The linearized perturbed compressible equations for aeroacoustic noise prediction at very low Mach numbers

The linearized perturbed compressible equations, based on a hydrodynamic/acoustic splitting method, are proposed for low Mach number aeroacoustics. In the hydrodynamic/acoustic splitting method, perturbed vorticity easily becomes unstable through coupling effects between the hydrodynamic vorticity and the perturbed velocities, and it consequently contaminates the acoustic solution. The generation of perturbed vorticity is firmly suppressed in the linearized perturbed compressible equations, which is able to secure consistent, grid-independent acoustic solution. The validity of the linearized perturbed compressible equations is demonstrated for a dipole tone from a circular cylinder at Reynolds number based on the cylinder diameter, Re_D=150 and free stream Mach number M_∞=0.1, a quadruple noise generated by Kirchhoff vortex at Mach number based on the rotating speed M_θ=0.1, and a quadruple noise from a temporal mixing layer at Reynolds number based on the shear layer thickness Re _δ=10000 and Mach number based on the shear rate M _s=0.1.