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

Physics of Fluids

Kittell, David E.; Yarrington, Cole Y.; Lechman, Jeremy B.; Baer, M.R.

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.

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TYPE Journal Article YEAR 2018
ScopusOSTIDOI

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

Journal of Applied Physics

Kittell, David E.; Yarrington, Cole Y.; Hobbs, Michael L.; Abere, Michael J.; Adams, David P.

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 model fidelity, excellent overall agreement is shown between the simulations and experimental results with a single calibrated parameter set. However, the burn front velocities of Al/Pt multilayers ignited on tungsten substrates are over-predicted. Possible sources of error are discussed and a higher activation energy (from 41.9 kJ/mol.at. to 47.5 kJ/mol.at.) is shown to bring the simulations into agreement with the velocity data observed on tungsten substrates. This higher activation energy suggests an inhibited diffusion mechanism present at lower heating rates.

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TYPE Journal Article YEAR 2018
ScopusOSTIDOI

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

Combustion Theory and Modelling

Kittell, David E.; Yarrington, Cole Y.

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.

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TYPE Journal Article YEAR 2016
ScopusOSTIDOI
Results 26–44 of 44
Results 26–44 of 44