Numerical computation of airfoil-gust lift response with applications to leading-edge noise generation

We propose a numerical framework to compute the airfoil-gust lift response and its subsequent leading-edge noise generation due to an incident compressible turbulent flow. This approach is valid for blades with large aspect ratios, general airfoil geometries, three-dimensional supercritical perturbations and compressible subsonic flows. The linearized equation for unsteady potential flow is rewritten as a Helmholtz equation in the transformed Prandtl-Glauert plane, leading to a boundary value problem prescribed by the linearized airfoil theory. The boundary element method is then employed iteratively to solve the Helmholtz equation for realistic airfoil configurations. Results show that non-zero thickness airfoils drastically reduce the pronounced acoustic radiation expected by oblique gusts. However, at moderate Mach numbers, the compressibility effects may increase the noise radiation in the upstream direction compared to Amiet’s analytical solution when thickness is addressed into the analysis.