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Self-excited oscillations of a confined flame, burning in the wake of a bluff-body flameholder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic waves. According to linear theory, flow disturbances grow exponentially with time. A theory for nonlinear oscillations is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially 'saturates'. The amplitudes of the pressure fluctuations are sufficiently small that the acoustic waves remain linear. The time evolution of the oscillations is determined by numerical integration and inclusion of nonlinear effects is found to lead to limit cycles of finite amplitude. The predicted limit cycles are compared with results from experiments and from linear theory. The amplitudes and spectra of the limit-cycle oscillations are in reasonable agreement with experiment. Linear theory is found to predict the frequency and mode shape of the nonlinear oscillations remarkably well. Moreover, we find that, for this type of nonlinearity, describing function analysis enables a good estimate of the limit-cycle amplitude to be obtained from linear theory.Active control has been successfully applied to eliminate these oscillations. We demonstrate the same effect by adding a feedback control system to our nonlinear model. This theory is used to explain why any linear controller capable of stabilizing the linear flow disturbances is also able to stabilize finite-amplitude oscillations in the nonlinear limit cycles.

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▪ Abstract  Early work and recent advances in feedback control of combustion oscillations are described. The physics of combustion oscillations, most commonly caused by a coupling between acoustic waves and unsteady heat release, are discussed, and the concept of using feedback control to interrupt these interactions is introduced. Factors affecting practical implementation of feedback control, including sensors, actuators, and controller design are described, and the historical development of control strategy for combustion oscillations is reviewed. Finally, demonstrations of feedback control on full-scale combustion systems are described, and it is concluded that there is potential to apply more systematic controller designs at full scale.