This paper considers the ensemble averaged propagation speed of turbulent flames that also have deterministic, harmonically oscillating wrinkles on them. Prior studies have shown that this "turbulent flame speed" varies along the flame and can be correlated with the instantaneous curvature of the coherent wrinkle. This sensitivity of the turbulent flame speed to curvature, the "Turbulent Markstein number", is quantified here for a much broader parameter range than in earlier work, using data from a turbulent premixed flame attached to a harmonically oscillating flame holder. High speed Particle Image Velocimetry is used to obtain velocity fields and the same Mie-scattering images are used to simultaneously track flame edges. Ensemble-averaged results are extracted by averaging the flame edges and velocity fields corresponding to the same phase with respect to the forcing cycle. Ensemble-averaged flame speed and curvature shows a negative correlation for negative values of curvature and a flattened to positive correlation for positive values of curvature. We quantify this with a turbulent Markstein length for a range of turbulence intensities and harmonic wrinkle wavelengths. The broader range of conditions clarifies some questions from Humphrey et al. [1] work, showing that the turbulent Markstein length decreases with the square root of turbulence intensity and decreased convective wavelength. One interpretation of this functional dependence, is that the turbulent Markstein length is a function of the ratio of the Taylor microscale and convective wavelength.
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