Effect of Acoustic Feedback on Lagrangian Coherent Structures in a Backward Facing Step Combustor With a Partially Premixed Flame

The thermoacoustic oscillations of a partially premixed flame stabilized in a backward facing step combustor are studied at a constant equivalence ratio in long and short combustor configurations corresponding to with and without acoustic feedback respectively. We perform simultaneous time-resolved particle image velocimetry (TR-PIV) and chemiluminescence for selected flow conditions based on the acoustic characterization in the long combustor. The acoustic characterization shows a transition in the dominant pressure amplitudes from low to high magnitudes with an increase in the inlet flow Reynolds number. This is accompanied by a shift in the dominant frequencies. For the intermittent pressure oscillations in the long combustor, the wavelet analysis indicates a switch between the acoustic and vortex modes with silent zones of relatively low-pressure amplitudes. The short combustor configuration indicates the presence of the vortex shedding frequency and an additional band comprising the Kelvin Helmholtz mode. Next, we apply the method of finite-time Lyapunov exponent (FTLE) to the time-resolved velocity fields to extract features of the Lagrangian coherent structures (LCS) of the flow. In the long combustor post transition with the time instants with dominant acoustic mode, a large-scale modulation of the FTLE boundaries over one cycle of pressure oscillation is evident. Further, the FTLEs and the flame boundaries align each other for all phases of the pressure oscillation. In the short combustor, the FTLEs indicate the presence of small wavelength waviness that overrides the large-scale vortex structure, which corresponds to the vortex shedding mode. This behaviour contrasts with the premixed flame in the short combustor reported earlier in which such large scales were found to be seldom present. The presence of the large-scale structures even in the absence of acoustic feedback in a partially premixed flame signifies its inherent unstable nature leading to large pressure amplitudes during acoustic feedback. Lastly, the FTLE boundaries provide the frequency information of the identified coherent structure and also acts as the surrogate flame boundaries that are estimated from just the velocity fields.