Pressure Evolution from Head-on Reflection of High-speed Deflagration in Hydrogen Mixtures

Our previous reported experiments revealed that the reflection of high-speed deflagrations in hydrogenair and hydrogen-oxygen mixtures produces higher mechanical loading and reflected pressures than reflecting detonations. This surprising result was shown to correlate with the onset of detonation in the gases behind the reflected shock. We revisit these experiments with the aim of developing a closed-form model for the pressure evolution due to the shock-induced ignition and rapid transition to detonation. We find that the reflection condition of fast deflagrations corresponds to the chain-branching crossover regime of hydrogen ignition, in which the reduced activation energy is very large and the reaction characteristic time is very short compared to the induction time. We formulate a closed-form model in the limit of fast reaction times as compared to the induction time, which is used to predict a square wave pressure profile generated by self-similar propagation of internal Chapman-Jouguet detonation waves followed by Taylor expansion waves. The model predictions are compared with Navier-Stokes numerical simulations with full chemistry, as well as simple Euler calculations using calibrated one-step, or twostep chain-branching models. Both simplified numerical models were found to be in good agreement with the full chemistry model. We thus demonstrate that the end pressure evolution due to the reflection of high-speed deflagrations can be well predicted analytically and numerically using relatively simple models in this ignition regime of main interest for safety analysis and explosion mitigations. The slight departures from the square wave model are investigated based on the physical wave processes occurring in the shocked gases, controlling the shock-to-detonation transition. Using the two-step model, we study how the variations of the rate of energy release control the pressure evolution in the end gas, extending the analysis of Sharpe to very large rates of energy release.