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An Analysis of the Initiation Process of Electroexplosive Devices

An Analysis of the Initiation Process of Electroexplosive Devices

Paulo C. C. Faria (Aeronautics Institute of Technology, Brazil)
Copyright: © 2018 |Pages: 12
DOI: 10.4018/978-1-5225-2903-3.ch015
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Abstract

Electroexplosive devices, EEDs or squibs (an electric resistance encapsulated by a primary explosive), fundamentally convert electrical energy into heat, solely to start off an explosive chemical reaction. Obviously, the EED activation shall not happen by accident or, even worse, by intentional exogenous influence. From an ordinary differential equation (ODE), which describes this device thermal behaviour for both continuous and pulsed electrical excitation, a remarkable, but certainly not intuitive, dependence of the temperature response on the heat transfer process time-constant is verified: the EED temperature profile dramatically changes as the time-constant spans a wide range of values, from much lesser than the pulse width to much greater than the pulse period. On the basis of this dependence, important recommendations, concerning the EED safety (and efficient) operation, are presented.
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A Convenient Analogy

Consider a barrel (a cylinder with transversal area 978-1-5225-2903-3.ch015.m01, height 978-1-5225-2903-3.ch015.m02, and top surface removed), initially empty, having a small hole in the center of its base. Assume that it is raining (uniform precipitation). Naturally, a question arises: how is the level of the water inside the barrel going to evolve as a function of time?

To facilitate the analysis of this problem, let the hole at the barrel base be modeled by a linear hydraulic resistance 978-1-5225-2903-3.ch015.m03 (actually, 978-1-5225-2903-3.ch015.m04, with 978-1-5225-2903-3.ch015.m05 adjusted to each specific case (Cochin, 1980)), and let the water flux through the hole, 978-1-5225-2903-3.ch015.m06, be proportional to 978-1-5225-2903-3.ch015.m07:

978-1-5225-2903-3.ch015.m08
(1)

On the other hand, the water volumetric flow that enters the barrel (it is raining) is constant and equal to 978-1-5225-2903-3.ch015.m09. From the cylindrical geometry, 978-1-5225-2903-3.ch015.m10, and from the mass-rate balance principle, 978-1-5225-2903-3.ch015.m11. Combining these two expressions, it results the ordinary differential equation (ODE):

978-1-5225-2903-3.ch015.m12
(2)

This ODE has 978-1-5225-2903-3.ch015.m13 for solution 978-1-5225-2903-3.ch015.m14. Obviously, the necessary condition for the water to overflow is 978-1-5225-2903-3.ch015.m15.

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