Homogenization of the acoustic transmission on periodically perforated plates interacting with potential mean flow

The paper is devoted to the homogenization of the acoustic waves interacting with background steady inviscid and irrotational flow in the neighbourhood of rigid peri- odically perforated plates. We present a model of an acoustic interface obtained by the asymptotic homogenization of a thin transmission layer in which the plate is embedded. To account for the presence of the mean flow, a decomposition of the fluid pressure and velocity in the steady and fluctuating parts is employed. This leads to a linearization and an efficient use of the homogenization method with the model order reduction effect. The acoustic perturbations of the velocity potential are governed by an extended wave equation depending on the advection velocity due to the mean flow. The coefficients of the homogenized interface depend on the flow. The derived model extended by natural coupling conditions provides an implicit Dirichlet-to-Neumann operator. Numerical simulations of wave propagation in a waveguide illustrate the flow speed influence on the acoustic transmission. Also geometrical features of the plate perforation are explored