Numerical simulation of a turbulent channel flow with an acoustic liner

Abstract

Numerical simulations of a compressible turbulent channel flow with an acoustic impedance boundary condition are performed to assess how the flow is modified compared with a channel flow with rigid walls. When the liner resonance frequency is not too large and the resistance sufficiently small, turbulent statistics deviate from those obtained with rigid walls and surface waves are found traveling along the liner surface. For small resonance frequencies these waves are two-dimensional, they have a large wavelength compared to the turbulent structures and modulate these structures. As a result, they transport momentum toward the impedance wall, causing a drag increase. When the resonance frequency increases, the waves along the liner surface progressively lose their spanwise coherence while their streamwise wavelength decreases to get close to the flow typical length scales, which may also result in a drag increase when the resistance is sufficiently small. In the cases in which the surface waves are two-dimensional, a connection is established between them and the unstable modes computed by using a linear stability analysis. Given the streamwise periodicity of the channel, a temporal stability analysis is performed rather than a spatial analysis, the latter being more frequently encountered in acoustic mode computations. This temporal analysis shows that the unstable mode in the vicinity of an acoustic liner arises from the A-branch of wall modes.