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Thermoacoustic instabilities are a cause for concern in combustion applications as diverse as small household burners, gas turbines or rocket engines. In this work, a feedback mechanism is analyzed, which couples combustion chamber acoustics with convectively transported fluctuations of entropy (entropy waves) generated within a premixed flame. Essential elements of this thermo-acoustic feedback loop are fluctuations in fuel concentration, induced by acoustic disturbances at the location of fuel injection, convective transport of fuel inhomogeneities through the premixing section of the burner, modulations in heat release rate and hot gas entropy resulting from the consumption of fuel/air mixture with varying fuel concentration by the flame, and the generation of sound through entropy non-uniformities at the turbine inlet. From a qualitative analysis based on relative phases, it is concluded that depending on the various convective and acoustic time lags involved, entropy waves may couple constructively as well as destructively with combustor acoustics. However, such qualitative analysis does not indicate whether the coupling between entropy and acoustic waves is strong enough to significantly influence thermo-acoustic stability. Therefore, a linear model has been constructed to estimate the effect of entropy waves on the thermo-acoustic response and stability of a combustor with a choked exit nozzle, as it might be found in a gas turbine. Note that phenomena like dispersion of convective waves, distributed heat release, vortical velocities, etc., have not been taken into account, as they would burden the presentation with unnecessary complexity. Results obtained indicate that the interaction between combustor acoustics and entropy waves can be significant, especially for the lowest non-axisymmetric modes, and even at frequencies higher than those usually associated with convective waves. As expected, it was observed that the coupling between pressure and entropy waves at the exit nozzle can enhance as well as reduce the thermo-acoustic stability of a combustor, or the responsiveness to an external or internal fluid-mechanic excitation mechanism. It is concluded that comprehensive thermo-acoustic analysis of a premixed combustor with a choked exit must in general include generation and propagation of entropy waves and coupling with combustor acoustics.

Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor with a Choked Exit