Fractal approach to the evaluation of burning rates in the vicinity of the piston in a spark-ignition engine

The burning rate in the vicinity of a piston is estimated from a fractal analysis. The fractal parameters are determined from laser sheet tomography flame images for methane-air mixtures with three equivalence ratios (1, 0.9, 0.8) in a transparent spark-ignition engine. Two imaging configurations were used: five horizontal planes placed at different distances from the piston (0, 1, 2, 3, and 5 mm) and a vertical one passed through the center of the combustion chamber. The methodology proposed by Foucher et al. [F. Foucher, S. Burnel, C. Mounaïm-Rousselle, Proc. Combust. Inst. 29 (2002) 751-757] allows the effect of cyclic variations to be avoided. The fractal formulation is modified to take into account the flame-piston distance and flame quenching. Far from the piston, evolution of the fractal dimension versus q′/SL0 is found to be in good agreement with literature results. Near the piston, the fractal dimension evolves significantly when the distance is about twice the integral length scale and tends toward 2, the fractal dimension of a laminar flame front. The quenching ratio parameter QR is introduced to consider the quenching of the flame by the piston. Finally, the burning rate is determined as a function of the distance between the wall and the mean flame contour and compared to a flame density approach, and similar results are found.