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

The intrinsic thermoacoustic (ITA) feedbackloop constitutes a coupling between flow, flame and acoustics that does not involve the natural acoustic modes of the system. One recent study showed that ITA modes in annular combustors come in significant number and with the peculiar behavior of clusters, i.e. several modes with close frequencies. In the present work an analytical model of a typical annular combustor is derived via Riemann invariants and Bloch theory. The resulting formulation describes the full annular system as a longitudinal combustor with an outlet reflection coefficient that depends on frequency and the azimuthal mode order. The model explains the underlying mechanism of the clustering phenomena and the structure of the clusters associated with ITA modes of different azimuthal orders. In addition, a phasor analysis is proposed, which enclose the conditions for which the 1D model remains valid when describing the thermoacoustic behavior of an annular combustor.