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.