A Mathematical Model for the Interaction of Anisotropic Turbulence with Porous Surfaces*

Leading-edge noise is a complex phenomenon that occurs when a turbulent fluid encounters a solid object and is a notable concern in various engineering applications. 

This presentation explores how existing theoretical leading-edge noise models can account for porosity at the leading edge and for anisotropic flow. 

The model has two key components. First, we adjust the velocity spectrum to account for the possibility of complex anisotropy ratios in the flow. Second, we adapt the fully analytical acoustic transfer function to account for different boundaries by implementing convective impedance boundary conditions when formulating the gust diffraction problem. We apply the Wiener–Hopf technique to solve the gust-diffraction problem along the semi-infinite boundary.

Each modification is inspired by leading-edge noise experimental data obtained using a series of different porous leading edges. Experimental data demonstrates the interplay between anisotropy and leading-edge modifications while achieving the characteristic

mid-frequency noise reduction expected from porous leading edges. Our model is adapted to best fit the trends of the data via a tailored impedance function, leading to good agreement with all data sets across an extended frequency range.