Acoustic Wave Focusing by Non-Uniform Mean Flow in a Rectangular Duct with Viscous Walls

Abstract

The high-frequency acoustic wave focusing by a viscous flow profile and reflective duct walls encasing the flow is considered. For a range of the non-uniform meanflow and duct parameters, the problem of image sources generation upstream of the physical source in a rectangular duct is investigated computationally and analytically. This is done first by solving the Navier-Stokes equations at high Reynolds number in the Eulerian framework, then by using a Lagrangian particle method based on the high-frequency approximation, and finally, with a simple analytical plug-flow-profile model based on geometrical acoustics. It is shown that both the meanflow-refraction and wall-reflection play a key role in the focusing of acoustic waves. The analogy with geometrical acoustics is further emphasized by comparing the Navier-Stokes simulation results with the experimental data from the literature on acoustic wave focusing by a lens made of a negatively refractive material.