Abstract
The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.
Highlights
Introduction of the Mach Reflection ofThe Mach reflection of detonation waves is a classical problem that attracts considerable research attention, even in problems with multi-interfaces [1,2,3]
Note that it usually takes a long time for a stable planar Zel’dovich–von Neumann–Döring (ZND) detonation to evolve into a fully established cellular detonation
The present study involved a numerical investigation of the problem of Mach reflection of ZND detonations to investigate qualitatively the onset of the Mach reflection in the near field
Summary
The Mach reflection of detonation waves is a classical problem that attracts considerable research attention, even in problems with multi-interfaces [1,2,3]. The triple-point trajectory of a detonation Mach reflection appears to maintain self-similarity under the frozen limit (non-reactive three-shock theory) for a relatively large distance (several λ in [12] or 30–40 ∆ in [13]) This violates the definition of the frozen limit, which requires that the Mach stem travel distance is sufficiently small compared to the characteristic length scales, so as to ensure the detonation front is “frozen”. We attempt to perform an accurate comparison between the Mach reflection of a ZND detonation with the self-similar shock case to Entropy 2021, 23, 314 study the self-similarity problem associated with the onset of the Mach reflection in detail, especially the range of the frozen limit, by focusing on a relatively smaller scale near the wedge apex.
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