Geometrical Properties of Turbulent Premixed Flames: Comparison Between Computed and Measured Quantities

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Abstract
The constant density scalar field equation for a converted unsteady interface is solved numerically under prescribed monochromatic pulsating two-dimensional flow fields, with spatial frequencies (κ), temporal frequencies (ω) and rms amplitudes (w) simulating a Kolmogorov spectrum with parameter β = ω/kw ranging between 0.1 and 100. The effect of multiple velocity scales on the interface, which is considered to be a flame front, is accounted for by applying the renormalization theory on the monochromatic flame responses. Numerical calculations are performed for values of uv′/uL (turbulent intensity to laminar flame speed) up to fifteen. The results are then compared with turbulent flame front structure measurements obtained in an Internal Combustion Engine. The contribution of small scales to the flame surface area increase is shown to be smaller in cases with larger values of uv′/uL. The flame front does not obey a simple fractal-like scaling behavior between the extreme scales of the Kolmogorov spectrum. However, fractal like behavior can be a good approximation for scales larger than a minimum cutoff scale which decreases with increasing uv′/uL. Computed values of the fractal dimension, Z>2, are in good agreement with the experimental results, showing a rapid increase of D2 with uv′/uL for uv′/uL less than four. In the range 4 < uv′/uL < 15, the fractal dimension increases much slower with uv′/uL and remains constant within 3% around 1.37 for β = 0.8. The range of scales with non-fractal behavior can be important in determining turbulent flame speeds at low uv′/uL (uv′/uL < 3). Simple turbulent flame speed models based on fractals are consistent with the computations only at large values of uv′/uL (uv′/uL > 7). The precise values of the extreme scales of the turbulent spectrum (integral length scale and Kolmogorov scale) have no significant effect on global combustion quantities such as fractal dimensions and turbulent flame speeds.

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