Low-Order Modeling to Investigate Clusters of ITA Modes in Annular Combustors

The coupling between the unsteady heat release and the acoustic modes of a given combustor can lead to thermoacoustic instabilities of acoustic origin. Recent studies showed that a flame in an anechoic environment can also be unstable: a feedback loop, intrinsic to the flame and not involving the acoustic modes, exists and may eventually be strong enough to modulate the dynamics of the flame. This intrinsic mechanism gives rise to thermoacoustic modes of intrinsic origin (ITA origin). These modes have been extensively studied in longitudinal combustors but little has been done for annular configurations. One recent study showed that ITA modes in annular combustors come in significant number and with the peculiar behavior of clusters, ie. modes with close frequencies. In the present work an analytical model of a typical annular combustor is derived via Riemann invariants and Bloch theory. In the proposed model, the full annular system is described by one longitudinal combustor and an outlet reflection coefficient that depends on frequency and the azimuthal order. Results obtained by the model are compared against results from a 3D Helmholtz solver. By means of the derived low-order model, it is possible to understand the structure of the clusters associated to ITA modes of different azimuthal orders. The model also explains the underlying mechanism of the clustering phenomena, signature of weakly coupled oscillators. Additionally, the model shows how these clusters are affected by the strength of the acoustic flame response. The present study demonstrates that simple 1D thermoacoustic models of annular configurations can be accurate and transparent enough so that a parametrical analysis and tracking of modes of acoustic and ITA origin is possible, which in turn allows to comprehend which physical mechanisms play a major role in the thermoacoustic behaviour of annular combustors.

Keywords : thermoacoustic instabilities, combustion dynamics, annular combustor, low order model, ITA modes, clusters