skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on November 13, 2020

Title: Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

Abstract

Although current phenomenological burn models are useful for describing the average or bulk reactive flow behaviour of heterogeneous explosives, one fundamental weakness inherent to these models is the loss of detailed microstructural information at the scale of the calculation. In order to include the effects of the microstructure, and in particular the underlying material heterogeneities that influence the build-up to detonation, a new paradigm is put forth for modelling sub-grid, reaction-induced fluctuations (i.e. “hot spots”) at the continuum level. This modelling approach assumes that the reaction rate is stochastic, rather than deterministic, and it uses Langevin-type equations with a mathematical framework built upon Itô calculus and Lambourn's CIM model for shocked heterogeneous explosives. This approach follows directly from our previous letter, Ref. [1], and is inspired by the probability density function (pdf) methods used in turbulent reactive flows. Here, the stochastic burn model is derived, implemented, and exercised far beyond what has been shown in previous work. New hydrocode simulation results demonstrate the role of stochastic fluctuations during shock initiation; these fluctuations are approximated by collections of discrete particles, that evolve with drift (i.e. deterministic) and diffusion (i.e. stochastic) coefficients. Furthermore, the particle values are propagated and averaged to calculatemore » the heat release, yield strength, and material impedance in each computational cell. Hydrocode simulation results further show how the fluctuating hot spot energy may or may not be transmitted to the wave front, and result in a detonation wave-like structure. The fundamental stochastic nature of this model permits simulations to have varying outcomes with the same initial conditions; this allows for go/no-go estimation (e.g., marginal or failed detonations), which might possibly be calibrated using the statistical distributions from real materials. Mesoscale calculations of shocked heterogeneous explosives also show that these fluctuations are physically justified (i.e., Ref. [2]), and it is hypothesized that the pdf functions provide a link between the meso(grain) and continuum scales for practical engineering calculations. Hence, our approach is a paradigm shift for building efficient, reduced order continuum burn models, that represent the sub-grid stochastic behaviour of shocked heterogeneous solid explosives.« less

Authors:
 [1];  [1];  [1];  [1];  [1]
  1. 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:
1595423
Report Number(s):
SAND-2020-0010J
Journal ID: ISSN 0721-3115; 681962
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Propellants, Explosives, Pyrotechnics
Additional Journal Information:
Journal Name: Propellants, Explosives, Pyrotechnics; Journal ID: ISSN 0721-3115
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
shock initiation; stochastic process; burn model; mesoscale

Citation Formats

Kittell, David E., Yarrington, Cole D., Lechman, Jeremy B., Damm, David L., and Baer, Melvin R. Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes. United States: N. p., 2019. Web. doi:10.1002/prep.201900209.
Kittell, David E., Yarrington, Cole D., Lechman, Jeremy B., Damm, David L., & Baer, Melvin R. Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes. United States. doi:10.1002/prep.201900209.
Kittell, David E., Yarrington, Cole D., Lechman, Jeremy B., Damm, David L., and Baer, Melvin R. Wed . "Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes". United States. doi:10.1002/prep.201900209.
@article{osti_1595423,
title = {Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes},
author = {Kittell, David E. and Yarrington, Cole D. and Lechman, Jeremy B. and Damm, David L. and Baer, Melvin R.},
abstractNote = {Although current phenomenological burn models are useful for describing the average or bulk reactive flow behaviour of heterogeneous explosives, one fundamental weakness inherent to these models is the loss of detailed microstructural information at the scale of the calculation. In order to include the effects of the microstructure, and in particular the underlying material heterogeneities that influence the build-up to detonation, a new paradigm is put forth for modelling sub-grid, reaction-induced fluctuations (i.e. “hot spots”) at the continuum level. This modelling approach assumes that the reaction rate is stochastic, rather than deterministic, and it uses Langevin-type equations with a mathematical framework built upon Itô calculus and Lambourn's CIM model for shocked heterogeneous explosives. This approach follows directly from our previous letter, Ref. [1], and is inspired by the probability density function (pdf) methods used in turbulent reactive flows. Here, the stochastic burn model is derived, implemented, and exercised far beyond what has been shown in previous work. New hydrocode simulation results demonstrate the role of stochastic fluctuations during shock initiation; these fluctuations are approximated by collections of discrete particles, that evolve with drift (i.e. deterministic) and diffusion (i.e. stochastic) coefficients. Furthermore, the particle values are propagated and averaged to calculate the heat release, yield strength, and material impedance in each computational cell. Hydrocode simulation results further show how the fluctuating hot spot energy may or may not be transmitted to the wave front, and result in a detonation wave-like structure. The fundamental stochastic nature of this model permits simulations to have varying outcomes with the same initial conditions; this allows for go/no-go estimation (e.g., marginal or failed detonations), which might possibly be calibrated using the statistical distributions from real materials. Mesoscale calculations of shocked heterogeneous explosives also show that these fluctuations are physically justified (i.e., Ref. [2]), and it is hypothesized that the pdf functions provide a link between the meso(grain) and continuum scales for practical engineering calculations. Hence, our approach is a paradigm shift for building efficient, reduced order continuum burn models, that represent the sub-grid stochastic behaviour of shocked heterogeneous solid explosives.},
doi = {10.1002/prep.201900209},
journal = {Propellants, Explosives, Pyrotechnics},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 13, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Modeling heterogeneous energetic materials at the mesoscale
journal, February 2002


Probabilistic models for reactive behaviour in heterogeneous condensed phase media
journal, February 2012


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
  • DOI: 10.1016/j.jcp.2016.10.070

Initiation and Growth of Explosion in Liquids and Solids
journal, April 1952

  • Bowden, F. P.; Yoffe, A. D.; Hudson, George E.
  • American Journal of Physics, Vol. 20, Issue 4
  • DOI: 10.1119/1.1933188

Shock Initiation of Solid Explosives
journal, January 1961

  • Campbell, A. W.; Davis, W. C.; Ramsay, J. B.
  • Physics of Fluids, Vol. 4, Issue 4
  • DOI: 10.1063/1.1706354

On the effect of grain size on shock sensitivity of heterogeneous high explosives
journal, April 1997

  • Khasainov, B. A.; Ermolaev, B. S.; Presles, H. -N.
  • Shock Waves, Vol. 7, Issue 2
  • DOI: 10.1007/s001930050066

Mesoscale simulation of reactive pressed energetic materials under shock loading
journal, December 2015

  • Rai, Nirmal K.; Udaykumar, H. S.
  • Journal of Applied Physics, Vol. 118, Issue 24
  • DOI: 10.1063/1.4938581

Multi-dimensional mesoscale simulations of detonation initiation in energetic materials with density-based kinetics
journal, December 2017


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
  • DOI: 10.1063/1.5022042

Prediction of shock initiation thresholds and ignition probability of polymer-bonded explosives using mesoscale simulations
journal, May 2018

  • Kim, Seokpum; Wei, Yaochi; Horie, Yasuyuki
  • Journal of the Mechanics and Physics of Solids, Vol. 114
  • DOI: 10.1016/j.jmps.2018.02.010

Quantification of probabilistic ignition thresholds of polymer-bonded explosives with microstructure defects
journal, October 2018

  • Wei, Yaochi; Kim, Seokpum; Horie, Yasuyuki
  • Journal of Applied Physics, Vol. 124, Issue 16
  • DOI: 10.1063/1.5031845

Relating microstructure, temperature, and chemistry to explosive ignition and shock sensitivity
journal, April 2018


Multi-scale shock-to-detonation simulation of pressed energetic material: A meso-informed ignition and growth model
journal, August 2018

  • Sen, O.; Rai, N. K.; Diggs, A. S.
  • Journal of Applied Physics, Vol. 124, Issue 8
  • DOI: 10.1063/1.5046185

PDF methods for turbulent reactive flows
journal, January 1985


Lagrangian PDF Methods for Turbulent Flows
journal, January 1994


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
  • DOI: 10.1021/jz500756s

Highly scalable discrete-particle simulations with novel coarse-graining: accessing the microscale
journal, May 2018


On the systematics of particle velocity histories in the shock-to-detonation transition regime
journal, October 2006

  • James, H. R.; Lambourn, B. D.
  • Journal of Applied Physics, Vol. 100, Issue 8
  • DOI: 10.1063/1.2354416

Phenomenological model of shock initiation in heterogeneous explosives
journal, January 1980

  • Lee, E. L.; Tarver, C. M.
  • Physics of Fluids, Vol. 23, Issue 12
  • DOI: 10.1063/1.862940

A Consistent Hybrid Finite-Volume/Particle Method for the PDF Equations of Turbulent Reactive Flows
journal, September 1999

  • Muradoglu, Metin; Jenny, Patrick; Pope, Stephen B.
  • Journal of Computational Physics, Vol. 154, Issue 2
  • DOI: 10.1006/jcph.1999.6316

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
  • DOI: 10.1063/1.340428