Effects of a significant boundary layer on the flame acceleration and transition to detonation in millimeter-scale tubes

Experiments using three different mixtures (ethylene–oxygen, methane–oxygen, and acetylene–oxygen–argon) and four different tube diameters (0.5, 1, 2, and 4 mm) were carried out to investigate the entire process of flame propagation in narrow tubes. Flame propagation in the four sizes of tubes was recorded synchronously by a high-speed camera. The results show that the deflagration-to-detonation transition (DDT) process goes through four stages according to velocity evolution, in the sequence of (i) exponential acceleration, (ii) “hesitation” period, (iii) linear acceleration, and (iv) velocity jump. The DDT run-up distance decreases with decreasing tube diameter, which arises from the effect of the significant boundary layer during flame acceleration. The area divergence is introduced by analyzing how tube diameter and initial pressure affect the DDT run-up distance. The critical value of 0.1 for the area divergence can be used to distinguish the variation characteristics of the normalized DDT run-up distance between millimeter-scale tubes and the large tubes (centimeter-scale). Moreover, an empirical formula with a unified form is obtained, which describes the DDT run-up distance as a function of tube diameter and initial pressure. It allows a good prediction of the experimental results regardless of the tube size as well as the type of mixture.