Comparison of strongly and weakly nonlinear flame models applied to thermoacoustic instability

Weakly nonlinear flame (or heater) dynamic models, only accounting for heat release rate disturbances from the flame (or heater) at forcing frequencies and omitting harmonic terms due to nonlinear mechanisms, are widely used in low-order tools for the analysis and prediction of thermoacoustic instabilities, because they have a numerical cost much cheaper than tools based on Navier-Stokes equations, and are easier to develop and validate. However, these models may lead to errors under certain conditions. The present work considers a Rijke tube model combustor, in which a classical third-order model is used to describe the flame dynamic response to the oncoming flow disturbance. We call this model the strongly nonlinear flame model. The weakly nonlinear flame model is then introduced. The wave-based approach is adopted as a low-order tool. The weakly and strongly nonlinear flame models are embedded in the low-order tool to reproduce the thermoacoustic instability of the model combustor. The natural frequency and growth rate of thermoacoustic instability are then determined by mode extracted methods. The differences between the results predicted by using the weakly and strongly nonlinear flame models are compared for a set of operating conditions, in order to find the conditions under which the weakly nonlinear flame model works. Short-time Fourier transform is adopted to analyze the extracted frequencies and growth rates of four selected cases. When the dominant acoustic mode strength is much stronger than the remaining modes, the weakly nonlinear models perform well. However, these models fail to capture the mode frequency and growth rate when multiple unstable modes are present.