Critical Dynamics of Direct Initiation of Spherical Detonations

International audience ; The asymptotic limit of small heat release is investigated in the context of the critical dynamics of detonation direct initiation. The analysis, limited to spherical geometry, includes unsteadiness, curvature effects, and the gradient of the burnt-gas flow. Numerical integration of the hyperbolic equation governing the dynamics provides the basis of the study. The critical trajectories "detonation velocity vs radius" are characterized by a decay well below the CJ velocity at a small radius followed by a re-acceleration process back to a CJ detonation. The key mechanism is identified as the slowdown produced as soon as the sonic point reaches the exit of the reaction zone. Under this condition, the time delay of the nonlinear response of the front to the rarefaction-wave-induced decay increases significantly. Detonation fails if the decay rate is strong enough to prevent the sonic point to catch the exit of the reaction zone.