Numerical study of cellular detonation wave reflection over a cylindrical concave wedge

Abstract

Numerical simulations were performed to study reflection of a stable detonation wave with regular cellular patterns over a cylindrical concave wedge. The dynamics of this reflection phenomenon was described by the two-dimensional reactive Euler equations with a two-step induction-reaction kinetic model and solved numerically using the adaptive mesh refinement code AMROC. The effects of various parameters on the reflection evolution were analyzed in detail. The results indicate that the reflection-type transition of a stable cellular detonation is similar to that of a planar shock wave over a concave wedge. The triple-point trajectory resulted from the Mach reflection when the cellular detonation first encounters the concave wedge coincides with that of the planar shock propagating for the case with the same incident Mach number. As the effective wedge angle continuously increases, the Mach reflection of cellular detonation deviates from that of a planar shock with a reduced Mach stem height, and the transition from Mach to regular reflection occurs at a smaller angle. This observation is further explored by adopting the length-scale (or “corner-signal”) concept, examining the velocity variation of corner signals generated by fluid particles around the wedge tip. The reflection dynamics is described qualitatively by the ratio of two length scales characterizing the detonation structure, namely, the induction-zone and reaction-zone lengths. The increase of these length scales raises the Mach stem height and transition angle. Apart from the detonation length scales, the wedge curvature radius is found to have an opposite effect since the increase of radius expands the region where the corner signals are generated by the particles behind the induction zone, and makes the corner signals persist in a state with attenuating velocity.