Abstract
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.
Highlights
The interaction of a density gradient rq as present at the interface between light and heavy fluids and a pressure gradient rp can lead to hydrodynamic instability, commonly referred to as the Richtmyer–Meshkov instability (RMI)[1,2] or the Rayleigh–Taylor instability (RTI).[3,4]
The first phase was characterized by an increase in Af, caused by the build up of fresh gas cusps and the development of wrinkled structures
It was found that the equivalence ratio / is an important factor in the development of the RMI, as it affects the reactivity, flame density gradient and speed of sound
Summary
The interaction of a density gradient rq as present at the interface between light and heavy fluids and a pressure gradient rp can lead to hydrodynamic instability, commonly referred to as the Richtmyer–Meshkov instability (RMI)[1,2] or the Rayleigh–Taylor instability (RTI).[3,4] In the case of RTI the pressure gradient is caused by constant (e.g. gravity) or time-varying acceleration,[5] while the RMI is caused by the pressure gradient across a shock wave (impulsive acceleration). The misalignment of rp and rq leads to the production of vorticity, amplifying small disturbances across the interface and subsequently causing wrinkling and increased mixing of heavy and light fluids. In many reactor safety scenarios, the gas mixture is typically assumed to be lean,[19] analyzing and understanding the influence of these flame characteristics is important for creating a subgrid model for this use-case. IV C, investigating the fractal behavior of the wrinkled flame brush
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