Impedance modelling and eduction for CAA using the improved multipole broadband model

Acoustic liners are widely used as acoustic damping elements in the inlet and bypass duct of aero-engines. Liner models are used to include lined surfaces in complex CAA simulations with flow. To reproduce the behaviour of a real liner, the model parameters must be adjusted, for example on the basis of the liner's impedance function. Currently, there is no method to directly measure that function under flow conditions. However, it can be calculated indirectly by an impedance eduction. This method is based on CAA simulations including a liner model, and on measurements of the transmission and reflection coefficients. The model's parameters are optimized to reproduce the measured coefficients. The liner's impedance function can then be calculated using the optimized parameters. For some novel liner concepts or non-locally reacting liners, the impedance function is too complex to be accurately reproduced by models based on simple physical assumptions. Therefore, the impedance eduction method produces inaccurate results. The objective of this study is to investigate whether the improved broadband multipole impedance boundary condition can be used to replace the Extended Helmholtz Resonator (EHR) model for the impedance eduction to handle such complicated cases. To compare both models in a practical application, an impedance eduction for a non-locally reacting resistive liner is carried out and the results are compared against each other. Particular attention is paid to the specific requirements of the improved broadband multipole impedance boundary condition. Therefore, a curve fitting method is used for the generation of initial values for the optimization, and two optimization methods are compared against each other. By using the improved broadband multipole impedance boundary condition for the impedance eduction, the residual deviation of the energy coefficients could be reduced by a factor of 3.