On periodic behavior of weakly turbulent premixed flame corrugations

Periodicity in evolution of premixed methane-air V-shaped flames in the space domain is investigated experimentally. The experiments were performed using the Mie scattering and Particle Image Velocimetry techniques. Three Reynolds numbers of 510, 790, and 1057 along with two fuel-air equivalence ratios of 0.6 and 0.7 were tested in the experiments. The analyses were performed using the Proper Orthogonal Decomposition (POD) technique for the flame front position as well as the velocity data pertaining to non-reacting flow condition. The POD analysis shows that the spectral characteristics of the mode shapes associated with the velocity and the flame front position data feature similarities; however, the corresponding temporal coefficients are significantly different. Specifically, the POD mode shapes pertaining to both velocity and flame front position data feature dominant instabilities. It was shown that the normalized wave number pertaining to these instabilities are similar and equal to the Strouhal number corresponding to non-reacting flow over a circular cylinder. Comparison of the normalized temporal coefficients show that, for the flame front position data, the normalized first and second coefficients are mainly centered close to the origin; however, those associated with the velocity data are positioned around a unity radius circle. This was argued to be linked to the ratio of the corresponding first and second eigenvalues. Specifically, it was shown that, as this ratio approached to unity, the signal energy becomes distributed between the first and the second POD modes. As a result, the normalized temporal coefficients follow a circular pattern.