8/3/2019 Eric O. Morano and Joseph E. Shepherd- Effect of Reaction Periodicity on Detonation Propagation

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EFFECT OF REACTION RATE PERIODICITYON DETONATION PROPAGATION

Eric O. Morano and Joseph E. Shepherd

Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125

Abstract. As an alternative to homogeneous reaction rates, we implement synthetic hot-spots through a depletion rate that is a function of the local pressure multiplied by a periodicfunction of the spatial coordinates. We investigate through numerical simulations how the

detonation propagation is affected by the heterogeneous rate.

INTRODUCTION

Numerical simulation of shock and detona-tion physics in explosives can be carried out atvarious levels of sophistication but must includethe essential features of unsteady compressibleflow with shock waves, equations of state for re-actants and products, and some model of thechemical reaction processes.

However, modeling of high explosives is not

straightforward. There are a number of unre-solved issues in modeling solid explosives and asa consequence, there is no universally acceptedmodel for the equations of state and the reactionprocess. One key issue is that solid high explo-sives often come in the form of pressed powdersand for continuum models, this microstructurehas always been modeled through an empiricalreaction rate. There is no general agreement onhow to construct such a rate. Other key issuesinclude the thermodynamic models of the reac-tants and products. Various approximate modelsexist but there is no accepted and accurate repre-

sentation of all thermodynamic states significantto the detonation process. Finally, the chemi-cal reactions occur in a dense fluid environmentand it is clear that the reaction models used forideal gases are deficient in not accounting for the

effects of neighboring molecules on the reactionprocesses.

In this paper, we use a simple model for theequation of state as introduced in [1] and westudy the issue of heterogeneity in reaction rate.

ENGINEERING MODELS AND ISSUES

Many solid explosives are not homogeneouslike gases or liquids; the explosive is a granu-lated material which is coated with a binder, an

elastomer, and pressed.Due to the granular structure, the reaction

process is expected to be dominated by the pres-ence of hot-spots, regions of intense reaction cre-ated at voids, grain boundaries, and defects.Such regions of intense reaction are the resultof locally high temperature due to void collapse,friction of HE crystal surfaces, shock focusing,etc [2].

The classical approach to modeling these ex-plosives is to completely homogenize the mate-rial and represent it as a simple fluid that is anequilibrium mixture of reactants and products.

Two models of this type are Lee and Tarver [3]and Johnson et al. [4]. The advantage of thisapproach is that the standard single-fluid hydro-dynamic (Euler) equations govern the flow evo-lution. This approach enables the use of tradi-

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propagating waves within the reaction zone re-sults in oscillations in the leading shock strength,visible in Fig. 3.

x [mm]

Pressure[GPa]

0.125 500.125 1000.12 1500.120

10

20

30

40

50

60

FIGURE 1. Pressure profile @ t 144.36 s ( = 1.0

and = 2.0).

t [ s ]

U

[km/s]

50 100 150

9.4

9.5

9.6

9.7

9.8

9.9

10

FIGURE 2. Front velocity as a function of time ( =

1.0 and = 2.0).

x [mm]

Pressure [GPa]

t [ s]

0.05.0

10.015.0

20.025.0

30.00.0

50.0100.0

150.0200.0

250.0300.0

350.0

35.0

40.0

45.0

50.0

55.0

60.0

65.0

70.0

75.0

80.0

85.0

FIGURE 3. Pressure profiles ( = 1.0 and = 2.0).

The effect of the spatial frequency was ex-amined for several values of the amplitude .Rather than the spatial frequency, it is moreconvenient to refer to , the number of peri-ods within the reaction zone. We have analyzed

the results by computing the average, maximum,and minimum shock wave speed for the latterportion of the simulation after the initial tran-sient has settled down. These values are depictedvs. in Fig. 4 through 7 for = 2.00, 1.00, 0.50,

0.25. As expected, the average velocity convergesto the uniform rate velocity as goes to zero.

U[km/s]

0 0.25 0.5 0.75 1

9

9.25

9.5

9.75

10

average

minimum

maximum

FIGURE 4. Front velocities for = 2.00.

U[km/s]

0 0.25 0.5 0.75 1

9

9.25

9.5

9.75

10

average

minimum

maximum

FIGURE 5. Front velocities for = 1.00.

U[km/s]

0 0.25 0.5 0.75 1

9

9.25

9.5

9.75

10

average

minimum

maximum

FIGURE 6. Front velocities for = 0.50.

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