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Thermoacoustic oscillations occur in combustion chambers when heat release oscillations lock into pressure oscillations. They were first observed in lamps in the 18th century, in rockets in the 1930s, and are now one of the most serious problems facing gas turbine manufacturers.
This theoretical and numerical study concerns an infinite-rate chemistry diffusion flame in a tube, which is a simple model for a flame in a combustion chamber. The problem is linearized around the non-oscillating state in order to derive the direct and adjoint equations governing the evolution of infinitesimal oscillations.
The direct equations are used to predict the frequency, growth rate, and mode shape of the most unstable thermoacoustic oscillations. The adjoint equations are then used to calculate how the frequency and growth rate change in response to (i) changes to the base state such as the flame shape or the composition of the fuel (ii) generic passive feedback mechanisms that could be added to the device. This information can be used to stabilize the system, which is verified by subsequent experiments.
This analysis reveals that, as expected from a simple model, the phase delay between velocity and heat-release fluctuations is the key parameter in determining the sensitivities. It also reveals that this thermo-acoustic system is exceedingly sensitive to changes in the base state. This analysis can be extended to more accurate models and is a promising new tool for the analysis and control of thermo-acoustic oscillations.