Quasi-steady stages in the process of premixed flame acceleration in narrow channels (original) (raw)

The present paper addresses the phenomenon of spontaneous acceleration of a premixed flame front propagating in micro-channels, with subsequent deflagration-todetonation transition. It has recently been shown experimentally R. Yetter, Proc. Combust. Inst. 31, 2429 (2007)], computationally [D. Valiev, V. Bychkov, V. Akkerman, and L.-E. Eriksson, Phys. Rev. E 80, 036317 (2009)], and analytically [V. Bychkov, V. Akkerman, D. Valiev, and C. K. Law, Phys. Rev. E 81, 026309 (2010)] that the flame acceleration undergoes different stages, from an initial exponential regime to quasi-steady fast deflagration with saturated velocity. The present work focuses on the final saturation stages in the process of flame acceleration, when the flame propagates with supersonic velocity with respect to the channel walls. It is shown that an intermediate stage may occur during acceleration with quasi-steady velocity, noticeably below the Chapman-Jouguet deflagration speed. The intermediate stage is followed by additional flame acceleration and subsequent saturation to the Chapman-Jouguet deflagration regime. We elucidate the intermediate stage by the joint effect of gas pre-compression ahead of the flame front and the hydraulic resistance. The additional acceleration is related to viscous heating at the channel walls, being of key importance at the final stages. The possibility of explosion triggering is also demonstrated. C 2013 AIP Publishing LLC. 096101-2 Valiev et al. Phys. Fluids 25, 096101 (2013) at the rough walls, and viscous drag in relation to DDT have been also discussed. 20-23 An important theoretical prediction of Refs. 18 and 19 was the fast flame front acceleration in narrow channels. Following this prediction, experiments on DDT in micro-channels with diameters about 1 mm have been performed 24-27 using ethylene-oxygen mixtures. In addition to supporting the main theoretical predictions, the experiments also demonstrated several additional features beyond the scope of the theory, such as the possibility of fast steady or quasi-steady deflagration propagating with supersonic speed with respect to the channel wall. Since the theory 18, 19 was restricted to the initial incompressible stage of flame acceleration, it did not account for compressibility effects.