Assessment of Numerical Tools for the Evaluation of the Acoustic Impedance of Multi-Perforated Plates

Multi-perforated liners, commonly employed in Gas Turbine combustors as cooling devices to control metal temperature, are recognized as very effective sound absorbers. Thus, in the innovative lean combustion technology, where the onset of thermoacoustic instabilities represents one of the most important issue, the multi-perforated plates can be exploited both for wall cooling and damping combustion instabilities. As a first step of a large experimental and numerical research program regarding multi-perforated liners, an investigation of different numerical methodologies to analyze acoustic damping is here reported. In particular three different numerical techniques to evaluate planar waves sound absorption of perforated plates are presented and validated with literature test cases. A quasi 1-D code, implementing the wall compliance concept, provides results for a large set of geometric and fluidynamic conditions. A large test matrix was investigated varying perforation hole angle and diameter with different overall porosities. The effect of bias and grazing flows Mach number was tested as well. A subset of considered geometries were then supported by a full reconstruction of the unsteady pressure field by means of a Large Eddy Simulation computed with an open-source code. Non-reflective boundaries with forcing term provide the wave to acoustically excite the perforated plate. Multi-microphone postprocessing technique allowed the reconstruction of a progressive and regressive planar wave to compute the reflection coefficient. All results were cross-checked with a Finite Element Model, able to solve the wave equation in the frequency domain with a background velocity field.