Detonability limits in thin annular channels

In this paper, detonability limits in two-dimensional annular channels are investigated. Since the channel heights are small in comparison to the tube diameter, curvature effects can be neglected and the annular channels can be considered to be essentially two-dimensional. Mixtures that are highly diluted with argon are used since previous investigations seem to indicate that detonations in such mixtures are “stable” in that cellular instabilities play minor roles on the propagation of the detonation. For stable detonations where the ZND structure is valid, boundary layer effects can be modeled as a flow divergence term in the conservation of mass equation following the pioneering work of Fay [J.A. Fay, Phys. Fluids 2(3) (1959) 283–289]. Expansion due to flow divergence in the reaction zone results in a velocity deficit. There exists a maximum deficit when an eigenvalue detonation velocity can no longer be found, which can be taken as the onset of the detonability limits. Experimentally, it was found that unlike “unstable” detonations, the detonability limits for “stable” detonations are well-defined. No unstable near-limit phenomena (e.g., galloping detonations) was observed. Good agreement is found between the theoretical predictions and the experimentally obtained velocity deficits and limits in the two channel heights of 2.2 and 6.9 mm for hydrogen–oxygen and acetylene–oxygen mixtures diluted with over 50% argon. It may be concluded that at least for these special mixtures where the detonation is “stable,” the failure mechanism is due to flow divergence caused by the negative displacement thickness of the boundary layer behind the leading shock front of the detonation wave.