Combustion instabilities: Issues in modeling and control

This study deals with various aspects in the development of active control of combustion instabilities. A low-order model is developed, reconciling along the way two different approaches taken by researchers to attack the description of combustion instabilities. The model is demonstrated with application to a Rijke tube and compared to experiments. The Rijke burner experiments suggest two major discrepancies with the model: the presence of a hysteresis loop is unaccounted for and the model does not describe the seemingly random fluctuations in the amplitude of the pressure oscillations in the ‘unstable’ regime. So far no explanation for the hysteresis can be given; however, this phenomenon is successfully exploited by using a novel nonlinear control technique to expand the stable operating range of the burner. The origin of the ‘noise’ in the pressure trace is explained by considering entropy and vorticity waves in the combustor. Their presence leads to a slight modification of the original model, introducing stochastic source terms into the oscillator equations. The consequences of the presence of these terms is analyzed by means of simulations. One interesting result is that they allow for the identification of model parameters from a single experimental run of a stable combustion system.; Finally, a unified approach to controlling combustion instabilities is presented. The formulation and analysis account for truncation to a few modes; uncertainties in the description of the system (including uncertain sensing and actuating); external disturbances; and intrinsic noise sources. An explicit expression is derived against which any controller can be checked for stability.