Geometric interpretation of fractal parameters measured in turbulent premixed Bunsen flames

Abstract

Fractal analyses have been conducted to investigate flame-front wrinkling of turbulent premixed Bunsen flames. Emphasis is placed on the geometric interpretation of measured fractal parameters and their relationship with parameters used in current combustion models. The outer cutoff scale is found to be four times the integral length scale of flame-front wrinkling defined in the Bray–Moss–Libby model. A revised Gibson length scale is derived by taking into account the curvature effect. Dependency of the revised Gibson scale on the Karlovitz number agrees better with the bulk of available data for the inner cutoff scale than the original definition. The term “self-similarity dimension” is proposed for the fractal dimension measured at finite spatial resolution to highlight the self-similarity feature of local flame fronts. The self-similarity dimension is found to increase linearly with time, and correlates well with the turbulent flame brush thickness.