Finite thickness effects and corrections for acoustic waves propagating through shear layers

Acoustic imaging methods like beamforming rely on the propagation delay between source and observer. For open jet measurements the propagation delay is computed by a method proposed by Amiet, which has been used successfully for acoustic wind tunnels since its first introduction. The sound waves are assumed to refracted on a planar velocity discontinuity-modeling the shear layer-which combined with ray theory yields the propagation path. Amiet’s method is valid when the shear layer thickness may be neglected and the shear layer is approximately planar. In this paper the Amiet correction methodology is extended to alleviate these requirements, based on a discretization of the flow in Mach iso-contours. The rays are defined as the paths that minimize the travel time between source and observer by use of Fermat’s principle. This establishes an easy mathematical optimization process. Two specific cases considered are common to all wind tunnels: (i) an expanding-slightly slanted-shear layer interface and (ii) a rounded jet core cross sectional shape. A self-similar shear layer flow model by Görtler, and an adaptation of this model that that accounts for a rounded jet core shape are used to describe the jet flow. The results of the extended model are compared to a ray-tracing solution, which is used to evaluated accuracy and the gain in computational effort. This comparison showed good agreement, while having a computational effort of two orders lower than the raytracing code. The extended model is particularly useful in large industrial wind tunnels which have thick shear layers (up to 1 m) and microphone arrays placed with an offset from the wind tunnel axis. An experimental evaluation of the method, applied to a known speaker source in a large industrial wind tunnel, shows that source location accuracy could be improved up to 6 cm.