Transient phenomena in the initiation of a mechanically driven plane detonation

Abstract

Significant exothermic chemical activity in a combustible gas is switched on by a strong plane shock wave created by mechanical-power input from a piston. The Euler equations, written in terms of a lagrangian coordinate system, are used to model behaviour in the space between piston and shock. Since a primary aim is to follow the development of additional shocks, created by the release of chemical power, numerical solution of the problem is sought via the Random Choice Method combined with time-operator-splitting. Some effort is expended in bringing together in the text a number of facts, including some mathematically exact statements that are central to the analysis and comprehension of the numerical results. Thermal runaway takes place first in a small region, adjacent to the piston face, within which there is found high pressure, high temperature and comparatively low density. As a consequence of the way in which gas has been conditioned in the unsteady induction domain downstream of the precursor shock, a quasi-steady weak detonation appears at the head of the runaway region, and travels quickly into the induction domain. Continuing chemical power release behind this, decelerating, weak detonation creates a region of high pressure, high temperature and, now, high density too. A consequence of all of this activity is a gas velocity significantly in excess of the piston velocity. There must therefore be a region of strong expansion, between the location of peak-pressure and the piston face, whose task is to reduce flow velocities. Since intense chemical activity continues throughout the region within which all of these events take place, part of the pressure drop is accomplished through the action of a quasi-steady fast flame. As reactant material is consumed, further reductions of pressure take place through an inert expansion wave. The reaction shock, the unsteady reactive domain adjacent to it downstream, and the fast flame downstream of that, make up the elements of the ‘triplet’ that has been observed in earlier studies to precede formation of Zeldovich–von-Neumann–Döring (ZND) detonation. Precisely the same thing happens here, although this is the first time that creation of the ‘triplet’ from purely mechanical power input has been observed. The ZND-wave is of Chapman–Jouguet strength, and the inert expansion soon resolves itself into the classical Taylor wave. This system is still travelling in the slightly perturbed induction domain behind the precursor shock at the time that numerical calculations cease.

Ignition of thermally sensitive explosives between a contact surface and a shock

“…Thus as in the piston case [4,5], we expect that for moderately large finite activation energies the solutions will be qualitatively different to the asymptotic predictions, since the main reaction zone times will not short compared to the asymptotic wave deceleration time, and hence unsteadiness needs to be considered [5]. Furthermore, since the length and time-scales involved in the asymptotic become shorter as α 0 increases, larger activation energies can be expected to be required for the quasi-steady assumption to become valid.…”

“…However, numerical simulations of the piston driven shock-to-detonation process with finite, but realistic activation energies [4,5] show qualitatively different evolution scenarios than that predicted by the asymptotic theory . For moderately large activation energies, the reaction wave which emerges from the piston face consists only partially of a quasi-steady weak detonation, with the remainder of the wave complex comprising an unsteady combustion zone followed by part of a quasi-steady fast-flame (an expansive, subsonic reaction wave).…”

“…Values of E at different initial temperatures (> 1000K) and pressures were found by considering changes of the constant volume explosion induction time with temperature [25], giving E ∼ 15 for methane-oxygen, In order to interpret the results of the simulations we use the diagnostic methods described in [29], which involve plotting the solutions in the pressure-specific volume, pV , and pressure concentration, pλ, planes. These pV and pλ diagrams allow one to identify components of quasi-steady reaction waves, induction zones, unsteady combustion zones and burnt regions in the solution, as well as where these various features occur [4,5,29].…”

“…For such rapid decelerations, the post-shock temperature scaled activation energy would need to be very high in order for the main reaction zone to be sufficiently thin that the quasi-steady approximation holds. For the finite activation energies considered in [4,5], the main reaction zone times are not short compared to the asymptotic wave deceleration time, and hence unsteadiness needs to be considered, which profoundly affects the evolution [5].…”

Some observations on the initiation and onset of detonation

“…In the work of Singh & Clarke [43], the required critical conditions arise owing to the action of a mechanical piston that leads to local gas-dynamic heating and chemical reaction. Experimentally, the generation of hot spots was demonstrated by Williams [21] (figure 5) for the case of initiation of detonation by a planar incident shock wave.…”