Comparison of non-modal-based and modalbased impedance eduction techniques

Abstract

A comparative study of four impedance eduction techniques is reported. Two of the techniques are based on numerically solving the 2-D convective Helmholtz equation as a non-modal-based boundary-value problem. The third technique is modal-based as it applies a mode expansion to reduce the dimension of the Helmholtz equation from 2-D to 1-D. The forth technique is also modal-based but the employed propagation model takes account of the boundary-layer viscothermal effects and allows for shear flow varying over a rectangular cross section. Measurements on a liner with and without mean-flow conditions are carried out using the DLR DUCT-R system. The measured data are used for the impedance eduction and the educed results are presented. The conclusions drawn from the limited number of test cases include: 1, all the eduction techniques, except for one, educe scattered impedance values when the resistance of the liner is low, 2, the non-modalbased and the modal-based techniques yield similar impedance values for the downstream-propagating waves (modes), but yield considerably different values for the upstream-propagating waves (modes), and 3, the model which includes a shear mean flow and the model which assumes uniform mean flow exhibit differences in their educed impedance; the differences are larger for the upstream-propagating modes than for the downstreampropagating modes.