Direct Initiation of Gascous Detonations

Abstract
A theoretical analysis of the direct initiation of gaseous detonations by an energy source has been published recently, the results are recalled here. Nonlinear curvature effects are proved to be essential mechanisms controlling the critical condition. These effects are first studied in a quasi-steady (q-s) state approximation valid for a characteristic time scale much larger than the reaction time scale. Two branches of q-s solutions are exhibited with a C-shaped curve and a critical radius below which generalised Chapman-Jouguet (CJ) solutions cannot exist. At ordinary conditions this critical radius is much larger than the thickness of the plane CJ detonation front (typically 300 to 500 times larger). Direct numerical simulations show that the upper branch of q-s solutions, acts as an attractor of the unsteady blast waves originating from a sufficiently strong energy source. The criterion of initiation derived here works to a good approximation and exhibits the huge numerical factor (10⁶ - 10⁸) which is observed in the experimental data of the critical energy source and which was not explained up to now. Transient may induce additional failure mechanisms close to the critical condition.