Boundary integral method for fundamental solution of non-compact aerodynamic noise propagating in half-space

A tailored Green’s function satisfying the corresponding acoustic boundary conditions on all scattering surfaces can be used as the fundamental solution to predict aerodynamic noise. For the noise induced by a low Mach number flow above an infinite impedance plane, the tailored Green’s function is obtained by solving the linear wave equation in frequency domain with the free-space Green’s function. Numerical solutions applicable for an arbitrary shape of the non-compact scattering body are achieved with the boundary element method. And the effect of the infinite impedance plane is handled with the image source and the complex equivalent source methods to avoid the singular integral when the reflecting plane is spring-like surface impedance. Furthermore, a theoretical model, which is suitable for a two-dimensional non-compact cylinder over an infinite plane with acoustic hard-wall or impedance boundary conditions, is obtained with the use of the equivalent source method. For acoustic scattering from a two-dimensional cylindrical in stationary medium, the numerical solution corresponding to a point monopole source are in a good agreement with the analytical solution for all observer angles and wave numbers. Moreover, the fundamental solutions of the noise induced by a low Mach number flow past the cylinder are evaluated with the numerical approach. The results show that the infinite half-space boundary strengthens the radiation ability of the sound sources, and the medium moving at low Mach number less than 0.2 has little influence on sound propagation.