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We propose a framework of Lagrangian Coherent Structures (LCS) to enable passive open-loop control of tonal sound generated during thermoacoustic instability. Experiments were performed in a laboratory-scale bluff-body stabilized turbulent combustor in the state of thermoacoustic instability. We use dynamic mode decomposition (DMD) on the flow-field to identify dynamical regions where the acoustic frequency is dominant. We find that the separating shear layer from the backward-facing step of the combustor envelops a cylindrical vortex in the outer recirculation zone (ORZ), which eventually impinging on the top wall of the combustor during thermoacoustic instability. We track the saddle points in this shear layer emerging from the backward facing step over several acoustic cycles. A passive control strategy is then developed by injecting a steady stream of secondary air targeting the identified optimal location where the saddle points spend a majority of their time in a statistical sense. After implementing the control action, the resultant flow-field is also analysed using LCS to understand the key differences in flow dynamics. We find that the shear layer emerging from the dump plane is deflected in a direction almost parallel to the axis of the combustor after the control action. This deflection in turn prevents the shear layer from enveloping the vortex and impinging on the combustor walls, resulting in a drastic reduction in the amplitude of the sound produced.

We develop a passive control strategy for suppressing thermoacoustic instability in a bluff-body stabilized premixed turbulent combustor. When the equivalence ratio is varied, there is a transition from combustion noise to thermoacoustic instability via intermittency in the combustor. We perform simultaneous acoustic pressure, 2D-PIV, and CH$^*$ chemiluminescence measurements to capture the pressure fluctuations, the velocity field, and the heat release rate (HRR) field during the transition. We measure the spatial distribution of the amplitude of turbulent velocity at the acoustic frequency, time-averaged vorticity, time-averaged HRR, and Rayleigh index and identify various regions of significance. We implement a passive control strategy by targeting these regions with a steady injection of secondary micro-jet of air to optimize the injection location and determine the critical region. Targeting the critical region with secondary air leads to greater than 20 dB suppression of the dominant thermoacoustic mode. We observe that the coherent structure forming from the shear layer following the dump plane gets suppressed, leading to an incoherent spatial distribution of HRR fluctuations. We find that the turbulent velocity amplitude correctly identifies the critical region for optimized passive control during thermoacoustic instability. In contrast, the Rayleigh index identifies the region of the most significant acoustic driving; however, it does not identify the region most sensitive to control. Finally, we extend our analysis by determining the spatial distribution of the Hurst exponent measured from the turbulent velocity field. We show that the Hurst exponent identifies the critical region during thermoacoustic instability and intermittency, unlike the other physical measures., Comment: 12 pages, 10 figures; Preprint under review in Combustion and Flame