Reduced order modeling of reacting shear flow

Thermoacoustic instability in premixed combustors occurs occasionally at multiple frequencies, especially in configurations where flames are stabilized on separating shear layers that form downstream of sudden expansions or bluff bodies. While some of these frequencies are related to the acoustic field, others appear to be related to shear flow instability phenomena. It is shown in this paper that shear flows can support self-sustained instabilities if they possess absolutely unstable modes. The associated frequencies are predicted using mean velocity profiles that resemble those observed in separating flows and for profiles obtained from numerical simulations, and are shown to match those derived from experimental and numerical investigations. It is also shown that the presence of density profiles compatible with premixed combustion can affect this frequency and can change the absolute instability mode into a convectively unstable mode thereby reducing the possibility of the generation of self-sustained oscillations. A qualitative prediction of the pressure amplitudes resulting from these shear layer modes is shown to be consistent with experimental measurements. The results from the stability analysis are combined with those using the Proper Orthogonal Decomposition (POD) method to yield a reduced-order model.