Three-dimensional structure of freely-propagating flame prior to deflagration-to-detonation transition

The paper analyzes numerically the development of the freely expanding flame before the transition to detonation in three-dimensional space. The risks related to the transition to detonation in unconfined space arise at launch places and near-Earth space during rocket engine accidents. Clear and adequate models for such scenarios are in demand for the elaboration of safety measures. Here it is shown that the process of transition to detonation involves multidimensional effects related to the generation of compression waves and their amplification when interacting with the developing flame. The necessary conditions for deflagration-to -detonation transition are flame acceleration up to near-sonic speed and generation of transversal compression waves (propagating along the flame front). So, while the subsonic stage of flame acceleration can be successfully described by the quasi one-dimensional model supplemented by a known self-similar law of the flame area growth (folding factor), the model for the pre-detonation stage should take into account considered multidimensional effects. The presented results imply that there is no unambiguous relation between the transition to detonation and the folding factor.