Estimation of 3D flame surface density and global fuel consumption rate from 2D PLIF images of turbulent premixed flame

Abstract

In premixed turbulent combustion, flame surface density (FSD) is a key parameter and can be used to estimate the system reaction rates. Even though laser diagnostic technics (Mie scattering or OH/CH-PLIF) on flame front provided very useful information of flame front wrinkles, the measurement is limited to a plane on which wrinkles in the third direction is unavailable. In this study, the estimation of 3D FSD (Σ) and the global fuel consumption rate (W) from planar measurements of 2D FSD (Σ2D) was conducted on a Bunsen-type burner fueled with methane/air mixture at the equivalence ratio of 0.9. Assuming symmetry of the mean flow, five different models designated as Method 1 to Method 5 (M1 to M5) based on different additional assumptions were utilized. M1 connected the 2D to 3D FSD with a typical value of 0.69. M2 and M3 were based on isotropic flame front normal vector distribution and identical ϕ and θ distribution which designate the direction angle of front normal in 3D space and the measurement plane. M4 and M5 assumed that normal vector fluctuation intensity of transverse direction was similar with x or y direction on the measurement plane, respectively. W was also obtained by integrating the Σ within the flame domain and the flame stretch factor, I0 was evaluated based on fractal analysis of the 2D measurements. For all methods, the results are satisfying. Results of M1 indicate that a typical direction cosine value of 0.69 is valid for the turbulent Bunsen flame in this study and the satisfied W estimation under higher turbulent intensities is provided. Results of M2 are relatively rough for overestimating W by about 40% under most conditions because of its intrinsic deficiency of the 1/〈cosϕ〉s evaluation. M3 based on the assumed identical cosine value of mean direction angle of 3D and 2D flame front presented by ϕ and θ gave rather good estimation as M4. M4 and M5 provide the best evaluation of W, absolute error within 17% except low turbulence conditions (u′/SL≈0.2 and 0.4) of M4, by the normal vector fluctuation analysis. 2D data, as expected, underestimates W. Better W can be obtained considering the flame stretch factor, I0.