Can describing function technique predict bifurcations in thermoacoustic systems?

Modeling thermoacoustic instabilities using inputs from experimental data usually employs a two-part approach: the response of the flame to perturbations in the flow is first obtained in terms of a flame transfer function, which then used as a source term in the acoustic equation. Within the framework of the two-part approach, an approximate modal analysis technique, known as describing function technique is used to model the nonlinearities in the flame dynamics. In this paper, we examine the consequences of employing a two-part approach in predicting the nonlinear behavior of a thermoacoustic system. Further, we examine the applicability of describing function technique for predicting the bifurcations of thermoacoustic systems. A toy model of thermoacoustic system was designed in order to analyze the effects of the two-part approach. It is found that the two-part approach modifies the dynamics of the system and cannot capture the intricate coupling between the combustion processes and acoustic field. A ducted diffusion flame model and a ducted premixed flame model are then studied as representative problems of thermoacoustic instability in combustors. The bifurcation plots obtained from the predictions using describing function technique were compared with the bifurcation plots obtained from the simulations in time domain for these models. The results show that the system behavior predicted by the describing function technique is quantitatively as well as qualitatively different from those obtained from time evolutions. © 2010 by Priya Subramanian, Vikrant Gupta, Bharat Tulsyan and R. I. Sujith.