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Effect of chemical composition, pressure, temperature, geometry, system physical scale, non-uniformity (SWACER) and presence of venting

Effect of non-uniformity (SWACER)

In DDT process energy required to initiate detonation is provided by rapid release of energy during combustion to produce a blast wave of sufficient strength to cause detonation. As described by Lee (LeeJHS:1980), such shock waves can be produced by prescribing a spatial and temporal coherence of the energy release. Theoretically, the required coherence can be achieved by pre-conditioning the explosive mixture so that the induction time \tau increases in a prescribed manner away from an initial ignition point to produce energy source which propagates at a velocity V_0 = (\partial \tau /\partial x)^{-1} . Spatial gradients in induction time are due to gradients in temperature and/or free radical concentrations. The so-called SWACER (Shock Wave Amplification by the Coherent Energy Release) mechanism was first proposed to account for photochemical initiation in H2-Cl2 mixtures. Gradients in temperature and free radicals are also produced by turbulent mixing of hot combustion products with unburned gas in turbulent eddies associated with flame propagation around obstacles or in turbulent flame jets. Knystautas et al. (KnystautasR:1979) achieved DDT by injecting a hot turbulent jet into a quiescent fuel-oxygen mixture. Coherent energy release by itself is not enough for DDT, the volume of coherent energy release must be also be large enough to produce a strong enough shock wave with long enough duration to initiate detonation in the surrounding unburned mixture. A lower bound of the volume required for transition to occur in an unconfined cloud can be obtained by equating the chemical energy in a spherical volume to the critical initiation energy by an external source:

E_{c} =\frac{\pi \rho _{0} QD_{c}^{3} }{6}

where Q is the chemical energy release per unit volume, \rho_0 is the density of the unburned mixture, and D_c is the critical explosion diameter.

Lee J.H.S. and Moen I. O. (1980) The mechanism of transition from deflagration to detonation in vapor cloud explosions. Progress in Energy Combustion Science, 6:359-389.(BibTeX)
Knystautas R., Lee J.H.S., Moen I.O. and Wagner H.Gh. (1979) Direct initiation of spherical detonation by a hot turbulent gas jet. In Proceedings of the Seventeenth Symposium (International) on Combustion. Pittsburgh. The Combustion Institute, pages 1235-1245.(BibTeX)

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