Critical Decay Time Model for Direct Detonation Initiation Energy in Gaseous Mixtures

Abstract

A critical decay time (CDT) model is developed to predict the critical energy of direct detonation initiation in gaseous mixtures. It is based on the global initiation criterion that the energy deposit should allow the decaying shock speed to stay in a specific range below the Chapman–Jouguet (CJ) speed at least for a critical decay time. The speed range is estimated with the sub-CJ Zel’dovich–von Neumann–Döring (ZND) simulations. The critical decay time is calculated as the minimum time to reach unity Mach number in the sub-CJ ZND simulations. The lower-speed bound is taken as a characteristic extinction speed below (which means the lower-speed bound) which the direct initiation should fail. This speed is calibrated using one-dimensional simulations for [Formula: see text] mixtures. The calibrated CDT model is then applied to estimate the critical initiation energy with the point-blast theory. The model yields better agreement with experimental data for hydrogen-fueled mixtures such as [Formula: see text] and [Formula: see text] mixtures than the well-known critical decay rate model. For small hydrocarbon-fueled mixtures such as [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] mixtures, the predicted critical energies also agree well with experimental results. The CDT model provides an efficient tool to evaluate the detonability of fuel–oxidizer mixtures, which could be beneficial for ignition initiation in propulsion and power devices such as rotating detonation engines.