Generalized coupled thermoacoustic modes in annular combustors introduced by Helmholtz resonators

The present work studies the impact of Helmholtz resonators (HRs) on the thermoacoustic instability in annular combustors. It has been known that annular combustors can see purely longitudinal thermoacoustic modes where the acoustic field involves only the modal component with circumferential wave number $n=0$, purely spinning modes where the acoustic field involves only one (clockwise or anti-clockwise) modal component with a particular circumferential wave number such as $n=+1$ or $-1$, standing or mixed modes where both the clockwise and anti-clockwise modal components of a given circumferential wave number coexist (such as $n=\pm 1$), and slanted modes where the acoustic field involves all three modal components with $n=0,\pm 1$. By employing both a 2D low-order network model and a 3D Helmholtz solver, we show for the first time that a type of generalized coupled thermoacoustic modes could result due to the presence of an HR. This type of modes could involve the coupling of even more circumferential modal components than that of the slanted modes. We first use an analytical model for an infinitely long annular duct to illustrate how the resonator’s characteristics, such as its inlet cross-sectional area and impedance, influence the acoustic modal coupling. An annular duct with finite length is then used to show that modes with this more general modal coupling can result due to the presence of an HR. We also confirm the HR’s bias flow Mach number and cavity volume as pivotal parameters in achieving exceptional points (EPs), where two acoustic modes merge. We show that, in the considered cases, the EPs are usually generalized coupled thermoacoustic modes. Further study considering the geometry of the MICCA combustor from the EM2C laboratory corroborates our findings, illustrating the HR’s capability in introducing the generalized coupled thermoacoustic modes in annular combustors, and the dependence of the EPs with different HR parameters. This investigation enhances understanding of HR-induced modal coupling, providing insights for designing acoustic dampers for advanced gas turbine combustors.