Hydrodynamic instability and sound amplification over a perforated plate backed by a cavity

The long-wavelength hydrodynamic behaviour over a cavity-backed perforated plate, in a duct with a mean shear flow, is studied numerically using the multimodal method, where the acoustic and hydrodynamic disturbances are calculated from the linearized Euler equations. The flow–acoustic coupling near the perforated plate is first solved hole by hole, and results indicate a well-defined large-scale hydrodynamic wave over the plate, with a wavelength close to the plate length at the peak sound amplification frequency when a plane acoustic wave is introduced from the upstream duct. Since the hydrodynamic wavelength is one order larger than the period of the perforation, the effect of the perforated plate is then described by a homogeneous plate impedance. It is shown that the homogenized approach approximately represents the discrete approach in this problem.