Nonlinear Dynamics of a Swirl-Stabilized Combustor under Acoustic Excitations: Influence of the Excited Combustor Natural Mode Oscillations

In this study, experimental measurements are performed on a swirl-stabilized combustor to study the nonlinear combustor dynamic characteristics under acoustic excitations. The imposed acoustic disturbances with different frequencies and amplitudes generated by a loudspeaker are applied to the combustion system. The acoustic pressure oscillations and heat release rate fluctuations are measured using acoustic pressure transducers and a photomultiplier tube equipped with a bandpass OH* filter, respectively. Various parametric studies are conducted to evaluate the effects of the equivalent ratio phi, amplitude A(f), and frequency f(f) of the acoustic excitations on the combustor dynamics. The obtained results indicate that the combustor experiences frequency locking-in phenomenon accompanied by high amplitude acoustic oscillations when f(f) is close to the natural frequency f(a) of the combustor quarter-wave mode. Such physical phenomena are observed even for a low forcing wave amplitude. However, heat release rate fluctuations reach saturation at high amplitude excitations. Moreover, the combustor experiences super-harmonic resonances when f(f) is close to f(a)/2 or f(a)/3. Under such conditions, high amplitude excitations are required to stimulate the natural resonant mode, while the heat release rate fluctuations rarely reach saturation. Cross-correlation and cross-power spectral density analyses on the OH* chemiluminescence and acoustic pressure signals reveal that super-harmonic resonances are caused by "quasi-couplings" between the acoustic pressure and unsteady heat release. Further, the results demonstrate that the excited natural mode oscillations affect the acoustic wave characteristics at the inlet section, while they hardly influence the heat release rate fluctuations. The obtained results indicate that the equivalence ratio has a negligible effect on the combustor dynamics under forced conditions. Finally, discussions are provided to address the influences of the excited natural mode oscillations on the experimental measurements of the flame describing function (FDF). The achieved acoustic velocity disturbances at the injector outlet are suppressed by excited natural mode oscillations, which confine the velocity disturbance amplitude within a narrow range when f(f) matches f(a). Hence, excited natural mode oscillations should be avoided in practice if we need to measure the FDF under a wide range of acoustic velocity amplitudes. The nonlinear characteristics of forced oscillations studied in this paper are crucial to the development of control strategy and FDF measurement.