Multimodal method for flow-induced acoustic resonance in successive deep axisymmetric cavities in a duct

Flow-induced pulsations in axisymmetric cavities with an incident sound wave are investigated. The underlying physics of the problem, which is the interaction between the shear layer instabilities and acoustic waves, is study by means of multimodal analysis. The configuration is considered as a series of duct segments with different radius. For a sheared mean flow, the radial modes of different duct segments are solved. Matching the modes at the interfaces between the segments gives the acoustic scattering matrix and the acoustic fields of the cavities-duct system for plan wave incidence. It is found that the sound amplification rate is determined by the intensity of the unstable hydrodynamic mode. Multi-cavity system tends to give more significant sound amplification than a single cavity.