On the critical initiation of planar detonation in Noble-Abel and van der Waals gas

The critical decay rate theory (C.A. Eckett, J.J. Quirk, J.E. Shepherd, Journal of Fluid Mechanics 421 (2000) 147–183) on detonation initiation in unsteady flow was extended from ideal to Noble-Abel and van der Waals gas, in which the finite molecular volume effect (or repulsion force) and the inter-molecular attraction effect (or attraction force) were included. Considering the reactive Euler equations, the reaction zone temperature-gradient equation was established independently of the equation of state and wave geometry, and then solved asymptotically by assuming large activation energy, planar wave front and a one-step irreversible reaction model. A critical decay time was derived as the critical condition for detonation initiation. It was found that the inter-molecular attraction effect makes initiation more difficult by increasing the critical decay time, whereas the finite molecular volume effect promotes initiation. The real gas effects are enhanced when increasing the reduced activation energy and/or decreasing the heat capacity ratio of perfect gas. The applicability and generality of the asymptotic solutions were evaluated by comparison with quasi-unsteady simulation employing detailed reaction models for hydrogen-air and ethylene-air mixtures, and with the further simplified, fully analytical solutions based on strong-shock assumption. The critical conditions of the asymptotic solutions are qualitatively consistent with those obtained with the detailed mechanisms. The asymptotic solutions can also be well reproduced by the simple analytical solutions in most conditions. This study thus establishes a simple, yet reliable, method to evaluate the real gas effect on detonation initiation in high-pressure conditions.