Precursors in two-phase detonation: An elementary model for the channel effect

Abstract

The paper is concerned with the channel effect: detonation-propelled shocks occurring in tubular charges. It is shown that some salient aspects of the phenomenon may be successfully reproduced within a simple one-dimensional model assuming the gas–solid system to be isothermal and the volume fraction of the solid phase to be small. Two modes of the channel effect, dependent on the level of the ignition pressure, are identified. Although the emerging detonations appear to be of the Chapman–Jouguet (CJ) type, their velocities are controlled by the system’s gasification kinetics rather than its thermodynamics. The structure of the emerging CJ detonation differs from that of conventional ZND detonation. There is no shock attached to the reaction zone. The precursor shock is the only shock in the event.

Keywords:

• detonation in tubular charges
• channel effect
• gas-permeable explosives
• two-phase detonation
• cavitated charges

Acknowledgements

Engaging discussions with Leonid Kagan and Peter Gordon are gratefully acknowledged.

Notes

1. In this sense detonation of tubular charges is dynamically akin to the polymorphic transition in crystals [11], sharing some of its features, including precursors.

2. The proposed formulation is akin to Riemann’s early theory of shock waves [12], based on the isentropic equation of state. While capturing much of the relevant structure, the theory does not maintain conservation of energy across the shock.

Additional information

Funding

These studies were supported by the US–Israel Binational Science Foundation [grant number 2012-057]; the Israel Science Foundation [grant number 335/13].