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The modeling of weak shock waves in highly porous powder beds and comments on its relevance to exploding bridgewire (EBW) detonators

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Abstract

A computer modeling study is reported about the constant-piston-velocity compaction response of a 50% porous fine particle and air mixture. It is established that for the 10-\(\upmu \hbox {m}\) average particle diameter powder chosen (sugar), over the piston velocity range 100–1000 \(\hbox {m}\,\hbox {s}^{-1}\), a self-similar shock is formed in 12–14 particle diameters of motion (\({\approx }\,140~\upmu \hbox {m}\)). The shock is found to be statistically bounded, but temporally and spatially variable. At the resulting shock velocities identified for this powder, this results in self-similar behavior if the shock is supported for approximately 100 ns. Therefore, the use of the shock jump equations to estimate the post-shock state is valid after this duration. Further, it is found that a linear shock- and particle-velocity relation works well to model the low-pressure compaction of the powder. The intercept of this relation (commonly called the bulk sound speed in solid materials) is very low (50–100 \(\hbox {m}\,\hbox {s}^{-1}\)), but positive. The implications of this powder response on the functioning of exploding bridgewire detonators and the porous pentaerythritol-tetranitrate fill commonly used in them are discussed and compared with other literature on the topic.

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Acknowledgements

The author wishes to thank Peter Dickson for several helpful suggestions about powder compression at low pressures. Research presented in this article was supported in part by the Laboratory Directed Research and Development program of Los Alamos National Laboratory under Project No. 20210189ER. Funding was provided by National Nuclear Security Administration.

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Rae, P.J. The modeling of weak shock waves in highly porous powder beds and comments on its relevance to exploding bridgewire (EBW) detonators. Shock Waves 31, 153–164 (2021). https://doi.org/10.1007/s00193-021-00995-y

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