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Ignition and detonation of solid explosives: a micromechanical burn model

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Abstract

This paper describes a new computational framework for modeling splid explosives and proof-of-concept calculations. Our goal is to expand predictive model capability through the inclusion of various micro-mechanical burn processes. We propose a model which is complicated enough to represent underlying physics, but simple enough for engineering scale computations. Key components of the model include energy localization, the growth of hot spots, micro-mechanics in/around hot spots, and a phase-averaged mixture equation of state. The nucleation and growth of locally heated regions is treated by a statistical model based on an exponential size distribution. Proof-of-concept calculations are limited to shock loading, but show the capability of simulating Pop-plots, initial temperature effect, detonation waves in 2D, detonation shock confinement test, and multi-dimensional effects in a unified fashion based on micro-physics.

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Abbreviations

Roman symbols :

 

a :

gas/solid boundary coordinate

A :

frequency factor

c :

length of hot spot cell

c p :

heat capacity at constant pressure

c v :

heat capacity at constant volume

d 0 :

half thickness of slab

E :

activation energy

G :

mass fraction of evaporating reactant

h :

enthalpy

k :

BKW EOS parameter

\(\dot{m}\) :

mass flux

n :

constant in repulsive force

p :

pressure

p B :

external boundary pressure

p N :

configurational stress

q :

specific heat release

R :

universal gas constant

r :

pressure exponent in bulk gas reaction rate

T :

temperature

W :

average molecular weight of gas mixture

w :

particle velocity

x :

BKW EOS parameter

x i :

mole fraction of species i

Y i :

mass fraction of species i

z :

coordinate

Δh f :

enthalpy of formation

Greek symbols :

 

α:

BKW EOS parameter

β:

BKW EOS parameter

δ:

width of locally heated site

δ g :

thermal layer thickness

ζ:

coordinate used in heat conduction calculation

θ:

BKW EOS parameter

κ:

thermal conductivity

μ:

viscosity

ρ:

density

σ:

BKW EOS parameter

τ:

deviatoric stress

ω:

reaction rate

Φhs :

deposited energy

Subscripts :

 

g :

gas

s :

solid

a :

gas/solid boundary

0:

initial value

Superscripts :

 

hy:

hydro cell quantity

hs:

hot-spot cell quantity

i :

species i

R :

reactant

I :

inert

P :

product

*:

reference state

Accents :

 

_:

volume average

˙:

time derivative

^:

quantity adjusted for the hot-spot cell

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Authors and Affiliations

  1. Research and Engineering Education Facility, University of Florida, Shalimar, FL, 32579, USA

    Y. Hamate

  2. Air Force Research Laboratory, Eglin AFB, FL, 32542, USA

    Y. Horie

Authors
  1. Y. Hamate
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  2. Y. Horie
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Correspondence to Y. Hamate.

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Communicated by Y. Horie.

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Hamate, Y., Horie, Y. Ignition and detonation of solid explosives: a micromechanical burn model. Shock Waves 16, 125–147 (2006). https://doi.org/10.1007/s00193-006-0038-x

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