Flame shape and spatially resolved Rayleigh criterion using proper orthogonal decomposition

Chemiluminescence imaging was performed for premixed flames with natural thermoacoustic instabilities in a Rijke tube. The images were phase locked to the natural pressure oscillations in the tube. The use of proper orthogonal decomposition (POD) to identify phase-resolved flame fronts and flame surface area is reported. The flame front results compare favorably to an Abel transform for axisymmetric cases but also work well for cases with non-axisymmetric contributions. The flame area perturbations are compared to previous work using OH planar laser induced fluorescence. The relatively-simpler chemiluminescence approach finds the same flame surface area correlations versus pressure. Additionally, the modes from POD are used to compute local acoustic coupling via the space and time resolved Rayleigh index. It is found that one mode in the decomposition is spatially the same as the Rayleigh index and can be used to characterize the thermoacoustic coupling. This similarity is due to the mode's time constant replicating the phase of the tube's natural pressure oscillations.