Low-order network modelling of the effect of Helmholtz resonators on nonlinear thermoacoustic modes in annular combustors

Abstract

Modern aero-engines and land-based gas turbines often use annular combustors where many burners are installed in the circumferential direction. These combustors are often operated under lean-premixed pre-vaporized (LPP) conditions in which the flames are more susceptible to acoustic perturbations than traditional combustion systems. The resulted thermoacoustic instabilities may involve mode patterns varying in both longitudinal and circumferential directions. When nonlinear flame models are considered, our previous work proved that a 2-D low-order network model can capture limit cycle oscillations involving uncoupled and nonlinearly coupled modes, including longitudinal, circumferentially spinning/standing, and slanted modes. This kind of low-order network modelling tool has been recognised as a computationally efficient way of analysing thermoacoustic instabilities in annular combustors. Helmholtz resonators (HRs) are widely used to damp acoustic oscillations. For thermoacoustic instabilities in annular combustors, the presence of the HRs causes modal coupling and mode shape change. For nonlinearly coupled thermoacoustic modes, it is difficult to predict the change of modality accurately. In this paper, HRs are incorporated into the aforementioned low-order network model. The effect of HRs on different nonlinear thermoacoustic mode patterns are studied in detail. This provides a powerful low-order network modelling tool for studying the damping performance of HRs on nonlinear thermoacoustic modes in annular combustors.