Far-field microphone array techniques for acoustic characterisation of aerofoils

This thesis is concerned with the acoustic characterisation of flat plate aerofoils interacting with turbulent flows, and the use of microphone array methods as an experimental tool to assess these characteristics. The main equations describing acoustic propagation and radiation in a moving medium are described, covering plane waves, point sources and distributed sources. The geometric far-field approximation, introduced here as the Fraunhofer approximation, is shown to relate the acoustic field seen by a distant observer to the Spatial Fourier Transform of the source distribution evaluated within the so-called “radiation ellipse” in the wavenumber domain. The Amiet model for turbulence-flat plate interaction noise is presented, and its surface pressure and acoustic radiation characteristics for single- and multiple-gust responses are discussed from a wavenumber-domain perspective. Three sources of near-field effects were identified in a flat plate: the fundamental dipole hydrodynamic near-field, considered significant contributor to the acoustic field at low frequencies; the geometric near-field, considered significant at high frequencies; and the response to subcritical gusts, considered significant at low frequencies for a finite-span aerofoil. The prediction model was validated via microphone array acoustic measurements of a flat plate in a wind tunnel, showing a good agreement between the predicted and the measured acoustic fields, particularly regarding the coherence between microphones. The same set of signals was processed with conventional beamforming and CLEAN-SC, and again a good agreement was observed between prediction and measurements. Finally, a far-field inversion method was proposed by inverting the above mentioned Fourier relationship between the far-field pressure and the source wavenumber spectrum; two formulations were proposed, and it was shown that the estimated source is effectively a band passed version of the original source and thus lacks fine spatial detail. This band-passing phenomenon in the far-field radiation effectively smears out the original source distribution, and the estimated source becomes larger than the physical source. It is shown that both forms have very similar formulations to frequency-domain delay-and-sum beamforming