Acoustic damping optimization of the injector based on dynamic mode decomposition in a subscale combustor

The acoustic tuning of a swirl coaxial jet injector mounted upstream a combustion chamber is investigated in the aspect of stabilization of unstable combustion. The injector, which has a primary function to mix the oxidizer injected through the central passage and the fuel injected through the peripheral holes, is designed to be used as a half-wave resonator. The least damped modes are extracted by applying Dynamic mode decomposition (DMD) and the injector length is tuned to damp the second longitudinal mode. Then, the sensitivity of the heat release perturbation to the velocity perturbation at the frequency of the second longitudinal mode is evaluated by flame transfer function calculated by DMD. The relation between these two quantities is achieved by combining two equations, that is, the Crocco’s model and the inhomogeneous wave equation, and enables us to compute Flame transfer function (FTF) at a specific mode. The gain field of FTF shows that the sensitivity of the heat release fluctuation to the inlet velocity fluctuation is minimal with the optimal injector length. The proposed approach for application of dynamic mode decomposition would be a valuable tool in tuning a resonator acoustically, computing efficiently flame transfer function, and quantifying the relative stability of a combustion chamber.