Numerical study of direct initiation for one-dimensional Chapman–Jouguet detonations by reactive Riemann problems

Direct initiation of one-dimensional Chapman–Jouguet detonations in a framework of reactive Riemann problems has been numerically studied with a detailed chemical reaction mechanism in a stoichiometric hydrogen/oxygen mixture diluted by 70% argon. The reactive Riemann problem, with reactants of high temperature and high pressure to the left of the diaphragm as an energy source with a finite length scale, is applied to initiate detonations downstream. Based on the length scales and initial thermodynamic parameters of the energy source, three different regimes of detonation initiation were found, namely supercritical, critical, and subcritical regimes, which is in accord with the classical blast initiation. The initiation process is essentially an inert shock tube problem nonlinearly coupled with a constant-volume explosion. When the auto-ignition delay time of the constant-volume explosion is large as compared to that behind the leading shock, the mechanism can be identified as an incident shock initiation because the explosion far behind the leading shock cannot affect it. This is essentially the same as the experiments of detonation initiation in a shock tube. Conversely, when the auto-ignition delay time of the constant-volume explosion is small as compared to that behind the leading shock, the initiation process is highly influenced by the heat release of chemical reaction occurring near the rear boundary. A pressure pulse is generated at the tail of the modified expansion fan because of localized maximum reaction rate and eventually evolves into a shock to interact with the leading shock to enhance it. The subsequent detonation downstream is also a result of the initiation of the enhanced leading shock. The numerical results also suggest that the critical energy scaled by the product of the initial pressure and the length scale of the energy source keeps constant with the change in length scale, but can be highly influenced by the initial temperature of the energy source. The scaled critical energy is found to be approximately between 1 and 2 for a wide temperature range above the auto-ignition temperature.