Abstract
We present a theory for the evolution of a one-dimensional, steady-state detonation reaction zone to a two-dimensional reaction zone, when the explosive experiences a sudden loss of side-on confinement as a boundary of the explosive is impulsively withdrawn. Our focus is on condensed-phase explosives, which we describe as having a constant adiabatic gamma equation of state and an irreversible, state-independent reaction rate. We consider two detonation models: (i) the instantaneous reaction heat release Chapman–Jouguet (CJ)-limit and (ii) the spatially resolved reaction heat-release Zel’dovich–von Neumann–Doring (ZND) model, in the limit where only a small fraction of the energy release is resolved (the SRHR-limit). Two competing rarefaction waves are generated by this loss of confinement: (i) a smooth wave coming off the full length of the withdrawn boundary and (ii) a singular fan spreading out from the point where the detonation shock and the withdrawn boundary meet. For the CJ-limit, in all cases the singular rarefaction fan eventually dominates the competition to control the steady-state behaviour. For the SRHR-limit, the spatially resolved heat release moderates this competition. When the withdrawal speed is fast, the rarefaction fan dominates; when the withdrawal speed is slower, the smooth rarefaction eventually dominates, although the flow features a fan at early times. By examining the mathematical properties of the steady two-dimensional fan-based solution, we set down a mechanism for this transition in behaviours.
Highlights
In its simplest, one-dimensional (1-D) idealized form, a free-running, high-explosive (HE) detonation is a shock supported by the release of energy, initiated by the passage of the detonation’s shock over fresh explosive
The structure of the flow in the energy-release zone was first described by Zel’dovich, von Neumann and Döring (ZND) (Fickett & Davis 1979, pp. 42–51), When measured in a reference frame attached to the shock, the flow at the point where the shock crosses a particle of fresh explosive, referred to as the von Neumann (N) point, is subsonic and becomes choked or sonic at the point where the reaction in that particle is completed, referred to as the Chapman–Jouguet (CJ) point
Because of the disparity in these two reaction-zone time scales and the disproportionate effect that the last 10 % of the energy release has on the pressure in an unsupported detonation reaction zone, we introduced the small-resolved heat-release (SRHR) model of
Summary
One-dimensional (1-D) idealized form, a free-running, high-explosive (HE) detonation is a shock supported by the release of energy, initiated by the passage of the detonation’s shock over fresh explosive. As the confinement deflects in response to the pressure in the explosive’s reaction zone, a steep rarefaction is able to propagate into the explosive’s reaction zone, since the flow in the reaction zone and near the detonation shock is initially subsonic in the detonation shock-attached reference frame. As we have argued before (Bdzil 1981; Bdzil & Stewart 1986; Aslam et al 1996), once the sonic locus contacts the detonation shock at the edge, that limits any further decrease of the shock pressure near the edge, Pe, and limits the strength of the rarefaction propagating into the reaction zone. Carried out in the detonation shock /confiner interface intersection reference frame, this analysis constructs the pressure, P, versus streamline turning angle, Θ, curves both for all shocks and all rarefactions. Since for the steady-detonation problems described above the phase velocity is only known after the complete problem is solved, D0 is set by the user as an available free parameter
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
