Two-Dimensional Gaseous Detonations: Velocity Deficit

The measured velocity of gaseous detonation waves is less than that predicted by the Chapman-Jouguet plane wave theory. The velocity deficit (difference between theoretical and measured velocities) has been found earlier to vary inversely with the tube diameter and initial pressure. A quantitative explanation of this effect is advanced by determining the growth of the viscous boundary layer on the tube wall and its effect upon the flow in the reaction zone of the detonation front. It is proposed that the boundary layer displacement effect within the reaction zone produces a uniform flow divergence throughout the detonation front. The velocity deficit due to this two-dimensional flow is determined, using measured values of reaction zone thickness. The agreement of the velocity deficit with measured values is within a factor of two for the five hydrogen-oxygen-inert gas mixtures and one acetylene-oxygen mixture for which sufficient data are available.