The diffraction of a planar detonation wave at an abrupt area change

Previous experimental work on the diffraction of a detonation wave at a large and abrupt area change in a tube, has shown that every system is characterized by a critical tube diameter at which quenching of the detonation occurs. Zeldovich, Kogarko & Simonov (1956) established that the critical tube diameter, for the oxy-acetylene system with varying dilution of nitrogen, lies between 500 and 700 times the one-dimensional induction zone length. Later, Mitrovanov & Soloukhin (1964) discovered that, for the same system, the critical diameter is 10 or 13 times the transverse wave spacing for a flat channel and cylindrical tube respectively. The two results are shown to be equivalent and are confirmed by further experiments in a 75 × 6 mm channel in which the flow is two-dimensional.Smoked foil and schlieren records show that, for supercritical waves, re-ignition occurs at sites along the wedge formed by the head of the expansion from the diffracting aperture and criticality is attained when the site is located at the apex of the wedge. A universal feature of re-initiation, which is also observed in liquid and solid explosives, is the sudden appearance of a transverse detonation which sweeps through the compressed, but unreacted, gas of the dissociated shock-reaction zone regime; this is signalled by the appearance of fine triple-point writing on smoked-foil records.A criterion for re-initiation is formulated by equating the critical velocity gradient which characterizes the decay of the wavefront in a cell, to that obtaining in the diffracted shock front at the head of the expansion fan; an expression for the latter is derived from Whitham's (1957) theory for non-reactive shocks. The prediction of the criterion is in good agreement with observation.