Investigation of the Impedance Along the Surface of the Acoustic Liner Sample Based On Numerical Simulation

The aim of the study is a comparative analysis of the impedance values of a single-layer locally reacting acoustic liner sample, obtained by different methods based on numerical simulation of physical processes in a duct with grazing sound waves. The study considers a liner sample with 23 honeycomb cells arranged in a line along the sample. Each cell contains one hole with a diameter 5.6 mm located in the center of the cell, which corresponds to a perforation degree 11.7%. A full-scale experiment on the grazing incidence of waves relative to the sample surface in a duct is simulated; flow effect is not taken into account. Numerical simulation is performed on the basis of solving the non-stationary compressible Navier-Stokes equations in a three-dimensional formulation. As a result of numerical simulation, the acoustic pressure and normal acoustic velocity are found on the surface of the each cell and hole, which makes it possible to calculate the impedance for each cell by a direct method. In addition, for each cell, the impedance is calculated by Dean's method. Impedance calculations are carried out in the frequency range 500–2500 Hz. The results obtained demonstrate that the impedance varies along the liner sample. In this case, in the region of resonant frequencies, the real part of the impedance for the cells at the end of the sample (from the 20th to the 23rd cell) becomes negative, i.e. the cells amplifies the sound. The numerical simulation also gives the acoustic pressure at points on the wall opposite the liner sample, which corresponds to the microphones located in a full-scale experiment. Based on the acoustic pressures recorded at these points, the impedance is calculated by an impedance eduction method. This method represents the minimization of the objective function, which is the residual between the calculated and experimental (in our case, taken from numerical simulation) acoustic pressure values at the microphone installation points. The calculated acoustic pressure is determined by solving the linearized Euler equations with the impedance boundary condition by the finite element method. The eduction of constant and variable impedance along the acoustic liner sample is considered. A comparison of the obtained impedance values reveals that the impedance calculated by the direct method is in good agreement with the known concepts of physical processes in the locally reacting acoustic liner. In turn, the impedance eduction method, which takes into account the impedance variability along the liner sample, requires imposing the additional conditions that are responsible for the correct description of the impedance behavior at high SPL.