagation of detonation waves in explosives or shock propagation in geological materials, employ continuum material and reactive burn model treatment. In an effort to highlight the grain-scale processes that underlie the observable effects in an energetic system, a grain-scale model for hexanitrostilbene (HNS) has been developed. The measured microstructures were used to produce synthetic computational representations of the pore structure, and a density functional theory molecular dynamics derived equation of state (EOS) was used for the fully dense HNS matrix. The explicit inclusion of the microstr...

Heating rate dependent ignition of Al/Pt nanolaminates through pulsed laser irradiation

Direct laser irradiation of sputter deposited Al/Pt nanolaminate multilayers results in rapid local heating and exothermic mixing of reactant layers. Milli- and microsecond pulsed laser irradiation under certain test conditions leads to single-point ignition of rapid, self-propagating, formation reactions. Multilayers having bilayer thicknesses of 328 nm, 164 nm, and 65 nm are characterized by their ignition onset times and temperatures. Smaller bilayer thickness multilayers require less laser intensity for ignition compared with larger bilayer designs (when utilizing a particular pulse duration). The relationship between laser intensity and ignition onset time is used to calibrate an activation energy for ignition within a finite element reactive heat transport model. The local heating rate is varied from 104 K/s to 106 K/s by selecting a laser intensity. Kissinger analysis was performed on the heating rate-dependent ignition temperatures measured with high speed pyrometry to experimentally determine an activation energy in the foils of (6.2 ± 1.6 × 104 J/mole atoms). This value is then compared to an activation energy produced from model fits to an ignition onset time of 7.2 × 104 J/mole atoms.Direct laser irradiation of sputter deposited Al/Pt nanolaminate multilayers results in rapid local heating and exothermic mixing of reactant layers. Milli- and microsecond pulsed laser irradiation under certain test conditions leads to single-point ignition of rapid, self-propagating, formation reactions. Multilayers having bilayer thicknesses of 328 nm, 164 nm, and 65 nm are characterized by their ignition onset times and temperatures. Smaller bilayer thickness multilayers require less laser intensity for ignition compared with larger bilayer designs (when utilizing a particular pulse duration). The relationship between laser intensity and ignition onset time is used to calibrate an activation energy for ignition within a finite element reactive heat transport model. The local heating rate is varied from 104 K/s to 106 K/s by selecting a laser intensity. Kissinger analysis was performed on the heating rate-dependent ignition temperatures measured with high speed pyrometry to experimentally determine an ...

Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations

A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.

Ignition and self-propagating reactions in Al/Pt multilayers of varied design

The different rate-limiting processes underlying ignition and self-propagating reactions in Al/Pt multilayers are examined through experiments and analytical modeling. Freestanding, ∼1.6 μm-thick Al/Pt multilayers of varied stoichiometries and nanometer-scale layer thicknesses ignite at temperatures below the melting point of both reactants (and eutectics) demonstrating that initiation occurs via solid-state mixing. Equimolar multilayers exhibit the lowest ignition temperatures when comparing structures having a specific bilayer thickness. An activation energy of 76.6 kJ/mol at. associated with solid state mass transport is determined from the model analysis of ignition. High speed videography shows that equimolar Al/Pt multilayers undergo the most rapid self-sustained reactions with wavefront speeds as large as 73 m/s. Al- and Pt-rich multilayers react at reduced rates (as low as 0.3 m/s), consistent with reduced heat of reaction and lower adiabatic temperatures. An analytical model that accounts for key thermodynamic properties, preliminary mixing along interfaces, thermal transport, and mass diffusion is used to predict the wavefront speed dependencies on bilayer thickness. Good fits to experimental data provide estimates for activation energy (51 kJ/mol at.) associated with mass transport subject to high heating rates and thermal diffusion coefficient of premixed interfacial volumes (2.8 × 10−6 m2/s). Pt dissolution into molten Al is identified as a rate-limiting step underlying high temperature propagating reactions in Al/Pt multilayers.The different rate-limiting processes underlying ignition and self-propagating reactions in Al/Pt multilayers are examined through experiments and analytical modeling. Freestanding, ∼1.6 μm-thick Al/Pt multilayers of varied stoichiometries and nanometer-scale layer thicknesses ignite at temperatures below the melting point of both reactants (and eutectics) demonstrating that initiation occurs via solid-state mixing. Equimolar multilayers exhibit the lowest ignition temperatures when comparing structures having a specific bilayer thickness. An activation energy of 76.6 kJ/mol at. associated with solid state mass transport is determined from the model analysis of ignition. High speed videography shows that equimolar Al/Pt multilayers undergo the most rapid self-sustained reactions with wavefront speeds as large as 73 m/s. Al- and Pt-rich multilayers react at reduced rates (as low as 0.3 m/s), consistent with reduced heat of reaction and lower adiabatic temperatures. An analytical model that accounts for key...

A diffusion-limited reaction model for self-propagating Al/Pt multilayers with quench limits

A diffusion-limited reaction model was calibrated for Al/Pt multilayers ignited on oxidized silicon, sapphire, and tungsten substrates, as well as for some Al/Pt multilayers ignited as free-standing foils. The model was implemented in a finite element analysis code and used to match experimental burn front velocity data collected from several years of testing at Sandia National Laboratories. Moreover, both the simulations and experiments reveal well-defined quench limits in the total Al + Pt layer (i.e., bilayer) thickness. At these limits, the heat generated from atomic diffusion is insufficient to support a self-propagating wave front on top of the substrates. Quench limits for reactive multilayers are seldom reported and are found to depend on the thermal properties of the individual layers. Here, the diffusion-limited reaction model is generalized to allow for temperature- and composition-dependent material properties, phase change, and anisotropic thermal conductivity. Utilizing this increase in mode...

Detonation corner turning in vapor-deposited explosives using the micromushroom test

Detonation corner turning describes the ability of a detonation wave to propagate into unreacted explosive that is not immediately in the path normal to the wave. The classic example of a corner tu...

Characterizing the growth to detonation in HNS with small-scale PDV “cutback” experiments

For many decades, cutback experiments have been used to characterize the equation of state and growth to steady detonation in explosive formulations. More recently, embedded gauges have been used to capture the growth to steady detonation in gas-gun impacted samples. Data resulting from these experiments are extremely valuable for parameterizing equation of state and reaction models used in hydrocode simulations. Due to the extremely fast growth to detonation in typical detonator explosives, cutback and embedded gauge experiments are particularly difficult, if not impossible. Using frequency shifted photonic Doppler velocimetry (PDV) we have measured particle velocity histories from vapor-deposited explosive films impacted with electrically driven flyers. By varying the sample thickness and impact conditions we were able to capture the growth from inert shock to full detonation pressure within distances as short as 100 µm. These data are being used to assess and improve burn-model parameterization and equ...