Impedance Characterization of Carbon-Carbon Ultrasonically Absorptive Coatings Via the Inverse Helmholtz Solver

The current study introduces a novel methodology to determine the spatial distribution of the complex acoustic impedance at the open surface of an arbitrarily shaped geometry, associated with an incident planar acoustic wave of assigned wavenumber vector and frequency. This is achieved by developing the first inverse Helmholtz Solver (iHS), which reconstructs the complex acoustic waveform, at a given frequency, in the cavity and up to the open surface or unknown impedance boundary (IB), hereby providing the complete spatial distribution of impedance as a result of the calculation for that given frequency. Multiple instances of the iHS can be executed in parallel for different frequencies, allowing for a rapid determination of the full broadband impedance at every point of the IB. The iHS is first validated against Rott's quasi one-dimensional thermoacoustic theory for viscous and inviscid planar wave propagation in constant cross-sectional-area rectangular and circular ducts. The impedance of an ultrasonically absorptive, geometrically complex two-dimensional cavity is then evaluated and implemented as a time-domain impedance boundary condition (TDIBC) to allow comparison with fully compressible Navier-Stokes simulations resolving the cavity geometry. Finally, the evaluation of the effective surface impedance of the carbon-carbon ultrasonically absorptive coating (C/C UAC) used in the hypersonic transition delay experiments by Wagner et al. (AIAA 2012-5865), manufactured in DLR-Stuttgart, is presented.