Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow

A new broadband impedance eduction method is introduced to identify the surface impedance of acoustic liners from in situ measurements on a test rig. Multimodal acoustic propagation is taken into account in order to reproduce realistic conditions. The present approach is based on the resolution of the linearized 3D Euler equations in the time domain. The broadband impedance time domain boundary condition is prescribed from a multipole impedance model, and is formulated as a differential form well-suited for high-order numerical methods. Numerical values of the model coefficients are determined by minimizing the difference between measured and simulated acoustic quantities, namely the insertion loss and wall pressure fluctuations at a few locations inside the duct. The minimization is performed through a multi-objective optimization thanks to the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The present eduction method is validated with benchmark data provided by NASA for plane wave propagation, and by synthesized numerical data for multimodal propagation.