Open-Loop Control of Combustion Instabilities and the Role of the Flame Response to Two-Frequency Forcing

Controlling combustion instabilities by means of open-loop forcing at non-resonant frequencies is attractive because neither a dynamic sensor signal nor a signal processor is required. On the other hand, since the mechanism by which this type of control suppresses an unstable thermoacoustic mode is inherently nonlinear, a comprehensive explanation for success (or failure) of open-loop control has not been found. The present work contributes to the understanding of this process in that it interprets open-loop forcing at non-resonant frequencies in terms of the flame’s nonlinear response to a superposition of two approximately sinusoidal input signals. For a saturation-type nonlinearity, the fundamental gain at one frequency may be decreased by increasing the amplitude of a secondary frequency component in the input signal. This effect is first illustrated on the basis of an elementary model problem. In addition, an experimental investigation is conducted at an atmospheric combustor test-rig to corroborate the proposed explanation. Open-loop acoustic and fuel-flow forcing at various frequencies and amplitudes is applied at unstable operating conditions that exhibit high-amplitude limit-cycle oscillations. The effectiveness of specific forcing parameters in suppressing self-excited oscillations is correlated with flame response measurements that include a secondary forcing frequency. The results demonstrate that a reduction in the fundamental harmonic gain at the instability frequency through the additional forcing at a non-resonant frequency is one possible indicator of successful open-loop control. Since this mechanism is independent of the system acoustics, an assessment of favorable forcing parameters, which stabilize thermoacoustic oscillations, may be based solely on an investigation of burner and flame.