Surface topologies and self interactions in reactive and nonreactive Richtmyer-Meshkov instability

The reactive Richtmyer-Meshkov instability (RMI) exhibits strong wrinkling of a reactive flame front after an interaction with a shock wave. High levels of deformation and wrinkling can cause the flame surface to intersect with itself, leading to the events of flame self interactions (FSI). As FSI can have a significant influence on the development and topology of the flame surface, it should be considered an important factor affecting the burning characteristics of the flame. The topological structure and statistics of FSI are analyzed using data from high-fidelity simulations of a planar shock wave interacting with a statistically planar hydrogen/air flame for stoichiometric, lean and nonreactive gas mixtures. FSI events are detected by searching for critical points in the field of the reaction progress variable c and divided into the following topological categories: burned gas mixture pocket (BP), unburned gas mixture pocket (UP), tunnel formation (TF) and tunnel closure (TC). It is found that reactivity and flame thickness are decisive factors, influencing the frequency and topological distribution of the detected FSI events. While in early RMI-stages the FSI is found to be mainly dependent on the flame thickness, later stages are heavily influenced by the reactivity, as high reactivity quickly burns out emerging wrinkled structures (in the stoichiometric case) leading to massively reduced levels of FSI. The findings are further supported by the results from the nonreactive case, which at later stages of the RMI closely resembles the less reactive lean case. Analysis of the topology distribution over time and conditioned over c, reveals further differences between the lean and stoichiometric case, as the strong wrinkling and mixing encountered with the lean case facilitates the build up of many pocket-type and tunnel-type interactions throughout the wrinkled flame front. For the stoichiometric case, mainly tunnel-type and unburned pocket topologies are found in the narrow flame funnels extending into the burned gas.