Geometrical effect on detonation initiation by a nonuniform hot pocket of reactive gas

The coupling between combustion processes and gasdynamic effects in reactive mixtures with nonuniform temperature or concentration distributions may lead to the formation of detonations, producing very large-pressure waves. This type of large-pressure wave generation is one of the main mechanisms responsible for the knocking phenomenon in internal combustion engines and for the transition from deflagation to detonation in accidental explosions. In this paper, both theoretical analysis and one-dimensional numerical simulation are carried out to determine the critical conditions for the large overpressure generations by a nonuniform hot pocket. The analysis based on the square wave model shows that due to the curvature effect, a self-sustained quasi-CJ spherical detonation may not exist when the radius of the detonation front is smaller than a critical radius. It is found that the critical conditions for the self-sustained propagation of detonations control the formation of detonations: it occurs only when the position of the formation determined by Zeldovich's condition is larger than this critical value. The order of magnitude of the so-determined critical size of the hot pocket for successful initiation is much larger than the critical size estimated from Zeldovich's condition. This point is confirmed by our direct numerical simulations. The magnitude of the critical size is also in good agreement with the experimental results.