Prediction of stability behaviors of longitudinal and circumferential eigenmodes in a choked thermoacoustic combustor

Many aero-engine and gas turbine combustion systems are in choked configuration. These combustors are more prone to thermoacoustic instability. Thus there is a need to characterize and predict the stability behaviors of the choked systems. In this work, stability analysis of both longitudinal and circumferential eigenmodes in a thermoacoustic system with a choked outlet is performed via two different approaches. One is an analytical method, which describes the choked outlet by using two analytical expressions. The main difference between these expressions is whether a length correction is considered. The other method is a numerical one, which is based on linear Euler equation (LEE). Comparison is then made between the analytical results and the numerical ones. It is found that when longitudinal eigenmodes are considered and the length of the choked nozzle is not small, the analytical expression with a length correction should be used. However, when the flow Mach number is large (>0.1), these analytical expressions can lead to significant errors, especially for the longitudinal eigenmodes at higher frequency. To further validate these methods, they are then applied to predict the stability behavior of circumferential eigenmodes. It is found that the expressions for the choked outlet can be used for the predictions of azimuthal thermoacoustic instabilities. However, non-negligible errors are also brought when the Mach number is large (>0.1).