Four-dimensional formulation of the acoustic frequency domain for Kirchhoff surfaces

Abstract

Flow-induced noise is a common problem in practical engineering. The classical acoustic analogy model is insufficient to evaluate the characteristic distribution of the acoustic field using only acoustic pressure as a reference. Proceeding from a four-dimensional linear wave equation with sound pressure and sound velocity vectors as variables, by choosing the Kirchhoff surfaces to enclose a nonlinear acoustic source as integral surface, and combining with the convective Green's function, the four-dimensional acoustic frequency-domain integral equation for a uniformly moving medium is given. Numerical prediction studies are conducted for stationary, rotating monopole and dipole sources. The results show that the distributions of the sound pressure and acoustic velocity obtained in this paper are in good agreement with the analytical solutions. In contrast to the stationary flow case, the acoustic field distribution of the stationary point source in the uniform flow exhibits a convection effect. On the other hand, the acoustic field distribution of the rotating point source exhibits a strong Doppler effect and convection effect due to the joint influence of the uniform flow, the self-excitation frequency, harmonic order, and rotational frequency of the point source.

Keywords

• wave equation
• uniform flow
• kirchhoff surfaces
• four-dimensional acoustic formulation
• aerodynamic noise