Theory of Mach reflection of detonation at glancing incidence

Abstract

We present a theory for Mach reflection of a detonation undergoing glancing incidence reflection off of a rigid wall. Our focus is on condensed-phase explosives, which we describe with a constant adiabatic gamma equation of state and an irreversible and either state-independent or weakly state-dependent reaction rate. We consider two detonation models: (1) the instantaneous reaction heat-release Chapman–Jouguet (CJ) limit and (2) the spatially resolved reaction heat-release Zeldovich–von Neumann–Dø̈ring (ZND) limit, where here we only consider that a small fraction of the detonation energy release is spatially resolved (the SRHR limit). We observe a three-shock reflection in the CJ limit case, with a Mach shock that is curved. We develop an analytical expression for the triple-point track angle as a function of the angle of incidence. For the SRHR model, we observe a smooth lead shock, akin to von Neumann reflection, with no reflected shock in the reaction zone. Only at larger angles of incidence is a three-shock Mach reflection observed.