Fractal Dimension Growth in Flame Front Wrinkles during the Early Phase of Flame Propagation in an SI Engine

Turbulent premixed flame fronts during the early phase of flame propagation were visualized by a laser-light sheet technique in an optically accessible spark ignition engine. Time-resolved continuous images of wrinkling flame fronts were captured by a high-speed video camera until roughly 20% of total fuel was consumed. The image data were processed to measure the fractal dimension D₂ in a time series for each cycle. The results show that the fractal dimension D₂ is close to unity just after the spark ignition and then increases with time as the flame propagates. It is also shown that the fractal dimension increases more quickly as engine speed increases. The temporal rate of increase in the fractal dimension, ΔD₂/Δt, was obtained from the D₂ data and the relationship between ΔD₂/Δt and D₂ was examined. The result reveals that the higher D₂ is, the lower ΔD₂/Δt becomes from a positive value to a minus value, crossing zero when D₂ reaches a critical value D_2C. The following empirical equation was derived from the average of the relationships over many cycles: dD₂/dt = -{D₂ - D_2C}/τ (τ : time constant). The critical fractal dimension D_2C and the time constant τ were correlated with unburned mixture turbulence intensities, which were measured by a cross-correlation PIV technique. Compared with other combustion models, the present model produced a reasonable result.