MODELLING OF ACOUSTIC INSTABILITIES IN A FLOW DUCT WITH THE GREEN'S FUNCTION APPROACH

Thermoacoustic instabilities and aeroacoustic instabilities are due to feedback between acoustic field and unsteady heat release or unsteady flow fluctuations. The Green's function approach is a robust and fast analytical tool to study self-excited acoustic oscillations in such systems. If the mean flow is included, the reciprocity of the Green's function is lost. This work aims to extend the framework of the Green's function approach for modelling thermoacoustic instabilities in the presence of mean flow by demonstrating the symmetry of the Green's function. The framework is applied to a one-dimensional combustion system with a compact flame whose heat release rate is described by a generalized nonlinear time-lag law. Our extended Green's function approach is able to capture the effect of mean flow on the instabilities as well as the nonlinear dynamics of the system, showing that increasing the mean flow can expand the stable region of the stability map.