Mode coupling due to the non-uniformly distributed heat release in combustion instabilities

Combustion instabilities in a chamber with circumferentially non-uniform heat release is investigated. A low-order model is developed to predict the combustion instabilities under the effects of a non-uniform heat source. A good agreement was observed between the results of the present model and the previous linear Euler equation method, which indicates that the present model can be used for the prediction of the combustion instabilities with the non-uniform heat source. The analysis shows that mode coupling can be brought by the non-uniformly distributed heat release in azimuthal direction. Results show that the oscillation frequency is less influenced by mode coupling. The growth rate, however, can be significantly affected by the non-uniformity of the heat release. For the instabilities of longitudinal-dominant mode, azimuthal acoustic modes are excited and coupled with the longitudinal mode. If the distribution type of the heat source is sin(jθ), the jth azimuthal mode are the strongest one, while other azimuthal modes are weak. Moreover, with the increase of the duct length, the oscillation frequency decreases and get close to the cutoff value of the azimuthal modes. Mode coupling becomes weak for this condition and the effects of the non-uniformity of the heat source on the combustion instabilities are also reduced.