F. Diegelmann, S. Hickel, N.A. Adams (2016)
Combustion and Flame 174: 85-99. doi: 10.1016/j.combustflame.2016.09.014

We present numerical simulations for a reactive shock–bubble interaction with detailed chemistry. The convex shape of the bubble leads to shock focusing, which generates spots of high pressure and temperature. Pressure and temperature levels are sufficient to ignite the stoichiometric H2–O2 gas mixture. Shock Mach numbers between Ma = 2.13 and Ma = 2.90 induce different reaction wave types (deflagration and detonation).

Depending on the shock Mach number, low-pressure reactions or high-pressure chemistry are prevalent. A deflagration wave is observed for the lowest shock Mach number. Shock Mach numbers of Ma = 2.30 or higher ignite the gas mixture after a short induction time, followed by a detonation wave. An intermediate shock strength of Ma = 2.19 induces deflagration that transitions into a detonation wave. Richtmyer–Meshkov and Kelvin–Helmholtz instability evolutions exhibit a high sensitivity to the reaction wave type, which in turn has distinct effects on the spatial and temporal evolution of the gas bubble. We observe a significant reduction in mixing for both reaction wave types, wherein detonation shows the strongest effect. Furthermore, we observe a very good agreement with experimental observations.


Temperature contours for reacting and inert shock-bubble interactions at Mach numbers Ma = 2.13, Ma = 2.3, and Ma = 2.9. The reacting cases (hot!) are shown on the upper half and the corresponding inert cases on the (cold) lower halves. 


Deflagration to detonation transition in the reacting shock-bubble interaction at Mach number Ma=2.19. The upper half shows temperature contours and the lower half the pressure.