Measured fractal properties of premixed flames on a low-swirl burner at high reynolds numbers and their relation to turbulent burning velocities

This work presents measured fractal properties of lean premixed methane-air flames on two weak-swirl jet burners with 25-mm and 50-mm diameter nozzles at high turbulent Reynolds numbers, Re_T = u'L_I/ν = 350 ~ 2,500 based on r.m.s. turbulent fluctuating velocities and the integral length scale of reacting turbulence, where ν is the kinematic viscosity of reactants. The nondimensional turbulence intensity (u′/S_L) and turbulent burning velocities (S_T/S_L) were measured via high-speed, high-resolution digital particle imaging velocimetry, where S_L is the laminar burning velocity. The fractal dimension (D₃) and cutoff length scales were determined by the caliper method from analyses of lifted stabilized wrinkled flame front images obtained by laser sheet tomography. It is found that values of D₃ are only 2.22 and independent of u′/S_L at least for 3 < u′/S_L < 18.5 even at high-Re_T reacting flows. This finding differs drastically with most previous studies using different burners that reported D₃ ≈ 2.33 when u′/S_L > 3, but it supports a recent study by Gülder and his co-workers using a Bunsen-type burner that found D₃ ≈ 2.18 for much lower values of Re_T ≈ 40 ~ 467. The outer cutoff scale (ε_o), which is comparable to L_I, varies from about 12 mm to 10 mm when u′/S_L increases from about 2 to 18.5, while the inner cutoff ε_i ≈ 0.1ε_o, suggesting that both ε_o and ε_i are rather insensitive to u′/S_L. Finally, these fractal parameters obtained at high values of Re_T cannot predict measured S_T/S_L data correctly when the available fractal area closure model is applied, indicating a need for further improvement of existing fractal models.