Measurement of Liner Impedance with Flow by an Inverse Method

The measurement of liner impedance with flow is a very difficultproblem especially when the liner is not a simple single degree of freedom (SDOF) liner. To bypass the problem of knowing the acoustical propagation inside the liner, a method called ”eduction method” has been developed at NASA; the propagation of sound inside a 2D lined duct is computed through a finite elements method, with the assumptions of uniform flow and of acoustical displacement continuity over the liner. An inverse method is then used to determine a value of the impedance that minimizes the discrepancy between predicted and measured acoustical pressure at some characteristic points. We propose a new multimodal method (MM) to compute the propagation in a 2D lined duct with flow. The basis of this method is to project the propagation equations on a complete basis of functions. Then the transmission and reflection matrices can be computed easily. One advantage is that the MM is quicker than a finite elements method. The axial boundary conditions in the MM are exact and easy to implement. Furthermore, the effect of the boundary layer of the main flow can be taken into account. The numerical results are compared to experimental results measured in a set up with a rectangular section. An inverse method is used to find the best fit of impedance.