Verification and validation of detonation-shock-dynamics relations for explosives described by general equation of state and chemical reaction models

Abstract

Detonation shock dynamics is a powerful method to model the behaviour of High Explosives (HE). However in order to use this method, the underlying relationship between the local radius of curvature and the detonation speed must be known. Previous work has developed methods to calculate this effect using simple, single-step Arrhenius and polytropic gas, models for the chemical reaction and the equation of state, respectively. In recent years, more complex models for both reaction rates and equations of state have been developed which show better agreement with experimental data than these simple models, especially when considering condensed phase explosives.. This work presents the governing equations for solving these problems in a way that is generalised to use arbitrary equations of state as well as reaction models which may have more than a single step and multiple product species. This implementation is verified against exact solutions, demonstrating that the equations were implemented properly. The verified algorithm is then validated against experimental data and high fidelity simulations, showing that it is able to make accurate predictions in a regime where the underlying assumptions of the governing equations are valid. This approach has many applications: from creating equivalent detonation shock dynamics models for existing reactive burn calibrations for HE; to developing new functional forms and calibrations of reactive burn models for condensed phase high explosives.

Keywords:

• verification
• validation
• detonation shock dynamics
• high explosives
• PBX 9501
• PBX 9502

Acknowledgments

The author would like to thank Tariq Aslam and Ralph Menikoff for their help in understanding the underlying $D_n\left(\kappa \right)$ relationships as well as Kirill Velizhanin. The author would also like to thank the developers of the following open source software packages which were used extensively in the preparation of this work Numpy [33] Matplotlib [34] and SciPy [35].

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Triaminotrinitrobenzene.

2 A composite high explosive containing 45% HMX (1,3,5,7-Tetranitro-1,3,5,7-tetrazocane), 35% aluminum, and 20% binder by mass.

3 should be mixture

4 the WSD burn model,

Additional information

Funding

This work was supported by the U.S. Department of Energy through the Los Alamos National Laboratory. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy [Contract No. 89233218CNA000001]. Approved for public release LA-UR-LA-UR-23-25246 and DOPSR Case 23-S-2066