A theoretical analysis of accelerating reaction waves and detonation induction distances

A theoretical model is developed to predict the acceleration of deflagration waves in one-dimensional gaseous systems. Detonations are predicted along with how far the deflagration wave travels before the detonation occurs for given composition of the initial mixture, initial temperature and pressure, and the surface condition of the detonation tube. The acceleration process is approximated by a series of quasi-steady steps. At each step, the unsteady nature of the problem is investigated separately from the irreversible effects. It is postulated that the time required to go from one step to the next is controlled by the time required to establish turbulent flow in the boundary layer. A continuous reaction wave acceleration process results. The reaction wave acceleration velocity is determined along with the distance traveled by the reaction wave.