A generalized straightforward method for liner impedance eduction in the presence of a 2D shear flow

This paper extends the well-known straightforward impedance eduction method to consider a more realistic grazing flow, a two-dimensional shear flow. This is realized by transforming the theoretical formula based or boundary value problem based wavenumber-to-impedance process in the original Straightforward Methods (SFMs) into solving a generalized eigenvalue problem where the liner impedance is just the eigenvalue, implying that the impedance eduction procedure is entirely straightforward. The generalized eigenvalue problem is derived by using the finite difference method where a two-dimensional shear flow with an impedance boundary condition can be applied. By utilizing the proposed method on NASA’s benchmark data, the grid convergence and the effect of shear flow are investigated for two kinds of shear flow models which implement slip and no-slip boundary conditions, respectively. It is found that the proposed method with a Chebyshev grid has a high accuracy while the uniform grid is incapable of handling a finite boundary layer. Even at the anti-resonant frequency near which the impedance deviation caused by flow dimensionality reduction is primarily observed, the mode shapes under a uniform flow, an equivalent one-dimensional shear flow and a two-dimensional shear flow are very consistent, suggesting that in the terms of impedance eduction, the effect of two-dimensional shear flow is minimal in the plane-wave frequency range (500-3 000 Hz) for the downstream propagation.