Asymptotic analysis of the critical dynamics of spherical gaseous detonations

International audienceThe critical dynamics of supersonic combustion waves is studied in the context of thedirect initiation of detonation in a spherical geometry. The study is performed by anasymptotic analysis in the limit of small heat release, including unsteadiness, curvatureand the gradient of the burnt-gas flow. Derivation of analytical expressions for therarefaction wave in the burnt-gas flow, combined with numerical studies, provides thebasis of the analysis. The critical trajectories ‘detonation velocity vs front radius’ D (r f ) arecharacterized by a decay well below the Chapman–Jouguet (CJ) velocity at a small radius(however, larger than the detonation thickness), followed by a re-acceleration processback to a CJ detonation. The phenomenon is explained by the dynamics of the sonicpoint inside the inert rarefaction wave behind the reaction zone. The key mechanism isa critical slowdown as soon as the sonic condition (relative to the lead shock) approachesthe reaction zone from behind, leading to an increase of the time delay in the nonlinearresponse of the combustion wave to the rarefaction-wave-induced decay. Detonation failsif the rate of decay is strong enough to prevent the sonic point catching the reactionzone. Concerning successful initiation, the link between the trajectories D (r f ) of thefully unsteady problem and of the self-similar CJ solution of the discontinuous modelis deciphered in the long-time limit