Interaction between coherent flow oscillations and the pre-mixed flame sheet in combustors can result in coherent unsteadiness in the global heat release response. These coherent flow oscillations can either be self-excited (eg. the Precessing Vortex Core) or result from the hydrodynamic response of the flow field to acoustic forcing. Recent work has focused on understanding the various instability modes and fundamental mechanisms that control hydrodynamic instability in single nozzle swirl flows. However, the effect of multiple closely spaced nozzles as well as the non-axisymmetric nature of the confinement imposed by the combustor liner on swirl nozzle flows remains as yet unexplored. We study the influence of inter-nozzle spacing and non-axisymmetric confinement on the local temporal and spatiotemporal stability characteristics of multi-nozzle flows in this paper. The base flow model for the multi nozzle case is constructed by superposing contributions from a base flow model for each individual nozzle. The influence of the flame is captured by specifying a spatially varying base flow density field. The non-axisymmetric local stability problem is posed in terms of a parallel base flow with spatial variations in the two directions perpendicular to the streamwise direction. We investigate the case of a single nozzle and three nozzles arranged in a straight line within a rectangular combustor. The results show that geometric confinement imposed by the combustor walls has a quantitative impact on the eigenvalues of the hydrodynamic modes. Decreasing nozzle spacing for a given geometric confinement configuration makes the flow more unstable. The presence of an inner shear layer stabilized flame results in an overall stabilization of the flow instability. We also discuss qualitatively, the underlying vorticity dynamics mechanisms that influence the characteristics of instability modes in triple nozzle flows.

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