Nonlinear Self-Excited Combustion Oscillations of a Premixed Laminar Flame

Abstract

Self-excited combustion oscillations are caused by a coupling between acoustic waves and unsteady heat release. A premixed laminar flame in a Rijke tube, anchored to a metal gauze, is considered in this work. The flame response to flow disturbances is investigated by developing a nonlinear kinematic model based on the classical-equation, with the assumption of a time-invariant laminar flame speed. Unsteady heat release from the flame is assumed to be caused by its surface variations, which results from the fluctuations of the oncoming flow velocity. The flame is acoustically compact, and its presence causes the mean temperature undergoing a jump, whose effect on the dynamics of the thermo-acoustic system is discussed. Coupling the flame model with a Galerkin series expansion of the acoustic waves present enables the time evolution of the flow disturbances to be calculated. It was found that the model can predict the mode shape and the frequencies of the excited combustion oscillations very well. Moreover, the fundamental mode is found to be the easiest one to be triggered among all acoustic modes. To gain insight about the mode selection and triggering, further numerical investigation is conducted by linearizing the flame model and recasting into the popular formulation.