Do we need non-linear corrections? On the boundary Forchheimer equation in acoustic scattering

Abstract This paper presents a rapid numerical method for predicting the aerodynamic noise generated by foam-like porous aerofoils. In such situations, particularly high-frequency sources, Darcy’s law may be unsuitable describing pressure jump across aerofoil. Therefore, an inertial Forchheimer correction is introduced. results in non-linear boundary condition relating material to fluid displacement. We aim provide quick, semi-analytical model that incorporates effects without requiring full turbulent simulation. The scheme implemented based on local Mathieu function expansions, leading spectral well-suited both linear and conditions (including more general than correction). latter case, Newton’s employed solve resulting system of equations unknown coefficients. Whilst physical simplified consider just scattering thin aerofoil with no background flow, when included good agreement seen between predictions experimental large eddy simulations. It found sufficiently low-permeability materials, inertia can outweigh attenuation viscosity. helps explain discrepancy previous (linear) low-fidelity simulations or analytical predictions, which typically overestimate reduction capabilities