Fractals and turbulent premixed engine flames

The fractal nature of premixed turbulent flames in an internal combustion engine is examined. A sheet of laser light, approximately 200 μm thick, is shone through the cylinder of a single-cylinder ported internal combustion engine. The homogeneous charge of propane and air is seeded with submicron TiO₂ particles and the scattered light is collected through a quartz window in the engine head and is imaged on a 100 × 100 diode array camera. The number density of the TiO₂ particles scales with the gas density so that a two-dimensional map of reactants and products is obtained. A field of view 2 × 2 cm in the center of the cylinder is examined and fractal analysis is performed on the front separating reactants from products. Results are presented for two equivalence ratios and three engine speeds, corresponding to different laminar flame speeds S₁, laminar flame thicknesses δ₁, turbulent intensities u′, and Kolmogorov scales η. The examined flames were found to exhibit fractal character within a range of length scales as low as 200 μm and as high as 4.5 mm, which is twice the measured lateral integral length scale in this engine configuration. At stoichiometric conditions, the fractal dimension of the flame surface is found to be statistically different for engine speeds of 300, 1200, and 2400 rpm ( u′ S₁ = 0.5, 2, and 4). It increases with increasing u′ S₁. At lean conditions (Φ = 0.59), when u′ S₁ ≫ 1, the fractal dimension does not change with engine speed. For 4 ≤ u′ S₁ < 50 and 0.1 < η δ₁ ≤ 1 (estimated ranges), the fractal dimension is 2.36 ± 3%. A turbulent flame speed model based on fractal analysis is also briefly examined.