A theory of deflagration-to-detonation transition in unconfined flames

This paper outlines a theoretical approach for predicting the onset of detonation in unconfined turbulent flames. Two basic assumptions are made: (1) the gradient mechanism is the inherent mechanism that leads to deflagration-to-detonation transition (DDT) in unconfined conditions and (2) the sole mechanism for preparing the gradient in induction time is by turbulent mixing and local flame quenching. The criterion for DDT is derived in terms of the one-dimensional detonation wave thickness, the laminar flame speed, and the laminar flame thickness in the reactive gas. This approach gives a lower-bound criterion for DDT for conditions where shock preheating, wall effects, and interactions with obstacles are absent. Regions in parameter space where unconfined DDT can and cannot occur are determined. Copyright (C) 1997 by The Combustion Institute.