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We present a numerical method to determine the complex acoustic impedance atthe open surface of an arbitrarily shaped cavity, associated to an impingingplanar acoustic wave with a given wavenumber vector and frequency. We haveachieved this by developing the first inverse Helmholtz Solver (iHS), whichimplicitly reconstructs the complex acoustic waveform--at a given frequency--upto the unknown impedance boundary, hereby providing the spatial distribution ofimpedance as a result of the calculation for that given frequency. We show thatthe algebraic closure conditions required by the inverse Helmholtz problem arephysically related to the assignment of the spatial distribution of thepressure phase over the unknown impedance boundary. The iHS is embarrassinglyparallelizable over the frequency domain allowing for the straightforwarddetermination of the full broadband impedance at every point of the targetboundary. In this paper, we restrict our analysis to two-dimensions only. Wefirst validate our results against Rott's quasi one-dimensional thermoacoustictheory for viscid and inviscid constant-area rectangular ducts, test our iHS ina fully unstructured fashion with a geometrically complex cavity, and finally,present a simplified, two-dimensional analysis of a sample of carbon-carbonultrasonically absorptive coatings (C/C UACs) manufactured in DLR-Stuttgart,and used in the hypersonic transition delay experiments by Wagner et al. inAIAA 2012-5865. The final goal is to model C/C UACs with multi-oscillator TimeDomain Impedance Boundary Conditions (TDIBC) developed by Lin et al. in JFM(2016) to be applied in direct numerical simulations (DNS) focused on theoverlying boundary layer, eliminating the need to simultaneously resolve themicroscopic porous structure of the C/C UACs.

Towards Impedance Characterization of Carbon-Carbon Ultrasonically Absorptive Cavities via the Inverse Helmholtz Problem