Linear stability analysis of a combustor model with a delayed feedback tube

We conducted a linear stability analysis of a laboratory-scale combustor to develop a delayed feedback method for mitigating combustion oscillations. We employed linearized hydrodynamic equations and a flame transfer function in the frequency domain to assess the stability under various feedback tube configurations, including changes in the length, radius, and connection position. The results of the stability analysis demonstrated a significant improvement in stability when the length of the feedback tube was 0.56 times the wavelength of the unstable mode. Furthermore, the tube radius had an optimal value for stabilizing the system. The connection position also played a crucial role in stability. The effective feedback tube conditions determined in the analysis were applied to a real combustor to demonstrate the successful suppression of oscillations experimentally. The suppression mechanism is discussed using the acoustic power based on the calculation results. The acoustic power profile of the system revealed that the oscillation suppression was not simply an addition of acoustic dissipation, but importantly, a reduction in acoustic power generation at the flame.