Initiation of reactive blast waves by external energy sources

This article is devoted to the analysis of the direct initiation, by concentrated centrally-symmetric external energy sources, of self-sustained detonation waves in gaseous reactive mixtures. The dynamics of the detonation front will be described in the fast reaction limit, when the thickness of the reaction layer that follows the shock front is very small compared with the shock radius. At early times, after starting the external thermal energy deposition, the detonation front, associated with a strongly expanding flow, is overdriven; thus it is reached by expansion waves that decrease its velocity towards the Chapman–Jouguet (CJ) value, for which the expansion waves can no longer reach the front. The decay occurs for detonation radii such that the energy released by the external source equals the heat released by the chemical reaction. For planar detonations the CJ velocity is only approached asymptotically for large times, while for cylindrical and spherical detonations the flow divergence provides an additional decay mechanism associated with the front curvature that causes the transition to the constant CJ velocity to occur at a finite value of the detonation radius. The time evolution of the flow field and the corresponding variation with deposition time of the transition radius is computed for energy sources of constant heating rate. The analysis includes a detailed quantitative description of the near-front flow structure for times close to the transition time, given here for the first time, along with the study of the evolution towards the Zelʼdovich–Taylor cylindrical or spherical self-similar flow structure, which corresponds to a CJ detonation front ideally initiated at the center without any external energy source. The asymptotic decay to CJ is also described for planar detonations initiated with energy sources of constant heating rate and finite nonzero deposition time. A brief discussion will be given on how the reaction may be quenched by the flow divergence effects if the initiating energy is smaller than a critical value, thus failing to generate a self-propagating detonation wave.