Shock-induced ignition with single step Arrhenius kinetics

Shock-initiated ignition is studied numerically for single step Arrhenius kinetics. This is relevant to hydrogen safety, because hydrogen detonates easily, and detonation in shocked mixture may occur in deflagration to detonation transition scenarios, due to shock reflections on obstacles subsequent to flame acceleration. Simulation of ignition behind a shock moving into combustible mixture is difficult because of the singular nature of the initial conditions. The solution method includes two components. First, space as an independent variable is replaced by the ratio space over time, and second, initial conditions at a small non-zero time are used, obtained in closed form from short time asymptotics. This way, the initial singularity is effectively removed and the early process is well resolved. This method was used to study how the leading shock strength, and the heat release, affects the shock-initiated ignition process. The Essentially Non-Oscillatory algorithm used captures ignition, hot spot growth, birth of a secondary shock and transition into a detonation. Results show that for weaker shock cases as well as for higher heat release the evolution is more rapid, that a secondary shock forms closer to the contact surface and quickly becomes a detonation wave.