Linearized perturbed compressible equations for low Mach number aeroacoustics

For efficient aeroacoustic computation at low Mach numbers, the linearized perturbed compressible equations (LPCE) are proposed. The derivation is based on investigation of the perturbed vorticity transport equations. In the original hydrodynamic/acoustic splitting method, perturbed vorticity is generated by a coupling effect between the hydrodynamic vorticity and the perturbed velocities. At low Mach numbers, the effect of perturbed vorticity on sound generation is not significant. However, the perturbed vorticity easily becomes unstable, and causes inconsistent acoustic solutions, based on grid dependence. The present LPCE ensures grid-independent acoustic solutions by suppressing the generation of perturbed vorticity in the formulation. The present method is validated for various dipole and quadruple vortex-sound problems at low Mach numbers: (i) laminar 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, (ii) quadruple sound of Kirchhoff vortex at Mach number based on the rotating speed, M_Θ = 0.1, and (iii) temporal mixing layer noise at Reynolds number based on the shear layer thickness, Re_δ = 10000 and Mach number based on the shear rate, M_s = 0.1.