Scattering of sound by a core vortex: Numerical simulations using a wide angle parabolic equation

Abstract

The generation and scattering of sound by flow inhomogeneities such as vortices are basic problems which have received much attention in the efforts to develop methods to detect the strength and location of noise sources. Recent experimental studies have demonstrated that acoustic scattering can serve as an efficient (direct and nonintrusive) probe of the vorticity field for the characterization of turbulent flows. In 1978 Candel presented the results of a numerical study based on a standard parabolic equation in which the sound speed variations are included through an effective celerity ceff=c0+vx where the x axis give the direction of propagation of the acoustic wave. However, the effective celerity model does not include the effects of the perpendiculary components of the velocity field and the importance of this components increases with the angle of propagation. A wide angle parabolic equation has been recently proposed [Dallois et al., 7thAIAA/CEAS paper N 2001-2256] to take into account the mean velocity effects up to second order in Mach number. To estimate the validity of this new parabolic equation (MW–WAPE), we considered a configuration with both strong gradient and high Mach number. Our results are compared to a reference solution obtained by solving the linearized Euler equations. The MW–WAPE solutions are in good agreement with the reference solutions. This parabolic equation gives accurate results up to M≊0.5 whereas the standard equation using an effective celerity failed to give good results above M≊0.2.