The failure of marginal detonations in expanding channels

Abstract

Critical conditions for detonation failure due to tube expansion have been observed in marginal detonations propagating in a 1 4 × 3 in. (6.35 × 76.2 mm) channel. In these experiments, a well established marginal detonation propagating in the narrow channel entered a test section in which one of the narrow walls was inclined to the central axis at positive angles which ranged from 10° to 45°. Experiments were performed at pressures ranging from 60 to 200 torr (8 to 26.7 kPa) in stoichiometric hydrogen-oxygen mixtures diluted with 20, 50 and 70% argon. Smoke track records obtained on the surface which is the major dimension of the tube, were used to determine failure, incipient failure or self-sustenance of the entering wave. Because of the narrow tube used in the studies the incident waves were marginal in that their velocity was below the expected CJ (Chapman-Jouguet) value, their transverse wave spacing was larger than one would see in a large tube, and the transverse waves were of greater strength than in an ordinary detonation. All of these indicators of marginal behavior became progressively more pronounced as the pressure dropped from 200 torr (26.7 kPa) to the limit pressure of approximately 58 torr (7.73 kPa). The most interesting result of this experimental investigation is that the theoretical analyses predicted that simple one-dimensional opening of the tube should not show a pressure dependence to failure, while the experiments showed a definite decrease in the opening angle required for failure as initial pressure decreased. This behavior is related to the marginality of the incident waves, which is observed to increase smoothly with decreased pressure. It is postulated that detonation failure in the hydrogen-oxygen system occurs when the shock velocity at the end of the cell drops to about 0.60 of the CJ value due either to marginal behavior or to an expansion of the cross section of the tube.