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European Journal of Applied Sciences – Vol. 9, No. 5

Publication Date: October 25, 2021

DOI:10.14738/aivp.95.10968. Partom, Y. (2021). Modeling Initiation and Detonation of Complex Explosive Formulations. European Journal of Applied Sciences,

9(5). 311-323.

Services for Science and Education – United Kingdom

Modeling Initiation and Detonation of Complex Explosive

Formulations

Yehuda Partom

Retired from RAFAEL, ISRAEL

ABSTRACT

Since 1980 we’ve developed and used our reactive flow model TDRR (= reactant

Temperature Dependent Reaction Rate). TDRR makes it possible to calculate

initiation and detonation of a single component explosive. It includes EOSs

(Equations of State) for the reactant and products, and a reaction rate equation for

the transition from reactant to products. As the EOSs and the reaction rate are

calibrated for a certain formulation, say HV5 (95% HMX+5% Viton), it’s not possible

to use them for a different formulation of the same materials, say HV15. Here we

expand TDRR to handle general formulations with any number of components

(explosives, binders and products). We call our expanded model TDRRF (F for

Formulation). We first write down the model equations and then use them with two

computed examples: 1) HVx and BFx formulations (x=explosive mass ratio, H=HMX,

V=Viton, B=TATB, F=kelF) and 2) BHx formulations (x=B mass ratio).

INTRODUCTION

Since 1980 we’ve developed and used our reactive flow model TDRR (= reactant Temperature

Dependent Reaction Rate) [1-4], to simulate initiation and detonation of non-homogeneous

explosives. Several reactive flow models have been reported in the literature [5], but most of

them are not reactant temperature dependent.

With TDRR we assume that: 1) a strong enough shock or pressure wave creates so called hot

spots in the explosive. These hotspots are mainly created at large enough voids, which are

usually located between explosive grains; 2) hot spots are created by the collapse of grains

around voids, and as a result of such collapse the void boundary is heated up to ignite the

explosive there; 3) the remaining void is then filled with hot reaction products; 4) a deflagration

wave starts out of each such hot spot; 5) the speed of each such deflagration wave becomes

steady after a short travel distance, and it increases with the reactant temperature in the grains

it travels into; 6) as long as neighboring deflagration fronts do not interact, the overall reaction

rate (of a computational cell) increases with time. But after deflagration fronts start to interact,

reaction rate decreases monotonously down to zero, when all the explosive in the cell has

reacted.

Our TDRR reactive flow model includes four kinds of equations: 1) equations of state (EOSs) of

the reactants and of the reaction products; 2) energy conservation equations; 3) mix rules, and

4) reaction rate equations. The first three mix rules are:

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European Journal of Applied Sciences (EJAS) Vol. 9, Issue 5, October-2021

Services for Science and Education – United Kingdom

(1)

Where s(=solid) refers to the unreacted part, g(=gas) refers to the reacted part, P is pressure, V

is specific volume, and E is specific internal energy. The 4th mix rule is actually a separation rule.

The reacted part joins the previously reacted products in the cell, and the remaining unreacted

solid part stays adiabatic. As a result, the solid and gas parts in the cell have different

temperatures. With TDRR the state of the gas is not needed as part of the model. We show later

that for formulations (a mixture of several explosives) this is not the case.

The reaction rate equation is:

(2)

Where W is the reaction progress parameter, and y(W) is the burn topology function,

normalized to 1 at its maximum. In [1] we’ve estimated y(W), and in [6] they evaluated y(W)

based on statistical arguments. Ts is the temperature of the unreacted part of the cell, and RT, T*

are the material parameters to be calibrated from tests (usually, run to detonation tests).

As described above, our TDRR model makes it possible to model initiation and detonation of a

single explosive witch a chemical reaction transforms from reactant to products. So, when

equations of state and reaction rate have been calibrated for a certain explosive (e.g.,

HV5=HMX+5%Viton), it’s not possible to use this calibration for a different explosive composed

of the same materials (like HV15). Also, if an explosive formulation contains several

components, like BHV 50/40/10 (B=TATB), we need to calibrate it as a new material, and

cannot predict its performance from the performance of its components.

In what follows we develop an extended TDRR model that can handle an explosive formulation

containing any number of components. We refer to this extended model as TDRRF (F for

Formulation). Our TDRRF model is based on the following assumptions: 1) we know the EOS of

each of the components of the formulation. This includes inert components; 2) we know the

EOS of each of the components of the formulation, after it has reacted and converted to

products; 3) we know the reaction rate of each of the components, and the form of those

reaction rates is the same as that of our TDRR reaction rate; 4) we assume that all components

have the same form of BTF (burn topology function); 5) we know the heats of reaction (Qj) of

each of the components. For the inert components the heat of reaction is minus the sum of the

heat of melting and the heat of evaporation. In addition, we assume (as a first step in our TDRRF

( )

( )

s g

s g

s g

PPP

V WV 1 W V

E WE 1 W E

= =

= + -

= + -

( ) *

T s ig

s

s ig

W R y W exp T T T

T

W0 T T

æ ö = ç ÷ - 3 è ø

= <

!

!