Towards the numerical simulation of airfoil noise

A two-dimensional computational aeroacoustic (CAA) code is developed based on solving the two-dimensional linearized Euler equation. The 7-point dispersion-relation-preserving scheme (DRP) is used for spatial discretization in order to minimize the dispersion errors. The four-level optimized time discretization scheme, the classical Runge-Kutta scheme have been implemented into the code for time discretization. Radiation and outflow boundaries based on the asymptotic solution have been used at the far-field boundaries. The code is firstly validated by several model problems for testing the dispersion and dissipation properties of the DRP scheme, the effectiveness of far-field and solid wall boundary conditions. Then several simple applications relevant to acoustic reflection and scattering, gust/airfoil interaction and trailing edge noise problems have been solved by using the CAA approach. Numerical results about the acoustic reflection of time periodic acoustic reflection and scattering phenomena can be simulated correctly. For the gust/airfoil interaction cases, the numerical results show that the far-field radiation directivity can be reasonably simulated even for relatively high reduced frequencies. For the simulation of trailing edge noise, a vortex passing near the trailing edge of a half-infinite plate and a finite plate have been formulated into a initial value problem. The numerical simulation results agree rather well with classical theory in both the far-field radiation directivity and the power law. The present simple applications show the capabilities and potential of the CAA approach for future numerical simulations of airfoil noise