Detailed structure and propagation of three-dimensional detonations

Abstract

Self-sustaining detonations exhibit a three-dimensional structure within the reaction zone which is much more complex than one-dimensional classical theory. While the structure of two-dimensional detonations is now fairly well understood, the details of the three-dimensional structure remain largely unknown. Numerical simulation, performed with the reactive Euler equations coupled to a single-step chemistry model, yields insight into the three-dimensional reaction zone structure. Simulations in a square channel show that, in the absence of wall losses, the three-dimensional transverse wave spacing is the same as in two dimensions. However, the transverse wave structure is much more intricate. Two perpendicular modes exist in this channel, and they are approximately one-quarter of a period out of phase. This phase shift accounts for the slapping wave phenomenon observed in experiments. The slapping wave imprints on smoke foils occur when the transverse wave collides with the wall. The curvature of the imprints is explained by the curvature of the slapping wave, which is convex toward the wall. The interaction of the two transverse waves results in a vorticity field that is much more complex than in two dimensions. In two dimensions, vorticity originates from a point singularity, which is now replaced by a line singularity that forms closed loops interconnecting the two sets of transverse waves. The interconnection changes after collisions, creating cuts and free edges on the sheet structure which otherwise remains globally interconnected. It is the vorticity in the part of the sheet initiating or ending along a free edge that rolls up into rings. The rings entrain unburned fluid behind the Mach stem, as in two dimensions. The vorticity system provides a strong coupling mechanism between the two orthogonal sets of transverse waves.