Numerical computation of aeroacoustic transfer functions for realistic airfoils

Based on Amiet's theory formalism, we propose a numerical framework to compute the aeroacoustic transfer function of realistic airfoil geometries. The aeroacoustic transfer function relates the amplitude and phase of an incoming periodic gust to the respective unsteady lift response permitting, therefore, the application of Curle's analogy to compute the radiated noise. The methodology is focused on the airfoil leading-edge noise problem being able to also consider the trailing-edge back-scattering and, consequently, airfoil compactness effects. The approach is valid for compressible subsonic flows and the airfoil blade is assumed of large aspect ratio subjected to three-dimensional periodic gusts with supersonic velocity trace at the airfoil leading edge (i.e. supercritical gusts). This work proposes the iterative application of the boundary element method to numerically solve the boundary value problem prescribed by the linearized airfoil theory. Details of the numerical implementation are discussed and include the application of boundary conditions in different steps of the iterative procedure, treatment of derivatives in the implementation of the Kutta condition and accurate representation of singularities present at the leading- and trailing-edges. This study validates the numerical approach by comparing results with Amiet's theory obtained analytically. Subsequently, effects of realistic airfoil geometries on the leading-edge airfoil radiated noise are presented.