Wavenumber scattering and the interactions of turbulent boundary layer flow with the structures exhibiting the acoustic black hole effect

Beam and plate-like structures with non-constant surface impedance are known to exhibit wavenumber scattering such that the wavenumber energy of a vibration mode of the structure is spread over a wide wavenumber band. The scattered energy can couple into partially correlated forcing functions, such as turbulent boundary layer (TBL) flow, which exhibit a broadband wavenumber spectrum centered at the convective wavenumber. The overall effect is an increased amount of radiated noise for certain flow speeds. Recently, structures with imbedded acoustic black holes (ABH) have shown good noise and vibration level reductions for point excitations. However, it will be shown that when excited by complex, partially correlated forcing functions such as TBL flow, the wavenumber scattering caused by the power-law taper of the ABH can lead to increased radiated noise levels. The flow speed and wavenumber dependence of the TBL/ABH interactions will be presented using dimensional analysis.