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We propose a framework of Lagrangian Coherent Structures (LCS) to enablepassive open-loop control of tonal sound generated during thermoacousticinstability. Experiments were performed in a laboratory-scale bluff-bodystabilized turbulent combustor in the state of thermoacoustic instability. Weuse dynamic mode decomposition (DMD) on the flow-field to identify dynamicalregions where the acoustic frequency is dominant. We find that the separatingshear layer from the backward-facing step of the combustor envelops acylindrical vortex in the outer recirculation zone (ORZ), which eventuallyimpinging on the top wall of the combustor during thermoacoustic instability.We track the saddle points in this shear layer emerging from the backwardfacing step over several acoustic cycles. A passive control strategy is thendeveloped by injecting a steady stream of secondary air targeting theidentified optimal location where the saddle points spend a majority of theirtime in a statistical sense.  After implementing the control action, the resultant flow-field is alsoanalysed using LCS to understand the key differences in flow dynamics. We findthat the shear layer emerging from the dump plane is deflected in a directionalmost parallel to the axis of the combustor after the control action. Thisdeflection in turn prevents the shear layer from enveloping the vortex andimpinging on the combustor walls, resulting in a drastic reduction in theamplitude of the sound produced.

Identifying optimal location for control of thermoacoustic instability through statistical analysis of saddle point trajectories