Structure and properties of detonation waves of heterogeneous explosives from the point of view of the hot spots mechanism

It is assumed that the chemical reaction of a detonation transformation, that is, burning, arises first in separate hot spots originated by the explosive compression behind or within the detonation wave front due to heterogeneity of charges, instability of the detonation wave, etc. Then the burning spreads around into the bulk of the explosive and is completed in the Chapman–Jouguet plane, where the detonation product velocity relative to the detonation front is equal to the sound velocity. A simple analytical method proposed early by the authors is used to calculate the expression for the detonation transformation time, from which it follows that there are at least two nondimensional numbers defining the possibility of the realization of the mechanism mentioned above. The first one is the Frank-Kamenetskii number, that is, the relation of the characteristic time of the cooling of the hot spot to the adiabatic induction period at some characteristic temperature of the hot spot. The hot spot mechanism is realized if the Frank-Kamenetskii number is greater than the critical one that determines the minimum possible size of hot spots capable of ignition. The second number is the relation of the detonation transformation time in the presence of hot spots to the reaction time in accordance with classical mechanism. The hot spot mechanism at detonation is realized if this number is less than unity. By means of the numbers proposed, some interpretations of available experimental data concerning the detonation process are given.