On the impact of the turbulent grazing flow development on the acoustic response of an acoustic liner

The interaction between acoustic waves and turbulent grazing flow over an acoustic liner is investigated using Lattice-Boltzmann Very-Large-Eddy simulations. A single-degree-of-freedom liner with 11 streamwise-aligned cavities is studied in a grazing flow impedance tube. The conditions replicate reference experiments from the Federal University of Santa Catarina. The influence of grazing flow (with a centerline Mach number of 0.32), acoustic wave amplitude, frequency, and propagation direction relative to the mean flow is analysed.  Impedance is computed using both direct (i.e. the in-situ method) and model-fitting inference (i.e. the mode-matching method) methods. The former reveals strong spatial variations; however, averaged values throughout the sample show minimal differences between upstream and downstream propagating waves, in contrast to what is obtained with the latter method. Flow analyses reveal that the orifices displace the flow away from the face sheet, with this effect amplified by acoustic waves and dependent on the wave propagation direction. Consequently, the boundary layer displacement thickness ($\delta^*$) increases along the streamwise direction compared to a smooth wall and exhibits localised humps downstream of each orifice. The growth of $\delta^*$ alters the flow dynamics within the orifices by weakening the shear layer at downstream positions. This influences the acoustic-induced mass flow rate through the orifices at equal Sound Pressure Level,  suggesting that acoustic energy is dissipated differently along the liner. The asymmetry of the flow field experienced by the acoustic wave, depending on its propagation direction, highlights the need to consider a spatially evolving turbulent flow when studying the acoustic–flow interaction and measuring impedance.