Criteria for transition to detonation in tubes

Abstract

Transition from high speed flame to detonation in tubes was studied in an extensive series of experiments with the aim being to establish quantitative limiting criteria for the onset of transition. The experiments were carried out in three long tubes each with a different diameter. The tubes were 18 meters each and had internal diameters of 5, 15 and 30 cm, respectively. A matrix of fuel-air mixtures at atmospheric initial pressure and room temperature was studied over a broad range of equivalence ratios. The fuels were hydrogen, acetylene, ethylene, propane and methane. High speed flame propagation and transition to detonation were achieved in a controlled manner within each tube using the well-known flame acceleration technique of obstructing obstacles pioneered long ago in the experiments of Wheeler. In the present experiments the entire tube length was filled with orifice ring obstacles, equispaced one tube diameter apart, to ensure that the maximum terminal flame speed is achieved in all cases within the available length of each tube. The results show that transition to detonation in tubes invariably occurs from a minimum level of flame speed corresponding roughly to the speed of sound of the combustion products. Since the flame speed in a tube is directly coupled to the flow field that it generates ahead of itself, this minimum flame velocity requirement implies that an adequate intensity of turbulent shear mixing is required to form the required explosive pocket of gas inherent in the genesis of detonation. There is also a necessary condition for transition to detonation in that the minimum transverse tube dimension, corresponding to the orifice opening diameter d in this study, must be sufficiently large to accomodate at least one transverse cell width characteristic of the mixture in the tube. That is, the quantitative criterion for transition is that λ/ d ≤1. Once established, the detonation wave in the tube within the obstacle field is observed to propagate at a steady velocity with a substantial velocity deficit which can be as high as 40% below the theoretical C-J value. In the limit when d /λ→13, the detonation propagation asymptotically approaches the C-J level as expected.