Parsimonious approaches for the laboratory synthesis of wall-pressure excitations

The experimental synthesis of acoustic or aerodynamic wall-pressure excitations over industrial structures, for instance an aircraft sidewall or a car window, is a cost-efficient approach in order to optimise the insulating performance of these structures under real-life forcing generated in a controlled environment. Several strategies like inverse filtering in the spatial or wavenumber domains, holophonic or holographic reproductions, have proved to be successful for the laboratory synthesis of an acoustic diffuse field. But they required a prohibitive number of control sources for the real-time synthesis of sub-wavelength scales such as those associated with the wall-pressures induced by a Turbulent Boundary Layer (TBL). The present study compares the performance of several strategies for a direct reproduction of TBL excitations, independently of the test panel physical properties and with a reasonable number of sources. A first approach, the focused synthesis, uses spatial windowing to reduce the surface over which the TBL is reproduced, thereby enlarging the range of synthesized wavenumbers in the subsonic domain, if possible beyond the convective ridge. The two other approaches aim at synthesizing a reduced-rank approximation to either the target TBL correlation function or the source-fields acoustical transfers. The efficiency of these methods will be examined in terms of both the reproduction accuracy and the required number of sources that can be used to achieve the synthesis over a broad frequency range.