Nonlinear coupling from acoustics to aerodynamics in perforated plates at normal incidence

• Effect of acoustic excitations on the aerodynamics of perforated plates • Low-order modelling of the acoustically-induced increase of the nonlinear flow resistance • Analytical solutions for the mean flow resistance, for one or multiple acoustic excitation(s) • Explanation of the physics causing the nonlinear coupling from acoustics to aerodynamics • Explanation and modelling of the non-monotonic variation in acoustic resistance versus acoustic amplitude This study addresses the mean nonlinear pressure loss through a perforated plate caused by the combination of the steady bias flow itself and high-amplitude acoustic excitations. An analytical treatment of this problem yields an explicit formula allowing one to estimate the mean flow resistance as a function of the steady flow velocity and unsteady velocity amplitudes. An increase in the unsteady velocity amplitude(s) yields an increase in the mean flow resistance, which highlights the presence of nonlinear coupling from acoustics to aerodynamics. For a given value of the mean flow velocity (or pressure drop), this causes an increase in the mean pressure loss (or a decrease in the steady flow velocity). The model highlights that for moderate acoustic disturbances, the mean flow and acoustic contributions to the mean flow pressure loss add up, whereas for large acoustic velocity amplitudes, the pressure loss is, to the leading order, proportional to the product of the mean flow velocity and the maximum acoustic velocity amplitude. Finally, the model is exploited to explain the presence in some acoustic studies of a valley in the acoustic resistance curve versus the acoustic velocity amplitude. The simplicity of the model makes it attractive to account for 1D flow oscillation effects in fluid flow network models, to understand the essential mechanisms at play in the acoustically induced increase in the mean flow resistance, and to take this phenomenon into account when estimating the acoustic impedance of perforated plates.