Ensemble-averaged kinematics of harmonically oscillating turbulent premixed flames

Direct numerical simulation (DNS) was used to characterize the kinematics of ensemble-averaged flame position in harmonically oscillating turbulent premixed flames. The flames are stabilized on a harmonically oscillating flame holder, and the fuel consists of methane and hydrogen at a volume ratio of 10:3 and is mixed with air at the stoichiometric ratio. Turbulence intensities of 3.7, 8.6, and 13.3% are simulated, and each turbulent flame is simulated for 20 forcing periods for ensemble averaging. A laminar flame speed calculation method is derived based on the G-equation framework; the new method reproduces the reference laminar flame speed and the laminar Markstein length. The turbulent flame speed shows strong linear correlation with the ensemble-averaged flame curvature. The turbulent flame speed at zero flame curvature increases proportional to the turbulence intensity, while the turbulent Markstein length is independent of turbulence intensity. When the flame is far from the oscillating flame holder, the correlations between the turbulent flame speed and the flame curvature exhibit either piecewise linear or power-law dependencies. At these locations, the turbulent Markstein length at high curvature is similar to the laminar Markstein length. When a power law model is applied, the turbulent flame speed dependency asymptotes to 0.7 powers of the ensemble-average flame curvature at the turbulence conditions considered here.