Ignition and mixing in a reacting shock-bubble interaction

In the present work the interaction between shock-induced hydrodynamic instabilities and reaction waves is examined within the generic setup of a reacting shock-bubble interaction (RSBI) with detailed hydrogen-oxygen reaction kinetics. A planar shock wave penetrates a gas bubble, filled with a reactive gas mixture. Due to the convex shape of the bubble, the shock is focused and spots of high pressure and temperature arise. Depending on the shock strength the bubble is ignited directly behind the shock wave or near the downstream pole after a distinct ignition delay time. The following reaction wave propagates either as a deflagration or detonation through the reactive bubble gas. The configuration of RSBI serves to investigate the influence of different reaction wave types on global flow field quantities, like mixing and enstrophy production, and on the spatial and temporal evolution of the bubble gas. Three main configurations of RSBI serve to study the shock-induced ignition of a diluted stoichiometric hydrogen-oxygen gas mixture and the subsequent interaction with hydrodynamic instabilities. The first study contains a two-dimensional RSBI, which is penetrated by a shock wave at a constant shock Mach number. Different reaction wave types are triggered by the change of the initial pressure at a constant initial temperature. A low initial pressure leads to a long ignition delay time, followed by a subsonic deflagration wave. An increase of the pressure shortens the ignition delay time and induces a supersonic detonation wave. The rapid propagation of the detonation wave leads to an intense interaction between the reaction wave and the arising hydrodynamic instabilities. Mixing is significantly reduced and the growth of secondary instabilities is decelerated. The deflagration wave is characterized by a minor influence on the flow field: Due to the low propagation velocity the mixing is less reduced and the bubble evolution is only affected in the long-term evolution. The second study of RSBI analyzes the variation of the shock strength in a RSBI, which generates complex thermodynamic post-shock conditions. Different reaction wave types are triggered, including multiple ignitions and transition processes from deflagration to detonation. Two limiting cases are observed: The lowest shock Mach number induces deflagration near the shock-focusing point and the highest shock strength detonation directly at the upstream pole of the bubble. Besides the limiting cases two special phenomena are observed for shock Mach number in between, which have not been discussed before: The transition from deflagration to detonation (DDT) and a simultaneous double detonation. The third configuration deals with the first three-dimensional simulation of RSBI so far and outlines the influence of three-dimensional effects on the bubble evolution. A strong shock wave ignites the bubble gas before the shock-focusing point and induces a detonation wave. The reaction wave decelerates the growth of Richtmyer-Meshkov and Kelvin-Helmholtz instabilities and highly influences the mixing of the bubble gas with its surrounding. Three-dimensional effects, like vortex stretching and decay, as well as Widnall-type instabilities of the main vortex ring are observed and thoroughly analyzed. The present dissertation outlines numerical results of RSBI with detailed chemistry, including the first three-dimensional RSBI of its kind, and contributes to a deeper understanding of the interaction between hydrodynamic instabilities and shock-induced combustion processes.