Approximate computation of acoustic reflection and shadow effects using the Kirchhoff method

\nThe article presents a fairly simple way to take solid bodies into account in acoustic radiation calculations using integral methods, while still using the free-space Green’s function. The approach is based on the Kirchhoff method and on a locally plane reflection assumption. It can be applied to both analytical noise sources and acoustic disturbances provided by numerical simulations, to fixed or mobile noise sources, concentrated or widely spread in a moving medium. The time-domain formulation is an important advantage for periodic signals rich in harmonics (rotors or propellers impulsive noise) and for broadband signals (profile or jet noise). The formulation and calculation algorithm are described in detail. The method’s accuracy and limitations are shown first by comparing the results with analytical solutions for the acoustic scattering of a point source by a sphere, for a fluid at rest. An application example is then given for a wing in a Mach 0.5 flow, and the results are compared with the numerical solution of the linearized Euler equations, in the presence of a mean flow. In addition, the article proposes expressions for direct calculation of the pressure gradient by Kirchhoff and Ffowcs Williams-Hawkings surface formulations.\n