Flow-induced cylinder noise formulated as a diffraction problem for low Mach numbers

The role of surfaces in the mechanism of sound generation by low Mach number flows interacting with solid nonvibrating surfaces is well established by the classical aeroacoustic papers by Powell, Doak, Ffowcs Williams, Crighton, or Howe. It can be formulated as a problem of diffraction of the flow sources by the rigid body. The present study illustrates this statement in the case of flow-induced cylinder noise. Curleʹs formulation is analytically and numerically compared to a formulation based on an exact Greenʹs function tailored to a cylindrical geometry. The surface integral of Curleʹs formulation represents exactly the diffraction effects by the rigid body. The direct and scattered parts of the sound field are studied. In this low Mach number configuration, the cylinder is compact, and the scattered (dipole) field dominates the direct (quadrupole) field. The classical properties of the scattering by a cylinder are retrieved by considering a point quadripole source near the cylinder surface.