A reduced-order model for the control of thermoacoustic instabilities in a dump combustor
Résumé
Combustion instabilities may develop, due to the formation of vortices at a geometrical change, as a step, which causes flame wrinkling. This may be preponderant for ramjets. In the literature, low-order models for pressure and velocity oscillations have been proposed, in which the oscillations are induced by the coupling between the flame wrinkling and the acoustics. These models have a nonlinear dynamics (kicked oscillator, limit cycle) with a complex frequency spectrum. In order to control the development of thermoacoustic instabilities using these models, they should be written as a state-space representation. However, writing these models under a state-space representation is difficult due to their formulation as kicked oscillators. For this reason, the objective of this paper is to reduce the model to its most simplified form: considering a one-way interaction between the combustor acoustic and the convection of vortices, adopting a deterministic model rather than a stochastic one as proposed by some previous authors. The main contribution of this paper is to propose a reduced-order model, derived from pre-existing models, which is suitable for control. This model is compared to the Nair and Sujith model in this paper and we find satisfactory results: similar
spectrum, close amplitude prediction for various operating conditions. This degree of similarity between the models is sufficient in order to develop a model-based control methodology.
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