Triggering of self-excited thermo-acoustic oscillations in a Rijke tube with a premixed laminar flame

Abstract

For a given Rijke tube, self-excited combustion oscillations could be caused by the transient growth of flow disturbances. A premixed laminar flame, anchored to a metal gauze, is considered to investigate the role of non-normality and the resulting transient growth in triggering such oscillations. The unsteady heat release is assumed to be caused by the flame surface variations, which results from the fluctuations of the oncoming flow. The flame is acoustically compact and its presence causes a jump in mean temperature. Coupling the flame model with a Galerkin series expansion of the acoustic waves enables the time evolution of the flow disturbances to be calculated. It was found that the nonlinear model can predict the mode shape and the frequencies of the excited oscillations very well. Moreover, the fundamental mode with the lowest frequency is the easiest one to be excited among all the acoustic modes. Linearizing the model and recasting it into the classical time-lag formulation provide insights on the mode selection and triggering. Finally, to gain insight about the stability behaviors of such non-normal Rijke tube, pseudo-spectra analysis is performed to obtain upper and lower bounds on the transient growth factor.