In this study, focusing on the geometry characteristics of spherical expanding flame, the turbulent premixed flames of natural gas/air mixtures were investigated in a fan-stirred turbulent combustor. The effects of initial temperature (T=300–400 K), initial pressure (P=0.1–0.3 MPa), turbulence intensity (u′=1.0–2.7 m/s), oxygen volumetric percentage (φ(O2)=15%–21%) and carbon dioxide volumetric percentage (φ(CO2)=0–20%) were delved into. The flame profile under the Cartesian coordinate system was derived from the schlieren images taken by the high-speed camera. Besides, from both macroscopic and microscopic perspectives, the influence of experimental conditions on the flame geometry characteristics was explored through flame front extraction, wavelet decomposition and network topology. The results demonstrate that for significant flame wrinkling, changes in species concentrations and turbulence intensity have more pronounced effects on the flame wrinkling ratio. The wrinkling of the flame front maintains a certain degree of similarity, as evidenced by the locally concentrated distribution of the angles of the maximum fluctuation radius. The disturbance energy under large-scale (D6–D8) disturbances exhibits relatively high values with a similar trend, exerting a significant impact on the geometry characteristics of the flame front. The peaks of correlation degree are scattered either with the decomposition scale or the development of flame radius, indicating no linear correlation between different detail components. Furthermore, the probability distribution of node degrees in key wrinkled regions exhibits different trends with that of large-scale wrinkling and disturbance energy, especially with changes in initial pressure. This occurs because the number of key wrinkles varies based on the perturbation’s strength or the region’s span. Consequently, an increase in the fluctuation frequency of the flame’s local radius may not necessarily lead to an increase in the number of key folded regions.
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