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Vortex dynamics and fractal structures in reactive and nonreactive Richtmyer–Meshkov instability

Hydrodynamic instabilities caused by shock-flame interactions are a fundamental challenge in the accurate prediction of explosion loads in the context of nuclear and process plant safety. To investigate the Richtmyer–Meshkov instability, a series of three-dimensional numerical simulations of shock-flame interactions are performed, including lean, stoichiometric, and nonreactive homogeneous H2/Air mixtures. The equivalence ratio has a strong influence on the achievable flame wrinkling and mixing, by impacting key physical parameters such as the heat release parameter, flame thickness, and reactivity. The reactivity is found to be a decisive factor in the evolution of the wrinkled flame brush, as it can cause burnout of the developing fresh gas cusps and wrinkled structures. The importance of reactivity is further emphasized by comparisons to a nonreactive case. Analysis of the enstrophy (energy equivalent of vorticity) transport terms shows that baroclinic torque is dominant during shock-flame interactions. After the shock interaction, the vortex stretching, dissipation, and dilatation terms gain in importance significantly. A power-law based modeling approach of the flame wrinkling is investigated by explicitly filtering the present simulation data. The values determined for the fractal dimension show a nonlinear dependency on the chosen equivalence ratio, whereas the inner cutoff scale is found to be approximately independent of the equivalence ratio for the investigated cases.