Computer simulation of initiation of detonation by shock focusing

Failure of containment and essential equipment due to post-accident hydrogen combustion is recognized as a potential safety concern. One of the hazards posed by hydrogen combustion is the possibility of a transition to detonation resulting from flame acceleration. It has been demonstrated that the collision of the leading shock wave associated with an accelerated flame with obstacles along its path can create local hot spots and trigger onset of detonation. The objective of this paper is, through computer simulation, to determine the critical conditions required for onset of detonation and to establish the criteria for transition to detonation in tubes filled with various types of obstacles. The simulations described in this paper model the initiation of detonation resulting from a collision of a shock wave with a hemispherical cup. Three different configurations were used to examine formation of local hot spots by shock focusing. The first configuration was a 6 cm-diameter hemispherical cup located at the closed end of the tube (also 6 cm in diameter). Hemispherical cups were used in the present study because their 3-dimensional structure produces strong shock focusing effects. This configuration also allows us to simulate a 3-D phenomenon with a 2-D computer code. The second case was similar to the first configuration except that a 2 cm shoulder was added to the side of the cup. The third configuration was a 2 cm-diameter orifice placed along the centre of the tube. This configuration represents the limiting case in which the effects created by the curvature of the cup are removed in the shock focusing process. The gas mixture used in the simulation was a stoichiometric hydrogen-oxygen mixture at an initial pressure of 13.2 kPa and a temperature of 300 K. The critical conditions in terms of incident shock Mach numbers were determined for these three configurations. These critical conditions for onset of detonation agree with experimental observations. The present results enable us to determine the critical flame speed an accelerated flame has to achieve for a transition to detonation to occur. (author). 7 refs., 3 figs