Acoustic transfer function of a combustion system with premixing chamber

In this study we develop an analytic thermoacoustic model of a combustor for gas turbines. The combustor under consideration is composed of a premixing chamber, a nozzle, and a combustion chamber. Our thermoacoustic model is given as an acoustic transfer function from a heat release perturbation to a velocity perturbation at a flame location. It is shown that the resonance frequencies are functions of three turnaround periods of acoustic waves at each stage, and the area ratios between stages. The resonance modes can be well captured by calculating the poles of the acoustic transfer function, our analytic results show a good agreement with existing measurement data in the literature.