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

The prediction of combustion instabilities is essential for modern annular combustors fed by multiple flames. A model based on the Green's function is established in a three-dimensional (3-D) geometry with interactions of different flame responses. The flames are described by the flame transfer function (FTF), which are considered as the multiple sources to produce the pressure in the plenum and chamber. With equality of the pressure at the neighboring sectors in the combustor, the eigenfunction is obtained in frequency domain. The relevant eigenvalue is used to give the unstable frequency and judge the stability behavior of combustion system. The effects of non-identical flame responses on complicated slanted mode under the condition of asymmetric are studied with the present model. In addition, the combustion instabilities of radial mode can also be predicted by this model when the radial position distributions of the heat sources move in the case of small hub ratio.