Scale analysis of the flame front in premixed combustion using Proper Orthogonal Decomposition

• Proper Orthogonal Decomposition is applied to the flame front coordinates.
• A linear relationship between the mode numbers and physical scales is highlighted.
• A parametric expression for describing Richardson plots is proposed.
• Pressure and equivalence ratio effects on the flame wrinkles is assessed.
• The contribution of each scale to the flame brush is emphasized.

The main objective of the present study is to explore the degree of interactions between turbulence and the flame front in the context of lean premixed combustion. Premixed methane Bunsen flames are investigated using Mie scattering at three different pressure magnitudes (0.1, 0.2, and 0.3 MPa) and equivalence ratios (0.6, 0.7, 0.8) through six operating conditions at the same mean bulk velocity (3.6 m/s). Nearly homogeneous and isotropic turbulence is generated by a multi-scale grid consisting of three distinct perforated plates. The multi-scale nature of the flame front is characterized using an original method based on Proper Orthogonal Decomposition (POD). Particular emphasis is shed to the scales responsible for the flame brush and the wrinkling of the flame front. The flame front curvilinear length is analyzed as a function of the mode (or equivalently the scale) and yields the well known Richardson plot that is usually observed using fractal analysis. The inner and outer cut-off length-scales, together with the fractal dimension can thus be evaluated using the present method. An analytical expression for unambiguously assessing the latter three parameters is introduced and compares favorably well with experimental data. Second, the reconstruction of the flame using only the first few modes suggests that, the flame brush is characteristic of a rather large-scale phenomena whilst the smallest scales act in decreasing the total flame brush.