Prediction of combustion instabilities based on the Green's function in a three-dimensional annular combustor with multiple flames

The prediction of combustion instabilities is essential for modern annular combustors fed by multiple flames. This paper develops a model based on Green's function to study the interaction of multiple flame responses with different types in a three-dimensional (3D) geometry. The flame responses are described by flame transfer functions and are recognized as monopole sources in 3D cavities. Then the dispersion relation equation in the form of matrix is performed with the condition of equality of pressure. Thermoacoustic complex frequencies, mode structure, as well as the stability behaviors in combustor can be obtained in this model and the analysis is accomplished using Rayleigh index. The results are compared to the values of existing theoretical models and a good agreement is achieved. Furthermore, the effects of non-identical flame responses on complicated slanted mode under the condition of asymmetric are studied. In addition, the combustion instabilities of radial mode can be predicted by this model when the radial position distributions of the heat sources move in the case of small ratio of inner wall to outer wall.