Numerical Investigation of Richtmyer-Meshkov Instability in Reactive Gas Mixtures

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The interaction of a shock wave with a bubble of reactive gas mixture triggers Richtmyer-Meshkov instabilities and chemical reactions. With inert shock-bubble interactions (SBI) vorticity is deposited near the interface by baroclinic production. The incident shock wave is transmitted and reflected at the interface. For a heavy-gas bubble immersed in light gas the transmitted shock focuses at the downstream pole of the bubble resulting in a strong increase of pressure and temperature. Vorticity deposition leads to a strong deformation of the interface. The flow develops a turbulent mixing zone around the material interface. Non-reacting SBI was intensely studied over the last decades. In 1983 Haas and Sturtevant investigated SBI for light- or heavy-gas bubbles in air, thus establishing an entire new class of canonical flow configurations. Temperature and pressure increase due to the impacting shock wave opens the way of igniting a reactive-gas mixture without direct contact. Ex-tending SBI to reactive SBI (RSBI), Haehn et al. investigated in 2012 a stoichiometric mixture of hydrogen and oxygen, diluted by the inert gas xenon, ignited upon shock-wave impact. It was found that with increasing shock Mach numbers different reaction-wave types develop, from deflagration to detonation. The complex experimental setup of Haehn et al. implies significant uncertainties. The uncertainty in Damköhler number is around 50%. At the smallest investigated Mach number 30% of all experiments did not ignite. It is evident that without complementary numerical simulations the understanding can only be incomplete. The objective of the current project is twofold. Based on pre-liminary work on two-dimensional RSBI direct numerical simulations, we first target systematic in-vestigation of initial-data and combustion-model uncertainties. We identify quantities of interest, such as the mixing rate, enstrophy, intermediate reaction product mass fractions, and predict by non-intrusive uncertainty-propagation methods the effect of initial-data variations. We assess the prediction capability of different reaction mechanisms. The initial-data uncertainty quantification also allows to estimate impact of imperfections in reproducing the nominal experimental setup in three dimensions which are the second objective, aiming at the first quantitative numerical prediction of the experiments of Haehn et al. The objective of the three-dimensional investigation is to identify how dominant mixing mechanisms, reaction, and bubble deformation parameters differ from the ide-alized two-dimensional case, and how these differences may be related to experimental uncertain-ties. In a possible second funding period we will further increase the complexity towards engineering applications, e.g. by considering the interaction of reacting bubble clusters.