Fractal Dimension Growth Model for SI Engine Combustion

Time-resolved continuous images of wrinkling flame front cross-sections were acquired by a laser-light sheet technique in an optically accessible spark ignition engine. The test engine was operated at various engine speeds and compression ratios. The fractal dimension of the curve, D₂, was measured in a time series for each cycle. Analysis of the data shows that as the flame propagates the fractal dimension, D₂, is close to unity a short time after spark ignition and then increases. Examination of the relationship between the growth rate of the fractal dimension, ΔD₂/Δt, and D₂ reveals that the higher D₂ is, the lower ΔD₂/Δt becomes. An Empirical equation for ΔD₂/Δt was derived as a function of the ratio of the turbulence intensity to the laminar burning velocity and pressure. This model was tested in an SI engine combustion simulation, and results compared favorably with experimental data.