Vector Aeroacoustics for Uniform Mean Flow: Acoustic Velocity and Vortical Velocity

Abstract

Acoustic and vortical disturbances in uniform mean flow bounded with solid surfaces are investigated in this paper. A convective vector wave equation and a convection equation that describe the acoustic velocity and vortical velocity in uniform mean flow, respectively, are deduced by combining the Helmholtz–Hodge decomposition method with the method of Mao et al. Analytical acoustic velocity integral formulations for the monopole and dipole sources in uniform mean flow are deduced from the developed vector wave equation and are also verified through numerical test cases. Moreover, this paper clarifies that aerodynamic sound is radiated from the monopole source as well as the irrotational components of the dipole and quadrupole sources. The solenoidal parts of the dipole and quadrupole sources are acoustically nonradiating, but they induce vortical disturbances in uniform mean flow.