Shock-induced ignition with three-step chain-branching kinetics

Simulation of shock-ignition is a challenging problem because of the singular nature of the initial conditions due to the initial non-existence of the region of shocked reactive mixture. A combination of techniques has been developed, and results are obtained for a three-step chain-branching kinetic scheme. These techniques include replacing space as an independent variable by the ratio space over time, using initial conditions obtained from short time asymptotics. The essentially non-oscillatory numerical scheme used captures the entire ignition process : hot spot and shock formation, and appearance of a detonation wave. Numerical simulations were performed based upon the reactive Euler formulation, for a contact surface separating non-reactive hot fluid from cold reactive mixture. Chain-branching results were obtained for crossover temperatures corresponding to shocked fluid states from close to the limit to well inside the chain-branching zone. Since ignition occurs in a very thin zone compared with the length of the computational domain, the computations are relatively large, even though the problem is one-dimensional. Well inside the chain-branching region, results are consistent with the strong ignition model of Souloukhin and Oppenheim. Conversely, as we approach the limit, it seems that our model fails to capture the weak ignition regime.