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

## Abstract

Here, 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 assignmore »

- 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)

- OSTI Identifier:
- 1371468

- Report Number(s):
- SAND-2015-7099J

Journal ID: ISSN 1364-7830; 655037

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Combustion Theory and Modelling

- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 5; Journal ID: ISSN 1364-7830

- Publisher:
- Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Mie–Gruneisen equation of state; shock Hugoniot; explosive modelling; hydrocode; heterogeneous impact

### Citation Formats

```
Kittell, David Erik, and Yarrington, Cole Davis. A physically-based Mie–Gruneisen equation of state to determine hot spot temperature distributions. United States: N. p., 2016.
Web. doi:10.1080/13647830.2016.1201145.
```

```
Kittell, David Erik, & Yarrington, Cole Davis. A physically-based Mie–Gruneisen equation of state to determine hot spot temperature distributions. United States. doi:10.1080/13647830.2016.1201145.
```

```
Kittell, David Erik, and Yarrington, Cole Davis. Thu .
"A physically-based Mie–Gruneisen equation of state to determine hot spot temperature distributions". United States. doi:10.1080/13647830.2016.1201145. https://www.osti.gov/servlets/purl/1371468.
```

```
@article{osti_1371468,
```

title = {A physically-based Mie–Gruneisen equation of state to determine hot spot temperature distributions},

author = {Kittell, David Erik and Yarrington, Cole Davis},

abstractNote = {Here, 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.},

doi = {10.1080/13647830.2016.1201145},

journal = {Combustion Theory and Modelling},

number = 5,

volume = 20,

place = {United States},

year = {2016},

month = {7}

}

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Works referenced in this record:

##
Modeling heterogeneous energetic materials at the mesoscale

journal, February 2002

- Baer, M. R.
- Thermochimica Acta, Vol. 384, Issue 1-2

##
Explicit Gibbs free energy equation of state applied to the carbon phase diagram

journal, April 2000

- Fried, Laurence E.; Howard, W. Michael
- Physical Review B, Vol. 61, Issue 13

##
Thermodynamic stability of the Mie–Grüneisen equation of state, and its relevance to hydrocode computations

journal, September 1991

- Segletes, Steven B.
- Journal of Applied Physics, Vol. 70, Issue 5

##
Equation of state and reaction rate for condensed-phase explosives

journal, September 2005

- Wescott, B. L.; Stewart, D. Scott; Davis, W. C.
- Journal of Applied Physics, Vol. 98, Issue 5

##
CTH: A three-dimensional shock wave physics code

journal, January 1990

- McGlaun, J. M.; Thompson, S. L.; Elrick, M. G.
- International Journal of Impact Engineering, Vol. 10, Issue 1-4

##
Pore collapse in an energetic material from the micro-scale to the macro-scale

journal, April 2015

- Jackson, Thomas Luther; Buckmaster, John David; Zhang, Ju
- Combustion Theory and Modelling, Vol. 19, Issue 3

##
Thermomechanical model and temperature measurements for shocked ammonium perchlorate single crystals

journal, May 2002

- Winey, J. M.; Gruzdkov, Y. A.; Dreger, Z. A.
- Journal of Applied Physics, Vol. 91, Issue 9

##
Initiation of Detonation by the Interaction of Shocks with Density Discontinuities

journal, January 1965

- Mader, Charles L.
- Physics of Fluids, Vol. 8, Issue 10