Mode Shape and Eigenfrequency Analysis based on Helmholtz Equation for Thermo-acoustic Combustion Instability

Abstract

The thermo-acoustic combustion instability is a key problem in combustion that stems from the interaction between the acoustic wave and fluctuations of heat release. In this paper, the finite element software COMSOL is used to identify the frequencies and the growth rates at which thermo-acoustic instabilities are excited. The Helmholtz equation combined with the classical n-τ flame model is solved to capture the thermo-acoustic features in simple geometry combustors with no mean flow. The accuracy of this method is demonstrated by studying the thermo-acoustic in various verification cases. The effect of the flame holder on acoustic pressure field is studied. The results show that the first transverse mode is concentrated around the flame holder. The mode frequencies will change as the temperature increases in the downstream of flame holder. In addition, when the upstream temperature of the flame holder is different from downstream, the longitudinal mode will transition to transverse mode. Furthermore, combustion instability in the combustion chamber of the model rocket is studied by using this method and compared with the experimental data. The unstable mode frequencies are 1451Hz, 1184.9Hz, 1704.7Hz and 1821.5Hz, respectively. This work demonstrates that the method can be applied to predict the thermo-acoustic behavior.