Prediction of thermoacoustic instabilities by the linearized Acoustic equations incorporated with the n-tau model

Combustion instabilities are frequently encountered in liquid rocket engines (LREs) and gas turbines, due to the coupling between unsteady heat release and pressure fluctuations in the combustor. Acoustic models based on Helmholtz equations equipped with specific heat release models are commonly adopted because of the low computational costs. In this paper, the stability analysis is constructed for the model based on the linearized acoustic equation equipped with a linear n-tau model for unsteady heat release. Linearized acoustic equations are solved in the frequency domain by using eigenfrequency analysis in COMSOL with Arnoldi algorithm, which enables the treatment of the combustion system with complex geometry. The proposed method is applied in a model LRE with longitudinal instabilities. To get the rocket chamber environment and flame model parameters, large eddy simulation has been used. Aiming at the phenomenon that the non-premixed gaseous flame combustion area is very long in the numerical simulation acoustic analysis is used to analyse the influence of different flame positions on the stability. The effects of flame position, on linear stability have been studied. The results show that when the peak area of flame heat release is located at the antinode of the mode, it is most likely to trigger combustion instability.