Analysis of a tractable model for combustion instability: the effect of delay and low pass filtering

In this paper a new analytically tractable model for combustion instability is proposed. The model is based on two coupled resonators in a feedforward path, and a feedback path composed of a delay, generalized Van der Pol term and a low pass filter. The model is analyzed and approximated using a refined Krylov-Bogoliubov (K-B) method. The analysis shows that the model captures the phenomenon of two coexisting oscillating modes which has been noted in combustion instability by Dunstan (2003). Conditions for the occurrence of various operation regimes have been established. The importance of delay and low pass filtering is discussed in this article. A frequency domain comparison between K-B approximations and the true outputs of the model has been provided in the end of the paper