Effects of strain rate and curvature on the propagation of a spherical flame kernel in the thin-reaction-zones regime

Strain rate and curvature effects on the propagation of turbulent premixed flame kernels have been investigated in the thin-reaction-zones regime using three-dimensional compressible direct numerical simulations (DNS) with single-step Arrhenius chemistry. An initially spherical laminar flame kernel is allowed to interact with the surrounding turbulent fluid motion to provide a propagating turbulent flame with a strong mean spherical curvature. The statistical behavior of the local displacement speed in response to strain and curvature is investigated in detail. The results demonstrate clearly that the mean curvature inherent to the flame kernel configuration has a significant influence on the propagation of the flame. It has been found that the mean density-weighted displacement speed ρSdρSd in the case of flame kernels varies significantly over the flame brush and remains different from ρ0SLρ0SL (where ρ0ρ0 is the reactant density and SLSL is laminar flame speed), unlike statistically planar flames. It is also shown that the magnitude of reaction progress variable gradient |∇c||∇c| is negatively correlated with curvature in the case of flame kernels, in contrast to the weak correlation between |∇c||∇c| and curvature in the case of planar flames. This correlation induces a net positive correlation between the combined reaction and normal diffusion components of displacement speed (Sr+Sn)(Sr+Sn) and curvature in flame kernels, whereas the previous studies based on statistically planar flames did not observe any appreciable correlation between (Sr+Sn)(Sr+Sn) and curvature.