Transmission of a detonation wave across an inert layer

The transmission of a detonation wave across a layer of inert gas is studied via one- and two-dimensional numerical simulations based on the reactive Euler equations. The resulting transient transmission process from the one-dimensional simulations is first explored in detail, and is analyzed via distance-time characteristic diagrams. The physics of this transient process is the same until the end of a quasi-steady period. Afterward, the energy release from the combustion may couple to the gas dynamics. Through this coupling, the pressure pulse accompanying the energy release can be rapidly amplified, and consequently, leads to detonation onset. If the inert layer is too thick, the detonation cannot be successfully re-initiated downstream. This inert-layer thickness beyond which a detonation fails to be re-initiated is determined as the critical thickness, δi,cr. The mechanisms underlying the scenarios with a successful and unsuccessful re-initiation are demonstrated in detail. A parametric study considering simplified and detailed chemical kinetics (i.e., a stoichiometric mixture of hydrogen and air at various initial pressure from 0.1−1atm) demonstrate that δi,cr normalized by the intrinsic ZND induction length, ΔI, asymptotically decreases with an increase of the effective activation energy, Ea. The one-dimensional simulations under-predict the experimental results [1, 2] of δi,cr/ΔI by at least one order of magnitude. In the two-dimensional scenarios, transverse-wave instabilities are present and allow the detonation wave to re-initiate in cases where re-initiation is unsuccessful in one dimension. The two-dimensional results of δi,cr are in a closer agreement with the experimental findings.