Theory of gaseous detonations

The objective of the present paper is to review some developments that have occurred in detonation theory over the last ten years. They concern nonlinear dynamics of detonation fronts, namely patterns of pulsating and/or cellular fronts, selection of the cell size, dynamical self-quenching, direct (blast) or spontaneous initiation, and transition from deflagration to detonation. These phenomena are all well documented by experiments since the sixties but remained unexplained until recently. In the first part of the paper, the patterns of cellular detonations are described by an asymptotic solution to nonlinear hyperbolic equations (reactive Euler equations) in the form of unsteady (sometime chaotic) and multidimensional traveling-waves. In the second part, turning points of quasi-steady solutions are shown to correspond to critical conditions of fully unsteady problems, either for (direct or spontaneous) initiation or for spontaneous failure (self-quenching). Physical insights are tentatively presented rather than technical aspects. The challenge is to identify the physical mechanisms with their relevant parameters, and more specifically to explain how the length-scales involved in detonation dynamics are larger by two order of magnitude (at least) than the length-scale involved in the steady planar traveling-wave solution (detonation thickness).