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

## Abstract

In this paper, 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. Finally, 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.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); SNL Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1469625

- Alternate Identifier(s):
- OSTI ID: 1436551

- Report Number(s):
- SAND-2018-3215J

Journal ID: ISSN 1070-6631; 661797

- Grant/Contract Number:
- NA0003525

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Fluids

- Additional Journal Information:
- Journal Volume: 30; Journal Issue: 5; Journal ID: ISSN 1070-6631

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; stochastic processes; finite volume methods; shock waves; chemically reactive flows; explosives; energetic materials

### Citation Formats

```
Kittell, D. E., Yarrington, C. D., Lechman, J. B., and Baer, M. R. Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations. United States: N. p., 2018.
Web. doi:10.1063/1.5031775.
```

```
Kittell, D. E., Yarrington, C. D., Lechman, J. B., & Baer, M. R. Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations. United States. doi:10.1063/1.5031775.
```

```
Kittell, D. E., Yarrington, C. D., Lechman, J. B., and Baer, M. R. Wed .
"Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations". United States. doi:10.1063/1.5031775. https://www.osti.gov/servlets/purl/1469625.
```

```
@article{osti_1469625,
```

title = {Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations},

author = {Kittell, D. E. and Yarrington, C. D. and Lechman, J. B. and Baer, M. R.},

abstractNote = {In this paper, 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. Finally, 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.},

doi = {10.1063/1.5031775},

journal = {Physics of Fluids},

number = 5,

volume = 30,

place = {United States},

year = {2018},

month = {5}

}

Other availability

#### Figures / Tables:

FIG. 1: Diagram for the Riemann problem. Characteristic equations are solved along

*$\overline{ab}$*and*$\overline{bc}$*to match the local pressure and particle velocity at point*b*.
All figures and tables
(3 total)

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

##
Coarse-Grain Model Simulations of Nonequilibrium Dynamics in Heterogeneous Materials

journal, June 2014

- Brennan, John K.; Lísal, Martin; Moore, Joshua D.
- The Journal of Physical Chemistry Letters, Vol. 5, Issue 12

##
Phenomenological model of shock initiation in heterogeneous explosives

journal, January 1980

- Lee, E. L.; Tarver, C. M.
- Physics of Fluids, Vol. 23, Issue 12

##
Prediction of probabilistic ignition behavior of polymer-bonded explosives from microstructural stochasticity

journal, May 2013

- Barua, A.; Kim, S.; Horie, Y.
- Journal of Applied Physics, Vol. 113, Issue 18

##
Shock interactions with heterogeneous energetic materials

journal, March 2018

- Yarrington, Cole D.; Wixom, Ryan R.; Damm, David L.
- Journal of Applied Physics, Vol. 123, Issue 10

##
PDF methods for turbulent reactive flows

journal, January 1985

- Pope, S. B.
- Progress in Energy and Combustion Science, Vol. 11, Issue 2

##
Shock Initiation of Solid Explosives

journal, January 1961

- Campbell, A. W.; Davis, W. C.; Ramsay, J. B.
- Physics of Fluids, Vol. 4, Issue 4

##
Measurements of shock initiation in the tri-amino-tri-nitro-benzene based explosive PBX 9502: Wave forms from embedded gauges and comparison of four different material lots

journal, June 2006

- Gustavsen, R. L.; Sheffield, S. A.; Alcon, R. R.
- Journal of Applied Physics, Vol. 99, Issue 11

##
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

journal, February 2017

- Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G.
- Journal of Computational Physics, Vol. 330

##
The Hugoniot and shock sensitivity of a plastic‐bonded TATB explosive PBX 9502

journal, May 1988

- Dick, J. J.; Forest, C. A.; Ramsay, J. B.
- Journal of Applied Physics, Vol. 63, Issue 10

##
Understanding the shock and detonation response of high explosives at the continuum and meso scales

journal, March 2018

- Handley, C. A.; Lambourn, B. D.; Whitworth, N. J.
- Applied Physics Reviews, Vol. 5, Issue 1

##
Probabilistic models for reactive behaviour in heterogeneous condensed phase media

journal, February 2012

- Baer, M. R.; Gartling, D. K.; DesJardin, P. E.
- Combustion Theory and Modelling, Vol. 16, Issue 1

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*